,body,value,explanation_new
679,Create a data set with at least 8 data values that match each set of given conditions. A data set where the IQR is equal to the range.,"There are many correct answers for this question. One example of a correct answer is: 10, 10, 10, 10, 10, 10, 10, 10 In this case, the range is 10 - 10 = 0, and the IQR must also be 10 - 10 = 0.","###Write an explanation to this problem:
Create a data set with at least 8 data values that match each set of given conditions. A data set where the IQR is equal to the range.
###Explanation:
There are many correct answers for this question. One example of a correct answer is: 10, 10, 10, 10, 10, 10, 10, 10 In this case, the range is 10 - 10 = 0, and the IQR must also be 10 - 10 = 0."
708,"A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project","Since the number of tables is unknown, we can use a variable, t, to represent this value. There are 8 students at each table, and the total number of students is 120. This means that: 8 students * number of tables = 120 students total 8t=120","###Write an explanation to this problem:
A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Since the number of tables is unknown, we can use a variable, t, to represent this value. There are 8 students at each table, and the total number of students is 120. This means that: 8 students * number of tables = 120 students total 8t=120"
635,Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project,"Your answer can be any statistical question, a question that asks for multiple data points that may vary.","###Write an explanation to this problem:
Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project
###Explanation:
Your answer can be any statistical question, a question that asks for multiple data points that may vary."
703,Solve the inequality. Represent the solution on a number line. 1.5y>9 The Utah Middle School Math Project,"Solve for y. The number line should be greater than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 1.5y>9 The Utah Middle School Math Project
###Explanation:
Solve for y. The number line should be greater than the solution, but not contain it."
314,"Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.",The slope shows that 2 are added for each muffin ordered. The intercept of 3 probably represents a 3 delivery fee or tip for the order.,"###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
###Explanation:
The slope shows that 2 are added for each muffin ordered. The intercept of 3 probably represents a 3 delivery fee or tip for the order."
311,"In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. Submit your drawing using the tools below.","The three angle measures must add to 180∘ but must all be equal. Therefore, each measure is 60∘, since 60 = 1/3 * 180. The answer is 60.","###Write an explanation to this problem:
In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. Submit your drawing using the tools below.
###Explanation:
The three angle measures must add to 180∘ but must all be equal. Therefore, each measure is 60∘, since 60 = 1/3 * 180. The answer is 60."
522,Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project,"Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project
###Explanation:
Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output"
442,The following equation is given: -3x ndash; 5 = -2 Provide a context/word problem for the given information. The Utah Middle School Math Project,Five less than the product of -3 and a number is -2.,"###Write an explanation to this problem:
The following equation is given: -3x ndash; 5 = -2 Provide a context/word problem for the given information. The Utah Middle School Math Project
###Explanation:
Five less than the product of -3 and a number is -2."
575,"Let's say that Mouse, Double-Dog and Triple-Threat-Tiger all have swimming pools. What would you predict about the scale factor of the volume as related to double or triple dimensions? Prove or adjust your prediction--say that Mouse has a pool which is 1 foot deep and 2 feet by 3 feet. The Utah Middle School Math Project",You would cube the scale factor of the lengths,"###Write an explanation to this problem:
Let's say that Mouse, Double-Dog and Triple-Threat-Tiger all have swimming pools. What would you predict about the scale factor of the volume as related to double or triple dimensions? Prove or adjust your prediction--say that Mouse has a pool which is 1 foot deep and 2 feet by 3 feet. The Utah Middle School Math Project
###Explanation:
You would cube the scale factor of the lengths"
411,"Suppose the cell phone company sells three different plans to its customers: Pay-as-you-go: The customer is charged per minute for each call. Unlimited minutes: The customer pays a flat fee per month and can make unlimited calls with no additional charges. Basic plan: The customer is not charged per minute unless the customer exceeds 500 minutes in the month; then, the customer is charged per minute for the extra minutes. Consider the chance experiment of selecting a customer at random and recording which plan she purchased. What outcomes are in the sample space for this chance experiment?",1 pay-as-you-go 2 unlimited minutes 3 basic plan,"###Write an explanation to this problem:
Suppose the cell phone company sells three different plans to its customers: Pay-as-you-go: The customer is charged per minute for each call. Unlimited minutes: The customer pays a flat fee per month and can make unlimited calls with no additional charges. Basic plan: The customer is not charged per minute unless the customer exceeds 500 minutes in the month; then, the customer is charged per minute for the extra minutes. Consider the chance experiment of selecting a customer at random and recording which plan she purchased. What outcomes are in the sample space for this chance experiment?
###Explanation:
1 pay-as-you-go 2 unlimited minutes 3 basic plan"
839,"The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.","10, -7; as the distance between -2 and 10 is 12 units. -14, -7; as the distance between -2 and -14 is 12 units. -2, 5; as the distance between 5 and -7 is 12 units. -2, -19; as the distance between -7 and -19 is 12 units.","###Write an explanation to this problem:
The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.
###Explanation:
10, -7; as the distance between -2 and 10 is 12 units. -14, -7; as the distance between -2 and -14 is 12 units. -2, 5; as the distance between 5 and -7 is 12 units. -2, -19; as the distance between -7 and -19 is 12 units."
67,"It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents.","The equation shows that after h hours, the temperature has become 14 degrees.","###Write an explanation to this problem:
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents.
###Explanation:
The equation shows that after h hours, the temperature has become 14 degrees."
558,The following problem is given to Miranda: 23.10*100 She states that since she is multiplying by 100 she simply must add two zeros to 23.10. Explain the error in Miranda's thinking and explain how to find the correct answer without using a calculator or long multiplication. The Utah Middle School Math Project,"Multiplying by 100 indicates moving the decimal two places to the right; this will give you 2,310.","###Write an explanation to this problem:
The following problem is given to Miranda: 23.10*100 She states that since she is multiplying by 100 she simply must add two zeros to 23.10. Explain the error in Miranda's thinking and explain how to find the correct answer without using a calculator or long multiplication. The Utah Middle School Math Project
###Explanation:
Multiplying by 100 indicates moving the decimal two places to the right; this will give you 2,310."
275,"1. Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice? Copied for free from openupresources.org",The angles go all the way around one point.,"###Write an explanation to this problem:
1. Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice? Copied for free from openupresources.org
###Explanation:
The angles go all the way around one point."
757,Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.,"Note that the area of a triangle is A = 1/2bh and the area of a parallelogram is A = bh. Therefore, to find the dimensions of a right triangle and a parallelogram with the same area, the base of the triangle should be double that of the parallelogram. Sample response: Right Triangle: b = 10 cm h = 8 cm A = 1/2bh = 1/210 cm8cm = 40 cm2 Parallelogram: b = 5 cm h = 8 cm A = bh = 5 cm8 cm = 40 cm2","###Write an explanation to this problem:
Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.
###Explanation:
Note that the area of a triangle is A = 1/2bh and the area of a parallelogram is A = bh. Therefore, to find the dimensions of a right triangle and a parallelogram with the same area, the base of the triangle should be double that of the parallelogram. Sample response: Right Triangle: b = 10 cm h = 8 cm A = 1/2bh = 1/210 cm8cm = 40 cm2 Parallelogram: b = 5 cm h = 8 cm A = bh = 5 cm8 cm = 40 cm2"
787,"Use tape diagrams and equations to solve the problem with visual models and algebraic methods. Alyssa is twice as old as Brittany, and Jazmyn is 15 years older than Alyssa. If Jazmyn is 35 years old, how old is Brittany? Let a represent Alyssa's age in years and b represent Brittany's age in years. Submit your work using the tools below.","According to this tape diagram, a+15=35 on Jazmyn's tape diagram. To solve for a, subtract 15 from 35. a is 20. b is half of a, so 20/2 = 10. b =10","###Write an explanation to this problem:
Use tape diagrams and equations to solve the problem with visual models and algebraic methods. Alyssa is twice as old as Brittany, and Jazmyn is 15 years older than Alyssa. If Jazmyn is 35 years old, how old is Brittany? Let a represent Alyssa's age in years and b represent Brittany's age in years. Submit your work using the tools below.
###Explanation:
According to this tape diagram, a+15=35 on Jazmyn's tape diagram. To solve for a, subtract 15 from 35. a is 20. b is half of a, so 20/2 = 10. b =10"
801,"120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.",Change percent to a decimal of means to multiply 1.20 x= 78,"###Write an explanation to this problem:
120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.
###Explanation:
Change percent to a decimal of means to multiply 1.20 x= 78"
768,"The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.","𝟏𝟎, -𝟕; as the distance between -2 and 10 is 12 units. -𝟏𝟒, -𝟕; as the distance between -2 and -14 is 12 units. -𝟐, 𝟓; as the distance between 5 and -7 is 12 units. -𝟐, -𝟏𝟗; as the distance between -7 and -19 is 12 units.","###Write an explanation to this problem:
The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.
###Explanation:
𝟏𝟎, -𝟕; as the distance between -2 and 10 is 12 units. -𝟏𝟒, -𝟕; as the distance between -2 and -14 is 12 units. -𝟐, 𝟓; as the distance between 5 and -7 is 12 units. -𝟐, -𝟏𝟗; as the distance between -7 and -19 is 12 units."
675,-7 x -2 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,This multiplication problem means the opposite of seven groups of negative 2.,"###Write an explanation to this problem:
-7 x -2 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem means the opposite of seven groups of negative 2."
326,A map of a park says its scale is 1 to 100. What do you think that means? copied for free from openupresources.org,That the actual park is 100 times larger than the map.,"###Write an explanation to this problem:
A map of a park says its scale is 1 to 100. What do you think that means? copied for free from openupresources.org
###Explanation:
That the actual park is 100 times larger than the map."
629,"In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: 6x = 54 Original Equation: x=9 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 6x has been divided by 6. On the right side, 54 has been divided by 6, to create the result of 9. The action was: Divide both sides of the equation by 6.","###Write an explanation to this problem:
In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: 6x = 54 Original Equation: x=9 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 6x has been divided by 6. On the right side, 54 has been divided by 6, to create the result of 9. The action was: Divide both sides of the equation by 6."
519,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project",Sarah: y= 400 - 15x Matthew: y= 50 + 20x where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project
###Explanation:
Sarah: y= 400 - 15x Matthew: y= 50 + 20x where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250."
468,210% of 60 Estimate the answer. The Utah Middle School Math Project,"210% means over twice as much as the whole thing, so 210% of 60 must be over 120.","###Write an explanation to this problem:
210% of 60 Estimate the answer. The Utah Middle School Math Project
###Explanation:
210% means over twice as much as the whole thing, so 210% of 60 must be over 120."
412,"Mr. Cortez drove at a constant rate for 5 hours. At the end of 2 hours he had driven 90 miles. After 5 hours, he had driven 225 miles. What is the dependent variable in this relationship? The Utah Middle School Math Project",The distance that was driven depends on the amount of time that he was driving. This means distance is the dependent variable in this equation.,"###Write an explanation to this problem:
Mr. Cortez drove at a constant rate for 5 hours. At the end of 2 hours he had driven 90 miles. After 5 hours, he had driven 225 miles. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The distance that was driven depends on the amount of time that he was driving. This means distance is the dependent variable in this equation."
588,Write a context to match the numeric expression given. 23 12 The Utah Middle School Math Project,"Angie is making key lime pie for a bake sale. Each pie can be cut into 12 slices. If she makes 3 pies and sells each slice for 2, how much money will she make?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 23 12 The Utah Middle School Math Project
###Explanation:
Angie is making key lime pie for a bake sale. Each pie can be cut into 12 slices. If she makes 3 pies and sells each slice for 2, how much money will she make?"
526,"Determine if the relation or situation defines a function. Justify your answer. You call the post office and ask for the zip code for the city of Salt Lake City, UT. Is zip code a function of the name of the city? The Utah Middle School Math Project","No, the data does not describe a function There are several zip codes for the city of Salt Lake, and therefore several outputs or zip codes for the one input of the city of Salt Lake","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. You call the post office and ask for the zip code for the city of Salt Lake City, UT. Is zip code a function of the name of the city? The Utah Middle School Math Project
###Explanation:
No, the data does not describe a function There are several zip codes for the city of Salt Lake, and therefore several outputs or zip codes for the one input of the city of Salt Lake"
718,"Imagine cutting a cube, parallel to the base. What shape is the plane section? The Utah Middle School Math Project",If a cube was cut parallel to the base the resulting cross-section would have to be a square,"###Write an explanation to this problem:
Imagine cutting a cube, parallel to the base. What shape is the plane section? The Utah Middle School Math Project
###Explanation:
If a cube was cut parallel to the base the resulting cross-section would have to be a square"
213,"The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.",The researchers might be correct because the data shows a large IQR.,"###Write an explanation to this problem:
The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.
###Explanation:
The researchers might be correct because the data shows a large IQR."
514,How do you read the expression --12? The Utah Middle School Math Project,The opposite of the opposite of twelve,"###Write an explanation to this problem:
How do you read the expression --12? The Utah Middle School Math Project
###Explanation:
The opposite of the opposite of twelve"
39,1. A balloon is floating above a lake and a sunken canoe is below the surface of the lake. The balloon's vertical position is 12 meters and the canoe's is -4.8 meters. The equation copied for free from openupresources.org,The difference in elevation between the balloon and the canoe.,"###Write an explanation to this problem:
1. A balloon is floating above a lake and a sunken canoe is below the surface of the lake. The balloon's vertical position is 12 meters and the canoe's is -4.8 meters. The equation copied for free from openupresources.org
###Explanation:
The difference in elevation between the balloon and the canoe."
766,Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e,"The greatest common factor of 4 and 12 is 4. 4 goes into 4 1 time, and 12/4=3. This means the coefficient of d will be 1 and the coefficient of e will be 3. Plugging this into the equation, and using the distributive property, the equation becomes 41d+3e.","###Write an explanation to this problem:
Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e
###Explanation:
The greatest common factor of 4 and 12 is 4. 4 goes into 4 1 time, and 12/4=3. This means the coefficient of d will be 1 and the coefficient of e will be 3. Plugging this into the equation, and using the distributive property, the equation becomes 41d+3e."
168,Write two division expressions that have the same value as 61.12 / 3.2.,"There are a variety of correct answers to this problem. These are just a few examples: 6,112/320 611.2/32 0.6112/0.032","###Write an explanation to this problem:
Write two division expressions that have the same value as 61.12 / 3.2.
###Explanation:
There are a variety of correct answers to this problem. These are just a few examples: 6,112/320 611.2/32 0.6112/0.032"
439,The following equation is given: x + x+3 + x + x+3 = 34 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project,"The length of a rectangle is 3 more than the width. If the perimeter is 34, what are the length and width?","###Write an explanation to this problem:
The following equation is given: x + x+3 + x + x+3 = 34 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
The length of a rectangle is 3 more than the width. If the perimeter is 34, what are the length and width?"
467,150% of 16 Estimate the answer. The Utah Middle School Math Project,"150% is in between 100% and 200%, so 150% of 16 must be in between 16 and 32.","###Write an explanation to this problem:
150% of 16 Estimate the answer. The Utah Middle School Math Project
###Explanation:
150% is in between 100% and 200%, so 150% of 16 must be in between 16 and 32."
30,A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.,6:8:10 9:12:15,"###Write an explanation to this problem:
A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.
###Explanation:
6:8:10 9:12:15"
338,Graph a system of linear equations with no solutions. Submit your graph using the tools below.,"The solution of a system of equations can be easily seen on a graph. It is the point where the lines intersect. To graph a system of linear equations with no solutions, graph 2 lines that are parallel. Parallel lines will never intersect, so there will not be a solution.","###Write an explanation to this problem:
Graph a system of linear equations with no solutions. Submit your graph using the tools below.
###Explanation:
The solution of a system of equations can be easily seen on a graph. It is the point where the lines intersect. To graph a system of linear equations with no solutions, graph 2 lines that are parallel. Parallel lines will never intersect, so there will not be a solution."
208,List the sample space the available options for the chance experiment given. Flipping a coin,"When you flip a coin, the two sides it could land on are heads or tails.","###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
When you flip a coin, the two sides it could land on are heads or tails."
139,What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB,"The sample space is the same for the two experiments because the words contain the same letters. Sample Space: A,B,L,M","###Write an explanation to this problem:
What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB
###Explanation:
The sample space is the same for the two experiments because the words contain the same letters. Sample Space: A,B,L,M"
829,Is there a triangle with 2 right angles? Explain your reasoning.,"There is no triangle with 2 right angles. The three angles in a triangle always add up 180 degrees, since 90 + 90 = 180 there is no way to make a triangle with 2 right angles.","###Write an explanation to this problem:
Is there a triangle with 2 right angles? Explain your reasoning.
###Explanation:
There is no triangle with 2 right angles. The three angles in a triangle always add up 180 degrees, since 90 + 90 = 180 there is no way to make a triangle with 2 right angles."
449,The following equation is given: 2/3x ndash; 20 = 280 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project,Paulo spent 2/3 of his savings on a new phone and then spent 20 on a new cover for it. He now has 280 left in his savings account. How much money did he start with?,"###Write an explanation to this problem:
The following equation is given: 2/3x ndash; 20 = 280 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
Paulo spent 2/3 of his savings on a new phone and then spent 20 on a new cover for it. He now has 280 left in his savings account. How much money did he start with?"
586,"Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800.","###Write an explanation to this problem:
Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800."
479,Create your own context or story that represents a relation that is not a function. Write your story.,"To create a story that is not a function, whatever you chose to be the independent variable x must have more than one corresponding dependent variable y.","###Write an explanation to this problem:
Create your own context or story that represents a relation that is not a function. Write your story.
###Explanation:
To create a story that is not a function, whatever you chose to be the independent variable x must have more than one corresponding dependent variable y."
597,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project","In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1,2, 5, 10, and so on is a correct answer.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project
###Explanation:
In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1,2, 5, 10, and so on is a correct answer."
260,Elena wants to know what proportion of people have cats as pets. Describe a process she could use to estimate an answer to her question.,"Example: Elena could ask a number of people whether or not they have a cat, then record how many people said yes. She would then divide the number of people who said yes by the total number of people she asked to get the proportion of people with cats.","###Write an explanation to this problem:
Elena wants to know what proportion of people have cats as pets. Describe a process she could use to estimate an answer to her question.
###Explanation:
Example: Elena could ask a number of people whether or not they have a cat, then record how many people said yes. She would then divide the number of people who said yes by the total number of people she asked to get the proportion of people with cats."
745,A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?,"Answers will vary, although it makes sense to count by 5's, since both values are multiples of 5.","###Write an explanation to this problem:
A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?
###Explanation:
Answers will vary, although it makes sense to count by 5's, since both values are multiples of 5."
424,Jasper has a coin collection consisting of quarters and dimes. He has 50 coins worth 8.60. How many of each coin does he have? First define your unknowns. The Utah Middle School Math Project,Explain what your variables will represent in your problem. For example: q = number of quarter d = number of dimes,"###Write an explanation to this problem:
Jasper has a coin collection consisting of quarters and dimes. He has 50 coins worth 8.60. How many of each coin does he have? First define your unknowns. The Utah Middle School Math Project
###Explanation:
Explain what your variables will represent in your problem. For example: q = number of quarter d = number of dimes"
667,Solve the inequality. Represent the solution on a number line. 5x<21 The Utah Middle School Math Project,"Solve for x. The number line should be less than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 5x<21 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than the solution, but not contain it."
23,Which of the numbers in problems 1-5 are not perfect squares? Explain.,The numbers 147 and 8 are not perfect squares because there is no integer x so that x2 = 147 OR x2 = 8,"###Write an explanation to this problem:
Which of the numbers in problems 1-5 are not perfect squares? Explain.
###Explanation:
The numbers 147 and 8 are not perfect squares because there is no integer x so that x2 = 147 OR x2 = 8"
210,"Rectangle ABCD is drawn on a coordinate plane. A = -6,9 and B = 5,9. What could be the locations of points C and D?","C could be -6,-9 and D could be 5,-9 or vice versa. This is because point A is at -6. 9 so your next point would have the same x but opposite y value. Point B is 5,9 so the new point would also have the same x but opposite y value.","###Write an explanation to this problem:
Rectangle ABCD is drawn on a coordinate plane. A = -6,9 and B = 5,9. What could be the locations of points C and D?
###Explanation:
C could be -6,-9 and D could be 5,-9 or vice versa. This is because point A is at -6. 9 so your next point would have the same x but opposite y value. Point B is 5,9 so the new point would also have the same x but opposite y value."
196,"For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7",We know that subtracting a number is the same as adding its opposite. That means we can transform the equation to: 20 - 9 + 8 - 7 20 + -9 + 8 + -7,"###Write an explanation to this problem:
For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7
###Explanation:
We know that subtracting a number is the same as adding its opposite. That means we can transform the equation to: 20 - 9 + 8 - 7 20 + -9 + 8 + -7"
732,Choose a situation that could be described by the following ratio. Write a sentence to describe the ratio in the context of the situation you chose. 1 to 2,"Answers will vary. You might write something like For every one nose, there are two eyes.","###Write an explanation to this problem:
Choose a situation that could be described by the following ratio. Write a sentence to describe the ratio in the context of the situation you chose. 1 to 2
###Explanation:
Answers will vary. You might write something like For every one nose, there are two eyes."
110,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. -3,?,0,5 The Utah Middle School Math Project","In this question, the ? falls between -3 and 0, so the integer that replaces the ? must be greater than -3 but less than 0. The only two integers where this is true are -2 and -1.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. -3,?,0,5 The Utah Middle School Math Project
###Explanation:
In this question, the ? falls between -3 and 0, so the integer that replaces the ? must be greater than -3 but less than 0. The only two integers where this is true are -2 and -1."
383,"The width of a rectangle is five less than three times the length of the rectangle. The perimeter of the rectangle is 70 inches. Write an expression to find the width of the rectangle, an expression to find the length of the rectangle, and an equation to show the relationship between these expressions and the perimeter of the rectangle. The Utah Middle School Math Project","The length of the rectangle is represented by l. The width of the rectangle is is 3 times the length minus 5, so the width is 3l-5. The perimeter of a rectangle is equal to the width times 2 plus the length times 2. Therefore, the equation of the perimeter of the rectangle is 23l-5+2l=70.","###Write an explanation to this problem:
The width of a rectangle is five less than three times the length of the rectangle. The perimeter of the rectangle is 70 inches. Write an expression to find the width of the rectangle, an expression to find the length of the rectangle, and an equation to show the relationship between these expressions and the perimeter of the rectangle. The Utah Middle School Math Project
###Explanation:
The length of the rectangle is represented by l. The width of the rectangle is is 3 times the length minus 5, so the width is 3l-5. The perimeter of a rectangle is equal to the width times 2 plus the length times 2. Therefore, the equation of the perimeter of the rectangle is 23l-5+2l=70."
227,Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han's sample is 59 inches. The mean height for Priya's sample is 61 inches. Does it surprise you that the two sample means are different?,"Even though they both selected a random sample, their samples probably included different people from the population. This is why it would make sense that the two sample means are different.","###Write an explanation to this problem:
Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han's sample is 59 inches. The mean height for Priya's sample is 61 inches. Does it surprise you that the two sample means are different?
###Explanation:
Even though they both selected a random sample, their samples probably included different people from the population. This is why it would make sense that the two sample means are different."
513,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project",Sarah: 𝑦 = 400 - 15𝑥 Matthew: 𝑦 = 50 + 20𝑥 where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project
###Explanation:
Sarah: 𝑦 = 400 - 15𝑥 Matthew: 𝑦 = 50 + 20𝑥 where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250."
653,"In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 14 Transformed Equation: x - 3 = 11 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 3 has been subtracted from x. On the right side, 3 has been subtracted from 14, which results in 11. The action was: Subtract 3 from both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 14 Transformed Equation: x - 3 = 11 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 3 has been subtracted from x. On the right side, 3 has been subtracted from 14, which results in 11. The action was: Subtract 3 from both sides of the equation."
86,Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume.,Calculating surface and calculating volume both involve measurement of 3 dimensional figures. The volume of a figure can help determine what can fit inside it. The surface area of a figure can help determine what is needed to cover the figure.,"###Write an explanation to this problem:
Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume.
###Explanation:
Calculating surface and calculating volume both involve measurement of 3 dimensional figures. The volume of a figure can help determine what can fit inside it. The surface area of a figure can help determine what is needed to cover the figure."
96,Sam was asked to evaluate the expression 5x + 3x + 20 for x = 100. Sam's work is shown below. Sam's Work: 5x + 3x + 20 = 100 8x + 20 = 100 8x = 80 x = 10 What mistake did Sam make? Help Sam to answer the question correctly. The Utah Middle School Math Project,"Sam was asked to find the value of the expression when x is equal to 100. The first step of Sam's work he sets the value of the expression equal to 100 instead of setting the value of x to 100. In order to find the actual value of the expression, the value 100 must be substituted into the expression for every instance of 'x'. 5x + 3x + 20 5100 + 3100 + 20 Now the equation can be simplified by multiplying the values in parenthesis. 5100 + 3100 + 20 500 + 300 + 20 Now the values can be added together. 500 + 300 + 20 800 + 20 820 The value of the expression when x = 100 is 820.","###Write an explanation to this problem:
Sam was asked to evaluate the expression 5x + 3x + 20 for x = 100. Sam's work is shown below. Sam's Work: 5x + 3x + 20 = 100 8x + 20 = 100 8x = 80 x = 10 What mistake did Sam make? Help Sam to answer the question correctly. The Utah Middle School Math Project
###Explanation:
Sam was asked to find the value of the expression when x is equal to 100. The first step of Sam's work he sets the value of the expression equal to 100 instead of setting the value of x to 100. In order to find the actual value of the expression, the value 100 must be substituted into the expression for every instance of 'x'. 5x + 3x + 20 5100 + 3100 + 20 Now the equation can be simplified by multiplying the values in parenthesis. 5100 + 3100 + 20 500 + 300 + 20 Now the values can be added together. 500 + 300 + 20 800 + 20 820 The value of the expression when x = 100 is 820."
752,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.,The temperature is 10 degrees below zero on the Fahrenheit scale.,"###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.
###Explanation:
The temperature is 10 degrees below zero on the Fahrenheit scale."
541,Write three expressions that are equivalent to the expression 4 + 32. The Utah Middle School Math Project,Example: 2x+2x+32; 1x+3x+216; 22x+16+16,"###Write an explanation to this problem:
Write three expressions that are equivalent to the expression 4 + 32. The Utah Middle School Math Project
###Explanation:
Example: 2x+2x+32; 1x+3x+216; 22x+16+16"
292,"Mai and Priya each played 10 games of bowling and recorded the scores. Mai's median score was 120, and her IQR was 5. Priya's median score was 118, and her IQR was 15. Whose scores probably had less variability? Explain how you know.","Since Mai's IQR was only 5, I believe she had less variability than Priya's IQR of 15.","###Write an explanation to this problem:
Mai and Priya each played 10 games of bowling and recorded the scores. Mai's median score was 120, and her IQR was 5. Priya's median score was 118, and her IQR was 15. Whose scores probably had less variability? Explain how you know.
###Explanation:
Since Mai's IQR was only 5, I believe she had less variability than Priya's IQR of 15."
136,Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. NOW there are 78 players on the field. Write an equation whose solution is the number of players on each team. copied for free from openupresources.org,15 6x-2 = 78 6x - 12 = 78 +12 +12 6x = 90 divide both sides by 6 x =15,"###Write an explanation to this problem:
Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. NOW there are 78 players on the field. Write an equation whose solution is the number of players on each team. copied for free from openupresources.org
###Explanation:
15 6x-2 = 78 6x - 12 = 78 +12 +12 6x = 90 divide both sides by 6 x =15"
109,"The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project","The equation for area of a parallelogram is area=base*height, or A=bh. Substitute the given values into this equation. 155.52=b*28.8.","###Write an explanation to this problem:
The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The equation for area of a parallelogram is area=base*height, or A=bh. Substitute the given values into this equation. 155.52=b*28.8."
209,Write two division expressions that have the same value as 36.8 / 2.3.,"There are multiple correct answers to this question. These are just a few examples: 3.68/0.23 368/23 3,680/230","###Write an explanation to this problem:
Write two division expressions that have the same value as 36.8 / 2.3.
###Explanation:
There are multiple correct answers to this question. These are just a few examples: 3.68/0.23 368/23 3,680/230"
660,-3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer -3 and multiply it 4 times, so -3 x 4 can be thought of as -3 + -3 + -3 + -3","###Write an explanation to this problem:
-3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -3 and multiply it 4 times, so -3 x 4 can be thought of as -3 + -3 + -3 + -3"
691,"Consider the following equations: 3x=18 x+5=12 When you are asked to solve these equations, what are you being asked to do? The Utah Middle School Math Project",Example answer: You are asked to find the value of the unknown that makes the equation true.,"###Write an explanation to this problem:
Consider the following equations: 3x=18 x+5=12 When you are asked to solve these equations, what are you being asked to do? The Utah Middle School Math Project
###Explanation:
Example answer: You are asked to find the value of the unknown that makes the equation true."
63,"It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents.","The equation shows that after h hours, the temperature has become 14 degrees below zero.","###Write an explanation to this problem:
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents.
###Explanation:
The equation shows that after h hours, the temperature has become 14 degrees below zero."
557,Write a phrase for the following algebraic expression 15 - 2x The Utah Middle School Math Project,15 - 2x is two times a number x less than fifteen.,"###Write an explanation to this problem:
Write a phrase for the following algebraic expression 15 - 2x The Utah Middle School Math Project
###Explanation:
15 - 2x is two times a number x less than fifteen."
849,Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.,"The length of Rectangle C is double the length of Rectangle B, but the width of Rectangle C is 1.5 times the width of Rectangle B.","###Write an explanation to this problem:
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.
###Explanation:
The length of Rectangle C is double the length of Rectangle B, but the width of Rectangle C is 1.5 times the width of Rectangle B."
328,A rectangular parking lot is 120 feet long and 75 feet wide. Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches. Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches. Explain or show how each scale would produce an 8 inch by 5 inch drawing. copied for free from openupresources.org,"For Lin's drawing, 1 in represents 15 ft, so 120 ft is 8 in 120/15=8 and 75 ft is 5 in 75/15=5. For Diego's drawing, 1 unit on the drawing represents 180 of the same unit in the actual distance, so 1 in represents 180 in. 180 in is equal to 15 ft 180/12=15.","###Write an explanation to this problem:
A rectangular parking lot is 120 feet long and 75 feet wide. Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches. Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches. Explain or show how each scale would produce an 8 inch by 5 inch drawing. copied for free from openupresources.org
###Explanation:
For Lin's drawing, 1 in represents 15 ft, so 120 ft is 8 in 120/15=8 and 75 ft is 5 in 75/15=5. For Diego's drawing, 1 unit on the drawing represents 180 of the same unit in the actual distance, so 1 in represents 180 in. 180 in is equal to 15 ft 180/12=15."
65,"Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ge; 500 and solved it to find the solution x ge; 55.25. Explain how you know Elena made a mistake based on her solution.","Elena's solution would mean that she has to put more than 55 movies on her hard drive. That doesn't make any sense because there should be a limit to how many movies she can put on the hard drive, it should not be unlimited.","###Write an explanation to this problem:
Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ge; 500 and solved it to find the solution x ge; 55.25. Explain how you know Elena made a mistake based on her solution.
###Explanation:
Elena's solution would mean that she has to put more than 55 movies on her hard drive. That doesn't make any sense because there should be a limit to how many movies she can put on the hard drive, it should not be unlimited."
807,Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.,"Since a loss of 500 in the stock market is worse than a gain of 200 in the stock market, the inequality is: -500 < 200","###Write an explanation to this problem:
Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.
###Explanation:
Since a loss of 500 in the stock market is worse than a gain of 200 in the stock market, the inequality is: -500 < 200"
78,Find 3 different ratios that are equivalent to 7 : 3,There are infinite amount of equivalent ratios to 7:3 as long as the ratio is being multiplied or divided by the same constant. Here are a couple of examples of equivalent ratios: 21:9 70:30 49:21,"###Write an explanation to this problem:
Find 3 different ratios that are equivalent to 7 : 3
###Explanation:
There are infinite amount of equivalent ratios to 7:3 as long as the ratio is being multiplied or divided by the same constant. Here are a couple of examples of equivalent ratios: 21:9 70:30 49:21"
300,"A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm. She wants to test the plants at the farm, but it will ruin the crop if she tests all of them. If the farm has 5,000 spinach plants, describe a method that would produce a random sample of 10 plants.","One way of getting a random sample would be if she could number the plants from 1 to 5,000 and have a computer select 10 random numbers between 1 and 5,000, then test the plants that correspond to the numbers the computer generated.","###Write an explanation to this problem:
A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm. She wants to test the plants at the farm, but it will ruin the crop if she tests all of them. If the farm has 5,000 spinach plants, describe a method that would produce a random sample of 10 plants.
###Explanation:
One way of getting a random sample would be if she could number the plants from 1 to 5,000 and have a computer select 10 random numbers between 1 and 5,000, then test the plants that correspond to the numbers the computer generated."
657,Sally spent 60 on ingredients for a bake sale. She had sold 35 in baked goods. Write an inequality to represent the amount she still needs to sell to make a profit. The Utah Middle School Math Project,"Sally has already sold 35 worth of baked goods, and needs 60 total. That means the inequality will be 35+s>60.","###Write an explanation to this problem:
Sally spent 60 on ingredients for a bake sale. She had sold 35 in baked goods. Write an inequality to represent the amount she still needs to sell to make a profit. The Utah Middle School Math Project
###Explanation:
Sally has already sold 35 worth of baked goods, and needs 60 total. That means the inequality will be 35+s>60."
689,One angle is five times larger than another angle. Together the angles sum to 1800. What is the measure of each angle? Write an equation to solve the problem. The Utah Middle School Math Project,"The measure of the smaller angle can be x, and the measure of the larger angle will be equal to 5x, because it is five times as large. Added together, these will be equal to 180. This means that: x+5x=180.","###Write an explanation to this problem:
One angle is five times larger than another angle. Together the angles sum to 1800. What is the measure of each angle? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The measure of the smaller angle can be x, and the measure of the larger angle will be equal to 5x, because it is five times as large. Added together, these will be equal to 180. This means that: x+5x=180."
346,Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project,w= 2r where w represents Will's distance and r represents Ruby's distance r + w= 18 Will ran 12 miles and Ruby ran 6 miles.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project
###Explanation:
w= 2r where w represents Will's distance and r represents Ruby's distance r + w= 18 Will ran 12 miles and Ruby ran 6 miles."
628,For what value of x does the expression + 6 evaluate to 8? Write an equation to represent the problem. The Utah Middle School Math Project,"To make an equation where the expression x+6 evaluates to 8, we need to say that the expression equals 8. x+6=8 Any equation that simplifies to this equation is a correct answer.","###Write an explanation to this problem:
For what value of x does the expression + 6 evaluate to 8? Write an equation to represent the problem. The Utah Middle School Math Project
###Explanation:
To make an equation where the expression x+6 evaluates to 8, we need to say that the expression equals 8. x+6=8 Any equation that simplifies to this equation is a correct answer."
451,Given information: c = cost of a shirt 0.25c = 25% of the cost of the shirt Equation: c ndash; 0.25c = 28.80 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,A shirt is on sale for 25% off the original price. The sale price is 28.80. What was the original cost of the shirt?,"###Write an explanation to this problem:
Given information: c = cost of a shirt 0.25c = 25% of the cost of the shirt Equation: c ndash; 0.25c = 28.80 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
A shirt is on sale for 25% off the original price. The sale price is 28.80. What was the original cost of the shirt?"
547,Ed burns 500 calories an hour running. He burns 650 calories an hour biking. Use the distributive property to write two different expressions that can be used to represent the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours. The Utah Middle School Math Project,"If Ed runs for two hours, he will burn 2500 calories. If he bikes for two hours, he will burn 2650 calories. So, the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours can be represented by the following expression: 2650 - 2500 Another way to think about this problem is that the difference between the number of calories Ed burns after running for an hour and the number of calories Ed burns after biking for an hour is 650 - 500 calories. Since he runs for two hours, an appropriate representation could be 2650 - 500","###Write an explanation to this problem:
Ed burns 500 calories an hour running. He burns 650 calories an hour biking. Use the distributive property to write two different expressions that can be used to represent the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours. The Utah Middle School Math Project
###Explanation:
If Ed runs for two hours, he will burn 2500 calories. If he bikes for two hours, he will burn 2650 calories. So, the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours can be represented by the following expression: 2650 - 2500 Another way to think about this problem is that the difference between the number of calories Ed burns after running for an hour and the number of calories Ed burns after biking for an hour is 650 - 500 calories. Since he runs for two hours, an appropriate representation could be 2650 - 500"
576,Write a context to match the numeric expression given. 40 + 625 The Utah Middle School Math Project,"Angie runs a company specializing in selling rare gems. For online orders, there is a 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 40 + 625 The Utah Middle School Math Project
###Explanation:
Angie runs a company specializing in selling rare gems. For online orders, there is a 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost?"
49,"If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.","The easiest way to compare recipes is to find the ratio of ingredients for multiple batches until you find a common measurement for a specific ingredient. In this case, the following tables show both recipes up to the point that they both have 2 cups of milk. First Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 2 1 2 4 2 Second Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 3 2 Since the first recipe uses more scoops of chocolate ice cream to the same amount of milk, it means it would have a stronger chocolate flavor.","###Write an explanation to this problem:
If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.
###Explanation:
The easiest way to compare recipes is to find the ratio of ingredients for multiple batches until you find a common measurement for a specific ingredient. In this case, the following tables show both recipes up to the point that they both have 2 cups of milk. First Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 2 1 2 4 2 Second Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 3 2 Since the first recipe uses more scoops of chocolate ice cream to the same amount of milk, it means it would have a stronger chocolate flavor."
120,"Lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. Explain some possible reasons why these measurements differ.","Two diameters of the same circle should have the same length. While the circle will always have the same diameter, the measured distance can change based on human error. Some errors that may have occurred when measuring the circle is: Lin not measuring across the widest part when measuring vertically the measurements could have been rounded instead of exact The thickness of the circle may have affected the measurements","###Write an explanation to this problem:
Lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. Explain some possible reasons why these measurements differ.
###Explanation:
Two diameters of the same circle should have the same length. While the circle will always have the same diameter, the measured distance can change based on human error. Some errors that may have occurred when measuring the circle is: Lin not measuring across the widest part when measuring vertically the measurements could have been rounded instead of exact The thickness of the circle may have affected the measurements"
559,Write a context to match the numeric expression given. 0.150 + 0.0150 + 0.0150 The Utah Middle School Math Project,"Dom is a very avid magnet collector. He has found a small shop that seems to have a very cool selection of magnets. They offer large rectangular magnets for 10 cents each and small spherical magnets for 1 cent each. Since Dom's likes to have 50 of each magnet, he buys 50 rectangle and 50 sphere magnets. As he is leaving, he remembered that he owes his friend Mike 50 sphere magnets as well, and goes back to buy some more. In total, how much did Dom spend?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 0.150 + 0.0150 + 0.0150 The Utah Middle School Math Project
###Explanation:
Dom is a very avid magnet collector. He has found a small shop that seems to have a very cool selection of magnets. They offer large rectangular magnets for 10 cents each and small spherical magnets for 1 cent each. Since Dom's likes to have 50 of each magnet, he buys 50 rectangle and 50 sphere magnets. As he is leaving, he remembered that he owes his friend Mike 50 sphere magnets as well, and goes back to buy some more. In total, how much did Dom spend?"
299,Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.,"There are several ways that Elena could simulate the power up. One way to simulate getting the power-up is having the computer program pick a number between 1 and 100, if the number is between 1 and 15, then they got the best power-up. The program can be run 3 times to see if they get the best power-up 2 out of the 3 times. If at least 2 of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and estimate the probability as the proportion of trials for which at least 2 of the numbers are between 1 and 15.","###Write an explanation to this problem:
Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.
###Explanation:
There are several ways that Elena could simulate the power up. One way to simulate getting the power-up is having the computer program pick a number between 1 and 100, if the number is between 1 and 15, then they got the best power-up. The program can be run 3 times to see if they get the best power-up 2 out of the 3 times. If at least 2 of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and estimate the probability as the proportion of trials for which at least 2 of the numbers are between 1 and 15."
137,Give a number between -1 and -2. The Utah Middle School Math Project,"Negative numbers are the opposite of positive numbers. This means that the opposites of -1 and -2 are 1 and 2. A number that is between -1 and -2 will have its opposite between 1 and 2. There are many numbers between 1 and 2. For example: 1.5, 1.76, 1 2/3, and so on If we take the opposite, then these numbers are between -1 and -2. For example: -1.5, -1.76, -1 2/3, and so on","###Write an explanation to this problem:
Give a number between -1 and -2. The Utah Middle School Math Project
###Explanation:
Negative numbers are the opposite of positive numbers. This means that the opposites of -1 and -2 are 1 and 2. A number that is between -1 and -2 will have its opposite between 1 and 2. There are many numbers between 1 and 2. For example: 1.5, 1.76, 1 2/3, and so on If we take the opposite, then these numbers are between -1 and -2. For example: -1.5, -1.76, -1 2/3, and so on"
265,"The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.","In this case, we are using the median as our measure of center. This means that our middle point of our data that our data tends to cluster up around is the median. When the median is used in this way, then we use the interquartile range IQR as the measure of variability. This is how much our data varies from each other. If the medians are less than 2 IQR's apart, then they would not have a meaningful difference. The medians are 14,000 apart. If the IQR is 7,000 or more, then the medians would be less than 2 IQR's apart.","###Write an explanation to this problem:
The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.
###Explanation:
In this case, we are using the median as our measure of center. This means that our middle point of our data that our data tends to cluster up around is the median. When the median is used in this way, then we use the interquartile range IQR as the measure of variability. This is how much our data varies from each other. If the medians are less than 2 IQR's apart, then they would not have a meaningful difference. The medians are 14,000 apart. If the IQR is 7,000 or more, then the medians would be less than 2 IQR's apart."
848,List the sample space the available options for the chance experiment given. Flipping a coin,The sample space for flipping a coin is heads or tails. You have a 1/2 chance of either flipping a coin on tales or flipping a coin on heads. This works out to be a 50% of each outcome occurring.,"###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
The sample space for flipping a coin is heads or tails. You have a 1/2 chance of either flipping a coin on tales or flipping a coin on heads. This works out to be a 50% of each outcome occurring."
440,The following equation is given: 4x + 2 = 30 Provide a context/word problem for the given information. The Utah Middle School Math Project,Four times a number increased by 2 is 30. What is the number?,"###Write an explanation to this problem:
The following equation is given: 4x + 2 = 30 Provide a context/word problem for the given information. The Utah Middle School Math Project
###Explanation:
Four times a number increased by 2 is 30. What is the number?"
777,What is the difference between 6z and z6?,"6z is z+z+z+z+z+z, and z^6 is z*z*z*z*z*z.","###Write an explanation to this problem:
What is the difference between 6z and z6?
###Explanation:
6z is z+z+z+z+z+z, and z^6 is z*z*z*z*z*z."
33,"In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.",There are multiple answers to this question. These are just a couple of examples. The ratio of cups of sparkling water to cups of grape juice concentrate is 6 to 2. The ratio of cups of sparkling water to cups of grape juice concentrate is 30 to 10.,"###Write an explanation to this problem:
In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
###Explanation:
There are multiple answers to this question. These are just a couple of examples. The ratio of cups of sparkling water to cups of grape juice concentrate is 6 to 2. The ratio of cups of sparkling water to cups of grape juice concentrate is 30 to 10."
31,A fisherman weighs an ahi tuna a very large fish on a scale and gets a reading of 135 pounds. The reading on the scale may have an error of up to 5%. What are two possible values for the actual weight of the fish?,"If there is a 1% error, the actual weight of the fish would be 133.65 pounds because 0.99135 = 133.65 or 136.35 pounds because 1.01135 = 136.35.","###Write an explanation to this problem:
A fisherman weighs an ahi tuna a very large fish on a scale and gets a reading of 135 pounds. The reading on the scale may have an error of up to 5%. What are two possible values for the actual weight of the fish?
###Explanation:
If there is a 1% error, the actual weight of the fish would be 133.65 pounds because 0.99135 = 133.65 or 136.35 pounds because 1.01135 = 136.35."
696,"The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project","The equation for area of a parallelogram is area=base*height, or A=bh. Plug the given values into this equation. 155.52=b*28.8.","###Write an explanation to this problem:
The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The equation for area of a parallelogram is area=base*height, or A=bh. Plug the given values into this equation. 155.52=b*28.8."
712,Solve the inequality. Represent the solution on a number line. 8xge;2 The Utah Middle School Math Project,Solve for x. The number line should be greater than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 8xge;2 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be greater than and equal to the solution."
367,"Write each expression as a multiple of a power of 10: 42,300 copied for free from openupresources.org","Sample Answer: 423*10^2, 4.23*10^4","###Write an explanation to this problem:
Write each expression as a multiple of a power of 10: 42,300 copied for free from openupresources.org
###Explanation:
Sample Answer: 423*10^2, 4.23*10^4"
76,"Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.","In drawing a triangle with three provided side lengths, there is only one way to draw the triangle. Once one length is drawn, the other two lengths are used to draw circles with the lengths as the respective radii of each circle, centered at either end of the segment drawn first. Regardless of which order of segments is used, there is only one unique triangle that can be drawn. In drawing a triangle with two side lengths and included angle provided, there is only one way to draw the triangle. Once the angle is drawn and the two side lengths are marked off on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle.","###Write an explanation to this problem:
Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.
###Explanation:
In drawing a triangle with three provided side lengths, there is only one way to draw the triangle. Once one length is drawn, the other two lengths are used to draw circles with the lengths as the respective radii of each circle, centered at either end of the segment drawn first. Regardless of which order of segments is used, there is only one unique triangle that can be drawn. In drawing a triangle with two side lengths and included angle provided, there is only one way to draw the triangle. Once the angle is drawn and the two side lengths are marked off on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle."
247,Explain how to make this calculation mentally. 99 * 15,"I would add 1 to 99 to get 100 x 15=1,500 and then subtract the extra group of 15 that we added and get 1,500-15=1,485.","###Write an explanation to this problem:
Explain how to make this calculation mentally. 99 * 15
###Explanation:
I would add 1 to 99 to get 100 x 15=1,500 and then subtract the extra group of 15 that we added and get 1,500-15=1,485."
477,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A child's wading pool is being inflated. The pool's size increases at a rate of 2 cubic feet per minute. The Utah Middle School Math Project,Time is the dependent variable. The size of the pool depends on the amount of time the pool has been inflating. The size is dependent.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A child's wading pool is being inflated. The pool's size increases at a rate of 2 cubic feet per minute. The Utah Middle School Math Project
###Explanation:
Time is the dependent variable. The size of the pool depends on the amount of time the pool has been inflating. The size is dependent."
235,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,Pages 1 through 428 are the sample space for this experiment.,"###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
Pages 1 through 428 are the sample space for this experiment."
72,A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour. Name two quantities in this situation that are in a functional relationship. Copied for free from openupresources.org,The amount of yeast and the amount of flour.,"###Write an explanation to this problem:
A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour. Name two quantities in this situation that are in a functional relationship. Copied for free from openupresources.org
###Explanation:
The amount of yeast and the amount of flour."
77,"For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7",20 + - 9 + 8 +-7 A subtraction sign is the same thing as adding the opposite. This expression could be combined to equal 12,"###Write an explanation to this problem:
For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7
###Explanation:
20 + - 9 + 8 +-7 A subtraction sign is the same thing as adding the opposite. This expression could be combined to equal 12"
739,Jane paid 40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was 48. How do you think Jane's friend arrived at this amount?,"Jane's friend found that 20% of 40 is 8. Then, she added 8 to the sale price: 40 + 8 = 48. That is how she determined that the original amount was 48.","###Write an explanation to this problem:
Jane paid 40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was 48. How do you think Jane's friend arrived at this amount?
###Explanation:
Jane's friend found that 20% of 40 is 8. Then, she added 8 to the sale price: 40 + 8 = 48. That is how she determined that the original amount was 48."
542,Write an ordered pair that would be on the y-axis when graphed. The Utah Middle School Math Project,"Any ordered pair x, y where x = 0 is on the y-axis. Examples: 0, 7 0, -7 0, 0","###Write an explanation to this problem:
Write an ordered pair that would be on the y-axis when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair x, y where x = 0 is on the y-axis. Examples: 0, 7 0, -7 0, 0"
409,"Make a list to find the GCF of this pair of numbers. 45 and 60 First, write the list here. The Utah Middle School Math Project","Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 45 and 60 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60"
286,"Decide if the data set below might produce one or more gaps when represented by a histogram. If you think the data set might produce gaps, briefly describe or give an example of how the values in the data set might do so. The ages of students in a sixth-grade class.",This would not have any gaps.,"###Write an explanation to this problem:
Decide if the data set below might produce one or more gaps when represented by a histogram. If you think the data set might produce gaps, briefly describe or give an example of how the values in the data set might do so. The ages of students in a sixth-grade class.
###Explanation:
This would not have any gaps."
174,"Over several months, the weight of a baby measured in pounds doubles. Does its weight measure in kilograms also double? Explain","Yes, the weight is doubled. Whatever measurement you are using, if one unit of measurement doubles, then all units of measurement will double. The weights will just be different since 1lb is equal to about 0.45 kilograms.","###Write an explanation to this problem:
Over several months, the weight of a baby measured in pounds doubles. Does its weight measure in kilograms also double? Explain
###Explanation:
Yes, the weight is doubled. Whatever measurement you are using, if one unit of measurement doubles, then all units of measurement will double. The weights will just be different since 1lb is equal to about 0.45 kilograms."
680,"Augusto tips 20% on his meals. If he tipped 4.80 on a meal, how much was the meal? Write an equation to solve the problem. The Utah Middle School Math Project",The percent tipped in decimal form times the original order is the amount tipped. This means 0.2*m=4.80,"###Write an explanation to this problem:
Augusto tips 20% on his meals. If he tipped 4.80 on a meal, how much was the meal? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The percent tipped in decimal form times the original order is the amount tipped. This means 0.2*m=4.80"
851,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,The sample space for this experiment is the pages in the book. You have an opportunity to land at any page in the book equally.,"###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
The sample space for this experiment is the pages in the book. You have an opportunity to land at any page in the book equally."
294,"Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.","There are multiple answers to this question, this is just an example: How many followers do you have on Twitter? It will produce numerical data because all of the answers we receive will be in number form.","###Write an explanation to this problem:
Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.
###Explanation:
There are multiple answers to this question, this is just an example: How many followers do you have on Twitter? It will produce numerical data because all of the answers we receive will be in number form."
381,"Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9",5 - 9 = 5 + -9,"###Write an explanation to this problem:
Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9
###Explanation:
5 - 9 = 5 + -9"
481,Create a representation of a table of data that represents a linear function. The Utah Middle School Math Project,There are many different tables that can be created that represent a linear function. One possible example is: x 1 2 3 4 5 6 y 2 4 6 8 10 12,"###Write an explanation to this problem:
Create a representation of a table of data that represents a linear function. The Utah Middle School Math Project
###Explanation:
There are many different tables that can be created that represent a linear function. One possible example is: x 1 2 3 4 5 6 y 2 4 6 8 10 12"
666,Solve the inequality. Represent the solution on a number line. x/0.5le;18 The Utah Middle School Math Project,Solve for x. The number line should be less than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. x/0.5le;18 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than and equal to the solution."
623,Give a number between -1 and -2. The Utah Middle School Math Project,"Your answer can be any negative number that is less than -1 and greater than -2. Possible answers: -1.01, -1.99, -1 1/4, -3/2","###Write an explanation to this problem:
Give a number between -1 and -2. The Utah Middle School Math Project
###Explanation:
Your answer can be any negative number that is less than -1 and greater than -2. Possible answers: -1.01, -1.99, -1 1/4, -3/2"
631,"In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: 0 = x - 5 Original Equation: 5=x Action: ______ The Utah Middle School Math Project","On the right side of the equation, 5 has been added to x-5. On the left side, 5 has been added to 0, which results in 5. The action was: Add 5 to both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: 0 = x - 5 Original Equation: 5=x Action: ______ The Utah Middle School Math Project
###Explanation:
On the right side of the equation, 5 has been added to x-5. On the left side, 5 has been added to 0, which results in 5. The action was: Add 5 to both sides of the equation."
344,The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org,"The first expression represents the volume of liquid in one of the containers. The second expression represents the volume of liquid in the other container. If you set the two expressions equal to each other, this means that the volume of liquid in both of the containers is equal. You are trying to solve for t to find how much time, t, must pass before the two containers have the same amount of liquid in them.","###Write an explanation to this problem:
The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org
###Explanation:
The first expression represents the volume of liquid in one of the containers. The second expression represents the volume of liquid in the other container. If you set the two expressions equal to each other, this means that the volume of liquid in both of the containers is equal. You are trying to solve for t to find how much time, t, must pass before the two containers have the same amount of liquid in them."
290,Invent a data set with five numbers that has a mean of 10 and a median of 12.,There are a variety of correct answers to this question.,"###Write an explanation to this problem:
Invent a data set with five numbers that has a mean of 10 and a median of 12.
###Explanation:
There are a variety of correct answers to this question."
644,Explain ratio in your own words. Give several examples of ratios. The Utah Middle School Math Project,Sample: A ratio expresses a relationship between two quantities.,"###Write an explanation to this problem:
Explain ratio in your own words. Give several examples of ratios. The Utah Middle School Math Project
###Explanation:
Sample: A ratio expresses a relationship between two quantities."
215,Priya has completed 9 exam questions. This is 60% of the questions on the exam. Write an equation representing this situation. Explain the meaning of any variables you use.,0.6x=9 x represents the total number of exam questions,"###Write an explanation to this problem:
Priya has completed 9 exam questions. This is 60% of the questions on the exam. Write an equation representing this situation. Explain the meaning of any variables you use.
###Explanation:
0.6x=9 x represents the total number of exam questions"
5,"Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.","Subtracting a negative number is the same as adding the positive version of that number. For example, 3 - -2 = 3 + 2. So -9.5 - -8 - 6.5 = -9.5 + 8 - 6.5.","###Write an explanation to this problem:
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.
###Explanation:
Subtracting a negative number is the same as adding the positive version of that number. For example, 3 - -2 = 3 + 2. So -9.5 - -8 - 6.5 = -9.5 + 8 - 6.5."
54,The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org,The two sides of the equation represent the volume in the two containers.,"###Write an explanation to this problem:
The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org
###Explanation:
The two sides of the equation represent the volume in the two containers."
422,"Justine and her family are floating down a river. After 1 hour, they have floated 1.25 miles, after 4 hours they have floated 5 miles, and after 6 hours they have floated 7.5 miles. Is the relationship between time in hours and distance in miles linear? Why or why not? The Utah Middle School Math Project","This data is linear, because the relationship between the number of hours that have passed, and the distance they have floated is constant.","###Write an explanation to this problem:
Justine and her family are floating down a river. After 1 hour, they have floated 1.25 miles, after 4 hours they have floated 5 miles, and after 6 hours they have floated 7.5 miles. Is the relationship between time in hours and distance in miles linear? Why or why not? The Utah Middle School Math Project
###Explanation:
This data is linear, because the relationship between the number of hours that have passed, and the distance they have floated is constant."
375,Use the expressions and equation below about the cost of clothes to answer the questions that follow Cost of a shirt: c Cost of a pair of jeans: + 12 3 + 2 + 12 = 164 Write a story that matches the expressions and equation in the space provided. The Utah Middle School Math Project,"A pair of jeans costs 12 dollars more than the cost of a shirt. Because of what these expressions are divided by in the final equation, we can see that 3 shirts were bought, and 2 pairs of jeans were bought.","###Write an explanation to this problem:
Use the expressions and equation below about the cost of clothes to answer the questions that follow Cost of a shirt: c Cost of a pair of jeans: + 12 3 + 2 + 12 = 164 Write a story that matches the expressions and equation in the space provided. The Utah Middle School Math Project
###Explanation:
A pair of jeans costs 12 dollars more than the cost of a shirt. Because of what these expressions are divided by in the final equation, we can see that 3 shirts were bought, and 2 pairs of jeans were bought."
244,Explain how to make this calculation mentally. 244 - 99,"I would add 1 to 99 to make it 244 - 100= 144 and since you took one more away than you needed to, you add that one back to get 144+1=145.","###Write an explanation to this problem:
Explain how to make this calculation mentally. 244 - 99
###Explanation:
I would add 1 to 99 to make it 244 - 100= 144 and since you took one more away than you needed to, you add that one back to get 144+1=145."
97,Make up your own pattern that is not linear. Prove that your pattern is not linear with at least 2 pieces of evidence. The Utah Middle School Math Project,"A pattern is determined to be linear if the same amount of objects is being added each time. The problem asks you to create a pattern that is not linear. In order to prove that your pattern is not linear, you could draw a graph or a diagram, show math work to back up your answer, and explain in text why the pattern is not linear.","###Write an explanation to this problem:
Make up your own pattern that is not linear. Prove that your pattern is not linear with at least 2 pieces of evidence. The Utah Middle School Math Project
###Explanation:
A pattern is determined to be linear if the same amount of objects is being added each time. The problem asks you to create a pattern that is not linear. In order to prove that your pattern is not linear, you could draw a graph or a diagram, show math work to back up your answer, and explain in text why the pattern is not linear."
552,Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project,"Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad.","###Write an explanation to this problem:
Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project
###Explanation:
Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad."
816,"In your own words, what is the least common multiple of two whole numbers? How can you find it?","The least common multiple of two whole numbers is the lowest number that is a multiple of both of the two whole numbers. For example, the lowest common multiple of 2 and 5 is 10, because the first few multiples for 2 are 2, 4, 6, 8, 10 and the first few multiples of 5 is 5 and 10. 10 is a number that is a multiple of both, but it is also the lowest multiple they have in common.","###Write an explanation to this problem:
In your own words, what is the least common multiple of two whole numbers? How can you find it?
###Explanation:
The least common multiple of two whole numbers is the lowest number that is a multiple of both of the two whole numbers. For example, the lowest common multiple of 2 and 5 is 10, because the first few multiples for 2 are 2, 4, 6, 8, 10 and the first few multiples of 5 is 5 and 10. 10 is a number that is a multiple of both, but it is also the lowest multiple they have in common."
464,Write a story that matches the expressions and equations. Fixing Your Car Time hours: h Cost of Mike's Mechanics dollars: 15h + 75 Cost of Bubba's Body Shop dollars: 25h 15h + 75 = 25h The Utah Middle School Math Project,"The cost of Mike's Mechanics is 15h + 75, meaning there must be an initial fee of 75 and for every hour you will pay an additional 15. The cost of Bubba's Body Shop is 25h, meaning you will pay 25 dollars per hour. So, when 15h +75 = 25h, the cost of Mike's Mechanics will be equal to the cost of Bubba's Body Shop. Solve for h to find out after how many hours will both shops charge the same rate to fix your car.","###Write an explanation to this problem:
Write a story that matches the expressions and equations. Fixing Your Car Time hours: h Cost of Mike's Mechanics dollars: 15h + 75 Cost of Bubba's Body Shop dollars: 25h 15h + 75 = 25h The Utah Middle School Math Project
###Explanation:
The cost of Mike's Mechanics is 15h + 75, meaning there must be an initial fee of 75 and for every hour you will pay an additional 15. The cost of Bubba's Body Shop is 25h, meaning you will pay 25 dollars per hour. So, when 15h +75 = 25h, the cost of Mike's Mechanics will be equal to the cost of Bubba's Body Shop. Solve for h to find out after how many hours will both shops charge the same rate to fix your car."
817,"A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered? Explain your answer, and how you got it.","Sample response: An even number of tiles fit on the30 foot length of the room 20 tiles, but the width requires 13 1/3 tiles. This accounts for a 20 tile by 13 tile array. 20 * 13 = 260 260 tiles need to be ordered. The remaining area is 30 ft. * 0.5 ft. 20 * 1/3 tile Since 20 of the 1/3 tiles are needed, 7 additional tiles must be cut to form 21/3. 20 of these will be used with 1/3 of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles.","###Write an explanation to this problem:
A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered? Explain your answer, and how you got it.
###Explanation:
Sample response: An even number of tiles fit on the30 foot length of the room 20 tiles, but the width requires 13 1/3 tiles. This accounts for a 20 tile by 13 tile array. 20 * 13 = 260 260 tiles need to be ordered. The remaining area is 30 ft. * 0.5 ft. 20 * 1/3 tile Since 20 of the 1/3 tiles are needed, 7 additional tiles must be cut to form 21/3. 20 of these will be used with 1/3 of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles."
828,Find 3 different ratios that are equivalent to 7 : 3,14:6 21:9 70:30,"###Write an explanation to this problem:
Find 3 different ratios that are equivalent to 7 : 3
###Explanation:
14:6 21:9 70:30"
84,Find a number that matches the description. A 4-digit number that is divisible by 5 and 9 but not divisible by 10. How do you know? The Utah Middle School Math Project,"There are many different correct answers to this question. We want a number that is divisible by 5 and 9, but not by 10. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 9, the digits must sum to a number that is divisible by 9. To be divisible by 10, the last digit must be a 0. If we want our number to be divisible by 5 but not 10, then the last digit must be a 5. _ _ _ 5 Finally, let's pick our other three digits so that all four digits add to a number divisible by 9. This could be 5445. 5 + 4 + 4 + 5 = 18, and 18 is divisible by 9. Our number could be 5445.","###Write an explanation to this problem:
Find a number that matches the description. A 4-digit number that is divisible by 5 and 9 but not divisible by 10. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 5 and 9, but not by 10. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 9, the digits must sum to a number that is divisible by 9. To be divisible by 10, the last digit must be a 0. If we want our number to be divisible by 5 but not 10, then the last digit must be a 5. _ _ _ 5 Finally, let's pick our other three digits so that all four digits add to a number divisible by 9. This could be 5445. 5 + 4 + 4 + 5 = 18, and 18 is divisible by 9. Our number could be 5445."
10,Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < <,-1 < 0 < 1,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < <
###Explanation:
-1 < 0 < 1"
664,Solve the inequality. Represent the solution on a number line. y/11<66 The Utah Middle School Math Project,"Solve for y. The number line should be less than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. y/11<66 The Utah Middle School Math Project
###Explanation:
Solve for y. The number line should be less than the solution, but not contain it."
355,"Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.","This is the original problem: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 Now we can see how this problem, which began as subtraction, can be rewritten as an addition problem.","###Write an explanation to this problem:
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.
###Explanation:
This is the original problem: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 Now we can see how this problem, which began as subtraction, can be rewritten as an addition problem."
382,"Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. -14 - -2",-14 - -2 = -14 + 2,"###Write an explanation to this problem:
Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. -14 - -2
###Explanation:
-14 - -2 = -14 + 2"
118,"120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.",120% is equivalent to the decimal 1.2. 1.2 * x = 78 ---> The word of means to multiply,"###Write an explanation to this problem:
120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.
###Explanation:
120% is equivalent to the decimal 1.2. 1.2 * x = 78 ---> The word of means to multiply"
362,"Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org","From 8:00 am to 9:20 am, the phone lost 10% battery. This is 80 minutes time, so every 8 minutes, she will lost 1% battery. After 800 total minutes from 8:00 am, she would lose all of her battery. 8 min/1%*100% = 800 minutes 800 minutes is 13 hours and 20 minutes. 13 hours and 20 minutes from 8:00 am is 9:20 pm. We can estimate her phone will die at around 9:20 pm.","###Write an explanation to this problem:
Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org
###Explanation:
From 8:00 am to 9:20 am, the phone lost 10% battery. This is 80 minutes time, so every 8 minutes, she will lost 1% battery. After 800 total minutes from 8:00 am, she would lose all of her battery. 8 min/1%*100% = 800 minutes 800 minutes is 13 hours and 20 minutes. 13 hours and 20 minutes from 8:00 am is 9:20 pm. We can estimate her phone will die at around 9:20 pm."
250,Suppose EF and GH are line segments of the same length. Describe a sequence of transformations that moves EF to GH . Copied for free from openupresources.org,"A translation of EF that moves E to G ,and then rotate EF with center G until the image of F lines up with H.","###Write an explanation to this problem:
Suppose EF and GH are line segments of the same length. Describe a sequence of transformations that moves EF to GH . Copied for free from openupresources.org
###Explanation:
A translation of EF that moves E to G ,and then rotate EF with center G until the image of F lines up with H."
29,Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true. Copied for free from openupresources.org,"40,100 20,140 10,160","###Write an explanation to this problem:
Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true. Copied for free from openupresources.org
###Explanation:
40,100 20,140 10,160"
709,Solve the inequality. Represent the solution on a number line. 32ge;8x The Utah Middle School Math Project,Solve for x. The number line should be less than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 32ge;8x The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than and equal to the solution."
751,Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < <,-1 < 0 < 1,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < <
###Explanation:
-1 < 0 < 1"
302,"A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M. What letters are possible to teach using this method? There are 15","List the days of the week and highlight each of the letters only once. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY These letters are M, O, N, D, A, Y, T, U, E, S, W, H, R, F, I. Put these in order. A,D,E,F,H,I,M,N,O,R,S,T,U,W,Y","###Write an explanation to this problem:
A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M. What letters are possible to teach using this method? There are 15
###Explanation:
List the days of the week and highlight each of the letters only once. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY These letters are M, O, N, D, A, Y, T, U, E, S, W, H, R, F, I. Put these in order. A,D,E,F,H,I,M,N,O,R,S,T,U,W,Y"
333,Here is an equation that is true for all values of x: 5x + 2 = 5x + 10. Elena saw this equation and says she can tell 20x + 2 + 31 = 45x + 10 + 31 is also true for any value of x. How can she tell? Explain your reasoning.,"Elena can tell that the equation, 20x + 2 + 31 = 45x + 10 + 31, is true for any value of x, because both sides of the equation are equal and will cancel out. While the two sides do not look equal at first, the equation can be rearranged using the distributive property. First the equation can be simplified to make it easier to compare both sides. 20x + 2 + 31 = 45x + 10 + 31 Both sides have 31 being added to them so that term cancels out after subtracting 31 from both sides. 20x + 2 = 45x + 10 Within the parenthesis on the right both terms are multiples of 5, so using the distributive property, a 5 can be taken out of the parenthesis. 20x + 2 = 4*5x + 2 20x + 2 = 20x + 2 Since both sides are the same, each term will cancel out and the equation will eventually simplify to 0 = 0, making all values of x true.","###Write an explanation to this problem:
Here is an equation that is true for all values of x: 5x + 2 = 5x + 10. Elena saw this equation and says she can tell 20x + 2 + 31 = 45x + 10 + 31 is also true for any value of x. How can she tell? Explain your reasoning.
###Explanation:
Elena can tell that the equation, 20x + 2 + 31 = 45x + 10 + 31, is true for any value of x, because both sides of the equation are equal and will cancel out. While the two sides do not look equal at first, the equation can be rearranged using the distributive property. First the equation can be simplified to make it easier to compare both sides. 20x + 2 + 31 = 45x + 10 + 31 Both sides have 31 being added to them so that term cancels out after subtracting 31 from both sides. 20x + 2 = 45x + 10 Within the parenthesis on the right both terms are multiples of 5, so using the distributive property, a 5 can be taken out of the parenthesis. 20x + 2 = 4*5x + 2 20x + 2 = 20x + 2 Since both sides are the same, each term will cancel out and the equation will eventually simplify to 0 = 0, making all values of x true."
81,Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project,"There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 4 + 0 = 4, so to get to the next number that is divisible by 3, 6, we have to add 2. 2 4 0 240 is divisible by 3 and 4. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144.","###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 4 + 0 = 4, so to get to the next number that is divisible by 3, 6, we have to add 2. 2 4 0 240 is divisible by 3 and 4. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144."
630,"In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x + 5 = 12 Original Equation: x=7 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 5 has been subtracted from x+5. On the right side, 5 has been subtracted from 12, which results in 7. The action was: Subtract 5 from both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x + 5 = 12 Original Equation: x=7 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 5 has been subtracted from x+5. On the right side, 5 has been subtracted from 12, which results in 7. The action was: Subtract 5 from both sides of the equation."
388,3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of as 3 + 3 + 3 + 3","###Write an explanation to this problem:
3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of as 3 + 3 + 3 + 3"
537,"In your own words, describe what it means for two figures to be congruent. The Utah Middle School Math Project","Two figures are congruent if the second can be obtained from the first by a rigid motion rotation, reflection, or translation or a sequence of rigid motions. If you can move one of the figures using one of these transformations or a series of these transformations so that it fits exactly on the other one, the two figures are congruent.","###Write an explanation to this problem:
In your own words, describe what it means for two figures to be congruent. The Utah Middle School Math Project
###Explanation:
Two figures are congruent if the second can be obtained from the first by a rigid motion rotation, reflection, or translation or a sequence of rigid motions. If you can move one of the figures using one of these transformations or a series of these transformations so that it fits exactly on the other one, the two figures are congruent."
551,Make a mapping of a relation that is a function. Explain how you know. The Utah Middle School Math Project,"There are many different mappings that represent functions, so answers will vary Each input should have exactly one output","###Write an explanation to this problem:
Make a mapping of a relation that is a function. Explain how you know. The Utah Middle School Math Project
###Explanation:
There are many different mappings that represent functions, so answers will vary Each input should have exactly one output"
756,Write a word problem whose solution is |20| = 20.,Kelli flew a kite 𝟐𝟎 feet above the ground. Determine the distance between the kite and the ground.,"###Write an explanation to this problem:
Write a word problem whose solution is |20| = 20.
###Explanation:
Kelli flew a kite 𝟐𝟎 feet above the ground. Determine the distance between the kite and the ground."
363,"Problem 7 Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 5:1 and 15:3 copied for free from openupresources.org","In order to find equivalent ratios, we multiply or divide the numbers in a ratio by the same number. So we can take one set of ratio numbers and see if we can find a number that we could multiply or divide to equal the other set of ratio numbers. If we use the 5:1 ratio, and multiply each of those by 3 we will get the 15:3 ratio. We could also take the 15:3 ratio and divide each of those by 3 to get the 5:1 ratio.","###Write an explanation to this problem:
Problem 7 Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 5:1 and 15:3 copied for free from openupresources.org
###Explanation:
In order to find equivalent ratios, we multiply or divide the numbers in a ratio by the same number. So we can take one set of ratio numbers and see if we can find a number that we could multiply or divide to equal the other set of ratio numbers. If we use the 5:1 ratio, and multiply each of those by 3 we will get the 15:3 ratio. We could also take the 15:3 ratio and divide each of those by 3 to get the 5:1 ratio."
516,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. The admission fee at a local zoo is 1.50 for children and 4.00 for adults. On a certain day, 2,200 people enter the zoo and 5,050 is collected. How many children and how many adults attended? The Utah Middle School Math Project","c + a = 2200 where c is number of children tickets and a is number of adult tickets 1.5c+ 4a = 5050 1,500 children attended and 700 adults attended","###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. The admission fee at a local zoo is 1.50 for children and 4.00 for adults. On a certain day, 2,200 people enter the zoo and 5,050 is collected. How many children and how many adults attended? The Utah Middle School Math Project
###Explanation:
c + a = 2200 where c is number of children tickets and a is number of adult tickets 1.5c+ 4a = 5050 1,500 children attended and 700 adults attended"
770,Describe a situation that could be modeled with the ratio 4:1.,"For every four customers at a restaurant, one orders dessert.","###Write an explanation to this problem:
Describe a situation that could be modeled with the ratio 4:1.
###Explanation:
For every four customers at a restaurant, one orders dessert."
447,61% of 20 Estimate the answer. The Utah Middle School Math Project,"50% of 20 is 10, so 61% of 20 must be greater than 10.","###Write an explanation to this problem:
61% of 20 Estimate the answer. The Utah Middle School Math Project
###Explanation:
50% of 20 is 10, so 61% of 20 must be greater than 10."
684,Create a context for the numeric representation. 601 + 60.75 = 601.75 = 105 The Utah Middle School Math Project,"Sample Answer: If a person has 60 apples, then gains 75% more apples than the original 60, this numeric expression describes the total number of apples.","###Write an explanation to this problem:
Create a context for the numeric representation. 601 + 60.75 = 601.75 = 105 The Utah Middle School Math Project
###Explanation:
Sample Answer: If a person has 60 apples, then gains 75% more apples than the original 60, this numeric expression describes the total number of apples."
457,Given information: m = height of a maple tree 0.15m = 15% of the height of the maple tree Equation: m + 0.15m = 97.75 feet Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,"Since January, the maple tree in front of my house has grown by15% of its original height. It's now 97.75 feet. How tall was my tree in January?","###Write an explanation to this problem:
Given information: m = height of a maple tree 0.15m = 15% of the height of the maple tree Equation: m + 0.15m = 97.75 feet Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Since January, the maple tree in front of my house has grown by15% of its original height. It's now 97.75 feet. How tall was my tree in January?"
266,"The inequalities h > 42 and h < 60 represent the height requirements for an amusement park ride, where h represents a person's height in inches. Write a sentence or draw a sign that describes these rules as clearly as possible.","You have to be at least 42 inches tall to ride, but you can not ride if you are taller than 60 inches.","###Write an explanation to this problem:
The inequalities h > 42 and h < 60 represent the height requirements for an amusement park ride, where h represents a person's height in inches. Write a sentence or draw a sign that describes these rules as clearly as possible.
###Explanation:
You have to be at least 42 inches tall to ride, but you can not ride if you are taller than 60 inches."
231,"Andre would like to estimate the mean number of books the students at his school read over the summer break. He has a list of the names of all the students at the school, but he doesn't have time to ask every student how many books they read. What should Andre do to estimate the mean number of books?","There are many things that Andre could do to estimate the mean number of books. Andre could estimate the mean by using the list he has to select a random sample of the students, then asking the students in the sample how many books they read over the summer. He could choose a sample size, but it would be better to take a larger sample if he can, because this probably gives him a more accurate estimate.","###Write an explanation to this problem:
Andre would like to estimate the mean number of books the students at his school read over the summer break. He has a list of the names of all the students at the school, but he doesn't have time to ask every student how many books they read. What should Andre do to estimate the mean number of books?
###Explanation:
There are many things that Andre could do to estimate the mean number of books. Andre could estimate the mean by using the list he has to select a random sample of the students, then asking the students in the sample how many books they read over the summer. He could choose a sample size, but it would be better to take a larger sample if he can, because this probably gives him a more accurate estimate."
323,Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8.,"The original equation and Andre's equation look like: 2x + 6 = 3x - 8 -x + 6 = -8 We can see that the constants 6 and -8 did not change, only the x's on both sides did. There is no longer 3x on the right hand side. Andre must have subtracted 3x from both sides of the equation. Remember that subtracting 3x is the same as adding -3x.","###Write an explanation to this problem:
Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8.
###Explanation:
The original equation and Andre's equation look like: 2x + 6 = 3x - 8 -x + 6 = -8 We can see that the constants 6 and -8 did not change, only the x's on both sides did. There is no longer 3x on the right hand side. Andre must have subtracted 3x from both sides of the equation. Remember that subtracting 3x is the same as adding -3x."
211,Find a value for x that makes -x less than 2x. copied for free from openupresources.org,"If x is any positive number, -x will be less than 2x.","###Write an explanation to this problem:
Find a value for x that makes -x less than 2x. copied for free from openupresources.org
###Explanation:
If x is any positive number, -x will be less than 2x."
259,Make up a situation where a quantity is changing. Explain what it means to have a negative change.,A negative change can be a loss or expenditure.,"###Write an explanation to this problem:
Make up a situation where a quantity is changing. Explain what it means to have a negative change.
###Explanation:
A negative change can be a loss or expenditure."
7,"Nathan is your school's star soccer player. When he takes a shot on goal, he typically scores half of the time. Suppose that he takes six shots in a game. To estimate the probability of the number of goals Nathan makes, use simulation with a number cube. One roll of a number cube represents one shot. For this problem, what represents a trial of taking six shots?","To simulate taking six shots, we will roll the number cube six times.","###Write an explanation to this problem:
Nathan is your school's star soccer player. When he takes a shot on goal, he typically scores half of the time. Suppose that he takes six shots in a game. To estimate the probability of the number of goals Nathan makes, use simulation with a number cube. One roll of a number cube represents one shot. For this problem, what represents a trial of taking six shots?
###Explanation:
To simulate taking six shots, we will roll the number cube six times."
281,"Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.","There are multiple answers to this question, this is just an example: Are you on Instagram? Answers: Yes or No","###Write an explanation to this problem:
Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.
###Explanation:
There are multiple answers to this question, this is just an example: Are you on Instagram? Answers: Yes or No"
155,A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.,"Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue.","###Write an explanation to this problem:
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.
###Explanation:
Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue."
786,Explain why 6:4 and 18:8 are not equivalent ratios.,"6:4 and 18:8 are not equivalent because 6 x 3= 18, but 4 x 3= 12, not 8. In order for two ratios to be equivalent, both numbers have to be multiplied or divided by the same number. 6 4 12 8 18 12","###Write an explanation to this problem:
Explain why 6:4 and 18:8 are not equivalent ratios.
###Explanation:
6:4 and 18:8 are not equivalent because 6 x 3= 18, but 4 x 3= 12, not 8. In order for two ratios to be equivalent, both numbers have to be multiplied or divided by the same number. 6 4 12 8 18 12"
101,Solve the inequality. Represent the solution on a number line. 2ge;0.4b The Utah Middle School Math Project,"Solve for b. Divide both sides of the inequality by 0.4, because this is the inverse of multiplying b by 0.4. 2/0.4 = 5 b<5 The number line should be less than and equal to the solution.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 2ge;0.4b The Utah Middle School Math Project
###Explanation:
Solve for b. Divide both sides of the inequality by 0.4, because this is the inverse of multiplying b by 0.4. 2/0.4 = 5 b<5 The number line should be less than and equal to the solution."
788,Choose an integer between -5 and -10. Label it R on a number line created and complete the following tasks. What is the opposite of R? Label it Q.,"Sample response: Let R be -6, then the opposite of R is 6. Therefore, Q is 6.","###Write an explanation to this problem:
Choose an integer between -5 and -10. Label it R on a number line created and complete the following tasks. What is the opposite of R? Label it Q.
###Explanation:
Sample response: Let R be -6, then the opposite of R is 6. Therefore, Q is 6."
530,Write an ordered pair that would be in Quadrant I when graphed. The Utah Middle School Math Project,"Any ordered pair x, y where both x and y are positive is in Quadrant I. Examples: 1, 1 5, 3 1/2, 3/4","###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant I when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair x, y where both x and y are positive is in Quadrant I. Examples: 1, 1 5, 3 1/2, 3/4"
430,A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project,The dependent variable is number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students.,"###Write an explanation to this problem:
A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The dependent variable is number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students."
444,50% of 21 Estimate the answer. The Utah Middle School Math Project,"50% of 20 is 10, so 50% of 21 must be greater than 10.","###Write an explanation to this problem:
50% of 21 Estimate the answer. The Utah Middle School Math Project
###Explanation:
50% of 20 is 10, so 50% of 21 must be greater than 10."
2,How can you find 50% of a number quickly in your head?,"50% is half of 100%, so finding 50% of a number quickly in your head would be the same thing as dividing by 2 half.","###Write an explanation to this problem:
How can you find 50% of a number quickly in your head?
###Explanation:
50% is half of 100%, so finding 50% of a number quickly in your head would be the same thing as dividing by 2 half."
192,"An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?",This simulation gives every flavor of ice cream a random chance of being selected. This would not accurately show the likelihood of each flavor being chose because people choose their ice cream flavor based on what they like.,"###Write an explanation to this problem:
An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?
###Explanation:
This simulation gives every flavor of ice cream a random chance of being selected. This would not accurately show the likelihood of each flavor being chose because people choose their ice cream flavor based on what they like."
462,Given information: s = the price of a pair of socks 5s ndash; 1 = the price of a pair of shoes Equation: 3s + 25s ndash; 1 = 56.50 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,Sally bought 3 pairs of socks and 2 pairs of shoes. A pair of shoes costs one dollar less than 5 times the price of a pair of socks. She spent 56.50. How much does a pair of socks cost and how much does a pair of shoes cost?,"###Write an explanation to this problem:
Given information: s = the price of a pair of socks 5s ndash; 1 = the price of a pair of shoes Equation: 3s + 25s ndash; 1 = 56.50 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Sally bought 3 pairs of socks and 2 pairs of shoes. A pair of shoes costs one dollar less than 5 times the price of a pair of socks. She spent 56.50. How much does a pair of socks cost and how much does a pair of shoes cost?"
497,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Whitney is training for a half marathon. She wants to know how long it will take her to run based on how far she has to run for. The Utah Middle School Math Project,How long it will take is the dependent variable The how far she has to run for is the independent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Whitney is training for a half marathon. She wants to know how long it will take her to run based on how far she has to run for. The Utah Middle School Math Project
###Explanation:
How long it will take is the dependent variable The how far she has to run for is the independent variable."
433,Jayden's soccer team wins 24 of the 30 games they play in a season. Find two equivalent ratios that are smaller than the one given in the problem. Explain how you found your smaller equivalent ratios. The Utah Middle School Math Project,Ratios equivalent to 24:30 12:15 Divide each side by 2 to get this. 4:5 Divide each side by 6 to get this.,"###Write an explanation to this problem:
Jayden's soccer team wins 24 of the 30 games they play in a season. Find two equivalent ratios that are smaller than the one given in the problem. Explain how you found your smaller equivalent ratios. The Utah Middle School Math Project
###Explanation:
Ratios equivalent to 24:30 12:15 Divide each side by 2 to get this. 4:5 Divide each side by 6 to get this."
761,A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?,Sample response: I would count by 5's,"###Write an explanation to this problem:
A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?
###Explanation:
Sample response: I would count by 5's"
485,A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project,The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example.,"###Write an explanation to this problem:
A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example."
795,"If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.","You would get a stronger chocolate flavor in the milkshake with 2 scoops of chocolate ice cream and 1 cup of milk because in the second milkshake they doubled the amount milk but only added 1 1/2 times the amount of chocolate ice cream. Therefore, the chocolate flavor would not be as strong as the first milkshake. If you doubled the recipe you would have 4 scoops/2 cups but instead the ratio is 3 scoops/2 cups which would be less ice cream therefore less chocolate flavor.","###Write an explanation to this problem:
If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.
###Explanation:
You would get a stronger chocolate flavor in the milkshake with 2 scoops of chocolate ice cream and 1 cup of milk because in the second milkshake they doubled the amount milk but only added 1 1/2 times the amount of chocolate ice cream. Therefore, the chocolate flavor would not be as strong as the first milkshake. If you doubled the recipe you would have 4 scoops/2 cups but instead the ratio is 3 scoops/2 cups which would be less ice cream therefore less chocolate flavor."
544,List 4 ordered pairs that when graphed would fall on the same vertical line. The Utah Middle School Math Project,"Any four ordered pairs that have the same x-value would fall on the same vertical line. Examples: 3, 0 3, 5 3, -2 These all fall on the vertical line at x = 3.","###Write an explanation to this problem:
List 4 ordered pairs that when graphed would fall on the same vertical line. The Utah Middle School Math Project
###Explanation:
Any four ordered pairs that have the same x-value would fall on the same vertical line. Examples: 3, 0 3, 5 3, -2 These all fall on the vertical line at x = 3."
331,"Your teacher will give you some cards with a scale on each card. Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards. Trade places with another group and check each other's work. If you disagree about how the scales should be sorted, work to reach an agreement. copied for free from openupresources.org","1 centimeter to 1 meter, and 1 to 100 1 centimeter to 1 kilometer, 1/2 cm to 500 m, and 1 to 100,000 1 inch to 8 feet, 1/8 inch to 1 foot, and 1 to 96 1 centimeter to 10 meters, 1 inch to 1,000 inches, and 1 millimeter to 1 meter 1 foot to 1 mile, and 1 to 5,280 1 inch to 1 mile, and 1 to 63,360","###Write an explanation to this problem:
Your teacher will give you some cards with a scale on each card. Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards. Trade places with another group and check each other's work. If you disagree about how the scales should be sorted, work to reach an agreement. copied for free from openupresources.org
###Explanation:
1 centimeter to 1 meter, and 1 to 100 1 centimeter to 1 kilometer, 1/2 cm to 500 m, and 1 to 100,000 1 inch to 8 feet, 1/8 inch to 1 foot, and 1 to 96 1 centimeter to 10 meters, 1 inch to 1,000 inches, and 1 millimeter to 1 meter 1 foot to 1 mile, and 1 to 5,280 1 inch to 1 mile, and 1 to 63,360"
501,Create a representation of an equation that defines a nonlinear function. The Utah Middle School Math Project,There are many different equations that can be created that represent a nonlinear function. One possible example is: y=x2+5,"###Write an explanation to this problem:
Create a representation of an equation that defines a nonlinear function. The Utah Middle School Math Project
###Explanation:
There are many different equations that can be created that represent a nonlinear function. One possible example is: y=x2+5"
569,"Here, write the fourth problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project","Sample Answer: Justin bought 8 bags of chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips. How many bags of chips did Justin eat? Solution: whole: 8 bags percent: 37.5% = 0.375 To find the number of bags of chips Justin ate on his way home, we multiply the whole by the percent: whole x percent = 8 bags x 0.375 = 3 bags We get that Justin ate 3 bags of the chips on his way home.","###Write an explanation to this problem:
Here, write the fourth problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Justin bought 8 bags of chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips. How many bags of chips did Justin eat? Solution: whole: 8 bags percent: 37.5% = 0.375 To find the number of bags of chips Justin ate on his way home, we multiply the whole by the percent: whole x percent = 8 bags x 0.375 = 3 bags We get that Justin ate 3 bags of the chips on his way home."
493,Write three expressions that are equivalent to 3x + 15 The Utah Middle School Math Project,Any equation that is equivalent to 3x + 15 would be a correct answer here. Some examples include 3x + 15 3x + 17 - 2 x + 2x + 15,"###Write an explanation to this problem:
Write three expressions that are equivalent to 3x + 15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 3x + 15 would be a correct answer here. Some examples include 3x + 15 3x + 17 - 2 x + 2x + 15"
450,The following equation is given: 3x + 2x = 85 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project,"The ratio of girls to boys on the track team is 3 to 2. If there are 85 people on the team, how many girls and boys are there?","###Write an explanation to this problem:
The following equation is given: 3x + 2x = 85 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
The ratio of girls to boys on the track team is 3 to 2. If there are 85 people on the team, how many girls and boys are there?"
368,Each statement contains a quantity. Rewrite each quantity using a power of 10. There are about 37 trillion cells in an average human body. copied for free from openupresources.org,Sample Answer: 37*10^12,"###Write an explanation to this problem:
Each statement contains a quantity. Rewrite each quantity using a power of 10. There are about 37 trillion cells in an average human body. copied for free from openupresources.org
###Explanation:
Sample Answer: 37*10^12"
603,Write the expression 6 + 42 as the product of two factors. The Utah Middle School Math Project,Example: 23x+21,"###Write an explanation to this problem:
Write the expression 6 + 42 as the product of two factors. The Utah Middle School Math Project
###Explanation:
Example: 23x+21"
79,Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org,"-7, -8 , -9 -3x > 18 x < -6 x needs to be a number that is less than -6","###Write an explanation to this problem:
Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org
###Explanation:
-7, -8 , -9 -3x > 18 x < -6 x needs to be a number that is less than -6"
148,A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.,"Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue.","###Write an explanation to this problem:
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.
###Explanation:
Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue."
393,Write a story that matches the expressions and equations. World Languages Number of years: t of students in French: 160 - 9t of students in Spanish: 85 + 6t 160 - 9t = 85 + 6t The Utah Middle School Math Project,"Initially at t = 0 years, there must be 160 students in French and 85 students in Spanish. Each year, the number of students in French will decrease by 9 and the number of students in Spanish will increase by 6. So 160 - 9t is the number of students in French after t years and 85 + 6t is the number of students in Spanish after t years. When 160 - 9t = 85 + 6t, there will be the same number of students will be in French class as there are in Spanish class. After how many years will the number of students in French class be the same as the number of students in Spanish class?","###Write an explanation to this problem:
Write a story that matches the expressions and equations. World Languages Number of years: t of students in French: 160 - 9t of students in Spanish: 85 + 6t 160 - 9t = 85 + 6t The Utah Middle School Math Project
###Explanation:
Initially at t = 0 years, there must be 160 students in French and 85 students in Spanish. Each year, the number of students in French will decrease by 9 and the number of students in Spanish will increase by 6. So 160 - 9t is the number of students in French after t years and 85 + 6t is the number of students in Spanish after t years. When 160 - 9t = 85 + 6t, there will be the same number of students will be in French class as there are in Spanish class. After how many years will the number of students in French class be the same as the number of students in Spanish class?"
218,Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.,"Elena could have the computer pick any 3 integers from 1 to 100. If either 2 or three of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and use the data to estimate the probability by finding the proportion of the trials that had a successful outcome.","###Write an explanation to this problem:
Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.
###Explanation:
Elena could have the computer pick any 3 integers from 1 to 100. If either 2 or three of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and use the data to estimate the probability by finding the proportion of the trials that had a successful outcome."
799,6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org,"60% of c means to multiply 60% and c. Is means equal to. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.6c=43.2","###Write an explanation to this problem:
6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org
###Explanation:
60% of c means to multiply 60% and c. Is means equal to. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.6c=43.2"
361,When is it better to use a table? When is it better to use a scatter plot? Copied for free from openupresources.org,Sample Answer: Scatter plots are best when looking for an overall pattern or lack of one. Tables are best when looking for the precise details of the data.,"###Write an explanation to this problem:
When is it better to use a table? When is it better to use a scatter plot? Copied for free from openupresources.org
###Explanation:
Sample Answer: Scatter plots are best when looking for an overall pattern or lack of one. Tables are best when looking for the precise details of the data."
352,"Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.","-9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 When we add two negative terms, the signs are both negative. Will the sum be negative or positive? Will we add or subtract the absolute values? We will add the absolute values and put the common sign, so our new equation is as follows: -9.5+ -6.5 + 8 -16 + 8 -16 has a greater absolute value than 8. -16 is negative. Will the final answer be negative or positive?","###Write an explanation to this problem:
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.
###Explanation:
-9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 When we add two negative terms, the signs are both negative. Will the sum be negative or positive? Will we add or subtract the absolute values? We will add the absolute values and put the common sign, so our new equation is as follows: -9.5+ -6.5 + 8 -16 + 8 -16 has a greater absolute value than 8. -16 is negative. Will the final answer be negative or positive?"
677,"Four families are renting a house together on vacation. If each family pays 75 per night to rent the house, what is the total cost of the house each night? Write an equation to solve the problem. The Utah Middle School Math Project","Each family spends 75 a night, and the total cost is split 4 ways, so the cost of the house is h/4=75","###Write an explanation to this problem:
Four families are renting a house together on vacation. If each family pays 75 per night to rent the house, what is the total cost of the house each night? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Each family spends 75 a night, and the total cost is split 4 ways, so the cost of the house is h/4=75"
309,"In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC is an acute triangle.","Sample response: To make an acute triangle, the other two angles must measure less than 90 degrees for example: 60, 70.","###Write an explanation to this problem:
In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC is an acute triangle.
###Explanation:
Sample response: To make an acute triangle, the other two angles must measure less than 90 degrees for example: 60, 70."
133,Name the parts of the expression. 14b,14 is the coefficient b is the variable 14b is a term and is the product of 14 and b,"###Write an explanation to this problem:
Name the parts of the expression. 14b
###Explanation:
14 is the coefficient b is the variable 14b is a term and is the product of 14 and b"
428,"You and your friends go to a BMX dirt-biking race. For one of the events, the competitors are going off a jump. The winner of the event is the competitor that gets the most air or jumps the highest. Do you think the relationship between the weight of the bike and the height of the jump can be modeled by a linear relationship? Why or why not? The Utah Middle School Math Project","Logically, it makes sense that as the weight of the bike increases, the height of the jump may decrease. This is linear, because - for example - for each 1 pound increase in weight, a biker jumps 1 cm lower or 0.5 cm lower.","###Write an explanation to this problem:
You and your friends go to a BMX dirt-biking race. For one of the events, the competitors are going off a jump. The winner of the event is the competitor that gets the most air or jumps the highest. Do you think the relationship between the weight of the bike and the height of the jump can be modeled by a linear relationship? Why or why not? The Utah Middle School Math Project
###Explanation:
Logically, it makes sense that as the weight of the bike increases, the height of the jump may decrease. This is linear, because - for example - for each 1 pound increase in weight, a biker jumps 1 cm lower or 0.5 cm lower."
254,6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org,"0.60c = 43.2 First, you need to change 60% to a decimal in order to be able to use it with an operation. 60% is equal to 0.60. Next, 60% of c means that you are multiplying because of implies multiplication. Lastly is implies what the expression is equal to.","###Write an explanation to this problem:
6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org
###Explanation:
0.60c = 43.2 First, you need to change 60% to a decimal in order to be able to use it with an operation. 60% is equal to 0.60. Next, 60% of c means that you are multiplying because of implies multiplication. Lastly is implies what the expression is equal to."
523,Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project,"Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output To better visualize this, try creating a table, graph, or equation that could represent the data given","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project
###Explanation:
Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output To better visualize this, try creating a table, graph, or equation that could represent the data given"
55,"Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org",9:20 pm,"###Write an explanation to this problem:
Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org
###Explanation:
9:20 pm"
507,"Use The Distributive Property to find the product. 719 First, show your work here. The Utah Middle School Math Project",719 = 720 - 1 = 720 - 71 = 140 - 7 = 133,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 719 First, show your work here. The Utah Middle School Math Project
###Explanation:
719 = 720 - 1 = 720 - 71 = 140 - 7 = 133"
643,"Beckham is interested in the hand span, the length from the tip of the pinky finger to the tip of the thumb, for people in his class. He asks the statistical question, How long is the hand span for people in my class? He decides to conduct a survey to answer his question. His data is shown below. Length of hand span in inches: 6, 6.5, 9, 7.5, 7.5, 7, 6.5, 7, 7, 9.5, 6, 8, 5.5, 7, 6.5 What is the attribute that is being measured?",The attribute being measured is the lengths of hand span.,"###Write an explanation to this problem:
Beckham is interested in the hand span, the length from the tip of the pinky finger to the tip of the thumb, for people in his class. He asks the statistical question, How long is the hand span for people in my class? He decides to conduct a survey to answer his question. His data is shown below. Length of hand span in inches: 6, 6.5, 9, 7.5, 7.5, 7, 6.5, 7, 7, 9.5, 6, 8, 5.5, 7, 6.5 What is the attribute that is being measured?
###Explanation:
The attribute being measured is the lengths of hand span."
525,Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project,A triangular prism cut parallel to the base will always result in a rectangular cross-section.,"###Write an explanation to this problem:
Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project
###Explanation:
A triangular prism cut parallel to the base will always result in a rectangular cross-section."
738,Create another possible ratio that describes the relationship between the amount of money in Pam's account and the amount of money in her brother's account.,"Answers will vary. You might something like 4:10, 8:20, etc.","###Write an explanation to this problem:
Create another possible ratio that describes the relationship between the amount of money in Pam's account and the amount of money in her brother's account.
###Explanation:
Answers will vary. You might something like 4:10, 8:20, etc."
432,"Complete the following statements: In scientific notation, as the exponent power goes up by 1, the standard number's decimal is... The Utah Middle School Math Project","In scientific notation, as the exponent power goes up by 1, the standard number's decimal is moved one place to the right. For each exponent added, another power of 10 is added.","###Write an explanation to this problem:
Complete the following statements: In scientific notation, as the exponent power goes up by 1, the standard number's decimal is... The Utah Middle School Math Project
###Explanation:
In scientific notation, as the exponent power goes up by 1, the standard number's decimal is moved one place to the right. For each exponent added, another power of 10 is added."
204,List the sample space the available options for the chance experiment given. Flipping a coin,"Heads, tails","###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
Heads, tails"
587,"Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800.","###Write an explanation to this problem:
Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800."
582,"Mr. Green is purchasing four new computers for the computer lab. Each computer costs 350. In addition, Mr. Green is purchasing a protection plan for each computer. The cost of the protection plan is 25 per computer. Use the distributive property to write two different expressions that can be used to represent the cost of the computers with the protection plans. The Utah Middle School Math Project","Since there are four computers that each cost 350 and four protection plans that each cost 25, one expression to represent the cost of the computers and protection plans is 4350 + 425 Another way to think about this is that the cost of a computer and protection plan is 350 + 25 and four computers with protection plans need to be bought, so another expression to represent the cost of the computers and protection plans is 4350 + 25","###Write an explanation to this problem:
Mr. Green is purchasing four new computers for the computer lab. Each computer costs 350. In addition, Mr. Green is purchasing a protection plan for each computer. The cost of the protection plan is 25 per computer. Use the distributive property to write two different expressions that can be used to represent the cost of the computers with the protection plans. The Utah Middle School Math Project
###Explanation:
Since there are four computers that each cost 350 and four protection plans that each cost 25, one expression to represent the cost of the computers and protection plans is 4350 + 425 Another way to think about this is that the cost of a computer and protection plan is 350 + 25 and four computers with protection plans need to be bought, so another expression to represent the cost of the computers and protection plans is 4350 + 25"
306,Jada applies two transformations to a polygon in the coordinate plane. One of the transformations is a translation and the other is a reflection. What information does Jada need to provide to communicate the transformations she has used?,"For the translation, Jada needs to provide the distance and direction of the vertical displacement and the distance and direction of the horizontal displacement. For the reflection, Jada needs to give the line of reflection. It is also important for Jada to communicate the order in which the transformations are applied.","###Write an explanation to this problem:
Jada applies two transformations to a polygon in the coordinate plane. One of the transformations is a translation and the other is a reflection. What information does Jada need to provide to communicate the transformations she has used?
###Explanation:
For the translation, Jada needs to provide the distance and direction of the vertical displacement and the distance and direction of the horizontal displacement. For the reflection, Jada needs to give the line of reflection. It is also important for Jada to communicate the order in which the transformations are applied."
332,"The point -3,6 is on a line with a slope of 4. Find two more points on the line.","The slope is equal to the change in y over the change in x. The slope of 4 means that for every 4 units the y changes, the x changes by 1. Two more points can be found by adding 1 to x and 4 to y, or subtracting 1 from x and 4 from y. -3, 6 +1 +4 -2, 10 +1 +4 -1, 14 Two more points on the line are -2, 10 and -1, 14.","###Write an explanation to this problem:
The point -3,6 is on a line with a slope of 4. Find two more points on the line.
###Explanation:
The slope is equal to the change in y over the change in x. The slope of 4 means that for every 4 units the y changes, the x changes by 1. Two more points can be found by adding 1 to x and 4 to y, or subtracting 1 from x and 4 from y. -3, 6 +1 +4 -2, 10 +1 +4 -1, 14 Two more points on the line are -2, 10 and -1, 14."
425,A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project,The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example.,"###Write an explanation to this problem:
A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example."
60,"Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org",In order to factor you need to look at the numbers and think about what is the greatest common factor that will go into those numbers. For example: 30x + 9 The common factor would be 3. 310x + 3 After you find the common factor you then need to put that number in front of the parenthesis The numbers that go inside the parenthesis are the numbers that you multiply by to equal the original expression. 12x - 4 = 43x -1,"###Write an explanation to this problem:
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org
###Explanation:
In order to factor you need to look at the numbers and think about what is the greatest common factor that will go into those numbers. For example: 30x + 9 The common factor would be 3. 310x + 3 After you find the common factor you then need to put that number in front of the parenthesis The numbers that go inside the parenthesis are the numbers that you multiply by to equal the original expression. 12x - 4 = 43x -1"
199,What information do you need to know to write an equation relating two quantities that have a proportional relationship?,You would need to know the constant of proportionality and the variables for the quantities.,"###Write an explanation to this problem:
What information do you need to know to write an equation relating two quantities that have a proportional relationship?
###Explanation:
You would need to know the constant of proportionality and the variables for the quantities."
638,"In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x - 3 = 11 Original Equation: x=14 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 3 has been added to x-3. On the right side, 3 has been added to 11, which results in 14. The action was: Add 3 to both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x - 3 = 11 Original Equation: x=14 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 3 has been added to x-3. On the right side, 3 has been added to 11, which results in 14. The action was: Add 3 to both sides of the equation."
685,Create a context for the numeric representation. 1201 ndash; 1201/4 = 1203/4 = 90 The Utah Middle School Math Project,"If a person has 120 apples, then loses 1/4 of the apples, this numeric expression describes how many apples they have left.","###Write an explanation to this problem:
Create a context for the numeric representation. 1201 ndash; 1201/4 = 1203/4 = 90 The Utah Middle School Math Project
###Explanation:
If a person has 120 apples, then loses 1/4 of the apples, this numeric expression describes how many apples they have left."
581,"Use The Distributive Property to find the product. 712 First, show your work here. The Utah Middle School Math Project",712 = 710 + 2 = 710 + 72 = 70 + 14 = 84,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 712 First, show your work here. The Utah Middle School Math Project
###Explanation:
712 = 710 + 2 = 710 + 72 = 70 + 14 = 84"
429,"Suppose a certain bank pays 4% interest at the end of each year on the money in an account. When Devon was born, his parents put 100 in the account and will leave it there until he goes to college. Is the relationship between time in years and the amount of money in the account in dollars linear or not? Why or why not? The Utah Middle School Math Project","This data is not linear, because the money with interest has interest added each year.","###Write an explanation to this problem:
Suppose a certain bank pays 4% interest at the end of each year on the money in an account. When Devon was born, his parents put 100 in the account and will leave it there until he goes to college. Is the relationship between time in years and the amount of money in the account in dollars linear or not? Why or why not? The Utah Middle School Math Project
###Explanation:
This data is not linear, because the money with interest has interest added each year."
445,61% of 20 Estimate the answer. The Utah Middle School Math Project,"61% = 50% + 10% + 1% 50% of 20 is 10, so the answer must be greater than 10.","###Write an explanation to this problem:
61% of 20 Estimate the answer. The Utah Middle School Math Project
###Explanation:
61% = 50% + 10% + 1% 50% of 20 is 10, so the answer must be greater than 10."
601,Describe absolute value in your own words. Use examples to support your explanation. The Utah Middle School Math Project,"The absolute value of a number is the number's distance from 0. Distance is always positive. You can think of it like a point on a number line. The distance from 0 is how many steps, or units, it takes to get to that point from 0. Even if that point has a negative value, it takes a positive number of steps to get to that point from 0. This distance/number of steps is the point's absolute value.","###Write an explanation to this problem:
Describe absolute value in your own words. Use examples to support your explanation. The Utah Middle School Math Project
###Explanation:
The absolute value of a number is the number's distance from 0. Distance is always positive. You can think of it like a point on a number line. The distance from 0 is how many steps, or units, it takes to get to that point from 0. Even if that point has a negative value, it takes a positive number of steps to get to that point from 0. This distance/number of steps is the point's absolute value."
494,"In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5x+ 4x - x 9x Explain the mistake The Utah Middle School Math Project","Notice that when combining like terms, the coefficients were added wrong. Since 5x + 4x - x = x5 + 4 - 1 =x8 does not equal 9x.","###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5x+ 4x - x 9x Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that when combining like terms, the coefficients were added wrong. Since 5x + 4x - x = x5 + 4 - 1 =x8 does not equal 9x."
791,"9. Noah raised 54 to support the animal shelter, which is 60% of his fundraising goal. a. Write an equation to represent the situation. copied for free from openupresources.org","To set up an equation to represent this situation, I know that the unknown value is Noah's fundraising goal which will be represented by x. Also, I know that the problem says 60% of his fundraising goal and of means to multiply. 60%x=54 is how this problem could be written, but the percent needs to change to a decimal in order to solve so the final equation would be 0.6x=54","###Write an explanation to this problem:
9. Noah raised 54 to support the animal shelter, which is 60% of his fundraising goal. a. Write an equation to represent the situation. copied for free from openupresources.org
###Explanation:
To set up an equation to represent this situation, I know that the unknown value is Noah's fundraising goal which will be represented by x. Also, I know that the problem says 60% of his fundraising goal and of means to multiply. 60%x=54 is how this problem could be written, but the percent needs to change to a decimal in order to solve so the final equation would be 0.6x=54"
633,"Yesterday, Ruth and Carl invited 10 friends to go out to lunch. Add one more statistical question of your own that relates to this situation. The Utah Middle School Math Project",One example of a statistical question would be: How many people were sitting at each table in the restaurant?,"###Write an explanation to this problem:
Yesterday, Ruth and Carl invited 10 friends to go out to lunch. Add one more statistical question of your own that relates to this situation. The Utah Middle School Math Project
###Explanation:
One example of a statistical question would be: How many people were sitting at each table in the restaurant?"
759,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.,The temperature is 22 degrees below zero on the Celcius scale.,"###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.
###Explanation:
The temperature is 22 degrees below zero on the Celcius scale."
615,Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school?,Answers will vary.,"###Write an explanation to this problem:
Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school?
###Explanation:
Answers will vary."
334,Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.,"To get a scaled copy, you have to be multiplying all of the dimensions of the original figure or shape by the same scale factor. In this case, the original figure is Rectangle B. Rectangle B measures 15 by 10. Rectangle C measures 30 by 15. We can see that Rectangle C's length is twice Rectangle B's length. BUT Rectangle C's width is not twice Rectangle B's width. This means Rectangle C cannot be a scaled copy of Rectangle B.","###Write an explanation to this problem:
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.
###Explanation:
To get a scaled copy, you have to be multiplying all of the dimensions of the original figure or shape by the same scale factor. In this case, the original figure is Rectangle B. Rectangle B measures 15 by 10. Rectangle C measures 30 by 15. We can see that Rectangle C's length is twice Rectangle B's length. BUT Rectangle C's width is not twice Rectangle B's width. This means Rectangle C cannot be a scaled copy of Rectangle B."
767,Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.,"Note that the area of a triangle is A = 1/2bh and the area of a parallelogram is A = bh. Sample response: To find the dimensions of a right triangle and a parallelogram with the same area, the base of the triangle should be double that of the parallelogram. Right Triangle: b = 10 cm h = 8 cm A = 1/2bh = 1/210 cm8cm = 40 cm2 Parallelogram: b = 5 cm h = 8 cm A = bh = 5 cm8 cm = 40 cm2","###Write an explanation to this problem:
Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.
###Explanation:
Note that the area of a triangle is A = 1/2bh and the area of a parallelogram is A = bh. Sample response: To find the dimensions of a right triangle and a parallelogram with the same area, the base of the triangle should be double that of the parallelogram. Right Triangle: b = 10 cm h = 8 cm A = 1/2bh = 1/210 cm8cm = 40 cm2 Parallelogram: b = 5 cm h = 8 cm A = bh = 5 cm8 cm = 40 cm2"
90,The equation d=3t represents the relationship between the distance d in inches that a snail is from a certain rock and the time t in minutes. What does the number 3 represent?,The 3 is the constant in the equation which is how fast the snail can travel in 1 minute which would be 3 inches in 1 minute.,"###Write an explanation to this problem:
The equation d=3t represents the relationship between the distance d in inches that a snail is from a certain rock and the time t in minutes. What does the number 3 represent?
###Explanation:
The 3 is the constant in the equation which is how fast the snail can travel in 1 minute which would be 3 inches in 1 minute."
800,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.,The temperature is -10oF. OR The temperature is 10 degrees below zero on the Fahrenheit scale.,"###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.
###Explanation:
The temperature is -10oF. OR The temperature is 10 degrees below zero on the Fahrenheit scale."
181,Explain how you could find the difference of 1 and 0.1978.,"To find the difference between 1 and 0.1978 you have to first add a decimal behind the 1. Since 0.1978 has 4 places behind the decimal, you have to add 4 zeros behind the 1 and the decimal. Then you can subtract the digits the same way you would if you were subtracting 1,978 from 10,000. Line up the decimals on top of each other and bring down a decimal in the same place of the difference. Therefore instead of getting a difference of 8,022, it is 0.8022 because of the decimal.","###Write an explanation to this problem:
Explain how you could find the difference of 1 and 0.1978.
###Explanation:
To find the difference between 1 and 0.1978 you have to first add a decimal behind the 1. Since 0.1978 has 4 places behind the decimal, you have to add 4 zeros behind the 1 and the decimal. Then you can subtract the digits the same way you would if you were subtracting 1,978 from 10,000. Line up the decimals on top of each other and bring down a decimal in the same place of the difference. Therefore instead of getting a difference of 8,022, it is 0.8022 because of the decimal."
456,Given information: v = Vicki's money 5v = Wally's money Equation: 5v + v = 72 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,Wally has five times more money than Vicki. Together they have 72. How much money do they each have?,"###Write an explanation to this problem:
Given information: v = Vicki's money 5v = Wally's money Equation: 5v + v = 72 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Wally has five times more money than Vicki. Together they have 72. How much money do they each have?"
500,Create a representation of an equation that defines a linear function. The Utah Middle School Math Project,There are many different equations that can be created that represent a linear function. One possible example is: y=2x+3,"###Write an explanation to this problem:
Create a representation of an equation that defines a linear function. The Utah Middle School Math Project
###Explanation:
There are many different equations that can be created that represent a linear function. One possible example is: y=2x+3"
744,Write a story problem that includes both integers -8 and 12.,Answers may vary. You might write something like One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat.,"###Write an explanation to this problem:
Write a story problem that includes both integers -8 and 12.
###Explanation:
Answers may vary. You might write something like One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat."
158,"Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.","Slope would represent the relationship between the side length and the perimeter. Since it is equilateral, to find the perimeter you would always multiply by 3 for the 3 sides. The y- intercept is 0 because if you don't have a side length 0, you would not have a perimeter to calculate.","###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
###Explanation:
Slope would represent the relationship between the side length and the perimeter. Since it is equilateral, to find the perimeter you would always multiply by 3 for the 3 sides. The y- intercept is 0 because if you don't have a side length 0, you would not have a perimeter to calculate."
69,"One end point of a line segment is -3, -6. The length of the line segment is 7 units. Find four points that could serve as the other end point of the given line segment.","-10, -6 4, -6 -3, 1 -3, -13","###Write an explanation to this problem:
One end point of a line segment is -3, -6. The length of the line segment is 7 units. Find four points that could serve as the other end point of the given line segment.
###Explanation:
-10, -6 4, -6 -3, 1 -3, -13"
319,"The Fabulous Fish Market orders tilapia, which costs 3 per pound, and salmon, which costs 5 per pound. The market budgets 210 to spend on this order each day. What are five different combinations of salmon and tilapia that the market can order?",70 pounds of tilapia and 0 pounds of salmon 0 pounds of tilapia and 42 pounds of salmon 20 pounds of tilapia and 30 pounds of salmon 10 pounds of tilapia and 36 pounds of salmon 30 pounds of tilapia and 24 pounds of salmon,"###Write an explanation to this problem:
The Fabulous Fish Market orders tilapia, which costs 3 per pound, and salmon, which costs 5 per pound. The market budgets 210 to spend on this order each day. What are five different combinations of salmon and tilapia that the market can order?
###Explanation:
70 pounds of tilapia and 0 pounds of salmon 0 pounds of tilapia and 42 pounds of salmon 20 pounds of tilapia and 30 pounds of salmon 10 pounds of tilapia and 36 pounds of salmon 30 pounds of tilapia and 24 pounds of salmon"
131,What does the expression + + + represent?,"This expression represents the perimeter of the rectangle, or the sum of the four sides of a rectangle.","###Write an explanation to this problem:
What does the expression + + + represent?
###Explanation:
This expression represents the perimeter of the rectangle, or the sum of the four sides of a rectangle."
44,30 + -30 = 0. Enter another sum of two numbers that equals 0. copied for free from openupresources.org,4 + -4 = 0,"###Write an explanation to this problem:
30 + -30 = 0. Enter another sum of two numbers that equals 0. copied for free from openupresources.org
###Explanation:
4 + -4 = 0"
596,"Here, write the third problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Last night, Jeff did not read 61.54% of the targetted number of pages. He fell asleep with 40 pages unread. What was the targetted number of pages to read that night? Solution: part: 40 pages percent: 61.54% We want to find the number of pages Jeff did not read that night. Note that 61.54% of the targetted number of pages is 40 pages. 61.54% of the targetted page is 0.6154 times the targetted page. With this information, we can write: 40 pages = targetted page x 0.6154 Now, we can solve for the targetted number of pages: 40 pages = targetted page x 0.6154 40 pages/0.6154 = targetted page 65 pages = targetted page We get that Jeff planned to read 65 pages that night.","###Write an explanation to this problem:
Here, write the third problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Last night, Jeff did not read 61.54% of the targetted number of pages. He fell asleep with 40 pages unread. What was the targetted number of pages to read that night? Solution: part: 40 pages percent: 61.54% We want to find the number of pages Jeff did not read that night. Note that 61.54% of the targetted number of pages is 40 pages. 61.54% of the targetted page is 0.6154 times the targetted page. With this information, we can write: 40 pages = targetted page x 0.6154 Now, we can solve for the targetted number of pages: 40 pages = targetted page x 0.6154 40 pages/0.6154 = targetted page 65 pages = targetted page We get that Jeff planned to read 65 pages that night."
70,"Two of the vertices of a rectangle are 1, -6 and -8, -6. If the rectangle has a perimeter of 26 units, what are the coordinates of its other two vertices?","1, -2 and -8, -2 or 1, -10 and -8, -10","###Write an explanation to this problem:
Two of the vertices of a rectangle are 1, -6 and -8, -6. If the rectangle has a perimeter of 26 units, what are the coordinates of its other two vertices?
###Explanation:
1, -2 and -8, -2 or 1, -10 and -8, -10"
436,The following equation is given: 0.2x + x = 240 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project,"In the last year Milo's saving account has increased by 20%. If he now has 240, how much did he start with?","###Write an explanation to this problem:
The following equation is given: 0.2x + x = 240 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
In the last year Milo's saving account has increased by 20%. If he now has 240, how much did he start with?"
806,Write an inequality that relates the rational numbers. Three and one-half yards of fabric is less than five and one-half yards of fabric,Three and one-half yards of fabric is less than five and one-half yards of fabric,"###Write an explanation to this problem:
Write an inequality that relates the rational numbers. Three and one-half yards of fabric is less than five and one-half yards of fabric
###Explanation:
Three and one-half yards of fabric is less than five and one-half yards of fabric"
398,On Saturday Fiona gets to work 15 minutes early and sells three sweaters before her shift even begins. She then sells 4 sweaters every hour for the rest of her shift. Find and describe the rate of change for this relationship. The Utah Middle School Math Project,The rate of change for this relationship is 4 sweaters sold for every hour worked. We do not need to include the three sweaters she sold before her shift began because she is not selling them at a constant rate during her shifts.,"###Write an explanation to this problem:
On Saturday Fiona gets to work 15 minutes early and sells three sweaters before her shift even begins. She then sells 4 sweaters every hour for the rest of her shift. Find and describe the rate of change for this relationship. The Utah Middle School Math Project
###Explanation:
The rate of change for this relationship is 4 sweaters sold for every hour worked. We do not need to include the three sweaters she sold before her shift began because she is not selling them at a constant rate during her shifts."
351,Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project,Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 + 2 2x + 4x - 16 + 1,"###Write an explanation to this problem:
Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 + 2 2x + 4x - 16 + 1"
707,Solve the inequality. Represent the solution on a number line. r-3.5>8.25 The Utah Middle School Math Project,"Solve for r. The number line should be greater than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. r-3.5>8.25 The Utah Middle School Math Project
###Explanation:
Solve for r. The number line should be greater than the solution, but not contain it."
239,A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population?,"A sample refers to a small portion of the entire population. In this example, in order to use the entire population, the doctor would have to test all of the blood in your body. That is probably not possible while keeping you healthy and even alive, so a smaller sample is better.","###Write an explanation to this problem:
A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population?
###Explanation:
A sample refers to a small portion of the entire population. In this example, in order to use the entire population, the doctor would have to test all of the blood in your body. That is probably not possible while keeping you healthy and even alive, so a smaller sample is better."
135,Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e,4d + 3e OR 41d + 3e,"###Write an explanation to this problem:
Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e
###Explanation:
4d + 3e OR 41d + 3e"
82,Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project,"There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240.","###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240."
165,"One day in Boston, MA, the high temperature was 60 degrees Fahrenheit, and the low temperature was 52 degrees. Write one or more inequalities to describe the temperatures T that are between the high and low temperatures on that day.",60>T>52 or T52 This is saying that T is less than 60 and T is greater than 52.,"###Write an explanation to this problem:
One day in Boston, MA, the high temperature was 60 degrees Fahrenheit, and the low temperature was 52 degrees. Write one or more inequalities to describe the temperatures T that are between the high and low temperatures on that day.
###Explanation:
60>T>52 or T52 This is saying that T is less than 60 and T is greater than 52."
164,A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs 24. copied for free from openupresources.org,"Strategy 1: Find what 25% of 24 is. 25% = 0.25 0.25*24 = 6 Subtract this value from 24 24 - 6 18 Strategy 2: You are taking away 25% from the whole. The whole is 1, or 100%. 100% - 25% = 75% Let's find what 75% of 24 is. 75% = 0.75 0.75*24 = 18","###Write an explanation to this problem:
A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs 24. copied for free from openupresources.org
###Explanation:
Strategy 1: Find what 25% of 24 is. 25% = 0.25 0.25*24 = 6 Subtract this value from 24 24 - 6 18 Strategy 2: You are taking away 25% from the whole. The whole is 1, or 100%. 100% - 25% = 75% Let's find what 75% of 24 is. 75% = 0.75 0.75*24 = 18"
28,The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.,"0 tables for 2 and 30 tables for 4 60 tables for 2 and 0 tables for 4 10 tables for 2 and 25 tables for 4 To find combinations, I chose a number of tables for 2 and multiplied that number by 2. I then subtracted that number from 120 and divided by 4 to determine how many tables of 4 I would need.","###Write an explanation to this problem:
The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.
###Explanation:
0 tables for 2 and 30 tables for 4 60 tables for 2 and 0 tables for 4 10 tables for 2 and 25 tables for 4 To find combinations, I chose a number of tables for 2 and multiplied that number by 2. I then subtracted that number from 120 and divided by 4 to determine how many tables of 4 I would need."
665,Solve the inequality. Represent the solution on a number line. x-2>7 The Utah Middle School Math Project,"Solve for x. The number line should be higher than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. x-2>7 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be higher than the solution, but not contain it."
193,"These three points form a horizontal line: -3.5,4, 0,4, and 6.2,4. Name two additional points that fall on this line.","2,4, -6.2, 4, and 342,4 Your answer may vary. You MUST have a 4 for the y-coordinate on the line.","###Write an explanation to this problem:
These three points form a horizontal line: -3.5,4, 0,4, and 6.2,4. Name two additional points that fall on this line.
###Explanation:
2,4, -6.2, 4, and 342,4 Your answer may vary. You MUST have a 4 for the y-coordinate on the line."
404,Callie and Jeff each have a job delivering newspapers. Jeff gets paid 140 dollars for delivering 350 papers. Callie gets paid 100 for delivering 200 papers. Find the unit rate for Callie The Utah Middle School Math Project,"The unit rate can be either the amount of dollars for every one newspaper or the amount of newspapers for every one dollar. Unlike just a rate, unit rates have a 1 in the denominator. To turn a rate into a unit rate, divide the numerator by the denominator. The rate that Callie was delivering papers is 100 per 200 papers or 100/200 papers. To get the unit rate divide 100 by 200 to get unit rate of 0.50/paper 0.50 is the unit rate of dollars to papers The rate that Callie delivered can also be expressed in papers per dollars. The rate would be 200 papers per 100. By simplifying the rate a unit rate of 2 papers per dollar is found. 2 is the unit rate of papers to dollars.","###Write an explanation to this problem:
Callie and Jeff each have a job delivering newspapers. Jeff gets paid 140 dollars for delivering 350 papers. Callie gets paid 100 for delivering 200 papers. Find the unit rate for Callie The Utah Middle School Math Project
###Explanation:
The unit rate can be either the amount of dollars for every one newspaper or the amount of newspapers for every one dollar. Unlike just a rate, unit rates have a 1 in the denominator. To turn a rate into a unit rate, divide the numerator by the denominator. The rate that Callie was delivering papers is 100 per 200 papers or 100/200 papers. To get the unit rate divide 100 by 200 to get unit rate of 0.50/paper 0.50 is the unit rate of dollars to papers The rate that Callie delivered can also be expressed in papers per dollars. The rate would be 200 papers per 100. By simplifying the rate a unit rate of 2 papers per dollar is found. 2 is the unit rate of papers to dollars."
465,99% of 75 Estimate the answer. The Utah Middle School Math Project,"99% is slightly less than 100%, so 99% of 75 is slightly less than 75.","###Write an explanation to this problem:
99% of 75 Estimate the answer. The Utah Middle School Math Project
###Explanation:
99% is slightly less than 100%, so 99% of 75 is slightly less than 75."
350,Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project,Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 - 2 2x + 4x - 16 + 1,"###Write an explanation to this problem:
Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 - 2 2x + 4x - 16 + 1"
140,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,The sample space would be the numbers 1-428.,"###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
The sample space would be the numbers 1-428."
173,Explain how to make this calculation mentally. 99 * 15,Round the 99 to 100 so you know have: 10015 = 1500,"###Write an explanation to this problem:
Explain how to make this calculation mentally. 99 * 15
###Explanation:
Round the 99 to 100 so you know have: 10015 = 1500"
6,"Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1.","When a slope is greater than 1, the vertical distance between two points will always be greater than the horizontal distance. When a slope is equal to 1, the vertical distance between two points will always be the same as the horizontal distance. When a slope is less than 1, the vertical distance between two points will always be less than the horizontal distance.","###Write an explanation to this problem:
Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1.
###Explanation:
When a slope is greater than 1, the vertical distance between two points will always be greater than the horizontal distance. When a slope is equal to 1, the vertical distance between two points will always be the same as the horizontal distance. When a slope is less than 1, the vertical distance between two points will always be less than the horizontal distance."
687,"The ratio of 6th graders to 7th graders to 8th graders in a middle school is 3:1:1. If there are 180 students in total, how many of the students are in each grade? Write an equation to solve the problem. The Utah Middle School Math Project","The variable x can represent the number of students in each grade, with the ratio 1 being the base. This means that 3x+1x+1x=180 students, or 3x+x+x=180.","###Write an explanation to this problem:
The ratio of 6th graders to 7th graders to 8th graders in a middle school is 3:1:1. If there are 180 students in total, how many of the students are in each grade? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The variable x can represent the number of students in each grade, with the ratio 1 being the base. This means that 3x+1x+1x=180 students, or 3x+x+x=180."
342,"In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.","If a triangle is an isosceles triangle, then two of its sides are the same length and the third side is different. This means two of the angles are the same and one is different. If A is 40, then this could be the same as one of the other angles. Angle B or Angle C could also measure 40 degrees. This means the other angle should measure 100 degrees. This is because all of the angles should add up to 180. 40 + 40 + 100 = 180 If A is 40 and is the different angle, then the other two angles together measure 140 degrees. 180 - 40 = 140 The angles must be congruent. 140/2 = 70 Angles B and C would be 70 degrees each.","###Write an explanation to this problem:
In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.
###Explanation:
If a triangle is an isosceles triangle, then two of its sides are the same length and the third side is different. This means two of the angles are the same and one is different. If A is 40, then this could be the same as one of the other angles. Angle B or Angle C could also measure 40 degrees. This means the other angle should measure 100 degrees. This is because all of the angles should add up to 180. 40 + 40 + 100 = 180 If A is 40 and is the different angle, then the other two angles together measure 140 degrees. 180 - 40 = 140 The angles must be congruent. 140/2 = 70 Angles B and C would be 70 degrees each."
73,"Find a number that matches the description. A 4-digit number that is not divisible by 2, 3, 5, or 10. The Utah Middle School Math Project","There are many different correct answers to this question. We want a number that is not divisible by 2, 3, 5, or 10. To be divisible by 2, the last digit must be an even number or 0. To be divisible by 3, the digits must sum to a number that is a multiple or 3. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 10, the last digit must be a 0. If we want our number to not be divisible by 2, 5, or 10, then the last digit cannot be an even number, 0, or 5. This leaves 1, 3, 7, and 9. For our example, we'll pick 7 _ _ _ 7 Finally, let's pick our other three digits so that all four digits do not add to a number divisible by 3. This could be 5447. 5 + 4 + 4 + 7 = 20, and 20 is not divisible by 3. Our number could be 5447.","###Write an explanation to this problem:
Find a number that matches the description. A 4-digit number that is not divisible by 2, 3, 5, or 10. The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is not divisible by 2, 3, 5, or 10. To be divisible by 2, the last digit must be an even number or 0. To be divisible by 3, the digits must sum to a number that is a multiple or 3. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 10, the last digit must be a 0. If we want our number to not be divisible by 2, 5, or 10, then the last digit cannot be an even number, 0, or 5. This leaves 1, 3, 7, and 9. For our example, we'll pick 7 _ _ _ 7 Finally, let's pick our other three digits so that all four digits do not add to a number divisible by 3. This could be 5447. 5 + 4 + 4 + 7 = 20, and 20 is not divisible by 3. Our number could be 5447."
591,"Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips.","###Write an explanation to this problem:
Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips."
602,"Use The Distributive Property to find the product. 4105 First, show your work here. The Utah Middle School Math Project",4105 = 4100 + 45 = 400 + 20 = 420,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 4105 First, show your work here. The Utah Middle School Math Project
###Explanation:
4105 = 4100 + 45 = 400 + 20 = 420"
734,Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.,There are many possible solutions. Here are some samples: The ratio of the number of male teachers to the number of female teachers is 15:35. The ratio of the number of female teachers to the number of male teachers is 35:15. The ratio of the number of female teachers to the total number of teachers in the school is 35:50. The ratio of the number of male teachers to the total number of teachers in the school is 15:50.,"###Write an explanation to this problem:
Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.
###Explanation:
There are many possible solutions. Here are some samples: The ratio of the number of male teachers to the number of female teachers is 15:35. The ratio of the number of female teachers to the number of male teachers is 35:15. The ratio of the number of female teachers to the total number of teachers in the school is 35:50. The ratio of the number of male teachers to the total number of teachers in the school is 15:50."
145,Mark the text by underlining key words. The sum of 25 and h is divided by f cubed.,The sum of 25 and h is divided by f cubed.,"###Write an explanation to this problem:
Mark the text by underlining key words. The sum of 25 and h is divided by f cubed.
###Explanation:
The sum of 25 and h is divided by f cubed."
234,"4. Take turns with your partner telling a story that might be represented by each equation. Then, for each equation, choose one story, state what quantity x describes, and solve the equation. If you get stuck, draw a diagram. a. 0.7 + x = 12 copied for free from openupresources.org","Here is an example, but answers may vary: First solve: 0.7 + x = 12-0.7 -0.7 --->Use inverse operation and subtract o.7 from each side to isolate xx = 11.3 Cara went to the store to buy pencils for school which cost 70 cents. She then bought some snacks to eat when she got home and her total was 12. When solving, the total Cara spent was 11.30 of her money and she used the 0.70 she found to pay the rest.","###Write an explanation to this problem:
4. Take turns with your partner telling a story that might be represented by each equation. Then, for each equation, choose one story, state what quantity x describes, and solve the equation. If you get stuck, draw a diagram. a. 0.7 + x = 12 copied for free from openupresources.org
###Explanation:
Here is an example, but answers may vary: First solve: 0.7 + x = 12-0.7 -0.7 --->Use inverse operation and subtract o.7 from each side to isolate xx = 11.3 Cara went to the store to buy pencils for school which cost 70 cents. She then bought some snacks to eat when she got home and her total was 12. When solving, the total Cara spent was 11.30 of her money and she used the 0.70 she found to pay the rest."
220,"A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm. She wants to test the plants at the farm, but it will ruin the crop if she tests all of them. If the farm has 5,000 spinach plants, describe a method that would produce a random sample of 10 plants.",She could put the map of the farm on a grid and number each section of the grid. She could have a computer program randomly select 10 grid numbers and choose a plant from inside the 10 grid numbers that the computer selected.,"###Write an explanation to this problem:
A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm. She wants to test the plants at the farm, but it will ruin the crop if she tests all of them. If the farm has 5,000 spinach plants, describe a method that would produce a random sample of 10 plants.
###Explanation:
She could put the map of the farm on a grid and number each section of the grid. She could have a computer program randomly select 10 grid numbers and choose a plant from inside the 10 grid numbers that the computer selected."
360,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A child's wading pool is being inflated. The pool's size increases at a rate of 2 cubic feet per minute. The Utah Middle School Math Project,Time is the dependent variable. The size of the pool depends on the amount of time the pool has been inflating. The size is independent.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A child's wading pool is being inflated. The pool's size increases at a rate of 2 cubic feet per minute. The Utah Middle School Math Project
###Explanation:
Time is the dependent variable. The size of the pool depends on the amount of time the pool has been inflating. The size is independent."
357,"Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org",Bananas cost 1.50 per pound. The cost for b pounds of bananas would be 1.5b. Guavas cost 3.00 per pound. The cost for g pounds of guavas would be 3g. The cost for b bananas and g guavas is 12. 12 = 1.5b + 3g,"###Write an explanation to this problem:
Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org
###Explanation:
Bananas cost 1.50 per pound. The cost for b pounds of bananas would be 1.5b. Guavas cost 3.00 per pound. The cost for g pounds of guavas would be 3g. The cost for b bananas and g guavas is 12. 12 = 1.5b + 3g"
132,What does the expression represent?,The expression represents the area of a rectangle.,"###Write an explanation to this problem:
What does the expression represent?
###Explanation:
The expression represents the area of a rectangle."
420,"Boris is setting up an exercise schedule. For five days each week, he would like to play a sport for 30 minutes, stretch for 5 minutes, and lift weights for 10 minutes. Write two different expressions that could be used to represent the total number of minutes he will exercise in five days. The Utah Middle School Math Project","To find the total number of minutes Boris exercises over the course of five days, add the number of minutes he exercises each day and multiplies the total by 5. This can be expressed in multiple ways. 1 530 + 5 + 10 2 530 + 55 + 510","###Write an explanation to this problem:
Boris is setting up an exercise schedule. For five days each week, he would like to play a sport for 30 minutes, stretch for 5 minutes, and lift weights for 10 minutes. Write two different expressions that could be used to represent the total number of minutes he will exercise in five days. The Utah Middle School Math Project
###Explanation:
To find the total number of minutes Boris exercises over the course of five days, add the number of minutes he exercises each day and multiplies the total by 5. This can be expressed in multiple ways. 1 530 + 5 + 10 2 530 + 55 + 510"
626,For what value of x does the expression 10 evaluate to 70? Write an equation to represent the problem. The Utah Middle School Math Project,"To make an equation where the expression 10x evaluates to 70, we need to say that the expression equals 70. 10x=70 Any equation that simplifies to this equation is a correct answer.","###Write an explanation to this problem:
For what value of x does the expression 10 evaluate to 70? Write an equation to represent the problem. The Utah Middle School Math Project
###Explanation:
To make an equation where the expression 10x evaluates to 70, we need to say that the expression equals 70. 10x=70 Any equation that simplifies to this equation is a correct answer."
813,"Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.",One question that would result in numerical data could be: How many hours did you sleep last night? This would produce numerical data because hours are a quantity that can be measured.,"###Write an explanation to this problem:
Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.
###Explanation:
One question that would result in numerical data could be: How many hours did you sleep last night? This would produce numerical data because hours are a quantity that can be measured."
41,"Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.","In drawing a triangle with three provided side lengths, there is only one way to draw the triangle. Once one length is drawn, the other two lengths are used to draw circles with the lengths as the respective radii of each circle, centered at either end of the segment drawn first. Regardless of which order of segments is used, there is only one unique triangle that can be drawn. In drawing a triangle with two side lengths and included angle provided, there is only one way to draw the triangle. Once the angle is drawn and the two side lengths are marked off on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle.","###Write an explanation to this problem:
Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.
###Explanation:
In drawing a triangle with three provided side lengths, there is only one way to draw the triangle. Once one length is drawn, the other two lengths are used to draw circles with the lengths as the respective radii of each circle, centered at either end of the segment drawn first. Regardless of which order of segments is used, there is only one unique triangle that can be drawn. In drawing a triangle with two side lengths and included angle provided, there is only one way to draw the triangle. Once the angle is drawn and the two side lengths are marked off on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle."
528,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Sally's track coach wants to know how far she can run based on the amount of time she runs for. The Utah Middle School Math Project,Time is the independent variable. The how far she can run is the dependent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Sally's track coach wants to know how far she can run based on the amount of time she runs for. The Utah Middle School Math Project
###Explanation:
Time is the independent variable. The how far she can run is the dependent variable."
108,"Sandy puts 6% of her income in a retirement account. If she made 1,500 in a pay period, how much of it will go into her retirement account? Write an equation to solve the problem. The Utah Middle School Math Project","Convert the percentage to a decimal. To convert a percent to a decimal, divide by 100. 6/100 = 0.06 This decimal should be multiplied by Sandy's income to reflect how much money goes into the account. The amount of money can be represented by r=0.061500.","###Write an explanation to this problem:
Sandy puts 6% of her income in a retirement account. If she made 1,500 in a pay period, how much of it will go into her retirement account? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Convert the percentage to a decimal. To convert a percent to a decimal, divide by 100. 6/100 = 0.06 This decimal should be multiplied by Sandy's income to reflect how much money goes into the account. The amount of money can be represented by r=0.061500."
779,"Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B","I can add two to the weeks each time to get the next number. I can add 350 to the money to get the next values. In the rows, we have 2:350, which is equal to 1:175. So the money is 175 times larger than the week. I can just multiply the week by 175 to get the amount of money in the account. The ratio used to create the table was 1:175.","###Write an explanation to this problem:
Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B
###Explanation:
I can add two to the weeks each time to get the next number. I can add 350 to the money to get the next values. In the rows, we have 2:350, which is equal to 1:175. So the money is 175 times larger than the week. I can just multiply the week by 175 to get the amount of money in the account. The ratio used to create the table was 1:175."
56,Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org,Lin Noah 7x+2=91 7x+14 = 91 7x = 77 x = 11 7x+2 =91 x+2 = 13 x = 11,"###Write an explanation to this problem:
Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org
###Explanation:
Lin Noah 7x+2=91 7x+14 = 91 7x = 77 x = 11 7x+2 =91 x+2 = 13 x = 11"
291,"Zookeepers recorded the ages, weights, genders, and heights of the 10 pandas at their zoo. Write two statistical questions that could be answered using these data sets.",There are multiple correct answers to this question. These are just a couple of examples: What is the average age of the pandas in the zoo? Are male pandas typically taller than female pandas?,"###Write an explanation to this problem:
Zookeepers recorded the ages, weights, genders, and heights of the 10 pandas at their zoo. Write two statistical questions that could be answered using these data sets.
###Explanation:
There are multiple correct answers to this question. These are just a couple of examples: What is the average age of the pandas in the zoo? Are male pandas typically taller than female pandas?"
316,"In an isosceles triangle, which is not equilateral, two side lengths are equal and two angle measures are equal. Sketch three different isosceles triangles. Submit your drawing using the tools below.",Triangles should each have two sides that are the same length but not three. Answer vary.,"###Write an explanation to this problem:
In an isosceles triangle, which is not equilateral, two side lengths are equal and two angle measures are equal. Sketch three different isosceles triangles. Submit your drawing using the tools below.
###Explanation:
Triangles should each have two sides that are the same length but not three. Answer vary."
840,"A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost 12. How much will the caterer pay for the pasta there? Write a ratio for the given information about the cost of pasta.",The ratio for the given information about the cost of pasta could be represented as 8pounds of pasta: 12 or 21 pounds of pasta: x,"###Write an explanation to this problem:
A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost 12. How much will the caterer pay for the pasta there? Write a ratio for the given information about the cost of pasta.
###Explanation:
The ratio for the given information about the cost of pasta could be represented as 8pounds of pasta: 12 or 21 pounds of pasta: x"
24,"Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9","The subtraction rule says that subtracting a number is the same as adding its opposite. To use this rule of subtraction, we start by switching the subtraction sign to an addition sign: 5 + 9 We then change the sign of 9 to its opposite and get: 5 + -9","###Write an explanation to this problem:
Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9
###Explanation:
The subtraction rule says that subtracting a number is the same as adding its opposite. To use this rule of subtraction, we start by switching the subtraction sign to an addition sign: 5 + 9 We then change the sign of 9 to its opposite and get: 5 + -9"
750,Fill in the blank with numbers that correctly complete the statement. Three rational numbers between -1 and -2 < <,-1.9 < -1.55 < -1.02,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three rational numbers between -1 and -2 < <
###Explanation:
-1.9 < -1.55 < -1.02"
394,"Write a story that matches the expressions and equation shown below. Felipe's age: f Felipe's sister's age: f - 6 Felipe's mom's age: 3f - 9 f + f - 6 + 3f - 9 = 60 Hint: When writing stories like the one above, be sure to relate the unknown to its meaning in the story. Don't use the actual unknown in the story. For example, in the situation above, do not write Felipe's sister is f minus 6 years old. Think about how Felipe's sister's age is related to Felipe's age which is represented by f in the expression. Also, remember that your story needs a question. The Utah Middle School Math Project","A possible story could be: Felipe's sister is six years younger than him. His mom's age is nine less than three ties his age. Together, their ages sum to 60, How old is each person? It is important that each age is addressed in the story, along with all known parts of the story. In this case, the known part of the story is the sum of the ages, and how old each person is based on Felipe's age.","###Write an explanation to this problem:
Write a story that matches the expressions and equation shown below. Felipe's age: f Felipe's sister's age: f - 6 Felipe's mom's age: 3f - 9 f + f - 6 + 3f - 9 = 60 Hint: When writing stories like the one above, be sure to relate the unknown to its meaning in the story. Don't use the actual unknown in the story. For example, in the situation above, do not write Felipe's sister is f minus 6 years old. Think about how Felipe's sister's age is related to Felipe's age which is represented by f in the expression. Also, remember that your story needs a question. The Utah Middle School Math Project
###Explanation:
A possible story could be: Felipe's sister is six years younger than him. His mom's age is nine less than three ties his age. Together, their ages sum to 60, How old is each person? It is important that each age is addressed in the story, along with all known parts of the story. In this case, the known part of the story is the sum of the ages, and how old each person is based on Felipe's age."
490,Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project,w= 2r where w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project
###Explanation:
w= 2r where w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles."
51,Write another ratio that is equivalent to the ratio 4:6.,"Some ratios that could be equivalent to 4:6 are 2:3, 8:12, 12:18 and 40:60","###Write an explanation to this problem:
Write another ratio that is equivalent to the ratio 4:6.
###Explanation:
Some ratios that could be equivalent to 4:6 are 2:3, 8:12, 12:18 and 40:60"
659,"Challenge: If two equal angles are supplements to each other, find the measure of each angle in terms of one variable. The Utah Middle School Math Project",The answer is x and 180-x This is because supplementary angles add to 180 so to find the angles you can do 180-x which will be one answer and x will be the other,"###Write an explanation to this problem:
Challenge: If two equal angles are supplements to each other, find the measure of each angle in terms of one variable. The Utah Middle School Math Project
###Explanation:
The answer is x and 180-x This is because supplementary angles add to 180 so to find the angles you can do 180-x which will be one answer and x will be the other"
811,Mark the text by underlining key words. The sum of 25 and h is divided by f cubed.,The sum of 25 and h is divided by f cubed.,"###Write an explanation to this problem:
Mark the text by underlining key words. The sum of 25 and h is divided by f cubed.
###Explanation:
The sum of 25 and h is divided by f cubed."
549,"In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. -32x-5-6x-15 Explain the mistake The Utah Middle School Math Project","Notice that -3 x -5 = 15, not -15. This means that the -3 was not distributed to the terms within the parentheses properly.","###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. -32x-5-6x-15 Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that -3 x -5 = 15, not -15. This means that the -3 was not distributed to the terms within the parentheses properly."
264,"The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100. Describe how the manager can select a fair sample of 5 packages.","There are several different correct ways the manager could select a fair sample of 5 packages. The manager should pick a method that will result in a random sample. One way is to write the numbers from 1 to 100 on slips of paper and put them in a bag. Mix them well, then select 5 slips of paper from the bag. Use the numbers on these slips to identify which packages in the shipment will be in the sample. ***Alternative: The manager might also use random digits or another type of random number generator.","###Write an explanation to this problem:
The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100. Describe how the manager can select a fair sample of 5 packages.
###Explanation:
There are several different correct ways the manager could select a fair sample of 5 packages. The manager should pick a method that will result in a random sample. One way is to write the numbers from 1 to 100 on slips of paper and put them in a bag. Mix them well, then select 5 slips of paper from the bag. Use the numbers on these slips to identify which packages in the shipment will be in the sample. ***Alternative: The manager might also use random digits or another type of random number generator."
774,A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.,Choice One: 𝟏 𝐜𝐦 * 𝟏 𝐜𝐦 * 𝟓𝟎 𝐜𝐦 Choice Two: 𝟏 𝐜𝐦 * 𝟐 𝐜𝐦 * 𝟐𝟓 𝐜𝐦 Choice Three: 𝟏 𝐜𝐦 * 𝟓 𝐜𝐦 * 𝟏𝟎 𝐜𝐦 Choice Four: 𝟐 𝐜𝐦 * 𝟓 𝐜𝐦 * 𝟓 𝐜m,"###Write an explanation to this problem:
A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.
###Explanation:
Choice One: 𝟏 𝐜𝐦 * 𝟏 𝐜𝐦 * 𝟓𝟎 𝐜𝐦 Choice Two: 𝟏 𝐜𝐦 * 𝟐 𝐜𝐦 * 𝟐𝟓 𝐜𝐦 Choice Three: 𝟏 𝐜𝐦 * 𝟓 𝐜𝐦 * 𝟏𝟎 𝐜𝐦 Choice Four: 𝟐 𝐜𝐦 * 𝟓 𝐜𝐦 * 𝟓 𝐜m"
590,"Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips.","###Write an explanation to this problem:
Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips."
671,-5 x 0 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer -5 and multiply it 0 times, so -5 x 0 means the opposite of five groups of 0.","###Write an explanation to this problem:
-5 x 0 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -5 and multiply it 0 times, so -5 x 0 means the opposite of five groups of 0."
482,Given the graphs of two or more lines how can you determine if they are parallel? The Utah Middle School Math Project,Lines are parallel if they have the same slope.,"###Write an explanation to this problem:
Given the graphs of two or more lines how can you determine if they are parallel? The Utah Middle School Math Project
###Explanation:
Lines are parallel if they have the same slope."
18,"Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.","The slope shows that for every 1 unit increase in side length of the triangle, the perimeter increases by 3 units.","###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
###Explanation:
The slope shows that for every 1 unit increase in side length of the triangle, the perimeter increases by 3 units."
617,Are all squares similar? Justify your answer. The Utah Middle School Math Project,The answer is yes. This is because the ratio between all sides of all squares is 1:1,"###Write an explanation to this problem:
Are all squares similar? Justify your answer. The Utah Middle School Math Project
###Explanation:
The answer is yes. This is because the ratio between all sides of all squares is 1:1"
833,"Why do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller?","As whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with.","###Write an explanation to this problem:
Why do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller?
###Explanation:
As whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with."
83,Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project,"There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240.","###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240."
61,Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org,"-7, -8, -9, -10","###Write an explanation to this problem:
Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org
###Explanation:
-7, -8, -9, -10"
272,A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?,"Both lights will blink the same after 20 seconds. Green- 4, 8, 12, 16, 20 Yellow- 5, 10, 15, 20","###Write an explanation to this problem:
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
###Explanation:
Both lights will blink the same after 20 seconds. Green- 4, 8, 12, 16, 20 Yellow- 5, 10, 15, 20"
285,Which data set is more likely to produce a histogram with a symmetric distribution? Explain your reasoning. Data on the number of seconds on a track of music in a pop album. Data on the number of seconds spent talking on the phone yesterday by everyone in the school.,"The data on the number of seconds on a track of music in a pop album is most likely to be symmetrical because pops songs are generally about the same length. The data about talking on the phone may have a wide spread because some people may only talk for a few seconds, but others may talk on the phone for hours.","###Write an explanation to this problem:
Which data set is more likely to produce a histogram with a symmetric distribution? Explain your reasoning. Data on the number of seconds on a track of music in a pop album. Data on the number of seconds spent talking on the phone yesterday by everyone in the school.
###Explanation:
The data on the number of seconds on a track of music in a pop album is most likely to be symmetrical because pops songs are generally about the same length. The data about talking on the phone may have a wide spread because some people may only talk for a few seconds, but others may talk on the phone for hours."
327,Which measurements would you need in order to draw a scale floor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specific as possible. copied for free from openupresources.org,The length and width of all the walls The measurements of doorways the measurements of all furniture in the classroom,"###Write an explanation to this problem:
Which measurements would you need in order to draw a scale floor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specific as possible. copied for free from openupresources.org
###Explanation:
The length and width of all the walls The measurements of doorways the measurements of all furniture in the classroom"
426,Homes in a certain neighborhood sell for 117 per square foot. Can the relationship between the number of square feet in the home and the sale price of the home be modeled by a linear function? Why or why not? The Utah Middle School Math Project,"This data can be modeled by a linear function, because the relationship between the number of square feet and the sale price is a constant.","###Write an explanation to this problem:
Homes in a certain neighborhood sell for 117 per square foot. Can the relationship between the number of square feet in the home and the sale price of the home be modeled by a linear function? Why or why not? The Utah Middle School Math Project
###Explanation:
This data can be modeled by a linear function, because the relationship between the number of square feet and the sale price is a constant."
499,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project",𝑥 + 𝑦 = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1𝑥 + 2.5𝑦 = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project
###Explanation:
𝑥 + 𝑦 = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1𝑥 + 2.5𝑦 = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982"
182,"Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org","Factoring is the distributive property in the other direction. Instead of expanding a product to a sum of terms, factoring first takes a sum of terms. It makes the sum of terms into a product by looking for common factors in the terms that can can be written outside the parentheses.","###Write an explanation to this problem:
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org
###Explanation:
Factoring is the distributive property in the other direction. Instead of expanding a product to a sum of terms, factoring first takes a sum of terms. It makes the sum of terms into a product by looking for common factors in the terms that can can be written outside the parentheses."
483,"Here, write the second problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project","Sample Answer: Richard prepares 24 fluid ounces of tea for his workday. In the first hour of work, he drank 25% of the tea. How many fluid ounces of tea did he drink? Solution: whole: 24 fl.oz. percent: 25% = 0.25 To find the amount of tea he drank, we multiply the whole by the percent: whole x percent = 24 fl. oz. x 0.25 = 6 fl. oz. We get that in the first hour of work, Richard drank 6 fl. oz. of tea.","###Write an explanation to this problem:
Here, write the second problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Richard prepares 24 fluid ounces of tea for his workday. In the first hour of work, he drank 25% of the tea. How many fluid ounces of tea did he drink? Solution: whole: 24 fl.oz. percent: 25% = 0.25 To find the amount of tea he drank, we multiply the whole by the percent: whole x percent = 24 fl. oz. x 0.25 = 6 fl. oz. We get that in the first hour of work, Richard drank 6 fl. oz. of tea."
533,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Jenny has 30 coins she has collected over 6 years. The Utah Middle School Math Project,The time 6 years is the independent variable The number of coins is the dependent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Jenny has 30 coins she has collected over 6 years. The Utah Middle School Math Project
###Explanation:
The time 6 years is the independent variable The number of coins is the dependent variable."
223,A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?,"20 seconds You need to find the least common multiple of each number 4: 4, 8, 12, 16, 205: 5, 10, 15, 20","###Write an explanation to this problem:
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
###Explanation:
20 seconds You need to find the least common multiple of each number 4: 4, 8, 12, 16, 205: 5, 10, 15, 20"
473,Create your own context or story that represents a relation that is not a function. Write your story.,"To be a function, whatever you chose to be the independent variable x must have only one corresponding dependent variable y.","###Write an explanation to this problem:
Create your own context or story that represents a relation that is not a function. Write your story.
###Explanation:
To be a function, whatever you chose to be the independent variable x must have only one corresponding dependent variable y."
604,"Use The Distributive Property to find the product. 4105 First, show your work here. The Utah Middle School Math Project",4105 = 4100 + 5 = 4100 + 45 = 400 + 20 = 420,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 4105 First, show your work here. The Utah Middle School Math Project
###Explanation:
4105 = 4100 + 5 = 4100 + 45 = 400 + 20 = 420"
359,"As part of a competition, Diego must spin around in a circle 6 times and then run to a tree. The time he spends on each spin is represented by s and the time he spends running is r. He gets to the tree 21 seconds after he starts spinning. Write an equation showing the relationship between s and r. Copied for free from openupresources.org","Diego has to spin 6 times. If it takes him s seconds per spin, then for all of his spins together he takes 6s seconds. If it takes him 21 seconds total to get to the tree, this means the time he spent spinning 6s plus the time he spent running r equals 21 seconds. 6s + r = 21","###Write an explanation to this problem:
As part of a competition, Diego must spin around in a circle 6 times and then run to a tree. The time he spends on each spin is represented by s and the time he spends running is r. He gets to the tree 21 seconds after he starts spinning. Write an equation showing the relationship between s and r. Copied for free from openupresources.org
###Explanation:
Diego has to spin 6 times. If it takes him s seconds per spin, then for all of his spins together he takes 6s seconds. If it takes him 21 seconds total to get to the tree, this means the time he spent spinning 6s plus the time he spent running r equals 21 seconds. 6s + r = 21"
487,"The number e is an important irrational number. In future math classes as well as science and socialscience, you will see and use this number quite a bit. Use the approximations of e and the calculationsgiven below to answer the questions that follow. e is between 2 and 3e is between 2.7 and 2.8e is between 2.71 and 2.72e is between 2.718 and 2.719 Find a number that is between 2 and e. The Utah Middle School Math Project","If e is between 2 and 3, then any number between 2 and 3 would be a correct answer.","###Write an explanation to this problem:
The number e is an important irrational number. In future math classes as well as science and socialscience, you will see and use this number quite a bit. Use the approximations of e and the calculationsgiven below to answer the questions that follow. e is between 2 and 3e is between 2.7 and 2.8e is between 2.71 and 2.72e is between 2.718 and 2.719 Find a number that is between 2 and e. The Utah Middle School Math Project
###Explanation:
If e is between 2 and 3, then any number between 2 and 3 would be a correct answer."
495,Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project,Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include 6x - 15 6x - 17 _ 2 2x + 4x - 16 + 1,"###Write an explanation to this problem:
Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include 6x - 15 6x - 17 _ 2 2x + 4x - 16 + 1"
527,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The value of your car decreases with age. The Utah Middle School Math Project,Value is dependent Age is independent,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The value of your car decreases with age. The Utah Middle School Math Project
###Explanation:
Value is dependent Age is independent"
176,Make up a situation where a quantity is changing. Explain what it means to have a negative change.,To have a negative change means that you are going down in something.,"###Write an explanation to this problem:
Make up a situation where a quantity is changing. Explain what it means to have a negative change.
###Explanation:
To have a negative change means that you are going down in something."
578,Write three expressions equivalent to the expression 4c. The Utah Middle School Math Project,There are many expressions that are equivalent to 4c. One example is the expression 2c + c + c.,"###Write an explanation to this problem:
Write three expressions equivalent to the expression 4c. The Utah Middle School Math Project
###Explanation:
There are many expressions that are equivalent to 4c. One example is the expression 2c + c + c."
812,"Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.",One question you could ask that would result in categorical data would be: What is your favorite color? This would produce categorical data because color is a category and is not a logical/measured quantity.,"###Write an explanation to this problem:
Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.
###Explanation:
One question you could ask that would result in categorical data would be: What is your favorite color? This would produce categorical data because color is a category and is not a logical/measured quantity."
163,Kiran drinks 6.4 oz of milk each morning. How many days does it take him to finish a 32 oz container of milk? Write and solve an equation for the situation.,"The equation will have to equal 32 oz, because that is the goal. Each day x he drinks 6.4 oz of milk. This will be multiplied. This means 6.4 times x will be equal to 32. 6.4x=32 To solve, divide both sides of the equation by 6.4, because this is the inverse of multiplying x by 6.4. 32/6.4 = 5, so x=5 days to finish a 32 oz container of milk.","###Write an explanation to this problem:
Kiran drinks 6.4 oz of milk each morning. How many days does it take him to finish a 32 oz container of milk? Write and solve an equation for the situation.
###Explanation:
The equation will have to equal 32 oz, because that is the goal. Each day x he drinks 6.4 oz of milk. This will be multiplied. This means 6.4 times x will be equal to 32. 6.4x=32 To solve, divide both sides of the equation by 6.4, because this is the inverse of multiplying x by 6.4. 32/6.4 = 5, so x=5 days to finish a 32 oz container of milk."
248,"Over several months, the weight of a baby measured in pounds doubles. Does its weight measure in kilograms also double? Explain",1 kg = 2.2 lbs This ratio remains the same even as the child gets heavier. A double is a number that is twice itself. For example: our baby's weight doubles from 12 lbs to 24 lbs 12 lb= 26.4 kgs Kilograms doubled that would be 52.8 kgs 24 lbs= 52.8 kgs It did double.,"###Write an explanation to this problem:
Over several months, the weight of a baby measured in pounds doubles. Does its weight measure in kilograms also double? Explain
###Explanation:
1 kg = 2.2 lbs This ratio remains the same even as the child gets heavier. A double is a number that is twice itself. For example: our baby's weight doubles from 12 lbs to 24 lbs 12 lb= 26.4 kgs Kilograms doubled that would be 52.8 kgs 24 lbs= 52.8 kgs It did double."
658,Write an equation that represents each description. The opposite of negative seven,--7 = 7,"###Write an explanation to this problem:
Write an equation that represents each description. The opposite of negative seven
###Explanation:
--7 = 7"
753,Write a statement relating the opposites of each of the given numbers. 7 is greater than 6,-7 is less than -6,"###Write an explanation to this problem:
Write a statement relating the opposites of each of the given numbers. 7 is greater than 6
###Explanation:
-7 is less than -6"
74,Find a value for x that makes -x less than 2x. copied for free from openupresources.org,"1, because -1 is less than 2*1","###Write an explanation to this problem:
Find a value for x that makes -x less than 2x. copied for free from openupresources.org
###Explanation:
1, because -1 is less than 2*1"
113,A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.,"The problem gives the ratio as: height : width 3 : 4.5 To find rectangles with dimensions that fit this ratio and can be scaled versions of the rectangle given in the problem we can multiply both sides of the ratio by the same factor. If we scale both sides by a factor of 2: 3*2 = 6 and 4.5*2 = 9 We get the dimensions 6 by 9. For a second rectangle, we can scale both sides by a different factor like 4: 3*4 = 12 and 4.5*4 = 18 We get the dimensions 12 by 18. There are many other dimensions that are correct answers, but as long as they fit the ratio given in the problem, they are correct.","###Write an explanation to this problem:
A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.
###Explanation:
The problem gives the ratio as: height : width 3 : 4.5 To find rectangles with dimensions that fit this ratio and can be scaled versions of the rectangle given in the problem we can multiply both sides of the ratio by the same factor. If we scale both sides by a factor of 2: 3*2 = 6 and 4.5*2 = 9 We get the dimensions 6 by 9. For a second rectangle, we can scale both sides by a different factor like 4: 3*4 = 12 and 4.5*4 = 18 We get the dimensions 12 by 18. There are many other dimensions that are correct answers, but as long as they fit the ratio given in the problem, they are correct."
486,A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project,The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example.,"###Write an explanation to this problem:
A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example."
453,Given information: 2m = Number of red marbles 3m = Number of blue marbles Equation: 2m + 3m = 155 marbles. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,The ratio of red marbles to blue marbles is 2:3. The total number of marbles is 155. How many red marbles and blue marbles are there?,"###Write an explanation to this problem:
Given information: 2m = Number of red marbles 3m = Number of blue marbles Equation: 2m + 3m = 155 marbles. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
The ratio of red marbles to blue marbles is 2:3. The total number of marbles is 155. How many red marbles and blue marbles are there?"
104,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. ?,-10,3,8 The Utah Middle School Math Project","In this question, the only requirement is than the number that replaces the ? is an integer that is less than -10. Any number that is farther from 0 than -10 is less than -10. Possible answers include: -11, -12, -25, and so on.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. ?,-10,3,8 The Utah Middle School Math Project
###Explanation:
In this question, the only requirement is than the number that replaces the ? is an integer that is less than -10. Any number that is farther from 0 than -10 is less than -10. Possible answers include: -11, -12, -25, and so on."
114,Explain a process you can use to create a number line from -5 to 5. What steps can you take? What tools can you use? The Utah Middle School Math Project,"To draw a number line from -5 to 5, you can start by using a ruler on a piece of paper and drawing a line that is a certain length, like 11 centimeters long. If we count from -5 to 5 ex: -5, -4, -3, -2..., we know that we will need 11 tick marks. We can draw 11 tick marks, equally spaced, along our line. If our line is 11 cm long, then there can be a tick mark starting at 0, and one at every centimeter mark after that. We know that -5 goes with the tick mark at the left end of the line. We know that 5 goes with the tick mark at the right end of the line. We know that 0 must go on the middle tick mark, since it is halfway between -5 and 5. Finally, we can fill in the rest of the tick marks.","###Write an explanation to this problem:
Explain a process you can use to create a number line from -5 to 5. What steps can you take? What tools can you use? The Utah Middle School Math Project
###Explanation:
To draw a number line from -5 to 5, you can start by using a ruler on a piece of paper and drawing a line that is a certain length, like 11 centimeters long. If we count from -5 to 5 ex: -5, -4, -3, -2..., we know that we will need 11 tick marks. We can draw 11 tick marks, equally spaced, along our line. If our line is 11 cm long, then there can be a tick mark starting at 0, and one at every centimeter mark after that. We know that -5 goes with the tick mark at the left end of the line. We know that 5 goes with the tick mark at the right end of the line. We know that 0 must go on the middle tick mark, since it is halfway between -5 and 5. Finally, we can fill in the rest of the tick marks."
572,Write an ordered pair that would be in Quadrant II when graphed. The Utah Middle School Math Project,Any ordered pair where x is negative and y is positive is in Quadrant II.,"###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant II when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair where x is negative and y is positive is in Quadrant II."
92,"Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project","Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 A factor is a number that you can multiply to get another larger number.","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 A factor is a number that you can multiply to get another larger number."
620,Write three numbers that are less than -1. The Utah Middle School Math Project,"Possible answers: -2, -4/3, -5.75","###Write an explanation to this problem:
Write three numbers that are less than -1. The Utah Middle School Math Project
###Explanation:
Possible answers: -2, -4/3, -5.75"
89,Write a pair of numbers whose LCM is 60. The Utah Middle School Math Project,"There are a few different numbers that have multiples of 15. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. From this list, the only pairs of numbers that have 60 as their least common multiple are: Any of the factors and 60 4 and 30 12 and 30 20 and 30 3 and 20 6 and 20 12 and 20 15 and 20 4 and 15 12 and 15 5 and 12 10 and 12","###Write an explanation to this problem:
Write a pair of numbers whose LCM is 60. The Utah Middle School Math Project
###Explanation:
There are a few different numbers that have multiples of 15. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. From this list, the only pairs of numbers that have 60 as their least common multiple are: Any of the factors and 60 4 and 30 12 and 30 20 and 30 3 and 20 6 and 20 12 and 20 15 and 20 4 and 15 12 and 15 5 and 12 10 and 12"
336,Here is an equation: 4x - 4 = 4x + __. What could you write in the blank so the equation would be true for: No values of x Copied for free from openupresources.org,"We have 4x on both sides of this equation. We know that if we insert a constant into this blank, then there would still only be 4x on both sides of the equation. If we subtract 4x from both sides, we get: -4 = ___ If we want this to not be true, then we would need for the constant in the blank to not equal -4. The answer is any constant not equal to -4.","###Write an explanation to this problem:
Here is an equation: 4x - 4 = 4x + __. What could you write in the blank so the equation would be true for: No values of x Copied for free from openupresources.org
###Explanation:
We have 4x on both sides of this equation. We know that if we insert a constant into this blank, then there would still only be 4x on both sides of the equation. If we subtract 4x from both sides, we get: -4 = ___ If we want this to not be true, then we would need for the constant in the blank to not equal -4. The answer is any constant not equal to -4."
548,"In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5-x-2 5-x-2 3-x Explain the mistake The Utah Middle School Math Project",Notice that the -1 was distributed to the x in the parentheses but not distributed to the -2 within the parentheses.,"###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5-x-2 5-x-2 3-x Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that the -1 was distributed to the x in the parentheses but not distributed to the -2 within the parentheses."
783,"How are the ordered pairs 4, 9 and 4,-9 similar?",The two ordered pairs are similar because their x-coordinates are the same.,"###Write an explanation to this problem:
How are the ordered pairs 4, 9 and 4,-9 similar?
###Explanation:
The two ordered pairs are similar because their x-coordinates are the same."
794,What does the expression represent?,"This is the area, because the area is length times width.","###Write an explanation to this problem:
What does the expression represent?
###Explanation:
This is the area, because the area is length times width."
693,Solve the inequality. Represent the solution on a number line. 12>x+11 The Utah Middle School Math Project,"Solve for x. The number line should be less than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 12>x+11 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than the solution, but not contain it."
529,Write an ordered pair that would be in Quadrant IV when graphed. The Utah Middle School Math Project,"Any ordered pair x, y where x is positive and y is negative is Quadrant IV. Examples: 1, -1 5, -3 1/2, -3/4","###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant IV when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair x, y where x is positive and y is negative is Quadrant IV. Examples: 1, -1 5, -3 1/2, -3/4"
94,"Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.",Kent knows that subtracting a number is the same as adding it's opposite. He then uses this idea to rewrite the problem changing all of the subtraction parts to adding the opposite: -9.5 - -8 - 6.5 can be rewritten as: -9.5 + 8 + -6.5 and now Kent can use only addition to solve this problem.,"###Write an explanation to this problem:
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.
###Explanation:
Kent knows that subtracting a number is the same as adding it's opposite. He then uses this idea to rewrite the problem changing all of the subtraction parts to adding the opposite: -9.5 - -8 - 6.5 can be rewritten as: -9.5 + 8 + -6.5 and now Kent can use only addition to solve this problem."
11,Fill in the blank with numbers that correctly complete the statement. Three rational numbers between -1 and -2 < <,-1.9 < -1.55 < -1.02,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three rational numbers between -1 and -2 < <
###Explanation:
-1.9 < -1.55 < -1.02"
396,Callie and Jeff each have a job delivering newspapers. Jeff gets paid 140 dollars for delivering 350 papers. Callie gets paid 100 for delivering 200 papers. Find the unit rate for Callie The Utah Middle School Math Project,"The unit rate can be either the amount of dollars for every one newspaper or the amount of newspapers for every one dollar. Unlike a regular rate, unit rates have a 1 in the denominator. To turn a rate into a unit rate, divide the numerator by the denominator. The rate that Callie was delivering papers is 100 per 200 papers or 100/200 papers. To get the unit rate divide 100 by 200 to get unit rate of 0.50/paper 0.50 is the unit rate of dollars to papers The rate that Callie delivered can also be expressed in papers per dollars. The rate would be 200 papers per 100. By simplifying the rate a unit rate of 2 papers per dollar is found. 2 is the unit rate of papers to dollars.","###Write an explanation to this problem:
Callie and Jeff each have a job delivering newspapers. Jeff gets paid 140 dollars for delivering 350 papers. Callie gets paid 100 for delivering 200 papers. Find the unit rate for Callie The Utah Middle School Math Project
###Explanation:
The unit rate can be either the amount of dollars for every one newspaper or the amount of newspapers for every one dollar. Unlike a regular rate, unit rates have a 1 in the denominator. To turn a rate into a unit rate, divide the numerator by the denominator. The rate that Callie was delivering papers is 100 per 200 papers or 100/200 papers. To get the unit rate divide 100 by 200 to get unit rate of 0.50/paper 0.50 is the unit rate of dollars to papers The rate that Callie delivered can also be expressed in papers per dollars. The rate would be 200 papers per 100. By simplifying the rate a unit rate of 2 papers per dollar is found. 2 is the unit rate of papers to dollars."
43,How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words east and west?,By using positive numbers for one direction and negative numbers for the other direction.,"###Write an explanation to this problem:
How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words east and west?
###Explanation:
By using positive numbers for one direction and negative numbers for the other direction."
42,"Nathan is your school's star soccer player. When he takes a shot on goal, he typically scores half of the time. Suppose that he takes six shots in a game. To estimate the probability of the number of goals Nathan makes, use simulation with a number cube. One roll of a number cube represents one shot. For this problem, what represents a trial of taking six shots?","Rolling the number cube six times would represent taking six shots, since one roll represents one shot.","###Write an explanation to this problem:
Nathan is your school's star soccer player. When he takes a shot on goal, he typically scores half of the time. Suppose that he takes six shots in a game. To estimate the probability of the number of goals Nathan makes, use simulation with a number cube. One roll of a number cube represents one shot. For this problem, what represents a trial of taking six shots?
###Explanation:
Rolling the number cube six times would represent taking six shots, since one roll represents one shot."
329,"Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.","To try to solve the puzzle, we can define each person's age in terms of Andre's age. Andre's age is x. He is 3 years younger than his brother, so his brother's age would be 3 more years than his age. His brother's age is x + 3. He is 2 years older than his sister. Her age would be his age minus 2 years. His sister's age is x - 2 His mom's age is 1 less than 3 times his brother's age. His brother's age is x + 3. 3 times his brother's age is 3x + 3 1 less than this is 3x + 3 - 1. If you add all of their ages, you get 87. x + x + 3 + x - 2 + 3x + 3 - 1 = 87 First, we should distribute the 3 to the terms in parentheses. x + x + 3 + x - 2 + 3x + 9 - 1 = 87 Next, we should combine like terms. 6x + 9 = 87 Now, we can solve for x by subtracting 9 from both sides. 6x = 78 x = 78/6 = 13 Andre is 13. His brother is 16. His sister is 11. His mother is 47.","###Write an explanation to this problem:
Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.
###Explanation:
To try to solve the puzzle, we can define each person's age in terms of Andre's age. Andre's age is x. He is 3 years younger than his brother, so his brother's age would be 3 more years than his age. His brother's age is x + 3. He is 2 years older than his sister. Her age would be his age minus 2 years. His sister's age is x - 2 His mom's age is 1 less than 3 times his brother's age. His brother's age is x + 3. 3 times his brother's age is 3x + 3 1 less than this is 3x + 3 - 1. If you add all of their ages, you get 87. x + x + 3 + x - 2 + 3x + 3 - 1 = 87 First, we should distribute the 3 to the terms in parentheses. x + x + 3 + x - 2 + 3x + 9 - 1 = 87 Next, we should combine like terms. 6x + 9 = 87 Now, we can solve for x by subtracting 9 from both sides. 6x = 78 x = 78/6 = 13 Andre is 13. His brother is 16. His sister is 11. His mother is 47."
167,List the sample space for selecting a letter a random from the word PINEAPPLE.,"P, I, N, E, A, L","###Write an explanation to this problem:
List the sample space for selecting a letter a random from the word PINEAPPLE.
###Explanation:
P, I, N, E, A, L"
746,Write a story problem using sea level that includes both integers -110 and 120.,"Answers may vary. On the beach, a man's kite flew at 120 feet above sea level, which is indicated by the water's surface. In the ocean, a white shark swims at 110 feet below the water's surface.","###Write an explanation to this problem:
Write a story problem using sea level that includes both integers -110 and 120.
###Explanation:
Answers may vary. On the beach, a man's kite flew at 120 feet above sea level, which is indicated by the water's surface. In the ocean, a white shark swims at 110 feet below the water's surface."
518,"Determine if the relation or situation defines a function. Justify your answer. {-1, 0, 1, 2, 1, 4, 5, 2} The Utah Middle School Math Project","No, the data does not describe a function For the x value of 1 there are two y values, 2 and 4 This means each input does not have exactly one output, and is therefore not a function","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. {-1, 0, 1, 2, 1, 4, 5, 2} The Utah Middle School Math Project
###Explanation:
No, the data does not describe a function For the x value of 1 there are two y values, 2 and 4 This means each input does not have exactly one output, and is therefore not a function"
651,"In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 9 Transformed Equation: 6x = 54 Action: ______ The Utah Middle School Math Project","On the left side of the equation, x has been multiplied by 6.","###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 9 Transformed Equation: 6x = 54 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, x has been multiplied by 6."
706,Create a context for the numeric representation. 801 + 80.40 = 801.40 = 112 The Utah Middle School Math Project,"Sample Answer: If a person has 80 apples, then gains 40% more apples than the original 80, this numeric expression describes the total number of apples.","###Write an explanation to this problem:
Create a context for the numeric representation. 801 + 80.40 = 801.40 = 112 The Utah Middle School Math Project
###Explanation:
Sample Answer: If a person has 80 apples, then gains 40% more apples than the original 80, this numeric expression describes the total number of apples."
178,Draw a square with side length 7 cm. Predict the perimeter.,"Use the information given in the problem to predict the perimeter of a square with a side length of 7 cm. Keep in mind that: A square has 4 side lengths of the same measurement The perimeter is the distance around the shape The problem says that the side length is 7 cm long To predict the perimeter, we can multiply the length of 1 side by 4 to get the sum of all of the lengths of the sides of the square. 7 cm * 4 sides = 28 cm A good prediction for the perimeter of the square would be 28 cm.","###Write an explanation to this problem:
Draw a square with side length 7 cm. Predict the perimeter.
###Explanation:
Use the information given in the problem to predict the perimeter of a square with a side length of 7 cm. Keep in mind that: A square has 4 side lengths of the same measurement The perimeter is the distance around the shape The problem says that the side length is 7 cm long To predict the perimeter, we can multiply the length of 1 side by 4 to get the sum of all of the lengths of the sides of the square. 7 cm * 4 sides = 28 cm A good prediction for the perimeter of the square would be 28 cm."
808,Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1,"-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2.","###Write an explanation to this problem:
Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1
###Explanation:
-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2."
598,"Determine whether the three given side lengths can form a triangle. If you chose no, explain why it doesn't work. 5.1 inches, 3.24 inches, 8.25 inches The Utah Middle School Math Project","By the Triangle Inequality Theorem, the sum of the lengths of two sides is greater than the length of the third side. 5.1 in + 3.24 in = 8.34 in > 8.25 in 5.1 in + 8.25 in = 13.35 in > 3.24 in 3.24 in + 8.25 in = 11.49 in > 5.1 in Therefore, by Triangle Inequality, the three side lengths can form a triangle.","###Write an explanation to this problem:
Determine whether the three given side lengths can form a triangle. If you chose no, explain why it doesn't work. 5.1 inches, 3.24 inches, 8.25 inches The Utah Middle School Math Project
###Explanation:
By the Triangle Inequality Theorem, the sum of the lengths of two sides is greater than the length of the third side. 5.1 in + 3.24 in = 8.34 in > 8.25 in 5.1 in + 8.25 in = 13.35 in > 3.24 in 3.24 in + 8.25 in = 11.49 in > 5.1 in Therefore, by Triangle Inequality, the three side lengths can form a triangle."
177,Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. NOW there are 78 players on the field. Write an equation whose solution is the number of players on each team. copied for free from openupresources.org,Sample Answer: An equation can be 6x-2 = 78.,"###Write an explanation to this problem:
Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. NOW there are 78 players on the field. Write an equation whose solution is the number of players on each team. copied for free from openupresources.org
###Explanation:
Sample Answer: An equation can be 6x-2 = 78."
585,"Simplify the following expressions using two different methods. 9100 + 10 + 1 First, show your work for each method. The Utah Middle School Math Project",One method is to first distribute the 9 to the terms within the parentheses: 9100 + 10 + 1 = 9100 + 910 + 91 = 900 + 90 + 9 = 999 Another method is to first add the terms in the parentheses and then distribute the 9: 9100 + 10 + 1 = 9111 = 999,"###Write an explanation to this problem:
Simplify the following expressions using two different methods. 9100 + 10 + 1 First, show your work for each method. The Utah Middle School Math Project
###Explanation:
One method is to first distribute the 9 to the terms within the parentheses: 9100 + 10 + 1 = 9100 + 910 + 91 = 900 + 90 + 9 = 999 Another method is to first add the terms in the parentheses and then distribute the 9: 9100 + 10 + 1 = 9111 = 999"
688,"Gavin is out shopping. After he buys 2 pairs of pants for 27 each, he has 60. How much money did he have before he bought the 2 pairs of pants? Write an equation to solve the problem. The Utah Middle School Math Project","Gavin has already spent 27 twice, and can spend 60 total. This means that m-227=60","###Write an explanation to this problem:
Gavin is out shopping. After he buys 2 pairs of pants for 27 each, he has 60. How much money did he have before he bought the 2 pairs of pants? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Gavin has already spent 27 twice, and can spend 60 total. This means that m-227=60"
737,Write two ratios that are equivalent to 3:11.,"Answers will vary. You might write the following ratios: 6:22, 9:33, etc.","###Write an explanation to this problem:
Write two ratios that are equivalent to 3:11.
###Explanation:
Answers will vary. You might write the following ratios: 6:22, 9:33, etc."
257,"9. Noah raised 54 to support the animal shelter, which is 60% of his fundraising goal. a. Write an equation to represent the situation. copied for free from openupresources.org",0.60x = 54 This is saying that 60% times some amount x is equal to 54.,"###Write an explanation to this problem:
9. Noah raised 54 to support the animal shelter, which is 60% of his fundraising goal. a. Write an equation to represent the situation. copied for free from openupresources.org
###Explanation:
0.60x = 54 This is saying that 60% times some amount x is equal to 54."
613,Write three expressions that are equivalent to the expression + + 4 + 3. The Utah Middle School Math Project,Example: 2x+4x+12; 6x+12; x+x+4x+43,"###Write an explanation to this problem:
Write three expressions that are equivalent to the expression + + 4 + 3. The Utah Middle School Math Project
###Explanation:
Example: 2x+4x+12; 6x+12; x+x+4x+43"
335,Draw two polygons that are similar but could be mistaken for not being similar. Submit your drawing using the tools below.,"There are many correct answers to this question. To be similar, the two polygons must be the same shape, but can involve some sorts of transformations to turn one into the other. For example, you could: Start with two triangles that are exactly the same and rotate one of them by however many degrees you want. You can then multiply all of the side lengths in the rotated triangle by a certain factor. Start with two triangles that are exactly the same and reflect one of them over a horizontal line. You can then multiply all of the side lengths in the reflected triangle by a certain factor.","###Write an explanation to this problem:
Draw two polygons that are similar but could be mistaken for not being similar. Submit your drawing using the tools below.
###Explanation:
There are many correct answers to this question. To be similar, the two polygons must be the same shape, but can involve some sorts of transformations to turn one into the other. For example, you could: Start with two triangles that are exactly the same and rotate one of them by however many degrees you want. You can then multiply all of the side lengths in the rotated triangle by a certain factor. Start with two triangles that are exactly the same and reflect one of them over a horizontal line. You can then multiply all of the side lengths in the reflected triangle by a certain factor."
532,Write a context to match the numeric expression given. 0.232 + 0.228 The Utah Middle School Math Project,"Dom is hungry at the store. He wants to buy fancy ham that is 32 a pound, and magic beans that are 28 a pound. He is going to buy 0.2 pounds of each. How much is this going to cost?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 0.232 + 0.228 The Utah Middle School Math Project
###Explanation:
Dom is hungry at the store. He wants to buy fancy ham that is 32 a pound, and magic beans that are 28 a pound. He is going to buy 0.2 pounds of each. How much is this going to cost?"
15,"Write an inequality that relates the rational numbers. In December, the total snowfall was 13.2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6.15 inches, respectively.",13.2 > 6.15 > 3.7,"###Write an explanation to this problem:
Write an inequality that relates the rational numbers. In December, the total snowfall was 13.2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6.15 inches, respectively.
###Explanation:
13.2 > 6.15 > 3.7"
3,Create a real-life example that can be modeled by the expression -2 * 4.,Your answer might vary. One example of a real life situation is: Tobi spends 2 each week on a candy bar for four weeks. Write an integer to represent Tobi's change in money after four weeks. Tobi's money changes by -2 X 4 after four weeks.,"###Write an explanation to this problem:
Create a real-life example that can be modeled by the expression -2 * 4.
###Explanation:
Your answer might vary. One example of a real life situation is: Tobi spends 2 each week on a candy bar for four weeks. Write an integer to represent Tobi's change in money after four weeks. Tobi's money changes by -2 X 4 after four weeks."
377,"Using circles and squares, create pictures that represent the ratio given. The ratio of squares to circles is 3:5. Draw your pictures on paper, take a picture, and upload it using the image upload icon If you do not have the ability to upload an image of your work type Picture is on paper. The Utah Middle School Math Project",DO NOT DO THIS ON SEPARATE PAPER. TYPE C for CIRCLE and S for SQUARE into the box making the correct ratio.,"###Write an explanation to this problem:
Using circles and squares, create pictures that represent the ratio given. The ratio of squares to circles is 3:5. Draw your pictures on paper, take a picture, and upload it using the image upload icon If you do not have the ability to upload an image of your work type Picture is on paper. The Utah Middle School Math Project
###Explanation:
DO NOT DO THIS ON SEPARATE PAPER. TYPE C for CIRCLE and S for SQUARE into the box making the correct ratio."
256,"Are you ready for more? The effects of each move can be undone by using another move. For example, to undo the effect of translating 3 units to the right, we could translate 3 units to the left. What move undoes each of the following moves? 1. Translate 3 units up. Copied for free from openupresources.org",Translate 3 units down.,"###Write an explanation to this problem:
Are you ready for more? The effects of each move can be undone by using another move. For example, to undo the effect of translating 3 units to the right, we could translate 3 units to the left. What move undoes each of the following moves? 1. Translate 3 units up. Copied for free from openupresources.org
###Explanation:
Translate 3 units down."
416,"Round 1 of a tennis tournament starts with 64 players. After each round, half the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 players, in round 3 there are 16 players and so on. What is the dependent variable in this relationship? The Utah Middle School Math Project",The number of players left is determined by the round number of the tournament. This means that players is the dependent variable in the equation.,"###Write an explanation to this problem:
Round 1 of a tennis tournament starts with 64 players. After each round, half the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 players, in round 3 there are 16 players and so on. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of players left is determined by the round number of the tournament. This means that players is the dependent variable in the equation."
554,Write a phrase for the following algebraic expression 7 - x The Utah Middle School Math Project,7 - x is a number x less than seven.,"###Write an explanation to this problem:
Write a phrase for the following algebraic expression 7 - x The Utah Middle School Math Project
###Explanation:
7 - x is a number x less than seven."
380,What is a net? Describe it in your own words.,Answers will vary but should capture the essence of the definition used in this lesson. A net is a two-dimensional figure which can be folded to create a three-dimensional solid with no gaps or overlaps.,"###Write an explanation to this problem:
What is a net? Describe it in your own words.
###Explanation:
Answers will vary but should capture the essence of the definition used in this lesson. A net is a two-dimensional figure which can be folded to create a three-dimensional solid with no gaps or overlaps."
222,A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?,"20 seconds You need to find the least common multiply of each number 4: 4, 8, 12, 16, 205: 5, 10, 15, 20","###Write an explanation to this problem:
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
###Explanation:
20 seconds You need to find the least common multiply of each number 4: 4, 8, 12, 16, 205: 5, 10, 15, 20"
843,Describe some things you could notice in two polygons that would help you decide that they were not scaled copies.,"I would check the angles in each polygon first. If any of the corresponding angle measures are not congruent they would not be scaled copies. After checking the angles, I would check the ratios of the corresponding sides to see if they are equivalent. If they are scaled copies, all of the ratios of the corresponding sides will be the same.","###Write an explanation to this problem:
Describe some things you could notice in two polygons that would help you decide that they were not scaled copies.
###Explanation:
I would check the angles in each polygon first. If any of the corresponding angle measures are not congruent they would not be scaled copies. After checking the angles, I would check the ratios of the corresponding sides to see if they are equivalent. If they are scaled copies, all of the ratios of the corresponding sides will be the same."
417,"Round 1 of a tennis tournament starts with 64 players. After each round, half the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 players, in round 3 there are 16 players and so on. What is the dependent variable in this relationship? The Utah Middle School Math Project",The number of players left is determined by the round of the tournament. This means that players is the dependent variable in the equation.,"###Write an explanation to this problem:
Round 1 of a tennis tournament starts with 64 players. After each round, half the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 players, in round 3 there are 16 players and so on. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of players left is determined by the round of the tournament. This means that players is the dependent variable in the equation."
836,Norman purchased 3.5 lb. of his favorite mixture of dried fruits to use in a trail mix. The total cost was 16.87. How much does the fruit cost per pound? Estimate the quotient.,Estimate: 16 / 4 = 4,"###Write an explanation to this problem:
Norman purchased 3.5 lb. of his favorite mixture of dried fruits to use in a trail mix. The total cost was 16.87. How much does the fruit cost per pound? Estimate the quotient.
###Explanation:
Estimate: 16 / 4 = 4"
324,The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.,"There are several combinations of tables that could be used to seat 120 customers. There could be no 2-seat and 30 4-seat, 10 2-seat and 25 4-seat, 40 2-seat and 10 4-seat. There are several ways to find the combinations, the number of 2-seat tables could be determined and then multiplied by 2 to find the number of people that could sit at those tables. Then the remaining number of people could be divided by 4 to get the number of 4-seat tables needed.","###Write an explanation to this problem:
The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.
###Explanation:
There are several combinations of tables that could be used to seat 120 customers. There could be no 2-seat and 30 4-seat, 10 2-seat and 25 4-seat, 40 2-seat and 10 4-seat. There are several ways to find the combinations, the number of 2-seat tables could be determined and then multiplied by 2 to find the number of people that could sit at those tables. Then the remaining number of people could be divided by 4 to get the number of 4-seat tables needed."
611,Are all rectangles scaled versions of each other? Justify your answer. The Utah Middle School Math Project,"The answer is no. This is because the ratios can differ. Rectangles all have the same angles, but consecutive sides are not always the same ratio.","###Write an explanation to this problem:
Are all rectangles scaled versions of each other? Justify your answer. The Utah Middle School Math Project
###Explanation:
The answer is no. This is because the ratios can differ. Rectangles all have the same angles, but consecutive sides are not always the same ratio."
9,Write a statement relating the opposites of each of the given numbers. 7 is greater than 6,-7 is less than -6,"###Write an explanation to this problem:
Write a statement relating the opposites of each of the given numbers. 7 is greater than 6
###Explanation:
-7 is less than -6"
249,"A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled win and 1 labeled lose. She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?","Sample Answer: She needs to repeat the process many more times to get a good estimate of the probability. She has only done it once right now. After she has repeated the simulation of the week many times, she could count the fraction of simulated weeks that included at least 2 wins and use that as an estimate for the probability.","###Write an explanation to this problem:
A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled win and 1 labeled lose. She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?
###Explanation:
Sample Answer: She needs to repeat the process many more times to get a good estimate of the probability. She has only done it once right now. After she has repeated the simulation of the week many times, she could count the fraction of simulated weeks that included at least 2 wins and use that as an estimate for the probability."
22,"In your own words, explain what a dilation is.",A dilation is a transformation that changes the size but not the shape of a figure.,"###Write an explanation to this problem:
In your own words, explain what a dilation is.
###Explanation:
A dilation is a transformation that changes the size but not the shape of a figure."
356,"Give an example of a rational number, and explain how you know it is rational. Copied for free from openupresources.org",A rational number is a fraction or its opposite or any number equivalent to a fraction or its opposite. Sample response: 2/3 is a rational number because rational numbers are fractions and their opposites and 2/3 is a fraction.,"###Write an explanation to this problem:
Give an example of a rational number, and explain how you know it is rational. Copied for free from openupresources.org
###Explanation:
A rational number is a fraction or its opposite or any number equivalent to a fraction or its opposite. Sample response: 2/3 is a rational number because rational numbers are fractions and their opposites and 2/3 is a fraction."
221,Your teacher will show you two rods. Does it take more green rods or blue rods lined up end to end to measure the width of a piece of printer paper? copied for free from openupresources.org,More green rods are used because they are shorter than the blue rods.,"###Write an explanation to this problem:
Your teacher will show you two rods. Does it take more green rods or blue rods lined up end to end to measure the width of a piece of printer paper? copied for free from openupresources.org
###Explanation:
More green rods are used because they are shorter than the blue rods."
579,"Simplify the following expression using two different methods. Four multiplied by the sum of thirty and six First, show your work for each method. The Utah Middle School Math Project","The sum of thirty and six is 30 + 6, so four multiplied by the sum of thirty and six is 430 + 6 One method is to first distribute the 4 to the terms within the parentheses: 430 + 6 = 430 + 46 = 120 + 24 = 144 Another method is to first add the terms in the parentheses and then distribute the 4: 430 + 6 = 436 = 144","###Write an explanation to this problem:
Simplify the following expression using two different methods. Four multiplied by the sum of thirty and six First, show your work for each method. The Utah Middle School Math Project
###Explanation:
The sum of thirty and six is 30 + 6, so four multiplied by the sum of thirty and six is 430 + 6 One method is to first distribute the 4 to the terms within the parentheses: 430 + 6 = 430 + 46 = 120 + 24 = 144 Another method is to first add the terms in the parentheses and then distribute the 4: 430 + 6 = 436 = 144"
733,Describe a situation that could be modeled with the ratio 4:1.,"Answers may vary. You might write something like For every four teaspoons of cream in a cup of tea, there is one teaspoon of honey.","###Write an explanation to this problem:
Describe a situation that could be modeled with the ratio 4:1.
###Explanation:
Answers may vary. You might write something like For every four teaspoons of cream in a cup of tea, there is one teaspoon of honey."
837,Divide: 994.14 / 18.9 Estimate the quotient.,Estimate: 100 / 2 = 50,"###Write an explanation to this problem:
Divide: 994.14 / 18.9 Estimate the quotient.
###Explanation:
Estimate: 100 / 2 = 50"
785,Name the parts of the expression. 30jk,"The parts of the expression are 30, j, k. 30 is the coefficient, and j and k are the variables, and 30jk is a term and the product of 30*j*k.","###Write an explanation to this problem:
Name the parts of the expression. 30jk
###Explanation:
The parts of the expression are 30, j, k. 30 is the coefficient, and j and k are the variables, and 30jk is a term and the product of 30*j*k."
340,Here is an inequality: -2x > 10. List some values for x that would make this inequality true.,"Any number less than -5 would make this inequality true. Some examples: If x = -6, then -2-6 = 12 > 10. If x = -7.5 then -2 -7.5 = 15 > 10. If x = -10 frac12; then -2-10 frac12; = 21 > 10. If x = -5, then -2-5 = 10 which is not greater than 10.","###Write an explanation to this problem:
Here is an inequality: -2x > 10. List some values for x that would make this inequality true.
###Explanation:
Any number less than -5 would make this inequality true. Some examples: If x = -6, then -2-6 = 12 > 10. If x = -7.5 then -2 -7.5 = 15 > 10. If x = -10 frac12; then -2-10 frac12; = 21 > 10. If x = -5, then -2-5 = 10 which is not greater than 10."
713,Solve the inequality. Represent the solution on a number line. 9<d/3 The Utah Middle School Math Project,"Solve for d. The number line should be greater than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 9<d/3 The Utah Middle School Math Project
###Explanation:
Solve for d. The number line should be greater than the solution, but not contain it."
203,There are 88 seats in a theater. The seating in the theater is split into 4 identical sections. Each section has 14 red seats and some blue seats. Draw a tape diagram to represent the situation. Submit your tape diagram using the tools below.,All together the tape diagram would equal the 88 seats. The tape diagram should be split into 4 equal pieces to represent the seating sections. Inside each equal piece you should see 14 + x. The 14 represents the red seats and the x represents how many blue seats are there.,"###Write an explanation to this problem:
There are 88 seats in a theater. The seating in the theater is split into 4 identical sections. Each section has 14 red seats and some blue seats. Draw a tape diagram to represent the situation. Submit your tape diagram using the tools below.
###Explanation:
All together the tape diagram would equal the 88 seats. The tape diagram should be split into 4 equal pieces to represent the seating sections. Inside each equal piece you should see 14 + x. The 14 represents the red seats and the x represents how many blue seats are there."
237,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,Pages 1 through 428 are the sample space for this experiment since you can pick any of those pages.,"###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
Pages 1 through 428 are the sample space for this experiment since you can pick any of those pages."
93,"Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project","Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 Factors are numbers that you can multiply together to get another number.","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 Factors are numbers that you can multiply together to get another number."
448,Given information: a = Measure of angle A a + 20 = Measure of angle B a ndash; 10 = Measure of angle C Equation: a + a + 20 + a ndash; 10 = 180deg;. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,"In a triangle, the largest angle is 20 degrees more than the medium angle. The smallest angle is 10 degrees less than the medium angles. What is the measure of the three angles?","###Write an explanation to this problem:
Given information: a = Measure of angle A a + 20 = Measure of angle B a ndash; 10 = Measure of angle C Equation: a + a + 20 + a ndash; 10 = 180deg;. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
In a triangle, the largest angle is 20 degrees more than the medium angle. The smallest angle is 10 degrees less than the medium angles. What is the measure of the three angles?"
405,"Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project","Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 The GCF is 4.","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 The GCF is 4."
695,Solve the inequality. Represent the solution on a number line. 2ge;0.4b The Utah Middle School Math Project,Solve for b. The number line should be less than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 2ge;0.4b The Utah Middle School Math Project
###Explanation:
Solve for b. The number line should be less than and equal to the solution."
284,"Below is a statistical question. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use. What is a typical height of female athletes on a team in the most recent international sporting event?",This question will provide numerical data and should use a unit of measurement like inches or centimeters.,"###Write an explanation to this problem:
Below is a statistical question. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use. What is a typical height of female athletes on a team in the most recent international sporting event?
###Explanation:
This question will provide numerical data and should use a unit of measurement like inches or centimeters."
184,"The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100. Describe how the manager can select a fair sample of 5 packages.",The manager could use a random number generator to pick a random number from 1 to 100 five times.,"###Write an explanation to this problem:
The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100. Describe how the manager can select a fair sample of 5 packages.
###Explanation:
The manager could use a random number generator to pick a random number from 1 to 100 five times."
705,Solve the inequality. Represent the solution on a number line. 8+n<11 The Utah Middle School Math Project,"Solve for n. The number line should be less than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 8+n<11 The Utah Middle School Math Project
###Explanation:
Solve for n. The number line should be less than the solution, but not contain it."
716,Imagine cutting a square based right pyramid parallel to the base. What shape is the plane section? The Utah Middle School Math Project,Cutting a square based right pyramid parallel to the base will result in a square cross-section,"###Write an explanation to this problem:
Imagine cutting a square based right pyramid parallel to the base. What shape is the plane section? The Utah Middle School Math Project
###Explanation:
Cutting a square based right pyramid parallel to the base will result in a square cross-section"
153,Each statement contains a quantity. Rewrite each quantity using a power of 10. There are about 37 trillion cells in an average human body. copied for free from openupresources.org,3.7*1013,"###Write an explanation to this problem:
Each statement contains a quantity. Rewrite each quantity using a power of 10. There are about 37 trillion cells in an average human body. copied for free from openupresources.org
###Explanation:
3.7*1013"
75,"Let and ' be two lines with the same slope passing through the same point . Show that there is only one line with a slope , where < 0, passing through the given point . Draw a diagram if needed.","First, assume that there are two different lines l and l' with the same negative slope passing through P. From point P, mark a point Q one unit to the right. Then, draw a line parallel to the y-axis through point Q. The intersection of this line and line l and l' are noted with points R and R' respectively. By definition of slope, the lengths |QR| and |QR'| represent the slopes of lines l and l', respectively. It has been given that the lines have the same slope, which means that lengths |QR| and |QR'| are equal. Since that is true, then points R and R' coincide and so do lines l and l'. therefore, our assumption that they are different lines is false; l and l' must be the same line. Therefore, there is only one line with slope m passing through the given point P.","###Write an explanation to this problem:
Let and ' be two lines with the same slope passing through the same point . Show that there is only one line with a slope , where < 0, passing through the given point . Draw a diagram if needed.
###Explanation:
First, assume that there are two different lines l and l' with the same negative slope passing through P. From point P, mark a point Q one unit to the right. Then, draw a line parallel to the y-axis through point Q. The intersection of this line and line l and l' are noted with points R and R' respectively. By definition of slope, the lengths |QR| and |QR'| represent the slopes of lines l and l', respectively. It has been given that the lines have the same slope, which means that lengths |QR| and |QR'| are equal. Since that is true, then points R and R' coincide and so do lines l and l'. therefore, our assumption that they are different lines is false; l and l' must be the same line. Therefore, there is only one line with slope m passing through the given point P."
678,Write a pair of numbers whose GCF is 10. The Utah Middle School Math Project,"Factors of 10: 1, 2, 5, 10 Factors of 20: 1, 2, 4, 5, 10, 20 GCF is 10","###Write an explanation to this problem:
Write a pair of numbers whose GCF is 10. The Utah Middle School Math Project
###Explanation:
Factors of 10: 1, 2, 5, 10 Factors of 20: 1, 2, 4, 5, 10, 20 GCF is 10"
531,"In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 2x+3+4x9x Explain the mistake The Utah Middle School Math Project","Notice that 2x + 3 + 4x = 6x + 3, since the 3 in this expression is not being multiplied by x.","###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 2x+3+4x9x Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that 2x + 3 + 4x = 6x + 3, since the 3 in this expression is not being multiplied by x."
277,"Below is a statistical question. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use. What is a typical height of female athletes on a team in the most recent international sporting event?",Collect data on the heights of female athletes in a sport and use inches as the units.,"###Write an explanation to this problem:
Below is a statistical question. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use. What is a typical height of female athletes on a team in the most recent international sporting event?
###Explanation:
Collect data on the heights of female athletes in a sport and use inches as the units."
68,How can you find 50% of a number quickly in your head?,50% is the same as half. The easy way to find 50% of a number is to divide it by 2.,"###Write an explanation to this problem:
How can you find 50% of a number quickly in your head?
###Explanation:
50% is the same as half. The easy way to find 50% of a number is to divide it by 2."
545,Imagine cutting a sphere with diameter 10 cm parallel to the table through the center. What shape will any plane section be? The Utah Middle School Math Project,The shape of any place section taken through the center of a sphere will be a circle.,"###Write an explanation to this problem:
Imagine cutting a sphere with diameter 10 cm parallel to the table through the center. What shape will any plane section be? The Utah Middle School Math Project
###Explanation:
The shape of any place section taken through the center of a sphere will be a circle."
188,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,The numbers 1 through 428,"###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
The numbers 1 through 428"
271,7. Write three expressions containing exponents so that each expression equals 81. copied for free from openupresources.org,Answers will vary Here are some examples. 92 = 81because 9 x 9 = 81 34 = 81because 3 x 3 x 3 x = 81 811because 81 x 1 = 81,"###Write an explanation to this problem:
7. Write three expressions containing exponents so that each expression equals 81. copied for free from openupresources.org
###Explanation:
Answers will vary Here are some examples. 92 = 81because 9 x 9 = 81 34 = 81because 3 x 3 x 3 x = 81 811because 81 x 1 = 81"
637,Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project,"Your answer can be any statistical question, a question that asks for multiple data points that may vary. Example question: How old were you when you lost your first tooth?","###Write an explanation to this problem:
Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project
###Explanation:
Your answer can be any statistical question, a question that asks for multiple data points that may vary. Example question: How old were you when you lost your first tooth?"
536,"In a 90˚ rotation, what happens to the slopes of the corresponding segments of the image and pre-image? How does the coordinate rule show this? In a 180˚ rotation, what happens to the slopes of the corresponding segments of the image and pre-image? How does the coordinate rule show this? The Utah Middle School Math Project","In a 90˚ rotation, the slopes of corresponding segments are opposite reciprocals or the product of the slopes is 1. The coordinate rule for a 90˚ rotation is x, y rarr; y, -x. The x- and y-coordinates change places therefore the slope is inverted. The sign is changed on only the x-coordinates therefore changing the sign of the slope. In a 180˚ rotation, the slopes of corresponding segments are the same. The coordinate rule for a 180˚ rotation is x, y rarr; -x, -y. The signs of both the x- and y-coordinates change therefore the net result is that the slope does not change.","###Write an explanation to this problem:
In a 90˚ rotation, what happens to the slopes of the corresponding segments of the image and pre-image? How does the coordinate rule show this? In a 180˚ rotation, what happens to the slopes of the corresponding segments of the image and pre-image? How does the coordinate rule show this? The Utah Middle School Math Project
###Explanation:
In a 90˚ rotation, the slopes of corresponding segments are opposite reciprocals or the product of the slopes is 1. The coordinate rule for a 90˚ rotation is x, y rarr; y, -x. The x- and y-coordinates change places therefore the slope is inverted. The sign is changed on only the x-coordinates therefore changing the sign of the slope. In a 180˚ rotation, the slopes of corresponding segments are the same. The coordinate rule for a 180˚ rotation is x, y rarr; -x, -y. The signs of both the x- and y-coordinates change therefore the net result is that the slope does not change."
236,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,Pages 1 through 428 are the sample space for this experiment because you can pick any of those pages.,"###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
Pages 1 through 428 are the sample space for this experiment because you can pick any of those pages."
88,Write a pair of numbers whose LCM is 60. The Utah Middle School Math Project,"There are a few different numbers that have multiples of 15. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. From this list, the only pairs of numbers that have 60 as their least common multiple are: Any of the factors and 60 4 and 30 12 and 30 20 and 30 3 and 20 6 and 20 12 and 20 15 and 20 4 and 15 12 and 15 5 and 12 10 and 12","###Write an explanation to this problem:
Write a pair of numbers whose LCM is 60. The Utah Middle School Math Project
###Explanation:
There are a few different numbers that have multiples of 15. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. From this list, the only pairs of numbers that have 60 as their least common multiple are: Any of the factors and 60 4 and 30 12 and 30 20 and 30 3 and 20 6 and 20 12 and 20 15 and 20 4 and 15 12 and 15 5 and 12 10 and 12"
758,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.,The temperature is 10 degrees below zero on the Farenheight scale.,"###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.
###Explanation:
The temperature is 10 degrees below zero on the Farenheight scale."
117,"During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60 / 5 in this context.","If there are 5 groups, how many students would be in each group? If there are 5 students in each group, how many groups would there be?","###Write an explanation to this problem:
During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60 / 5 in this context.
###Explanation:
If there are 5 groups, how many students would be in each group? If there are 5 students in each group, how many groups would there be?"
125,"Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope is increased or decreased while the y-intercept is held constant. The Utah Middle School Math Project","If the slope is increased or decreased while the y-intercept is held constant, then we know the only thing that is changing about the line is its steepness. If the steepness is changing, but the y-intercept remains the same, this transformation is described as a rotation about the y-intercept.","###Write an explanation to this problem:
Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope is increased or decreased while the y-intercept is held constant. The Utah Middle School Math Project
###Explanation:
If the slope is increased or decreased while the y-intercept is held constant, then we know the only thing that is changing about the line is its steepness. If the steepness is changing, but the y-intercept remains the same, this transformation is described as a rotation about the y-intercept."
760,A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?,Sample response: I would count by 5's because both numbers are multiples of 5,"###Write an explanation to this problem:
A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?
###Explanation:
Sample response: I would count by 5's because both numbers are multiples of 5"
289,"In an archery competition, scores for each round are calculated by averaging the distance of 3 arrows from the center of the target. An archer has a mean distance of 1.6 inches and a MAD distance of 1.3 inches in the first round. In the second round, the archer's arrows are farther from the center but are more consistent. What values for the mean and MAD would fit this description for the second round? Explain your reasoning.","In the second round, the archer's arrows are farther from the center but are more consistent. If the mean for the first round was 1.6 inches from the center, this number would be lower for this round. So any number less than 1.6 inches would be closer to the center. The fact that they are more consistent lets us know that the MAD is smaller than what it was. If the MAD for the first round is 1.3, then the MAD for the second round would be less than 1.3.","###Write an explanation to this problem:
In an archery competition, scores for each round are calculated by averaging the distance of 3 arrows from the center of the target. An archer has a mean distance of 1.6 inches and a MAD distance of 1.3 inches in the first round. In the second round, the archer's arrows are farther from the center but are more consistent. What values for the mean and MAD would fit this description for the second round? Explain your reasoning.
###Explanation:
In the second round, the archer's arrows are farther from the center but are more consistent. If the mean for the first round was 1.6 inches from the center, this number would be lower for this round. So any number less than 1.6 inches would be closer to the center. The fact that they are more consistent lets us know that the MAD is smaller than what it was. If the MAD for the first round is 1.3, then the MAD for the second round would be less than 1.3."
238,A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org,"Pages 1 through 428 are the sample space for this experiment, since you can pick any of those pages.","###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
Pages 1 through 428 are the sample space for this experiment, since you can pick any of those pages."
0,"From 2010 to 2011, the population of Queens increased by 16,075. Brooklyn's population increased by 11,870 more than the population increase of Queens. Estimate the total combined population increase of Queens and Brooklyn from 2010 to 2011. Round the addends to estimate","The problem gives information about the increase in the population from the years 2010 to 2011. Queens increased by 16,075 Brooklyn's population increased by 11, 870 more than Queens. This means figuring out Brooklyn's population involves adding 11 870 + 16,075 = 27,945 The problem is asking you to estimate the total combined population increase of Queens and Brooklyn. 16,075 + 27, 945 You can estimate the total population by rounding up to the nearest 1000. If below 500, round down, if above 500 round up. 16,000 +30,000 = 46.000","###Write an explanation to this problem:
From 2010 to 2011, the population of Queens increased by 16,075. Brooklyn's population increased by 11,870 more than the population increase of Queens. Estimate the total combined population increase of Queens and Brooklyn from 2010 to 2011. Round the addends to estimate
###Explanation:
The problem gives information about the increase in the population from the years 2010 to 2011. Queens increased by 16,075 Brooklyn's population increased by 11, 870 more than Queens. This means figuring out Brooklyn's population involves adding 11 870 + 16,075 = 27,945 The problem is asking you to estimate the total combined population increase of Queens and Brooklyn. 16,075 + 27, 945 You can estimate the total population by rounding up to the nearest 1000. If below 500, round down, if above 500 round up. 16,000 +30,000 = 46.000"
844,"Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 600 : 450 and 60:45","To get from 600:450 to 60:45 you would divide by the same constant of 10. 600 divided by 10= 60 450 divided by 10=45 Because they are being divided by the same constant, they are equivalent ratios.","###Write an explanation to this problem:
Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 600 : 450 and 60:45
###Explanation:
To get from 600:450 to 60:45 you would divide by the same constant of 10. 600 divided by 10= 60 450 divided by 10=45 Because they are being divided by the same constant, they are equivalent ratios."
431,Traveling between countries means exchanging currencies money. Look up the current exchange rate for Europe or replace Euros with the currency of a country of your choice. How many Euros would you receive for 1 dollar? The Utah Middle School Math Project,Set up the ratio according the exchange rate and find the unit rate to determine the solution.,"###Write an explanation to this problem:
Traveling between countries means exchanging currencies money. Look up the current exchange rate for Europe or replace Euros with the currency of a country of your choice. How many Euros would you receive for 1 dollar? The Utah Middle School Math Project
###Explanation:
Set up the ratio according the exchange rate and find the unit rate to determine the solution."
743,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.,"We don't say that a negative temperature is also below zero. In this case, we can either say the temperature is -22deg;C or we can say the temperature is 22 degrees below zero Celsius.","###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.
###Explanation:
We don't say that a negative temperature is also below zero. In this case, we can either say the temperature is -22deg;C or we can say the temperature is 22 degrees below zero Celsius."
395,"Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.","When we are given three sides that satisfy the triangle inequality theorem, there is only one way to draw the triangle. After drawing one length, use the other two lengths to draw circles with the lengths as the radii of each circle, centered at either end of the segment that we drew at the beginning. Regardless of which order you draw the segments in, there is only one unique triangle that can be drawn. When we draw a triangle with two side lengths with the included angle, there is only one way to draw the triangle. After drawing the angle and marking off the two side lengths on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle.","###Write an explanation to this problem:
Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.
###Explanation:
When we are given three sides that satisfy the triangle inequality theorem, there is only one way to draw the triangle. After drawing one length, use the other two lengths to draw circles with the lengths as the radii of each circle, centered at either end of the segment that we drew at the beginning. Regardless of which order you draw the segments in, there is only one unique triangle that can be drawn. When we draw a triangle with two side lengths with the included angle, there is only one way to draw the triangle. After drawing the angle and marking off the two side lengths on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle."
512,Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Blake has some quarters and dimes. He has 20 coins worth a total of 2.90. How many of each type of coin does he have? The Utah Middle School Math Project,𝑞 + 𝑑 = 20 where q is the number of quarters and d is the number of dimes 0.25𝑞 + 0.10𝑑 = 2.90 Blake has 14 dimes and 6 quartersEnter your explanation text here.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Blake has some quarters and dimes. He has 20 coins worth a total of 2.90. How many of each type of coin does he have? The Utah Middle School Math Project
###Explanation:
𝑞 + 𝑑 = 20 where q is the number of quarters and d is the number of dimes 0.25𝑞 + 0.10𝑑 = 2.90 Blake has 14 dimes and 6 quartersEnter your explanation text here."
126,"Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope is increased or decreased while the y-intercept is held constant. The Utah Middle School Math Project","The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the slope is increased or decreased while the y-intercept is held constant, then we know the only thing that is changing about the line is its steepness. If the steepness is changing, but the y-intercept remains the same, this transformation is described as a rotation about the y-intercept.","###Write an explanation to this problem:
Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope is increased or decreased while the y-intercept is held constant. The Utah Middle School Math Project
###Explanation:
The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the slope is increased or decreased while the y-intercept is held constant, then we know the only thing that is changing about the line is its steepness. If the steepness is changing, but the y-intercept remains the same, this transformation is described as a rotation about the y-intercept."
278,1. Which one doesn't belong? Explain your reasoning. 2 * 2 * 2 * 2 16 24 4 * 2 copied for free from openupresources.org,Answers may vary here is an example: Problem D because it equals 8 while the other expressions equal 16.,"###Write an explanation to this problem:
1. Which one doesn't belong? Explain your reasoning. 2 * 2 * 2 * 2 16 24 4 * 2 copied for free from openupresources.org
###Explanation:
Answers may vary here is an example: Problem D because it equals 8 while the other expressions equal 16."
662,"Boris is setting up an exercise schedule. For five days each week, he would like to play a sport for 30 minutes, stretch for 5 minutes, and lift weights for 10 minutes. Write two different expressions that could be used to represent the total number of minutes he will exercise in five days. The Utah Middle School Math Project","To find the total number of minutes Boris exercises over the course of five days, add the number of minutes he exercises each day and multiplies the total by 5. This can be expressed in multiple ways. 1. 530 + 5 + 10 2. 530 + 55 + 510","###Write an explanation to this problem:
Boris is setting up an exercise schedule. For five days each week, he would like to play a sport for 30 minutes, stretch for 5 minutes, and lift weights for 10 minutes. Write two different expressions that could be used to represent the total number of minutes he will exercise in five days. The Utah Middle School Math Project
###Explanation:
To find the total number of minutes Boris exercises over the course of five days, add the number of minutes he exercises each day and multiplies the total by 5. This can be expressed in multiple ways. 1. 530 + 5 + 10 2. 530 + 55 + 510"
116,Give two numbers with an absolute value greater than three. The Utah Middle School Math Project,"The absolute value of a number is always positive. This question is asking: |x| > 3 We could pick a number that is already greater than 3, like 5, since taking the absolute value of a positive number is just the number itself. We could also pick a number that is negative, but whose opposite is greater than 3. One possible example is -5. |-5| = 5, and 5 is greater than 3, so -5 is another possible answer. Any number that is greater than 3 or less than -3 is a possible answer.","###Write an explanation to this problem:
Give two numbers with an absolute value greater than three. The Utah Middle School Math Project
###Explanation:
The absolute value of a number is always positive. This question is asking: |x| > 3 We could pick a number that is already greater than 3, like 5, since taking the absolute value of a positive number is just the number itself. We could also pick a number that is negative, but whose opposite is greater than 3. One possible example is -5. |-5| = 5, and 5 is greater than 3, so -5 is another possible answer. Any number that is greater than 3 or less than -3 is a possible answer."
228,An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?,"By standard number cube, the problem is referring to an average die. A standard number cube only has 6 sides and therefore only 6 possible outcomes. For this experiment, we need 10 possible outcomes. The standard number cue could not produce all 10 possibilities from the experiment.","###Write an explanation to this problem:
An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?
###Explanation:
By standard number cube, the problem is referring to an average die. A standard number cube only has 6 sides and therefore only 6 possible outcomes. For this experiment, we need 10 possible outcomes. The standard number cue could not produce all 10 possibilities from the experiment."
599,Replace the ? in the fraction ?/12 with a number that would make the fraction greater than 2/3 but less than 1. The Utah Middle School Math Project,"If you multiply both parts of 2/3 by 4, you get 8/12. If you turn 1 into a fraction over 12, you get 12/12. Thus, you need to choose a number that makes ?/12 greater than 8/12 but less than 12/12. The ? needs to be greater than 8 but less than 12. The only integers that are greater than 8 but less than 12 are 9, 10, and 11.","###Write an explanation to this problem:
Replace the ? in the fraction ?/12 with a number that would make the fraction greater than 2/3 but less than 1. The Utah Middle School Math Project
###Explanation:
If you multiply both parts of 2/3 by 4, you get 8/12. If you turn 1 into a fraction over 12, you get 12/12. Thus, you need to choose a number that makes ?/12 greater than 8/12 but less than 12/12. The ? needs to be greater than 8 but less than 12. The only integers that are greater than 8 but less than 12 are 9, 10, and 11."
818,"A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered? Explain your answer, and how you got it.","Sample response: An even number of tiles fit on the30 foot length of the room 20 tiles, but the width requires 13 1/3 tiles. This accounts for a 20 tile by 13 tile array. 20 * 13 = 260 260 tiles need to be ordered. The remaining area is 30 ft. * 0.5 ft. 20 * 1/3 tile Since 20 of the 1/3 tiles are needed, 7 additional tiles must be cut to form 21/3. 20 of these will be used with 1/3 of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles.","###Write an explanation to this problem:
A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered? Explain your answer, and how you got it.
###Explanation:
Sample response: An even number of tiles fit on the30 foot length of the room 20 tiles, but the width requires 13 1/3 tiles. This accounts for a 20 tile by 13 tile array. 20 * 13 = 260 260 tiles need to be ordered. The remaining area is 30 ft. * 0.5 ft. 20 * 1/3 tile Since 20 of the 1/3 tiles are needed, 7 additional tiles must be cut to form 21/3. 20 of these will be used with 1/3 of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles."
847,"List three different combinations of coins, each with a value of 30% of a dollar.","For the value to equal 30% of a dollar, you would need to have the coins equal to 0.30 Combo 1: 1 dime, 3 nickels, 5 pennies Combo 2: 1 quarter, 5 pennies Combo 3: 2 dimes, 1 nickel, 5 pennies","###Write an explanation to this problem:
List three different combinations of coins, each with a value of 30% of a dollar.
###Explanation:
For the value to equal 30% of a dollar, you would need to have the coins equal to 0.30 Combo 1: 1 dime, 3 nickels, 5 pennies Combo 2: 1 quarter, 5 pennies Combo 3: 2 dimes, 1 nickel, 5 pennies"
274,"In your own words, what is the greatest common factor of two whole numbers? How can you find it?",The greatest common factor of two whole numbers is a factor of both numbers. It is also the largest factor that they have in common. You find it by listing the common factors of both numbers and find the greatest common factor.,"###Write an explanation to this problem:
In your own words, what is the greatest common factor of two whole numbers? How can you find it?
###Explanation:
The greatest common factor of two whole numbers is a factor of both numbers. It is also the largest factor that they have in common. You find it by listing the common factors of both numbers and find the greatest common factor."
318,Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.,"This equation is in slope-intercept form: y = mx + b This means that we know the y-intercept: 0,b 0,-1 We also know the slope of the line: -4. This means that for every 1 unit we go to the right, the line goes down 4 units. Start with the intercept 0,-1, and use the slope of -4 to move down 1 and 4 to the right or up 1 and 4 to the left to find other points. Or, find two or more solutions to the equation by substituting in a number for x and solving for y","###Write an explanation to this problem:
Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.
###Explanation:
This equation is in slope-intercept form: y = mx + b This means that we know the y-intercept: 0,b 0,-1 We also know the slope of the line: -4. This means that for every 1 unit we go to the right, the line goes down 4 units. Start with the intercept 0,-1, and use the slope of -4 to move down 1 and 4 to the right or up 1 and 4 to the left to find other points. Or, find two or more solutions to the equation by substituting in a number for x and solving for y"
583,"Simplify the following expression using two different methods. 710 + 3 First, show your work for each method. The Utah Middle School Math Project",One method is to first distribute the 7 to the terms within the parentheses: 710 + 3 = 710 + 73 = 70 + 21 = 91 Another method is to first add the terms in the parentheses and then distribute the 7: 710 + 3 = 713 = 91,"###Write an explanation to this problem:
Simplify the following expression using two different methods. 710 + 3 First, show your work for each method. The Utah Middle School Math Project
###Explanation:
One method is to first distribute the 7 to the terms within the parentheses: 710 + 3 = 710 + 73 = 70 + 21 = 91 Another method is to first add the terms in the parentheses and then distribute the 7: 710 + 3 = 713 = 91"
144,List the sample space the available options for the chance experiment given. Flipping a coin,Sample space is the range of values for a random variable. Flipping a coin has two possibilities: Heads or tails,"###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
Sample space is the range of values for a random variable. Flipping a coin has two possibilities: Heads or tails"
610,Write a situation that can be represented by the rational number. 2 The Utah Middle School Math Project,"Any situation that could be represented by the rational number 2 just needs to involve words like deposit, increase, profit, and so on that would indicate a positive number. One example of a correct situation would be: 2 miles above sea level","###Write an explanation to this problem:
Write a situation that can be represented by the rational number. 2 The Utah Middle School Math Project
###Explanation:
Any situation that could be represented by the rational number 2 just needs to involve words like deposit, increase, profit, and so on that would indicate a positive number. One example of a correct situation would be: 2 miles above sea level"
539,Write an ordered pair that would be on the x-axis when graphed. The Utah Middle School Math Project,"Any ordered pair x, y where y = 0 is on the x-axis. Examples: 7, 0 -7, 0 0, 0","###Write an explanation to this problem:
Write an ordered pair that would be on the x-axis when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair x, y where y = 0 is on the x-axis. Examples: 7, 0 -7, 0 0, 0"
784,Name the parts of the expression. 14b,"The parts of the expression are 14 and b. 14 is the coefficient, b is the variable, and 14b is a term and the product of 14*b.","###Write an explanation to this problem:
Name the parts of the expression. 14b
###Explanation:
The parts of the expression are 14 and b. 14 is the coefficient, b is the variable, and 14b is a term and the product of 14*b."
618,"Write a situation that can be represented by the rational number. -15,000 The Utah Middle School Math Project","Any situation that could be represented by the rational number -15,000 just needs to involve words like withdrawal, decrease, loss, and so on that would indicate a negative number. One example of a correct situation would be: 15,000 miles below sea level","###Write an explanation to this problem:
Write a situation that can be represented by the rational number. -15,000 The Utah Middle School Math Project
###Explanation:
Any situation that could be represented by the rational number -15,000 just needs to involve words like withdrawal, decrease, loss, and so on that would indicate a negative number. One example of a correct situation would be: 15,000 miles below sea level"
369,A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.,Choice 1: 1 cm x 1 cm x 50 cm Choice 2: 1 cm x 2 cm x 25 cm Choice 3: 1 cm x 5 cm x 10 cm Choice 4: 2 cm x 5 cm x 5 cm,"###Write an explanation to this problem:
A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.
###Explanation:
Choice 1: 1 cm x 1 cm x 50 cm Choice 2: 1 cm x 2 cm x 25 cm Choice 3: 1 cm x 5 cm x 10 cm Choice 4: 2 cm x 5 cm x 5 cm"
268,A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.,"To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue. Example mixture: 1 yellow, 1.75 blue","###Write an explanation to this problem:
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.
###Explanation:
To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue. Example mixture: 1 yellow, 1.75 blue"
797,7. 38% of e is 190. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org,"38% of e means to multiply 38% and e. Is means equal to. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.38e=190","###Write an explanation to this problem:
7. 38% of e is 190. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org
###Explanation:
38% of e means to multiply 38% and e. Is means equal to. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.38e=190"
307,"In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.","Sample Answer: If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day.","###Write an explanation to this problem:
In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.
###Explanation:
Sample Answer: If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day."
423,Tickets for a matinee are 5 for children and 8 for adults. The theater sold a total of 142 tickets for one matinee. Ticket sales were 890. How many of each type of ticket did the theater sell? First define your unknowns. The Utah Middle School Math Project,Explain what your variables will represent in your problem. For example: c = number of children tickets a = number of adult tickets,"###Write an explanation to this problem:
Tickets for a matinee are 5 for children and 8 for adults. The theater sold a total of 142 tickets for one matinee. Ticket sales were 890. How many of each type of ticket did the theater sell? First define your unknowns. The Utah Middle School Math Project
###Explanation:
Explain what your variables will represent in your problem. For example: c = number of children tickets a = number of adult tickets"
310,Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.,"To get a scaled copy, you have to be multiplying all of the dimensions of the original figure or shape by the same scale factor. In this case, the original figure is Rectangle B. Rectangle B measures 15 by 10. Rectangle C measures 30 by 15. We can see that Rectangle C's length is twice Rectangle B's length. BUT Rectangle C's width is not twice Rectangle B's width. This means Rectangle C cannot be a scaled copy of Rectangle B.","###Write an explanation to this problem:
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.
###Explanation:
To get a scaled copy, you have to be multiplying all of the dimensions of the original figure or shape by the same scale factor. In this case, the original figure is Rectangle B. Rectangle B measures 15 by 10. Rectangle C measures 30 by 15. We can see that Rectangle C's length is twice Rectangle B's length. BUT Rectangle C's width is not twice Rectangle B's width. This means Rectangle C cannot be a scaled copy of Rectangle B."
567,Give two numbers with an absolute value greater than three. The Utah Middle School Math Project,"The absolute value of a number is always positive. This question is asking: |x| > 3 We could pick a number that is already greater than 3, like 5, since taking the absolute value of a positive number is just the number itself. We could also pick a number that is negative, but whose opposite is greater than 3. One possible example is -5. |-5| = 5, and 5 is greater than 3, so -5 is another possible answer. Any number that is greater than 3 or less than -3 is a possible answer.","###Write an explanation to this problem:
Give two numbers with an absolute value greater than three. The Utah Middle School Math Project
###Explanation:
The absolute value of a number is always positive. This question is asking: |x| > 3 We could pick a number that is already greater than 3, like 5, since taking the absolute value of a positive number is just the number itself. We could also pick a number that is negative, but whose opposite is greater than 3. One possible example is -5. |-5| = 5, and 5 is greater than 3, so -5 is another possible answer. Any number that is greater than 3 or less than -3 is a possible answer."
46,"These three points form a horizontal line: -3.5,4, 0,4, and 6.2,4. Name two additional points that fall on this line.","Since the points are in a horizontal line, the y value would always be the same. So, any point with a y value of 4 would work. 2 points that could work would be 9,4 and -100, 4.","###Write an explanation to this problem:
These three points form a horizontal line: -3.5,4, 0,4, and 6.2,4. Name two additional points that fall on this line.
###Explanation:
Since the points are in a horizontal line, the y value would always be the same. So, any point with a y value of 4 would work. 2 points that could work would be 9,4 and -100, 4."
349,"In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5x+ 4x - x 9x Explain the mistake The Utah Middle School Math Project","Notice that when combining like terms, the coefficients were added wrong. 5x + 4x - x x5 + 4 - 1 x8 This expression simplifies to 8x, which does not equal 9x.","###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5x+ 4x - x 9x Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that when combining like terms, the coefficients were added wrong. 5x + 4x - x x5 + 4 - 1 x8 This expression simplifies to 8x, which does not equal 9x."
371,"Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 600 : 450 and 60:45","If we divide both numbers in the first ratio by 10, it will equal the second ratio, showing that the two are equivalent. Ratio 1 Ratio 2 / by 1st number 2nd number 1st number 2nd number 600 450 60 45 10 60 45","###Write an explanation to this problem:
Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 600 : 450 and 60:45
###Explanation:
If we divide both numbers in the first ratio by 10, it will equal the second ratio, showing that the two are equivalent. Ratio 1 Ratio 2 / by 1st number 2nd number 1st number 2nd number 600 450 60 45 10 60 45"
682,Create a context for the numeric representation. 5001 ndash; 5001/5 = 400 The Utah Middle School Math Project,"If a person has 500 apples, then loses 1/5 of the apples, this numeric expression describes how many apples they have left.","###Write an explanation to this problem:
Create a context for the numeric representation. 5001 ndash; 5001/5 = 400 The Utah Middle School Math Project
###Explanation:
If a person has 500 apples, then loses 1/5 of the apples, this numeric expression describes how many apples they have left."
261,The mean weight for a sample of a certain kind of ring made from platinum is 8.21 grams. The mean weight for a sample of a certain kind of ring made from gold is 8.61 grams. Is there a meaningful difference in the weights of the two types of rings? Explain your reasoning.,"The answer is unknown with this information. For example, if the MAD for each is 0.1 grams, then there would be a meaningful difference. If the MAD is greater than 0.2 grams, then there is not a meaningful difference.","###Write an explanation to this problem:
The mean weight for a sample of a certain kind of ring made from platinum is 8.21 grams. The mean weight for a sample of a certain kind of ring made from gold is 8.61 grams. Is there a meaningful difference in the weights of the two types of rings? Explain your reasoning.
###Explanation:
The answer is unknown with this information. For example, if the MAD for each is 0.1 grams, then there would be a meaningful difference. If the MAD is greater than 0.2 grams, then there is not a meaningful difference."
195,"The inequalities h > 42 and h < 60 represent the height requirements for an amusement park ride, where h represents a person's height in inches. Write a sentence or draw a sign that describes these rules as clearly as possible.",60>h>42 This is saying that a person's height must be taller than 42 inches or 3 feet 6 inches or they must be shorter than 60 inches or 5 feet tall.,"###Write an explanation to this problem:
The inequalities h > 42 and h < 60 represent the height requirements for an amusement park ride, where h represents a person's height in inches. Write a sentence or draw a sign that describes these rules as clearly as possible.
###Explanation:
60>h>42 This is saying that a person's height must be taller than 42 inches or 3 feet 6 inches or they must be shorter than 60 inches or 5 feet tall."
852,What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB,"If you select a letter at random from each word 'ALABAMA' or 'LAMB' you have the same opportunity to select a letter of L, A, M, B from the two words. The word 'LAMB' is in the word 'ALABAMA'.","###Write an explanation to this problem:
What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB
###Explanation:
If you select a letter at random from each word 'ALABAMA' or 'LAMB' you have the same opportunity to select a letter of L, A, M, B from the two words. The word 'LAMB' is in the word 'ALABAMA'."
714,Create a context for the numeric representation. 1201 ndash; 1201/4 = 1203/4 = 90 The Utah Middle School Math Project,"Sample Answer: If a person has 120 apples, then loses 1/4 of the apples, this numeric expression describes how many apples they have left.","###Write an explanation to this problem:
Create a context for the numeric representation. 1201 ndash; 1201/4 = 1203/4 = 90 The Utah Middle School Math Project
###Explanation:
Sample Answer: If a person has 120 apples, then loses 1/4 of the apples, this numeric expression describes how many apples they have left."
107,"Augusto tips 20% on his meals. If he tipped 4.80 on a meal, how much was the meal? Write an equation to solve the problem. The Utah Middle School Math Project",The percent tipped in decimal form times the original order is the amount tipped. This means 0.2*m=4.80,"###Write an explanation to this problem:
Augusto tips 20% on his meals. If he tipped 4.80 on a meal, how much was the meal? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The percent tipped in decimal form times the original order is the amount tipped. This means 0.2*m=4.80"
59,A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?,The rate at which water is falling into the bucket and the volume of the bucket.,"###Write an explanation to this problem:
A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?
###Explanation:
The rate at which water is falling into the bucket and the volume of the bucket."
634,The Washington Monument is 555 feet and 5 1/8 feet tall. Bob wants to create a scale model of it that is no more than 6 feet tall. What scale would you suggest Bob use for his model? The Utah Middle School Math Project,"The problem gives the Washington monuments to be 560.167 feet tall. The maximum height of the scale model should be 6 feet. To find the scale factor needed, divide the desired height by the original height 6 / 560.167 = 0.011 is the ideal scale factor.","###Write an explanation to this problem:
The Washington Monument is 555 feet and 5 1/8 feet tall. Bob wants to create a scale model of it that is no more than 6 feet tall. What scale would you suggest Bob use for his model? The Utah Middle School Math Project
###Explanation:
The problem gives the Washington monuments to be 560.167 feet tall. The maximum height of the scale model should be 6 feet. To find the scale factor needed, divide the desired height by the original height 6 / 560.167 = 0.011 is the ideal scale factor."
830,"In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC is an acute triangle.",angles A and C could both be 65 degrees since 65 is less than 90 and 50 + 65 + 65 = 180.,"###Write an explanation to this problem:
In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC is an acute triangle.
###Explanation:
angles A and C could both be 65 degrees since 65 is less than 90 and 50 + 65 + 65 = 180."
100,"The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project","The equation for area of a parallelogram is area=base*height, or A=bh. Substitute the given values into this equation. 155.52=b*28.8.","###Write an explanation to this problem:
The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The equation for area of a parallelogram is area=base*height, or A=bh. Substitute the given values into this equation. 155.52=b*28.8."
443,Given information: s = small angle 4s = larger angle Equation: s + 4s = 70 degrees Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,The sum of two angles is 70 degrees. The larger angle is 4 times bigger than the smaller angle. What is the measure of the two angles?,"###Write an explanation to this problem:
Given information: s = small angle 4s = larger angle Equation: s + 4s = 70 degrees Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
The sum of two angles is 70 degrees. The larger angle is 4 times bigger than the smaller angle. What is the measure of the two angles?"
584,"Simplify the following expression using two different methods. 830 - 1 First, show your work for each method. The Utah Middle School Math Project",One method is to first distribute the 8 to the terms within the parentheses: 830 - 1 = 830 - 81 = 240 - 8 = 232 Another method is to first add the terms in the parentheses and then distribute the 8: 830 - 1 = 829 = 232,"###Write an explanation to this problem:
Simplify the following expression using two different methods. 830 - 1 First, show your work for each method. The Utah Middle School Math Project
###Explanation:
One method is to first distribute the 8 to the terms within the parentheses: 830 - 1 = 830 - 81 = 240 - 8 = 232 Another method is to first add the terms in the parentheses and then distribute the 8: 830 - 1 = 829 = 232"
765,What is the difference between 4x and x4?,"4x means four times x; this is the same as x + x + x + x. On the other hand, x4 means x to the fourth power, or x*x*x*x.","###Write an explanation to this problem:
What is the difference between 4x and x4?
###Explanation:
4x means four times x; this is the same as x + x + x + x. On the other hand, x4 means x to the fourth power, or x*x*x*x."
616,Write a situation that can be represented by the rational number. -10 The Utah Middle School Math Project,"Any situation that could be represented by the rational number -10 just needs to involve words like withdrawal, decrease, loss, and so on that would indicate a negative number. One example of a correct situation would be: 10 degrees below freezing","###Write an explanation to this problem:
Write a situation that can be represented by the rational number. -10 The Utah Middle School Math Project
###Explanation:
Any situation that could be represented by the rational number -10 just needs to involve words like withdrawal, decrease, loss, and so on that would indicate a negative number. One example of a correct situation would be: 10 degrees below freezing"
506,Create a representation of a table of data that represents a nonlinear function. The Utah Middle School Math Project,There are many different tables that can be created that represent a nonlinear function. One possible example is: x 1 2 3 4 5 y 1 4 9 16 25,"###Write an explanation to this problem:
Create a representation of a table of data that represents a nonlinear function. The Utah Middle School Math Project
###Explanation:
There are many different tables that can be created that represent a nonlinear function. One possible example is: x 1 2 3 4 5 y 1 4 9 16 25"
179,Describe a situation where the following quantities might be useful. -20 gallons per hour,One situation where the quantity -20 gallons per hour may be useful is when talking about a problem where water is being drained from a pool.,"###Write an explanation to this problem:
Describe a situation where the following quantities might be useful. -20 gallons per hour
###Explanation:
One situation where the quantity -20 gallons per hour may be useful is when talking about a problem where water is being drained from a pool."
304,List two different possibilities for the angle measures of an isosceles triangle.,"Sample responses: 70∘, 70∘, 40∘ and 30∘, 30∘, 120∘.","###Write an explanation to this problem:
List two different possibilities for the angle measures of an isosceles triangle.
###Explanation:
Sample responses: 70∘, 70∘, 40∘ and 30∘, 30∘, 120∘."
478,Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Blake has some quarters and dimes. He has 20 coins worth a total of 2.90. How many of each type of coin does he have? The Utah Middle School Math Project,q + d = 20 where q is the number of quarters and d is the number of dimes 0.25q + 0.10d = 2.90 Blake has 14 dimes and 6 quarters,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Blake has some quarters and dimes. He has 20 coins worth a total of 2.90. How many of each type of coin does he have? The Utah Middle School Math Project
###Explanation:
q + d = 20 where q is the number of quarters and d is the number of dimes 0.25q + 0.10d = 2.90 Blake has 14 dimes and 6 quarters"
57,"In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. There are enough tables to fit 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria.",10+4nge;200,"###Write an explanation to this problem:
In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. There are enough tables to fit 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria.
###Explanation:
10+4nge;200"
822,3b. Explain what a perfect cube is. copied for free from openupresources.org,"A perfect cube is a number that is the result of multiplying an original number by itself 3 times. For example, 8 is a perfect cube because 2 x 2 x 2 = 8.","###Write an explanation to this problem:
3b. Explain what a perfect cube is. copied for free from openupresources.org
###Explanation:
A perfect cube is a number that is the result of multiplying an original number by itself 3 times. For example, 8 is a perfect cube because 2 x 2 x 2 = 8."
149,"For each equation, enter two more equations using the same numbers that express the same relationship in a different way. 3+2=5 copied for free from openupresources.org",3 Sample Answers: 5-3=2; 5-2=3; 2+3=5,"###Write an explanation to this problem:
For each equation, enter two more equations using the same numbers that express the same relationship in a different way. 3+2=5 copied for free from openupresources.org
###Explanation:
3 Sample Answers: 5-3=2; 5-2=3; 2+3=5"
124,"Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The y-intercept is decreased while the slope is held constant. The Utah Middle School Math Project","The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the y-intercept is decreased while the slope is held constant, then we know that the line is being moved down. This can be described as a vertical translation down.","###Write an explanation to this problem:
Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The y-intercept is decreased while the slope is held constant. The Utah Middle School Math Project
###Explanation:
The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the y-intercept is decreased while the slope is held constant, then we know that the line is being moved down. This can be described as a vertical translation down."
735,Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.,There are many possible solutions. Here are some samples: The ratio of the number of male teachers to the number of female teachers is 15:35. The ratio of the number of female teachers to the number of male teachers is 35:15. The ratio of the number of female teachers to the total number of teachers in the school is 35:50. The ratio of the number of male teachers to the total number of teachers in the school is 15:50.,"###Write an explanation to this problem:
Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.
###Explanation:
There are many possible solutions. Here are some samples: The ratio of the number of male teachers to the number of female teachers is 15:35. The ratio of the number of female teachers to the number of male teachers is 35:15. The ratio of the number of female teachers to the total number of teachers in the school is 35:50. The ratio of the number of male teachers to the total number of teachers in the school is 15:50."
740,Write a story context that would be represented by the ratio 1:4,Sample response: Kendra's mom pays her four dollars for every load of laundry she washes and dries.,"###Write an explanation to this problem:
Write a story context that would be represented by the ratio 1:4
###Explanation:
Sample response: Kendra's mom pays her four dollars for every load of laundry she washes and dries."
185,"A group of 100 people is divided into 5 groups with 20 people in each. One person's name is chosen, and everyone in their group wins a prize. Noah simulates this situation by writing 100 different names on papers and putting them in a bag, then drawing one out. Kiran suggests there is a way to do it with fewer paper slips. Explain a method that would simulate this situation with fewer than 100 slips of paper.",A simpler way to do this is just put 5 slips of paper in the bag with each group's number written on a slip of paper.,"###Write an explanation to this problem:
A group of 100 people is divided into 5 groups with 20 people in each. One person's name is chosen, and everyone in their group wins a prize. Noah simulates this situation by writing 100 different names on papers and putting them in a bag, then drawing one out. Kiran suggests there is a way to do it with fewer paper slips. Explain a method that would simulate this situation with fewer than 100 slips of paper.
###Explanation:
A simpler way to do this is just put 5 slips of paper in the bag with each group's number written on a slip of paper."
809,The volume of Box D subtracted from the volume of Box C is 23.14 cubic centimeters. Box D has a volume of 10.115 cubic centimeters. Let C be the volume of Box C in cubic centimeters. Write an equation that could be used to determine the volume of Box C.,C - 10.1115 cm3 = 23.14 cm3,"###Write an explanation to this problem:
The volume of Box D subtracted from the volume of Box C is 23.14 cubic centimeters. Box D has a volume of 10.115 cubic centimeters. Let C be the volume of Box C in cubic centimeters. Write an equation that could be used to determine the volume of Box C.
###Explanation:
C - 10.1115 cm3 = 23.14 cm3"
50,"If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.","The easiest way to compare recipes is to find the ratio of ingredients for multiple batches until you find a common measurement for a specific ingredient. In this case, the following tables show both recipes up to the point that they both have 2 cups of milk. First Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 2 1 2 4 2 Second Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 3 2 Since the first recipe uses more scoops of chocolate ice cream to the same amount of milk, it means it would have a stronger chocolate flavor.","###Write an explanation to this problem:
If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.
###Explanation:
The easiest way to compare recipes is to find the ratio of ingredients for multiple batches until you find a common measurement for a specific ingredient. In this case, the following tables show both recipes up to the point that they both have 2 cups of milk. First Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 2 1 2 4 2 Second Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 3 2 Since the first recipe uses more scoops of chocolate ice cream to the same amount of milk, it means it would have a stronger chocolate flavor."
341,"In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.","Sample Answer: If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day. This is because 15/50 = 30/100, or 30%.","###Write an explanation to this problem:
In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.
###Explanation:
Sample Answer: If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day. This is because 15/50 = 30/100, or 30%."
446,61% of 20 Estimate the answer. The Utah Middle School Math Project,"50% of 20 is 10, so the 61% of 20 must be greater than 10.","###Write an explanation to this problem:
61% of 20 Estimate the answer. The Utah Middle School Math Project
###Explanation:
50% of 20 is 10, so the 61% of 20 must be greater than 10."
842,"Diego made a graph of two quantities that he measured and said, The points all lie on a line except one, which is a little bit above the line. This means that the quantities can't be proportional. Do you agree with Diego? Explain.",I don't agree with Diego. A relationship can be considered proportional if the point fall in approximately a straight line and go through the origin. The measurements could be off just a little bit because Diego measured them himself.,"###Write an explanation to this problem:
Diego made a graph of two quantities that he measured and said, The points all lie on a line except one, which is a little bit above the line. This means that the quantities can't be proportional. Do you agree with Diego? Explain.
###Explanation:
I don't agree with Diego. A relationship can be considered proportional if the point fall in approximately a straight line and go through the origin. The measurements could be off just a little bit because Diego measured them himself."
535,Write an ordered pair that would be in Quadrant I when graphed. The Utah Middle School Math Project,"Any ordered pair with two positive numbers is in Quadrant I. Examples: 1, 1 5, 3 1/2, 3/4","###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant I when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair with two positive numbers is in Quadrant I. Examples: 1, 1 5, 3 1/2, 3/4"
321,Draw two polygons that are not similar but could be mistaken for being similar. Submit your drawing using the tools below.,"There are many correct answers to this question. To be similar, the two polygons must be the same shape, but can involve some sorts of transformations to turn one into the other. If two polygons are not similar, then their angle measures could match up but their side lengths could be not proportional. For example: A triangle with angles 45, 35, 100 and side lengths of 4, 3, and 8, and a triangle with angles 45, 35, 100 and side lengths of 5, 4, and 9. They could also have side lengths that are proportional but angles that do not match up. For example: A triangle with angles 45, 35, 100 and side lengths of 4, 3, and 8, and a triangle with angles 55, 25, 100 and side lengths of 8, 6, and 16.","###Write an explanation to this problem:
Draw two polygons that are not similar but could be mistaken for being similar. Submit your drawing using the tools below.
###Explanation:
There are many correct answers to this question. To be similar, the two polygons must be the same shape, but can involve some sorts of transformations to turn one into the other. If two polygons are not similar, then their angle measures could match up but their side lengths could be not proportional. For example: A triangle with angles 45, 35, 100 and side lengths of 4, 3, and 8, and a triangle with angles 45, 35, 100 and side lengths of 5, 4, and 9. They could also have side lengths that are proportional but angles that do not match up. For example: A triangle with angles 45, 35, 100 and side lengths of 4, 3, and 8, and a triangle with angles 55, 25, 100 and side lengths of 8, 6, and 16."
353,Create a real-life example that can be modeled by the expression -2 * 4.,Maria spends 2.00 each week on coffee. She tracks her spending for 4 weeks. Write an integer to represent the change in Maria's money as a result of buying coffee for 4 weeks. ndash;24 = -8 Maria will have spent 8.00 on coffee after 4 weeks.,"###Write an explanation to this problem:
Create a real-life example that can be modeled by the expression -2 * 4.
###Explanation:
Maria spends 2.00 each week on coffee. She tracks her spending for 4 weeks. Write an integer to represent the change in Maria's money as a result of buying coffee for 4 weeks. ndash;24 = -8 Maria will have spent 8.00 on coffee after 4 weeks."
789,Explain why 6:4 and 18:8 are not equivalent ratios.,"6:4 and 18:8 are not equivalent because 6 x 3= 18, but 4 x 3= 12, not 8. In order for two ratios to be equivalent, both numbers have to be multiplied or divided by the same number. 6 4 12 8 18 12","###Write an explanation to this problem:
Explain why 6:4 and 18:8 are not equivalent ratios.
###Explanation:
6:4 and 18:8 are not equivalent because 6 x 3= 18, but 4 x 3= 12, not 8. In order for two ratios to be equivalent, both numbers have to be multiplied or divided by the same number. 6 4 12 8 18 12"
142,"An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?",This is randomly selecting a flavor and does not take into account the customers and what they choose. Some flavors may be chosen than others by customers compared to randomly choosing from a bag because flavor choice is a bias based off of the customers.,"###Write an explanation to this problem:
An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?
###Explanation:
This is randomly selecting a flavor and does not take into account the customers and what they choose. Some flavors may be chosen than others by customers compared to randomly choosing from a bag because flavor choice is a bias based off of the customers."
470,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A car that has more gas in its tank can drive a farther distance. The Utah Middle School Math Project,Gas is independent variable. Distance depends on the amount of gas that is left in the tank. Distance is the dependent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A car that has more gas in its tank can drive a farther distance. The Utah Middle School Math Project
###Explanation:
Gas is independent variable. Distance depends on the amount of gas that is left in the tank. Distance is the dependent variable."
370,"In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.","In order to make sure the mixture tastes the same as this recipe, we have to keep the ratios equivalent. We can do this by multiplying or dividing both numbers in this 3 to 1 ratio by the same number. 3 bull; 2 = 6 and 1 bull; 2 = 2 so a new ratio could be 6 to 2. We could also divide 3 / 2 = 1 1/2 and 1 / 2 = 1/2 so another ratio could be 1 1/2 to 1/2.","###Write an explanation to this problem:
In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
###Explanation:
In order to make sure the mixture tastes the same as this recipe, we have to keep the ratios equivalent. We can do this by multiplying or dividing both numbers in this 3 to 1 ratio by the same number. 3 bull; 2 = 6 and 1 bull; 2 = 2 so a new ratio could be 6 to 2. We could also divide 3 / 2 = 1 1/2 and 1 / 2 = 1/2 so another ratio could be 1 1/2 to 1/2."
780,Jane paid 40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was 48. How do you think Jane's friend arrived at this amount?,Jane's friend found that 20% of 40 is 8. 0.20 * 40 = 8 Then she added 8 to the sale price: 40 + 8 = 48. Then she determined that the original amount was 48,"###Write an explanation to this problem:
Jane paid 40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was 48. How do you think Jane's friend arrived at this amount?
###Explanation:
Jane's friend found that 20% of 40 is 8. 0.20 * 40 = 8 Then she added 8 to the sale price: 40 + 8 = 48. Then she determined that the original amount was 48"
141,An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?,This would be a bad simulation because a standard number cube only has 6 sides options when the experiment has 10 different outcomes and would not be represented on a number cube.,"###Write an explanation to this problem:
An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?
###Explanation:
This would be a bad simulation because a standard number cube only has 6 sides options when the experiment has 10 different outcomes and would not be represented on a number cube."
399,"At Shoes for Less, a pair of shoes is 15 less than a pair of boots. Cho purchased three pairs of shoes and two pairs of boots for 120. How much does a pair of boots cost? Write an equation to answer the equation. The Utah Middle School Math Project","A pair of boots can be represented by the variable b. A pair of shoes can be represented by b-15, because shoes are 15 dollars less than boots. The cost of shoes must be multiplied by 3, and the cost of boots must be multiplied by two. These total costs must be added together, and set equal to 120. The equation is 3b-15+2b=120.","###Write an explanation to this problem:
At Shoes for Less, a pair of shoes is 15 less than a pair of boots. Cho purchased three pairs of shoes and two pairs of boots for 120. How much does a pair of boots cost? Write an equation to answer the equation. The Utah Middle School Math Project
###Explanation:
A pair of boots can be represented by the variable b. A pair of shoes can be represented by b-15, because shoes are 15 dollars less than boots. The cost of shoes must be multiplied by 3, and the cost of boots must be multiplied by two. These total costs must be added together, and set equal to 120. The equation is 3b-15+2b=120."
263,"A steel beam can be cut to different lengths for a project. Assuming the weight of a steel beam is proportional to its length, what information would you need to know to write an equation that represents this relationship?",Sample response: Are the length of the steel beam and its weight in a proportional relationship? The weight of steel per 1 meter length of beam. The length of a steel beam that weighs 1 kilogram. The weight and length of a certain steel beam.,"###Write an explanation to this problem:
A steel beam can be cut to different lengths for a project. Assuming the weight of a steel beam is proportional to its length, what information would you need to know to write an equation that represents this relationship?
###Explanation:
Sample response: Are the length of the steel beam and its weight in a proportional relationship? The weight of steel per 1 meter length of beam. The length of a steel beam that weighs 1 kilogram. The weight and length of a certain steel beam."
320,Draw two polygons that are similar but could be mistaken for not being similar. Submit your drawing using the tools below.,"There are many correct answers to this question. To be similar, the two polygons must be the same shape, but must involve some sorts of transformations to turn one into the other. For example, you could: start with two triangles that are exactly the same and rotate one of them by however many degrees you want. You can then multiply all of the side lengths in the rotated triangle by a certain factor. start with two triangles that are exactly the same and reflect one of them over a horizontal line. You can then multiply all of the side lengths in the reflected triangle by a certain factor.","###Write an explanation to this problem:
Draw two polygons that are similar but could be mistaken for not being similar. Submit your drawing using the tools below.
###Explanation:
There are many correct answers to this question. To be similar, the two polygons must be the same shape, but must involve some sorts of transformations to turn one into the other. For example, you could: start with two triangles that are exactly the same and rotate one of them by however many degrees you want. You can then multiply all of the side lengths in the rotated triangle by a certain factor. start with two triangles that are exactly the same and reflect one of them over a horizontal line. You can then multiply all of the side lengths in the reflected triangle by a certain factor."
19,"Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.","The slope shows that for every 1 unit increase in side length of the equilateral triangle, the perimeter increases by 3 units. The y intercept means that an equilateral triangle with side lengths of 0 units would have a perimeter of 0 units.","###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
###Explanation:
The slope shows that for every 1 unit increase in side length of the equilateral triangle, the perimeter increases by 3 units. The y intercept means that an equilateral triangle with side lengths of 0 units would have a perimeter of 0 units."
172,Explain how to make this calculation mentally. 99 * 6,Round the 99 to 100 so you know have: 1006 = 600.,"###Write an explanation to this problem:
Explain how to make this calculation mentally. 99 * 6
###Explanation:
Round the 99 to 100 so you know have: 1006 = 600."
694,"A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project","There are 8 students at each table, and the total number of students is 120. This means that 8t=120.","###Write an explanation to this problem:
A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
There are 8 students at each table, and the total number of students is 120. This means that 8t=120."
312,"Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.","The slope of 3 shows that the triangle has 3 sides. For each increase of 1 unit of the side length, the perimeter increases by 3 units. The intercept of 0 shows that the relationship is proportional--a triangle with sides of length 0 has a perimeter of length 0.","###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
###Explanation:
The slope of 3 shows that the triangle has 3 sides. For each increase of 1 unit of the side length, the perimeter increases by 3 units. The intercept of 0 shows that the relationship is proportional--a triangle with sides of length 0 has a perimeter of length 0."
390,Write a story that matches the expressions and equations. Fixing Your Car Time hours: h Cost of Mike's Mechanics dollars: 15h + 75 Cost of Bubba's Body Shop dollars: 25h 15h + 75 = 25h The Utah Middle School Math Project,"The cost of Mike's Mechanics is 15h + 75, meaning there must be an initial fee of 75 and for every hour you will pay an additional 15. The cost of Bubba's Body Shop is 25h, meaning you will pay 25 dollars per hour. So, when 15h +75 = 25h, the cost of Mike's Mechanics will be equal to the cost of Bubba's Body Shop. Solve for h to find out after how many hours will both shops charge the same rate to fix your car.","###Write an explanation to this problem:
Write a story that matches the expressions and equations. Fixing Your Car Time hours: h Cost of Mike's Mechanics dollars: 15h + 75 Cost of Bubba's Body Shop dollars: 25h 15h + 75 = 25h The Utah Middle School Math Project
###Explanation:
The cost of Mike's Mechanics is 15h + 75, meaning there must be an initial fee of 75 and for every hour you will pay an additional 15. The cost of Bubba's Body Shop is 25h, meaning you will pay 25 dollars per hour. So, when 15h +75 = 25h, the cost of Mike's Mechanics will be equal to the cost of Bubba's Body Shop. Solve for h to find out after how many hours will both shops charge the same rate to fix your car."
796,"To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.","To make 2 batches, you could use the ratio of 12 to 10 which would be 12 cups of pink paint and 10 cups of blue paint. To make 1/2 of a batch you could use the ratio of 3 to 2.5 which would be 3 cups of pink paint and 2.5 cups of blue paint.","###Write an explanation to this problem:
To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.
###Explanation:
To make 2 batches, you could use the ratio of 12 to 10 which would be 12 cups of pink paint and 10 cups of blue paint. To make 1/2 of a batch you could use the ratio of 3 to 2.5 which would be 3 cups of pink paint and 2.5 cups of blue paint."
12,Fill in the blank with numbers that correctly complete the statement. Three rational numbers between 16 and 15 < <,15.3 < 15.6 < 15.7,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three rational numbers between 16 and 15 < <
###Explanation:
15.3 < 15.6 < 15.7"
407,"Make a list to find the GCF of this pair of numbers. 14 and 35 First, write the list here. The Utah Middle School Math Project","Factors of 14: 1, 2, 7, 14 Factors of 35: 1, 5, 7, 35","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 14 and 35 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 14: 1, 2, 7, 14 Factors of 35: 1, 5, 7, 35"
408,Adam is trying to solve the following riddle: The sum of three consecutive integers is -36. What are the integers? Write an equation to solve this riddle. The Utah Middle School Math Project,"Consecutive integers are numbers that directly follow each other, and are whole numbers. The first integer will be set as n. The next integer follows directly after, so it can be n+1. The next integer will be n+2. These three values added together equal -36. The equation is n+n+1+n+2=-36.","###Write an explanation to this problem:
Adam is trying to solve the following riddle: The sum of three consecutive integers is -36. What are the integers? Write an equation to solve this riddle. The Utah Middle School Math Project
###Explanation:
Consecutive integers are numbers that directly follow each other, and are whole numbers. The first integer will be set as n. The next integer follows directly after, so it can be n+1. The next integer will be n+2. These three values added together equal -36. The equation is n+n+1+n+2=-36."
305,"In your own words, explain what a dilation is.",Sample responses: A dilation expands things. It makes scaled copies. It blows things up. It works by pushing things outward from a center. A dilation multiplies distances from the center to change the size of the figure.,"###Write an explanation to this problem:
In your own words, explain what a dilation is.
###Explanation:
Sample responses: A dilation expands things. It makes scaled copies. It blows things up. It works by pushing things outward from a center. A dilation multiplies distances from the center to change the size of the figure."
354,"Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.","This is the original problem: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 Now we can see how this problem, which began as subtraction, can be rewritten as an addition problem.","###Write an explanation to this problem:
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.
###Explanation:
This is the original problem: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 Now we can see how this problem, which began as subtraction, can be rewritten as an addition problem."
25,"Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. -14 - -2","The subtraction rule says that subtracting a number is the same as adding its opposite. To use this rule of subtraction, we start by switching the subtraction sign to an addition sign: -14 + -2 We then change the sign of -2 to its opposite and get: -14 + 2","###Write an explanation to this problem:
Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. -14 - -2
###Explanation:
The subtraction rule says that subtracting a number is the same as adding its opposite. To use this rule of subtraction, we start by switching the subtraction sign to an addition sign: -14 + -2 We then change the sign of -2 to its opposite and get: -14 + 2"
669,Solve the inequality. Represent the solution on a number line. 1.2<x-9/10 The Utah Middle School Math Project,"Solve for x. The number line should be greater than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 1.2<x-9/10 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be greater than the solution, but not contain it."
169,Name 4 points that would form a square with the origin at its center.,"Here is an example, answers will vary. Check your work by graphing or ask your teacher 3, 5, -3, 5, 3, -5, and -3, -5.","###Write an explanation to this problem:
Name 4 points that would form a square with the origin at its center.
###Explanation:
Here is an example, answers will vary. Check your work by graphing or ask your teacher 3, 5, -3, 5, 3, -5, and -3, -5."
538,"Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800.","###Write an explanation to this problem:
Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800."
38,A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?,"Find the multiples of 4 and of 5. The first one they have in common will be when the lights will blink at the same time. Multiples of 4: 4,8,12,16,20 Multiples of 5: 5,10,15,20 The lights will blink at the same time after 20 seconds.","###Write an explanation to this problem:
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
###Explanation:
Find the multiples of 4 and of 5. The first one they have in common will be when the lights will blink at the same time. Multiples of 4: 4,8,12,16,20 Multiples of 5: 5,10,15,20 The lights will blink at the same time after 20 seconds."
175,Make up a situation where a quantity is changing. Explain what it means to have a negative change.,"To have a negative change means that you are going down in something. For example, you may be selling lemonade so your amount of lemonade goes down.","###Write an explanation to this problem:
Make up a situation where a quantity is changing. Explain what it means to have a negative change.
###Explanation:
To have a negative change means that you are going down in something. For example, you may be selling lemonade so your amount of lemonade goes down."
245,Explain how to make this calculation mentally. 99 * 6,I would add 1 more to make it 100 x 6=600 and then I would subtract the extra group of six that we added to make it 600-6=594.,"###Write an explanation to this problem:
Explain how to make this calculation mentally. 99 * 6
###Explanation:
I would add 1 more to make it 100 x 6=600 and then I would subtract the extra group of six that we added to make it 600-6=594."
298,"Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ge; 500 and solved it to find the solution x ge; 55.25. Explain how you know Elena made a mistake based on her solution.",x ge; 55.25 means Elena has to put more than 55 movies on her hard drive. This doesn't make sense because there should be a maximum limit on movies rather than a minimum limit.,"###Write an explanation to this problem:
Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ge; 500 and solved it to find the solution x ge; 55.25. Explain how you know Elena made a mistake based on her solution.
###Explanation:
x ge; 55.25 means Elena has to put more than 55 movies on her hard drive. This doesn't make sense because there should be a maximum limit on movies rather than a minimum limit."
710,"Solve the inequality. Represent the solution on a number line. t+3ge;9 The Utah Middle School Math Project Solve the inequality. Represent the solution on a double number line. Then, write two solutions of the inequality. The Utah Middle School Math Project Solve the inequality. Represent the solution on a double number line. Then, write two solutions of the inequality. The Utah Middle School Math Project",Solve for t. The number line should be higher than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. t+3ge;9 The Utah Middle School Math Project Solve the inequality. Represent the solution on a double number line. Then, write two solutions of the inequality. The Utah Middle School Math Project Solve the inequality. Represent the solution on a double number line. Then, write two solutions of the inequality. The Utah Middle School Math Project
###Explanation:
Solve for t. The number line should be higher than and equal to the solution."
580,"Use The Distributive Property to find the product. 712 First, show your work here. The Utah Middle School Math Project",710 + 2 = 710 + 72 = 70 + 14 = 84,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 712 First, show your work here. The Utah Middle School Math Project
###Explanation:
710 + 2 = 710 + 72 = 70 + 14 = 84"
649,"Suppose you were to roll a fair 6-sided number cube once, then flip a coin. List all the possible outcomes.","Possible Outcomes: 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T","###Write an explanation to this problem:
Suppose you were to roll a fair 6-sided number cube once, then flip a coin. List all the possible outcomes.
###Explanation:
Possible Outcomes: 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T"
731,Write a story context that would be represented by the ratio 1:4,Answers will vary. For example: Kendra's mom pays her four dollars for every load of laundry she washes and dries.,"###Write an explanation to this problem:
Write a story context that would be represented by the ratio 1:4
###Explanation:
Answers will vary. For example: Kendra's mom pays her four dollars for every load of laundry she washes and dries."
154,"Water is running into a bathtub at a constant rate. After 2 minutes, the tub is filled with 2.5 gallons of water. Write two equations for this proportional relationship. Use w for the amount of water gallons and t for time minutes. In each case, what does the constant of proportionality tell you about the situation?","two equations can be made using the rate given in the question. One equation has w alone on one side of he equation, the second equation has t alone on one side of hte equation.","###Write an explanation to this problem:
Water is running into a bathtub at a constant rate. After 2 minutes, the tub is filled with 2.5 gallons of water. Write two equations for this proportional relationship. Use w for the amount of water gallons and t for time minutes. In each case, what does the constant of proportionality tell you about the situation?
###Explanation:
two equations can be made using the rate given in the question. One equation has w alone on one side of he equation, the second equation has t alone on one side of hte equation."
287,"10. In each list, find expressions that are equivalent to each other and explain to your partner why they are equivalent. Your partner listens to your explanation. If you disagree, explain your reasoning until you agree. Switch roles for each list. There may be more than two equivalent expressions in each list. a. 5 * 5 25 52 2 * 5 copied for free from openupresources.org",5 x 5 = 52 ---> Both of these expression are equal to 25.,"###Write an explanation to this problem:
10. In each list, find expressions that are equivalent to each other and explain to your partner why they are equivalent. Your partner listens to your explanation. If you disagree, explain your reasoning until you agree. Switch roles for each list. There may be more than two equivalent expressions in each list. a. 5 * 5 25 52 2 * 5 copied for free from openupresources.org
###Explanation:
5 x 5 = 52 ---> Both of these expression are equal to 25."
521,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. As the size of your family increases so does the cost of groceries. The Utah Middle School Math Project,Size is independent Cost is dependent,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. As the size of your family increases so does the cost of groceries. The Utah Middle School Math Project
###Explanation:
Size is independent Cost is dependent"
17,Write an inequality that relates the rational numbers. Sixteen degrees Celsius is warmer than zero degrees Celsius.,16 > 0,"###Write an explanation to this problem:
Write an inequality that relates the rational numbers. Sixteen degrees Celsius is warmer than zero degrees Celsius.
###Explanation:
16 > 0"
127,Use a geometric tool to draw a circle. Draw and measure a radius and a diameter of the circle. Submit your drawing using the tools below.,"A geometric tool that can be used to draw a circle is a compass. A compass can be used to draw a circle by putting the tip pointy part at the center of the circle and rotating the compass to move the pencil tip in a circle. To make the circle have a specific size, the distance between the needle tip and the pencil tip can be set to the radius of the circle.","###Write an explanation to this problem:
Use a geometric tool to draw a circle. Draw and measure a radius and a diameter of the circle. Submit your drawing using the tools below.
###Explanation:
A geometric tool that can be used to draw a circle is a compass. A compass can be used to draw a circle by putting the tip pointy part at the center of the circle and rotating the compass to move the pencil tip in a circle. To make the circle have a specific size, the distance between the needle tip and the pencil tip can be set to the radius of the circle."
322,Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true. Copied for free from openupresources.org,"There are many different combinations of x and y that will create a triangle, as long as the sum of the angles is equal to 180deg;, it will create a triangle. Some examples of angle measurements that can be used are x=y=60, or x=30 and y=120 or x=45 and y=90.","###Write an explanation to this problem:
Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true. Copied for free from openupresources.org
###Explanation:
There are many different combinations of x and y that will create a triangle, as long as the sum of the angles is equal to 180deg;, it will create a triangle. Some examples of angle measurements that can be used are x=y=60, or x=30 and y=120 or x=45 and y=90."
255,7. 38% of e is 190. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org,".38e = 190 First, you need to change 38% to a decimal in order to be able to use it with an operation. 38% is equal to 0.38. Next, 60% of e means that you are multiplying because of implies multiplication. Lastly is implies what the expression is equal to.","###Write an explanation to this problem:
7. 38% of e is 190. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org
###Explanation:
.38e = 190 First, you need to change 38% to a decimal in order to be able to use it with an operation. 38% is equal to 0.38. Next, 60% of e means that you are multiplying because of implies multiplication. Lastly is implies what the expression is equal to."
570,Will the product of 2 and 3 be bigger or smaller than each factor? Explain. The Utah Middle School Math Project,"23 means two groups of 3 or three groups of two. Two groups of 3 is bigger than 3 which equals to one group of 3 Three groups of two is bigger than 2 which equals to one group of 2 Alternatively, we can find the product: 23 = 6 Then, we can compare 6 to 2 and 3. 6 is bigger than 2 and 3.","###Write an explanation to this problem:
Will the product of 2 and 3 be bigger or smaller than each factor? Explain. The Utah Middle School Math Project
###Explanation:
23 means two groups of 3 or three groups of two. Two groups of 3 is bigger than 3 which equals to one group of 3 Three groups of two is bigger than 2 which equals to one group of 2 Alternatively, we can find the product: 23 = 6 Then, we can compare 6 to 2 and 3. 6 is bigger than 2 and 3."
820,Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.,Sample response: The ratio of the number of male teachers to the number of female teachers is 15: 35. The ratio of the number of female teachers to the number of male teachers is 35: 15. The ratio of the number of female teachers to the total number of teachers in the school is 35: 50. The ratio of the number of male teachers to the total number of teachers in the school is 15: 50.,"###Write an explanation to this problem:
Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.
###Explanation:
Sample response: The ratio of the number of male teachers to the number of female teachers is 15: 35. The ratio of the number of female teachers to the number of male teachers is 35: 15. The ratio of the number of female teachers to the total number of teachers in the school is 35: 50. The ratio of the number of male teachers to the total number of teachers in the school is 15: 50."
190,Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org,"First we need to simplify the inequality. -3x > 18 Divide each side of the inequality by -3. Remember that when you are dividing by a negative number, the inequality sign will flip. x < -18/3 x < -6 This inequality says that x is less than -6. A value for x that would make this inequality true is any number that is less than -6. Some examples are -7, -10, -88, and -100.","###Write an explanation to this problem:
Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org
###Explanation:
First we need to simplify the inequality. -3x > 18 Divide each side of the inequality by -3. Remember that when you are dividing by a negative number, the inequality sign will flip. x < -18/3 x < -6 This inequality says that x is less than -6. A value for x that would make this inequality true is any number that is less than -6. Some examples are -7, -10, -88, and -100."
115,The following problem is given to Miranda: 23.10*100 She states that since she is multiplying by 100 she simply must add two zeros to 23.10. Explain the error in Miranda's thinking and explain how to find the correct answer without using a calculator or long multiplication. The Utah Middle School Math Project,"Multiplying by 100 indicates moving the decimal two places to the right; this will give you 2,310.","###Write an explanation to this problem:
The following problem is given to Miranda: 23.10*100 She states that since she is multiplying by 100 she simply must add two zeros to 23.10. Explain the error in Miranda's thinking and explain how to find the correct answer without using a calculator or long multiplication. The Utah Middle School Math Project
###Explanation:
Multiplying by 100 indicates moving the decimal two places to the right; this will give you 2,310."
534,Write an ordered pair that would be in Quadrant II when graphed. The Utah Middle School Math Project,"Any ordered pair where x is negative and y is positive is in Quadrant II. Examples: -1, 1 -5, 3 -1/2, 3/4","###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant II when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair where x is negative and y is positive is in Quadrant II. Examples: -1, 1 -5, 3 -1/2, 3/4"
180,What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB,"The sample space is A, L, M, and B for both experiments.","###Write an explanation to this problem:
What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB
###Explanation:
The sample space is A, L, M, and B for both experiments."
301,Lin wants to know how many games teenagers in the United States have on their phones. What is the population for Lin's question?,The population is the group of people Lin wants to know the information about. Lin's population is all people who are 13 to 19 years old teenagers in the United States who have a phone.,"###Write an explanation to this problem:
Lin wants to know how many games teenagers in the United States have on their phones. What is the population for Lin's question?
###Explanation:
The population is the group of people Lin wants to know the information about. Lin's population is all people who are 13 to 19 years old teenagers in the United States who have a phone."
697,Write a pair of numbers whose GCF is 8. The Utah Middle School Math Project,"Factors of 8: 1, 2, 4, 8 Factors of 16: 1, 2, 4, 8, 16 GCF is 8","###Write an explanation to this problem:
Write a pair of numbers whose GCF is 8. The Utah Middle School Math Project
###Explanation:
Factors of 8: 1, 2, 4, 8 Factors of 16: 1, 2, 4, 8, 16 GCF is 8"
845,What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB,"If you select a letter at random from the words, 'ALABAMA' or 'LAMB' you have the same opportunity to select a letter of L, A, M, B from the two words. The word 'LAMB' is in the word 'ALABAMA'.","###Write an explanation to this problem:
What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB
###Explanation:
If you select a letter at random from the words, 'ALABAMA' or 'LAMB' you have the same opportunity to select a letter of L, A, M, B from the two words. The word 'LAMB' is in the word 'ALABAMA'."
625,For what value of x does the expression - 9 evaluate to 3? Write an equation to represent the problem. The Utah Middle School Math Project,"To make an equation where the expression x-9 evaluates to 3, we need to say that the expression equals 3. x-9=3 Any equation that simplifies to this equation is a correct answer.","###Write an explanation to this problem:
For what value of x does the expression - 9 evaluate to 3? Write an equation to represent the problem. The Utah Middle School Math Project
###Explanation:
To make an equation where the expression x-9 evaluates to 3, we need to say that the expression equals 3. x-9=3 Any equation that simplifies to this equation is a correct answer."
593,"Here, write the third problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project","Sample Answer: Last night, Jeff planned to read 65 pages of the report before he goes to bed. However, he fell asleep with 61.54% of his targetted 65 pages not read. How many pages did he read that night? Solution: whole: 65 pages percent: 61.54% = 0.6154 To find the number of pages Jeff have left to read that night, we multiply the whole by the percent: whole x percent = 65 pages x 0.6154 = 40 pages unread To get the number of pages Jeff read that night: Pages Read = Page Targetted - Page Unread = 65 page - 40 pages = 25 pages We get that Jeff read 25 pages that night.","###Write an explanation to this problem:
Here, write the third problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Last night, Jeff planned to read 65 pages of the report before he goes to bed. However, he fell asleep with 61.54% of his targetted 65 pages not read. How many pages did he read that night? Solution: whole: 65 pages percent: 61.54% = 0.6154 To find the number of pages Jeff have left to read that night, we multiply the whole by the percent: whole x percent = 65 pages x 0.6154 = 40 pages unread To get the number of pages Jeff read that night: Pages Read = Page Targetted - Page Unread = 65 page - 40 pages = 25 pages We get that Jeff read 25 pages that night."
704,Solve the inequality. Represent the solution on a number line. x-57le;429 The Utah Middle School Math Project,Solve for x. The number line should be less than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. x-57le;429 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than and equal to the solution."
517,Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project,𝑤 = 2𝑟 where w represents Will's distance and r represents Ruby's distance 𝑟 + 𝑤 = 18 Will ran 12 miles and Ruby ran 6 miles.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project
###Explanation:
𝑤 = 2𝑟 where w represents Will's distance and r represents Ruby's distance 𝑟 + 𝑤 = 18 Will ran 12 miles and Ruby ran 6 miles."
838,Write a word problem whose solution is |20| = 20.,Answers will vary. Kelli flew a kite 20 feet above the ground. Determine the distance between the kite and the ground.,"###Write an explanation to this problem:
Write a word problem whose solution is |20| = 20.
###Explanation:
Answers will vary. Kelli flew a kite 20 feet above the ground. Determine the distance between the kite and the ground."
45,Describe a situation where the following quantities might be useful. -20 gallons per hour,Water draining out of a pool.,"###Write an explanation to this problem:
Describe a situation where the following quantities might be useful. -20 gallons per hour
###Explanation:
Water draining out of a pool."
773,"Write your own problem, and solve it. Be ready to share the question tomorrow.",Answers will vary.,"###Write an explanation to this problem:
Write your own problem, and solve it. Be ready to share the question tomorrow.
###Explanation:
Answers will vary."
157,"Priya says I can figure out 50 by looking at other powers of 5. 53 is 125, 52 is 25, then 51 is 5. What pattern do you notice? Copied for free from openupresources.org","As the exponent decreases by 1, the power is being divided by the base.","###Write an explanation to this problem:
Priya says I can figure out 50 by looking at other powers of 5. 53 is 125, 52 is 25, then 51 is 5. What pattern do you notice? Copied for free from openupresources.org
###Explanation:
As the exponent decreases by 1, the power is being divided by the base."
640,"In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 7 Transformed Equation: x + 5 = 12 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 5 has been added to x. On the right side, 5 has been added to 7, which results in 12. The action was: Add 5 to both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 7 Transformed Equation: x + 5 = 12 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 5 has been added to x. On the right side, 5 has been added to 7, which results in 12. The action was: Add 5 to both sides of the equation."
171,Explain how to make this calculation mentally. 244 - 99,"To estimate, first round the 99 to 100 so you now hae 244-100 = 144 This makes it easier to do the math mentally.","###Write an explanation to this problem:
Explain how to make this calculation mentally. 244 - 99
###Explanation:
To estimate, first round the 99 to 100 so you now hae 244-100 = 144 This makes it easier to do the math mentally."
16,Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.,-500 < 200,"###Write an explanation to this problem:
Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.
###Explanation:
-500 < 200"
511,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project",𝑥 + 𝑦 = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1𝑥 + 2.5𝑦 = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project
###Explanation:
𝑥 + 𝑦 = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1𝑥 + 2.5𝑦 = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982"
48,Find three different ratios that are equivalent to the ratio 3:11.,There are a variety of correct answers for this one. Here are a few examples: 6:22 9:33 30:110 15:55,"###Write an explanation to this problem:
Find three different ratios that are equivalent to the ratio 3:11.
###Explanation:
There are a variety of correct answers for this one. Here are a few examples: 6:22 9:33 30:110 15:55"
826,"In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.",One possibility is that either angle B or C measure 40 degrees and the other measures 100 degrees since 100 + 40 + 40 = 180. The only other possibility is that angle B and angle C both measure 70 degrees since 70 + 70 + 40 = 180. These are the only two possibilities because the three angles have to add up to 180 degrees.,"###Write an explanation to this problem:
In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.
###Explanation:
One possibility is that either angle B or C measure 40 degrees and the other measures 100 degrees since 100 + 40 + 40 = 180. The only other possibility is that angle B and angle C both measure 70 degrees since 70 + 70 + 40 = 180. These are the only two possibilities because the three angles have to add up to 180 degrees."
515,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. The admission fee at a local zoo is 1.50 for children and 4.00 for adults. On a certain day, 2,200 people enter the zoo and 5,050 is collected. How many children and how many adults attended? The Utah Middle School Math Project","𝑐 + 𝑎 = 2200 where c is number of children tickets and a is number of adult tickets 1.5𝑐 + 4𝑎 = 5050 1,500 children attended and 700 adults attended","###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. The admission fee at a local zoo is 1.50 for children and 4.00 for adults. On a certain day, 2,200 people enter the zoo and 5,050 is collected. How many children and how many adults attended? The Utah Middle School Math Project
###Explanation:
𝑐 + 𝑎 = 2200 where c is number of children tickets and a is number of adult tickets 1.5𝑐 + 4𝑎 = 5050 1,500 children attended and 700 adults attended"
594,"Here, write the third problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project","Sample Answer: Last night, Jeff planned to read 65 pages of the report before he goes to bed. However, he fell asleep with 61.54% of his targetted 65 pages not read. How many pages did he read that night? Solution: whole: 65 pages percent: 61.54% = 0.6154 To find the number of pages Jeff has unread that night, we multiply the whole by the percent: whole x percent = 65 pages x 0.6154 = 40 pages unread To get the number of pages Jeff read that night: Pages Read = Page Targetted - Page Unread = 65 page - 40 pages = 25 pages We get that Jeff read 25 pages that night.","###Write an explanation to this problem:
Here, write the third problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Last night, Jeff planned to read 65 pages of the report before he goes to bed. However, he fell asleep with 61.54% of his targetted 65 pages not read. How many pages did he read that night? Solution: whole: 65 pages percent: 61.54% = 0.6154 To find the number of pages Jeff has unread that night, we multiply the whole by the percent: whole x percent = 65 pages x 0.6154 = 40 pages unread To get the number of pages Jeff read that night: Pages Read = Page Targetted - Page Unread = 65 page - 40 pages = 25 pages We get that Jeff read 25 pages that night."
480,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project",x+y= 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1x+ 2.5y= 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project
###Explanation:
x+y= 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1x+ 2.5y= 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982"
283,"Sixth-grade students were asked, What grade are you in? Explain why this is not a statistical question.","This is not a statistical question because there is no variability. Since they only asked sixth-grade students, they will all have the same answer, 6.","###Write an explanation to this problem:
Sixth-grade students were asked, What grade are you in? Explain why this is not a statistical question.
###Explanation:
This is not a statistical question because there is no variability. Since they only asked sixth-grade students, they will all have the same answer, 6."
568,"Here, write the third problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project","Sample Answer: Last night, Jeff planned to read 65 pages of the report before he goes to bed. However, he fell asleep with 61.54% of his targetted 65 pages not read. How many pages did he not read that night? Solution: whole: 65 pages percent: 61.54% = 0.6154 To find the number of pages Jeff has unread that night, we multiply the whole by the percent: whole x percent = 65 pages x 0.6154 = 40 pages unread We get that Jeff has 40 pages unread that night.","###Write an explanation to this problem:
Here, write the third problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Last night, Jeff planned to read 65 pages of the report before he goes to bed. However, he fell asleep with 61.54% of his targetted 65 pages not read. How many pages did he not read that night? Solution: whole: 65 pages percent: 61.54% = 0.6154 To find the number of pages Jeff has unread that night, we multiply the whole by the percent: whole x percent = 65 pages x 0.6154 = 40 pages unread We get that Jeff has 40 pages unread that night."
225,"Using only the values you computed in the previous two activities, compare your sample to your partner's. Is it reasonable to conclude that the measures of center for each of your populations are meaningfully different? Explain or show your reasoning. copied for free from openupresources.org","They are less than 2 MAD's apart, so they are not meaningfully different.","###Write an explanation to this problem:
Using only the values you computed in the previous two activities, compare your sample to your partner's. Is it reasonable to conclude that the measures of center for each of your populations are meaningfully different? Explain or show your reasoning. copied for free from openupresources.org
###Explanation:
They are less than 2 MAD's apart, so they are not meaningfully different."
26,"The point -3,6 is on a line with a slope of 4. Find two more points on the line.","-2, 10 and -1, 14. I found these points by adding 4 to the y coordinate and 1 to the x coordinate.","###Write an explanation to this problem:
The point -3,6 is on a line with a slope of 4. Find two more points on the line.
###Explanation:
-2, 10 and -1, 14. I found these points by adding 4 to the y coordinate and 1 to the x coordinate."
670,-1 x -1 = ____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer -1 and multiply it -1 times, so -1 x -1 can be thought of as the opposite of -1 x 1, which is -1. The opposite of -1 is 1","###Write an explanation to this problem:
-1 x -1 = ____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -1 and multiply it -1 times, so -1 x -1 can be thought of as the opposite of -1 x 1, which is -1. The opposite of -1 is 1"
437,The following equation is given: m ndash; 26 = 15 Provide a context/word problem for the given information. The Utah Middle School Math Project,A number decreased by 26 is 15,"###Write an explanation to this problem:
The following equation is given: m ndash; 26 = 15 Provide a context/word problem for the given information. The Utah Middle School Math Project
###Explanation:
A number decreased by 26 is 15"
364,"Priya says I can figure out 50 by looking at other powers of 5. 53 is 125, 52 is 25, then 51 is 5. What pattern do you notice? Copied for free from openupresources.org","You should notice that every time you take away 1 from the exponent, the number gets divided by 5. For example, if you go from 53 to 52, you divide 125 by 5 to get 25.","###Write an explanation to this problem:
Priya says I can figure out 50 by looking at other powers of 5. 53 is 125, 52 is 25, then 51 is 5. What pattern do you notice? Copied for free from openupresources.org
###Explanation:
You should notice that every time you take away 1 from the exponent, the number gets divided by 5. For example, if you go from 53 to 52, you divide 125 by 5 to get 25."
229,"An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?","Drawing from the bag is random, but people do not usually randomly choose ice cream flavors. When picking a piece of paper from a bag, you do not get to choose what you get. At an ice cream shop, people choose to order their favorite flavors.","###Write an explanation to this problem:
An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?
###Explanation:
Drawing from the bag is random, but people do not usually randomly choose ice cream flavors. When picking a piece of paper from a bag, you do not get to choose what you get. At an ice cream shop, people choose to order their favorite flavors."
37,"Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.","If Kiran was truly doubling Clare's recipe, he should have used the following ingredients: 2 cups of yogurt 6 tablespoons of peanut butter 4 teaspoons of chocolate syrup 4 cups of crushed ice He had all of the ingredients correct, except for the chocolate syrup. He has an extra teaspoon of chocolate syrup than he should have. His recipe would have a stronger chocolate flavor than Clare's.","###Write an explanation to this problem:
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
###Explanation:
If Kiran was truly doubling Clare's recipe, he should have used the following ingredients: 2 cups of yogurt 6 tablespoons of peanut butter 4 teaspoons of chocolate syrup 4 cups of crushed ice He had all of the ingredients correct, except for the chocolate syrup. He has an extra teaspoon of chocolate syrup than he should have. His recipe would have a stronger chocolate flavor than Clare's."
821,"Jada earns money from babysitting, walking her neighbor's dogs, and running errands for her aunt. Every four weeks, she combines her earnings and divides them into three equal parts--one for spending, one for saving, and one for donating to a charity. Jada donated 26.00 of her earnings from the past four weeks to charity. How much could she have earned from each job? Make two lists of how much she could have earned from the three jobs during the past four weeks.","There are various ways to represent how much she could have earned from her three jobs in the past four weeks. But, since she divides her earnings into 3 equal parts her total earnings would be 26 x 3= 78. Each row should equal 78 total for all 3 jobs earnings combined. Babysitting Walking dog Running Errands Total Earnings 35 35 8 78 10 40 28 78","###Write an explanation to this problem:
Jada earns money from babysitting, walking her neighbor's dogs, and running errands for her aunt. Every four weeks, she combines her earnings and divides them into three equal parts--one for spending, one for saving, and one for donating to a charity. Jada donated 26.00 of her earnings from the past four weeks to charity. How much could she have earned from each job? Make two lists of how much she could have earned from the three jobs during the past four weeks.
###Explanation:
There are various ways to represent how much she could have earned from her three jobs in the past four weeks. But, since she divides her earnings into 3 equal parts her total earnings would be 26 x 3= 78. Each row should equal 78 total for all 3 jobs earnings combined. Babysitting Walking dog Running Errands Total Earnings 35 35 8 78 10 40 28 78"
374,Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes. Draw a graph with two lines that represent the bike rides of Lin and Andre. Submit your graph using the tools below.,"Lin and Andre both biked a different distance and at a different rate. Lin went 1.5 km in 5 minutes at a speed of 0.3 d = rt 1.5 = 5r divide 1.5 by 5 = 0.3 Her k value is 1.5 x 3.33 =5 Andre went 2 km in 8 minutes at a speed of 0.25 d = rt 2 = 8r divide 2/8 = 0.25 for speed His k value is 4 On a graph Lin would start at 0,0 She would have a point at 1, 3.33 1.5, 5 On a graph Andre would start at 0,0 He would have a point a 1,4 2, 8","###Write an explanation to this problem:
Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes. Draw a graph with two lines that represent the bike rides of Lin and Andre. Submit your graph using the tools below.
###Explanation:
Lin and Andre both biked a different distance and at a different rate. Lin went 1.5 km in 5 minutes at a speed of 0.3 d = rt 1.5 = 5r divide 1.5 by 5 = 0.3 Her k value is 1.5 x 3.33 =5 Andre went 2 km in 8 minutes at a speed of 0.25 d = rt 2 = 8r divide 2/8 = 0.25 for speed His k value is 4 On a graph Lin would start at 0,0 She would have a point at 1, 3.33 1.5, 5 On a graph Andre would start at 0,0 He would have a point a 1,4 2, 8"
469,"Round 1 of a tennis tournament starts with 64 players. After each round, half the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 players, in round 3 there are 16 players and so on. What is the dependent variable in this relationship? The Utah Middle School Math Project",The number of players left is determined by the round number of the tournament. This means that the number of players is the dependent variable in the equation.,"###Write an explanation to this problem:
Round 1 of a tennis tournament starts with 64 players. After each round, half the players have lost and are eliminated from the tournament. Therefore, in round 2 there are 32 players, in round 3 there are 16 players and so on. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of players left is determined by the round number of the tournament. This means that the number of players is the dependent variable in the equation."
823,"Think about your work today, and write your best definition of area.",Area is the amount of space inside a shape or polygon. It is measured in square units.,"###Write an explanation to this problem:
Think about your work today, and write your best definition of area.
###Explanation:
Area is the amount of space inside a shape or polygon. It is measured in square units."
725,Write two ratios that are equivalent to 3:11.,Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 3x2:11x2 = 6:22 3x3:11x3 = 9:33 Or any ratio that simplifies to 3:11,"###Write an explanation to this problem:
Write two ratios that are equivalent to 3:11.
###Explanation:
Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 3x2:11x2 = 6:22 3x3:11x3 = 9:33 Or any ratio that simplifies to 3:11"
668,Solve the inequality. Represent the solution on a number line. 0.25xge;6 The Utah Middle School Math Project,Solve for x. The number line should be greater than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 0.25xge;6 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be greater than and equal to the solution."
194,"For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.",Prices for apples at all stores in our state; Prices for all fruit at these two stores.,"###Write an explanation to this problem:
For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.
###Explanation:
Prices for apples at all stores in our state; Prices for all fruit at these two stores."
727,Write two ratios that are equivalent to 1:1.,Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 1x2:1x2 = 2:2 1x50:1x50 = 50:50 Or any ratio that simplifies to 1:1,"###Write an explanation to this problem:
Write two ratios that are equivalent to 1:1.
###Explanation:
Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 1x2:1x2 = 2:2 1x50:1x50 = 50:50 Or any ratio that simplifies to 1:1"
736,Write two ratios that are equivalent to 1:1.,"Answers will vary. You might write the following ratios: 2:2, 50:50, etc.","###Write an explanation to this problem:
Write two ratios that are equivalent to 1:1.
###Explanation:
Answers will vary. You might write the following ratios: 2:2, 50:50, etc."
503,Create a representation of a context story that can be modeled by a linear function. The Utah Middle School Math Project,"There are many different stories that can be created that represent a linear function. One possible example is: Sarah is baking cupcakes for her school bake sale. Every hour she bakes two dozen cupcakes, and she bakes for 3 hours. How many cupcakes does she prepare for the bake sale?","###Write an explanation to this problem:
Create a representation of a context story that can be modeled by a linear function. The Utah Middle School Math Project
###Explanation:
There are many different stories that can be created that represent a linear function. One possible example is: Sarah is baking cupcakes for her school bake sale. Every hour she bakes two dozen cupcakes, and she bakes for 3 hours. How many cupcakes does she prepare for the bake sale?"
825,Explain why 6:4 and 18:8 are not equivalent ratios.,The ratios are not equivalent because there is not a common scale factor that you can multiply/divide by to get the ratios to be equal. To get from 6 to 18 you multiply by 3 and to get from 4 to 8 you multiply by 2. In order for the ratios to be equivalent you would need to multiply both numbers in the ratio by the same thing.,"###Write an explanation to this problem:
Explain why 6:4 and 18:8 are not equivalent ratios.
###Explanation:
The ratios are not equivalent because there is not a common scale factor that you can multiply/divide by to get the ratios to be equal. To get from 6 to 18 you multiply by 3 and to get from 4 to 8 you multiply by 2. In order for the ratios to be equivalent you would need to multiply both numbers in the ratio by the same thing."
711,Solve the inequality. Represent the solution on a number line. 2/9x<36 The Utah Middle School Math Project,"Solve for x. The number line should be less than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 2/9x<36 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than the solution, but not contain it."
824,Jada applies two transformations to a polygon in the coordinate plane. One of the transformations is a translation and the other is a reflection. What information does Jada need to provide to communicate the transformations she has used?,"For the translation, Jada needs to give the distance and direction of the vertical and horizontal slides. For the reflection, she needs to give the line of reflection. It is also important that she provides information about which order the transformations need to be completed in.","###Write an explanation to this problem:
Jada applies two transformations to a polygon in the coordinate plane. One of the transformations is a translation and the other is a reflection. What information does Jada need to provide to communicate the transformations she has used?
###Explanation:
For the translation, Jada needs to give the distance and direction of the vertical and horizontal slides. For the reflection, she needs to give the line of reflection. It is also important that she provides information about which order the transformations need to be completed in."
162,How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words east and west?,"East and west are opposite directions of each other. This means you could distinguish between them without giving compass directions by giving them opposite signs. For example, 5 mph east would be 5, and 5 mph west would be -5.","###Write an explanation to this problem:
How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words east and west?
###Explanation:
East and west are opposite directions of each other. This means you could distinguish between them without giving compass directions by giving them opposite signs. For example, 5 mph east would be 5, and 5 mph west would be -5."
606,"Use The Distributive Property to find the product. 647 First, show your work here. The Utah Middle School Math Project",647 = 640 + 7 = 640 + 67 = 240 + 42 = 282,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 647 First, show your work here. The Utah Middle School Math Project
###Explanation:
647 = 640 + 7 = 640 + 67 = 240 + 42 = 282"
152,"Write each expression as a multiple of a power of 10: 42,300 copied for free from openupresources.org",4.23*104,"###Write an explanation to this problem:
Write each expression as a multiple of a power of 10: 42,300 copied for free from openupresources.org
###Explanation:
4.23*104"
589,"Here, write the second problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Richard prepares tea for his workday. In the first hour of work, he drank 6 fl. oz. of the tea, which was 25% of the tea he prepared. How many fluid ounces of tea did he prepare? Solution: part: 6 fl.oz. percent: 25% = 0.25 We want to find the amount of tea Richard prepared started with. Note that 25% of the original amount is 6 fl. oz. 25% of the original amount is 0.25 times the original amount. With this information, we can write: 6 fl. oz. = original amount x 0.25 Now, we can solve for the original price: 6 fl. oz. = original amount x 0.25 6 fl. oz./0.25 = original amount 24 fl. oz. = original amount We get that Richard prepared 24 fl. oz. of tea.","###Write an explanation to this problem:
Here, write the second problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Richard prepares tea for his workday. In the first hour of work, he drank 6 fl. oz. of the tea, which was 25% of the tea he prepared. How many fluid ounces of tea did he prepare? Solution: part: 6 fl.oz. percent: 25% = 0.25 We want to find the amount of tea Richard prepared started with. Note that 25% of the original amount is 6 fl. oz. 25% of the original amount is 0.25 times the original amount. With this information, we can write: 6 fl. oz. = original amount x 0.25 Now, we can solve for the original price: 6 fl. oz. = original amount x 0.25 6 fl. oz./0.25 = original amount 24 fl. oz. = original amount We get that Richard prepared 24 fl. oz. of tea."
605,"Use The Distributive Property to find the product. 324 First, show your work here. The Utah Middle School Math Project",324 = 320 + 4 = 320 + 34 = 60 + 12 = 72,"###Write an explanation to this problem:
Use The Distributive Property to find the product. 324 First, show your work here. The Utah Middle School Math Project
###Explanation:
324 = 320 + 4 = 320 + 34 = 60 + 12 = 72"
650,"Find all the possible outcomes of flipping a coin heads or tails FOUR times. In other words, how many different ways are there to get heads and/or tails in four flips? Make sure your work is written so that you can use it for the next question The Utah Middle School Math Project",There are 16 possible outcomes of flipping the coin four times 1. H H H H 2. H H H T 3. H H T H 4. H T H H 5. T H H H 6. H H T T 7. H T T H 8. T T H H 9. H T T T 10. T T T H 11. T T T T 12. H T T T 13. T H T T 14. T T H T 15. T H T H 16. H T H T,"###Write an explanation to this problem:
Find all the possible outcomes of flipping a coin heads or tails FOUR times. In other words, how many different ways are there to get heads and/or tails in four flips? Make sure your work is written so that you can use it for the next question The Utah Middle School Math Project
###Explanation:
There are 16 possible outcomes of flipping the coin four times 1. H H H H 2. H H H T 3. H H T H 4. H T H H 5. T H H H 6. H H T T 7. H T T H 8. T T H H 9. H T T T 10. T T T H 11. T T T T 12. H T T T 13. T H T T 14. T T H T 15. T H T H 16. H T H T"
111,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project","In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1,2, 5, 10, and so on is a correct answer.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project
###Explanation:
In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1,2, 5, 10, and so on is a correct answer."
226,What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB,"Both experiments involve selecting a letter at random from a word, and both have the same sample space, since the words ALABAMA and LAMB only have the letters A, B, L, and M.","###Write an explanation to this problem:
What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB
###Explanation:
Both experiments involve selecting a letter at random from a word, and both have the same sample space, since the words ALABAMA and LAMB only have the letters A, B, L, and M."
595,"Write your own algebraic expression with four terms that is not simplified. Then, simply the expression. The Utah Middle School Math Project",One example of an algebraic expression is x + x + x + 3. The expression can be simplified to 3x + 3.,"###Write an explanation to this problem:
Write your own algebraic expression with four terms that is not simplified. Then, simply the expression. The Utah Middle School Math Project
###Explanation:
One example of an algebraic expression is x + x + x + 3. The expression can be simplified to 3x + 3."
103,Is there an association between the weight of a candle and the amount of time it burns? Make a prediction. The Utah Middle School Math Project,The burn time will increase as the starting weight increases.,"###Write an explanation to this problem:
Is there an association between the weight of a candle and the amount of time it burns? Make a prediction. The Utah Middle School Math Project
###Explanation:
The burn time will increase as the starting weight increases."
421,The ratio of rabbits to birds at the pet store is 5:2. Find three equivalent rabbit to bird ratios. The Utah Middle School Math Project,"Three ratios equivalent to 5:2 are 10:4, 15:6, and 20:8","###Write an explanation to this problem:
The ratio of rabbits to birds at the pet store is 5:2. Find three equivalent rabbit to bird ratios. The Utah Middle School Math Project
###Explanation:
Three ratios equivalent to 5:2 are 10:4, 15:6, and 20:8"
419,"Niona needs 50 to go on a school trip. She sells necklaces for 15 each and bracelets for 5 each. If she raises the money by selling half as many necklaces as bracelets, how many necklaces and bracelets does she sell? Write a system of linear equations that represent this problem. The Utah Middle School Math Project Define your Unknowns:","You know how much money Niona needs, which is 50 dollars. You do not know how many of each item she has sold. b = number of bracelets n = number of necklaces","###Write an explanation to this problem:
Niona needs 50 to go on a school trip. She sells necklaces for 15 each and bracelets for 5 each. If she raises the money by selling half as many necklaces as bracelets, how many necklaces and bracelets does she sell? Write a system of linear equations that represent this problem. The Utah Middle School Math Project Define your Unknowns:
###Explanation:
You know how much money Niona needs, which is 50 dollars. You do not know how many of each item she has sold. b = number of bracelets n = number of necklaces"
119,A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population?,Because the only person in this situation is you and not an entire population of people. The data is only specific to you and not a large population.,"###Write an explanation to this problem:
A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population?
###Explanation:
Because the only person in this situation is you and not an entire population of people. The data is only specific to you and not a large population."
53,A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs 24. copied for free from openupresources.org,0.75*24 = x 24 - 0.2524 = x,"###Write an explanation to this problem:
A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs 24. copied for free from openupresources.org
###Explanation:
0.75*24 = x 24 - 0.2524 = x"
151,"The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?","5,280 represents how many feet are in 1 mile.","###Write an explanation to this problem:
The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?
###Explanation:
5,280 represents how many feet are in 1 mile."
403,"Make a list to find the GCF of this pair of numbers. 30 and 50 First, write the list here. The Utah Middle School Math Project","Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 50: 1, 2, 5, 10, 25, 50","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 30 and 50 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 50: 1, 2, 5, 10, 25, 50"
804,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.,The temperature is -22oC. OR The temperature is 22 degrees below zero on the Celcius scale.,"###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.
###Explanation:
The temperature is -22oC. OR The temperature is 22 degrees below zero on the Celcius scale."
207,List the sample space the available options for the chance experiment given. Flipping a coin,"When you flip a coin, the two sides it could land on are heads or tails","###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
When you flip a coin, the two sides it could land on are heads or tails"
720,Solve the inequality. Represent the solution on a number line. x+4>5.2 The Utah Middle School Math Project,"Solve for x. The number line should be greater than the solution, but not contain it.","###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. x+4>5.2 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be greater than the solution, but not contain it."
656,"Beckham is interested in the hand span, the length from the tip of the pinky finger to the tip of the thumb, for people in his class. He asks the statistical question, How long is the hand span for people in my class? He decides to conduct a survey to answer his question. His data is shown below. Length of hand span in inches: 6, 6.5, 9, 7.5, 7.5, 7, 6.5, 7, 7, 9.5, 6, 8, 5.5, 7, 6.5 What is the attribute that is being measured?",The attribute being measured is the length of hand span.,"###Write an explanation to this problem:
Beckham is interested in the hand span, the length from the tip of the pinky finger to the tip of the thumb, for people in his class. He asks the statistical question, How long is the hand span for people in my class? He decides to conduct a survey to answer his question. His data is shown below. Length of hand span in inches: 6, 6.5, 9, 7.5, 7.5, 7, 6.5, 7, 7, 9.5, 6, 8, 5.5, 7, 6.5 What is the attribute that is being measured?
###Explanation:
The attribute being measured is the length of hand span."
8,"If two rational numbers, a and b, are ordered such that a is less than b, then what must be true about the order for their opposites: -a and -b?","The order will be reversed for the opposites, which means that -a will be greater than -b.","###Write an explanation to this problem:
If two rational numbers, a and b, are ordered such that a is less than b, then what must be true about the order for their opposites: -a and -b?
###Explanation:
The order will be reversed for the opposites, which means that -a will be greater than -b."
692,"The ratio of 6th graders to 7th graders to 8th graders in a middle school is 3:1:1. If there are 180 students in total, how many of the students are in each grade? Write an equation to solve the problem. The Utah Middle School Math Project","The variable x can represent the number of students in each grade, with the ratio 1 being the base. This means that 3x+1x+1x=180 students, or 3x+x+x=180.","###Write an explanation to this problem:
The ratio of 6th graders to 7th graders to 8th graders in a middle school is 3:1:1. If there are 180 students in total, how many of the students are in each grade? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The variable x can represent the number of students in each grade, with the ratio 1 being the base. This means that 3x+1x+1x=180 students, or 3x+x+x=180."
36,"9. Priya finds 1.05*2.8 by calculating 105*28, then moving the decimal point three places to the left. a Why does Priya's method make sense? copied for free from openupresources.org","Yes, Priya's method would work because when you multiply decimals, the decimals do not to be lined up and you would need to move the decimal place over the amount of total decimal values in the problem. 1.05 has 2 decimal places and 2.8 has 1 decimal place which is a total of 3 decimal places.","###Write an explanation to this problem:
9. Priya finds 1.05*2.8 by calculating 105*28, then moving the decimal point three places to the left. a Why does Priya's method make sense? copied for free from openupresources.org
###Explanation:
Yes, Priya's method would work because when you multiply decimals, the decimals do not to be lined up and you would need to move the decimal place over the amount of total decimal values in the problem. 1.05 has 2 decimal places and 2.8 has 1 decimal place which is a total of 3 decimal places."
452,The following equation is given: 2/5x + 1/5x = 360 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project,"Noel made some money working at her parents shop over the summer. She's going to put 2/5 of it in a savings account of a car when she gets her license and 1/5 of it on clothes. If she uses a total of 360 for these two, how much did she start with?","###Write an explanation to this problem:
The following equation is given: 2/5x + 1/5x = 360 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
Noel made some money working at her parents shop over the summer. She's going to put 2/5 of it in a savings account of a car when she gets her license and 1/5 of it on clothes. If she uses a total of 360 for these two, how much did she start with?"
253,35 equals 243. Explain how to use that fact to quickly evaluate 36.,"If 35=243, all you have to do is multiply 243 x 3. 35=3 x 3 x 3 x 3 x 3 36=3 x 3 x 3 x 3 x 3 x 3","###Write an explanation to this problem:
35 equals 243. Explain how to use that fact to quickly evaluate 36.
###Explanation:
If 35=243, all you have to do is multiply 243 x 3. 35=3 x 3 x 3 x 3 x 3 36=3 x 3 x 3 x 3 x 3 x 3"
303,Is there a triangle with 2 right angles? Explain your reasoning.,"Sample Answer: No, the three angles in a triangle add up to 180 degrees. Two right angles would already make 180 degrees, and so the third angle of the triangle would have to be 0 degrees--this is not possible.","###Write an explanation to this problem:
Is there a triangle with 2 right angles? Explain your reasoning.
###Explanation:
Sample Answer: No, the three angles in a triangle add up to 180 degrees. Two right angles would already make 180 degrees, and so the third angle of the triangle would have to be 0 degrees--this is not possible."
715,Explain how you can find 19% of 450 using the following information. 20% of 450 is 90. 1% of 450 is 4.5. The Utah Middle School Math Project,20% - 1% = 90 - 4.5 = 85.5,"###Write an explanation to this problem:
Explain how you can find 19% of 450 using the following information. 20% of 450 is 90. 1% of 450 is 4.5. The Utah Middle School Math Project
###Explanation:
20% - 1% = 90 - 4.5 = 85.5"
571,Will the product of 2 and 3 be bigger or smaller than each factor? Explain. The Utah Middle School Math Project,"23 means two groups of 3 or three groups of two. Two groups of 3 is bigger than 3 which equals to one group of 3 Three groups of two is bigger than 2 which equals to one group of 2 Alternatively, we can find the product: 23 = 6 Then, we can compare 6 to 2 and 3. 6 is bigger than 2 and bigger than 3.","###Write an explanation to this problem:
Will the product of 2 and 3 be bigger or smaller than each factor? Explain. The Utah Middle School Math Project
###Explanation:
23 means two groups of 3 or three groups of two. Two groups of 3 is bigger than 3 which equals to one group of 3 Three groups of two is bigger than 2 which equals to one group of 2 Alternatively, we can find the product: 23 = 6 Then, we can compare 6 to 2 and 3. 6 is bigger than 2 and bigger than 3."
802,"120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.",Change percent to a decimal of means to multiply Write out your equation as it is written above. 1.20 x= 78,"###Write an explanation to this problem:
120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.
###Explanation:
Change percent to a decimal of means to multiply Write out your equation as it is written above. 1.20 x= 78"
621,"If a < b and |a| = |b|, what is true of a and b? The Utah Middle School Math Project","This means that a must be the opposite of b. For example, if a = -3 and b = 3: a < b, -3 < 3 |a| = |b|, |-3| = |3|, 3 = 3","###Write an explanation to this problem:
If a < b and |a| = |b|, what is true of a and b? The Utah Middle School Math Project
###Explanation:
This means that a must be the opposite of b. For example, if a = -3 and b = 3: a < b, -3 < 3 |a| = |b|, |-3| = |3|, 3 = 3"
262,A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.,"To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue. Example mixture: 1 yellow, 1.75 blue","###Write an explanation to this problem:
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.
###Explanation:
To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue. Example mixture: 1 yellow, 1.75 blue"
297,"Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home. ​Andre wrote the inequality 3x + 10 le; 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.",The variable x represents the number of small paper cranes Andre will make. 10 is the number of minutes it takes to make the centerpiece. 3x is the amount of time it takes to make x small cranes it takes 3 minutes to make one crane. 30 is Andre's time limit in minutes.,"###Write an explanation to this problem:
Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home. ​Andre wrote the inequality 3x + 10 le; 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.
###Explanation:
The variable x represents the number of small paper cranes Andre will make. 10 is the number of minutes it takes to make the centerpiece. 3x is the amount of time it takes to make x small cranes it takes 3 minutes to make one crane. 30 is Andre's time limit in minutes."
414,The expression 25x ndash; 3 can be written as 10x ndash; 6 OR 10x + ndash;6. Write the following expressions in two different ways as the example shows: 43x ndash; 5 The Utah Middle School Math Project,"43x - 5 means four groups of 3x - 5 3x - 5 + 3x - 5 + 3x - 5 + 3x - 5 Then, combine like terms: 3x + 3x + 3x + 3x = 12x -5 + -5 + -5 + -5 = -20 The answer is 12x - 20 = 12x + -20","###Write an explanation to this problem:
The expression 25x ndash; 3 can be written as 10x ndash; 6 OR 10x + ndash;6. Write the following expressions in two different ways as the example shows: 43x ndash; 5 The Utah Middle School Math Project
###Explanation:
43x - 5 means four groups of 3x - 5 3x - 5 + 3x - 5 + 3x - 5 + 3x - 5 Then, combine like terms: 3x + 3x + 3x + 3x = 12x -5 + -5 + -5 + -5 = -20 The answer is 12x - 20 = 12x + -20"
150,"The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?",It is the constant of proportionality. It represents the number of feet in one mile.,"###Write an explanation to this problem:
The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?
###Explanation:
It is the constant of proportionality. It represents the number of feet in one mile."
676,Solve the inequality. Represent the solution on a number line. 42le;x-36 The Utah Middle School Math Project,Solve for x. The number line should be greater than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 42le;x-36 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be greater than and equal to the solution."
755,Write an equation that represents each description. The opposite of negative seven,The opposite of negative seven can be written as --7. The opposite of -7 is 7. This can be written into an expression of --7=7.,"###Write an explanation to this problem:
Write an equation that represents each description. The opposite of negative seven
###Explanation:
The opposite of negative seven can be written as --7. The opposite of -7 is 7. This can be written into an expression of --7=7."
550,Make a mapping of a relation that is a function. Explain how you know. The Utah Middle School Math Project,There are many different mappings that represent functions Each input should have exactly one output,"###Write an explanation to this problem:
Make a mapping of a relation that is a function. Explain how you know. The Utah Middle School Math Project
###Explanation:
There are many different mappings that represent functions Each input should have exactly one output"
488,What does the sign of the slope tell us about the line? The Utah Middle School Math Project,The sign of the slope determines if the line is going up or down from left to right.,"###Write an explanation to this problem:
What does the sign of the slope tell us about the line? The Utah Middle School Math Project
###Explanation:
The sign of the slope determines if the line is going up or down from left to right."
147,Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org,7x + 2 = 91 Lin used the distributive property to solve the equation. To solve she would have to multiply 7 times x and then 7 times 2. 7x + 14. Then subtract 14 from both sides. 7x = 77 Divide both sides by 7 x = 11 For Noah's method he took the same equation but divided each side by 7 first. 7x + 2 = 91 x + 2 = 91/7 x + 2 = 13 -2 - 2 x = 11 Both Lin and Noah solved the equations differently but still were able to come up with the same solution which was 11.,"###Write an explanation to this problem:
Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org
###Explanation:
7x + 2 = 91 Lin used the distributive property to solve the equation. To solve she would have to multiply 7 times x and then 7 times 2. 7x + 14. Then subtract 14 from both sides. 7x = 77 Divide both sides by 7 x = 11 For Noah's method he took the same equation but divided each side by 7 first. 7x + 2 = 91 x + 2 = 91/7 x + 2 = 13 -2 - 2 x = 11 Both Lin and Noah solved the equations differently but still were able to come up with the same solution which was 11."
146,The equation d=3t represents the relationship between the distance d in inches that a snail is from a certain rock and the time t in minutes. What does the number 3 represent?,"The number 3 is a coefficient. It is what we are multiplying our time by to get distance. Since we are getting units of distance from units of time, we must be multiplying by a rate of distance per unit time. This means that 3 is the constant of proportionality or the speed of the snail, 3 inches per minute.","###Write an explanation to this problem:
The equation d=3t represents the relationship between the distance d in inches that a snail is from a certain rock and the time t in minutes. What does the number 3 represent?
###Explanation:
The number 3 is a coefficient. It is what we are multiplying our time by to get distance. Since we are getting units of distance from units of time, we must be multiplying by a rate of distance per unit time. This means that 3 is the constant of proportionality or the speed of the snail, 3 inches per minute."
622,Give a number between -1 and -2. The Utah Middle School Math Project,"Your answer can be any negative number that is less than -1 and greater than -2. Possible answers: -1 1/4, -1.01, -1.99, -3/2","###Write an explanation to this problem:
Give a number between -1 and -2. The Utah Middle School Math Project
###Explanation:
Your answer can be any negative number that is less than -1 and greater than -2. Possible answers: -1 1/4, -1.01, -1.99, -3/2"
792,Write a word problem whose solution is |20| = 20.,Sample response: Kelli flew a kite 20 feet above the ground. Determine the distance between the kite and the ground.,"###Write an explanation to this problem:
Write a word problem whose solution is |20| = 20.
###Explanation:
Sample response: Kelli flew a kite 20 feet above the ground. Determine the distance between the kite and the ground."
636,Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project,"Your answer can be any statistical question, a question that asks for multiple data points that may vary. Example question: How old were you when you lost your first tooth?","###Write an explanation to this problem:
Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project
###Explanation:
Your answer can be any statistical question, a question that asks for multiple data points that may vary. Example question: How old were you when you lost your first tooth?"
348,Write three expressions that are equivalent to 3x + 15 The Utah Middle School Math Project,Any equation that is equivalent to 3x + 15 would be a correct answer here. Some examples include: 3x + 5 3x + 17 - 2 x + 2x + 15,"###Write an explanation to this problem:
Write three expressions that are equivalent to 3x + 15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 3x + 15 would be a correct answer here. Some examples include: 3x + 5 3x + 17 - 2 x + 2x + 15"
463,22% of 54 Estimate the answer. The Utah Middle School Math Project,"20% of 50 is 10, so 22% of 54 is close to 10.","###Write an explanation to this problem:
22% of 54 Estimate the answer. The Utah Middle School Math Project
###Explanation:
20% of 50 is 10, so 22% of 54 is close to 10."
325,"Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.","To try to solve the puzzle, we can define each person's age in terms of Andre's age. Andre's age is x. He is 3 years younger than his brother, so his brother's age would be 3 more years than his age. His brother's age is x + 3. He is 2 years older than his sister. Her age would be his age minus 2 years. His sister's age is x - 2 His mom's age is 1 less than 3 times his brother's age. His brother's age is x + 3. 3 times his brother's age is 3x + 3 1 less than this is 3x + 3 - 1. If you add all of their ages, you get 87. x + x + 3 + x - 2 + 3x + 3 - 1 = 87 First, we should distribute the 3 to the terms in parentheses. x + x + 3 + x - 2 + 3x + 9 - 1 = 87 Next, we should combine like terms. 6x + 9 = 87 Now, we can solve for x by subtracting 9 from both sides. 6x = 78 x = 78/6 = 13 Andre is 13. His brother is 16. His sister is 11. His mother is 47.","###Write an explanation to this problem:
Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.
###Explanation:
To try to solve the puzzle, we can define each person's age in terms of Andre's age. Andre's age is x. He is 3 years younger than his brother, so his brother's age would be 3 more years than his age. His brother's age is x + 3. He is 2 years older than his sister. Her age would be his age minus 2 years. His sister's age is x - 2 His mom's age is 1 less than 3 times his brother's age. His brother's age is x + 3. 3 times his brother's age is 3x + 3 1 less than this is 3x + 3 - 1. If you add all of their ages, you get 87. x + x + 3 + x - 2 + 3x + 3 - 1 = 87 First, we should distribute the 3 to the terms in parentheses. x + x + 3 + x - 2 + 3x + 9 - 1 = 87 Next, we should combine like terms. 6x + 9 = 87 Now, we can solve for x by subtracting 9 from both sides. 6x = 78 x = 78/6 = 13 Andre is 13. His brother is 16. His sister is 11. His mother is 47."
186,Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han's sample is 59 inches. The mean height for Priya's sample is 61 inches. Does it surprise you that the two sample means are different?,"No, because the students would be a variety of heights. I would expect the sample means to be close but not necessarily exactly the same.","###Write an explanation to this problem:
Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han's sample is 59 inches. The mean height for Priya's sample is 61 inches. Does it surprise you that the two sample means are different?
###Explanation:
No, because the students would be a variety of heights. I would expect the sample means to be close but not necessarily exactly the same."
123,Draw a diagram to represent each situation: The number of miles driven this month was a 30% decrease of the number of miles driven last month. Submit your diagram using the tools below.,"Sample Answer: A tape diagram showing 10 equal pieces labeled number of miles driven last month on the top with one below it that is just 7 pieces long and is labeled, number of miles driven this month.","###Write an explanation to this problem:
Draw a diagram to represent each situation: The number of miles driven this month was a 30% decrease of the number of miles driven last month. Submit your diagram using the tools below.
###Explanation:
Sample Answer: A tape diagram showing 10 equal pieces labeled number of miles driven last month on the top with one below it that is just 7 pieces long and is labeled, number of miles driven this month."
762,"Why do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller?","As whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with.","###Write an explanation to this problem:
Why do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller?
###Explanation:
As whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with."
608,Write your own absolute value statement for which there is not a number that makes the statement true. The Utah Middle School Math Project,"One example of an absolute value statement for which there is not a number that makes the statement true is: |x| = -6 The absolute value of x, our number, must always be positive, so -6 makes the statement impossible","###Write an explanation to this problem:
Write your own absolute value statement for which there is not a number that makes the statement true. The Utah Middle School Math Project
###Explanation:
One example of an absolute value statement for which there is not a number that makes the statement true is: |x| = -6 The absolute value of x, our number, must always be positive, so -6 makes the statement impossible"
143,List the sample space for selecting a letter a random from the word PINEAPPLE.,"Sample Space is the letters that make up the word: A,E,I,L,N,P","###Write an explanation to this problem:
List the sample space for selecting a letter a random from the word PINEAPPLE.
###Explanation:
Sample Space is the letters that make up the word: A,E,I,L,N,P"
815,"Below is a statistical question. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use. What is a typical height of female athletes on a team in the most recent international sporting event?",What you would collect is heights of female athletes and you would gather numerical data. The unit of measurement would be both feet and inches.,"###Write an explanation to this problem:
Below is a statistical question. What data would you collect and analyze to answer each question? For numerical data, include the unit of measurement that you would use. What is a typical height of female athletes on a team in the most recent international sporting event?
###Explanation:
What you would collect is heights of female athletes and you would gather numerical data. The unit of measurement would be both feet and inches."
197,"For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7",We know that subtracting a number is the same as adding its opposite. That means we can transform the expression: 20 - 9 + 8 - 7 20 + -9 + 8 + -7,"###Write an explanation to this problem:
For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7
###Explanation:
We know that subtracting a number is the same as adding its opposite. That means we can transform the expression: 20 - 9 + 8 - 7 20 + -9 + 8 + -7"
609,"Here, write the second problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project","Sample Answer: Richard prepares tea for his workday. In the first hour of work, he drank 6 fl. oz. of the tea, which was 25% of the tea he prepared. How many fluid ounces of tea did he prepare? Solution: part: 6 fl.oz. percent: 25% = 0.25 We want to find the amount of tea Richard prepared started with. Note that 25% of the original amount is 6 fl. oz. 25% of the original amount is 0.25 times the original amount. With this information, we can write: 6 fl. oz. = original amount x 0.25 Now, we can solve for the original price: 6 fl. oz. = original amount x 0.25 6 fl. oz./0.25 = original amount 24 fl. oz. = original amount We get that Richard prepared 24 fl. oz. of tea.","###Write an explanation to this problem:
Here, write the second problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Richard prepares tea for his workday. In the first hour of work, he drank 6 fl. oz. of the tea, which was 25% of the tea he prepared. How many fluid ounces of tea did he prepare? Solution: part: 6 fl.oz. percent: 25% = 0.25 We want to find the amount of tea Richard prepared started with. Note that 25% of the original amount is 6 fl. oz. 25% of the original amount is 0.25 times the original amount. With this information, we can write: 6 fl. oz. = original amount x 0.25 Now, we can solve for the original price: 6 fl. oz. = original amount x 0.25 6 fl. oz./0.25 = original amount 24 fl. oz. = original amount We get that Richard prepared 24 fl. oz. of tea."
279,Here is an inequality: -2x > 10. List some values for x that would make this inequality true.,"Note that we can simplify the inequality: -2x > 10 We can divide both sides by -2 to get one side equal to x. Since we are dividing both sides by a negative number, change the inequality sign from > to <. -2x/-2 < 10/-2 x < -5 Therefore, any number less than -5 is a solution.","###Write an explanation to this problem:
Here is an inequality: -2x > 10. List some values for x that would make this inequality true.
###Explanation:
Note that we can simplify the inequality: -2x > 10 We can divide both sides by -2 to get one side equal to x. Since we are dividing both sides by a negative number, change the inequality sign from > to <. -2x/-2 < 10/-2 x < -5 Therefore, any number less than -5 is a solution."
293,"Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.","There are multiple answers to this question, this is just an example: Are you on Instagram? Answers: Yes or No It will produce categorical data because they will be given answer choices to choose from. It will not be an open-ended question.","###Write an explanation to this problem:
Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.
###Explanation:
There are multiple answers to this question, this is just an example: Are you on Instagram? Answers: Yes or No It will produce categorical data because they will be given answer choices to choose from. It will not be an open-ended question."
400,"At Discovery Preschool, parents who have two students enrolled get a discount on the second child. The second child's tuition is 10 dollars less per day than the first child's. If Tess has her two children enrolled for 5 days and her total bill for both children is 200, how much does she pay each day for her second child to attend daycare? Write an equation to solve the question. The Utah Middle School Math Project","The tuition for one day for the first child is t and the tuition for one day for the second child is t-10. Both of these prices must be multiplied by 5, for the 5 days the children are in attendance. Then these values must be added together, and set equal to the total bill. This equation will be 5t+5t-10=200.","###Write an explanation to this problem:
At Discovery Preschool, parents who have two students enrolled get a discount on the second child. The second child's tuition is 10 dollars less per day than the first child's. If Tess has her two children enrolled for 5 days and her total bill for both children is 200, how much does she pay each day for her second child to attend daycare? Write an equation to solve the question. The Utah Middle School Math Project
###Explanation:
The tuition for one day for the first child is t and the tuition for one day for the second child is t-10. Both of these prices must be multiplied by 5, for the 5 days the children are in attendance. Then these values must be added together, and set equal to the total bill. This equation will be 5t+5t-10=200."
122,"Diego made a graph of two quantities that he measured and said, The points all lie on a line except one, which is a little bit above the line. This means that the quantities can't be proportional. Do you agree with Diego? Explain.","Sample answer: I don't agree with Diego, since the quantities could be proportional if the line goes through the origin. Measurements are not perfect and the relationship could be proportional.","###Write an explanation to this problem:
Diego made a graph of two quantities that he measured and said, The points all lie on a line except one, which is a little bit above the line. This means that the quantities can't be proportional. Do you agree with Diego? Explain.
###Explanation:
Sample answer: I don't agree with Diego, since the quantities could be proportional if the line goes through the origin. Measurements are not perfect and the relationship could be proportional."
183,"Kiran wrote the expression x - 10 for this number puzzle: Pick a number, add -2, and multiply by 5. Lin thinks Kiran made a mistake. How can she convince Kiran he made a mistake?","We can choose a value for x and then solve for the answer using Kiran's expression and using the number puzzle's phrasing. If x = 1, then the number puzzle should result in -5: Add -2: 1 + -2 = -1 Multiply by 5: -1 * 5 = -5 The number puzzle gives an answer of -5. If x = 1, then Kiran's expression would give: x - 10 1 - 10 = -9 Kiran's expression gives an answer of -9. The two answers do not match because Kiran's expression is wrong.","###Write an explanation to this problem:
Kiran wrote the expression x - 10 for this number puzzle: Pick a number, add -2, and multiply by 5. Lin thinks Kiran made a mistake. How can she convince Kiran he made a mistake?
###Explanation:
We can choose a value for x and then solve for the answer using Kiran's expression and using the number puzzle's phrasing. If x = 1, then the number puzzle should result in -5: Add -2: 1 + -2 = -1 Multiply by 5: -1 * 5 = -5 The number puzzle gives an answer of -5. If x = 1, then Kiran's expression would give: x - 10 1 - 10 = -9 Kiran's expression gives an answer of -9. The two answers do not match because Kiran's expression is wrong."
202,Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.,Answers will vary.,"###Write an explanation to this problem:
Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.
###Explanation:
Answers will vary."
438,The following equation is given: x/2 ndash; 5 = 10 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project,"I spent half my money on clothes and then 5 on lunch. If I have 10 left over, how much did I start with?","###Write an explanation to this problem:
The following equation is given: x/2 ndash; 5 = 10 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
I spent half my money on clothes and then 5 on lunch. If I have 10 left over, how much did I start with?"
246,"A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games. Design a simulation for this event.","There are several ways that the event can be simulated. One way to simulate the event is to make a spinner with 4 equal sections labeled 1, 2, 3, and 4. Spin the spinner, and record the outcomes as wins if the spinner lands on 1, 2, or 3 or losses when the spinner lands on 4 until one team wins the series. This process can be repeated several times. Other simulations can be used as long as the odds of winning and losing are the same.","###Write an explanation to this problem:
A hockey team has a 75% chance of winning against the opposing team in each game of a playoff series. To win the series, the team must be the first to win 4 games. Design a simulation for this event.
###Explanation:
There are several ways that the event can be simulated. One way to simulate the event is to make a spinner with 4 equal sections labeled 1, 2, 3, and 4. Spin the spinner, and record the outcomes as wins if the spinner lands on 1, 2, or 3 or losses when the spinner lands on 4 until one team wins the series. This process can be repeated several times. Other simulations can be used as long as the odds of winning and losing are the same."
415,"Think about this... In this lesson, you were given the slope and a point on the line and used this information to write the equation of the line in slope-intercept form. In the next lesson, you will be given 2 points and asked to write the equation in slope-intercept form. Write down your thoughts on how you might do this. The Utah Middle School Math Project",First find the slope and then plug in the slope and one of the points to find b. Now you have the slope and y-intercept needed to create the equation in slope-intercept form.,"###Write an explanation to this problem:
Think about this... In this lesson, you were given the slope and a point on the line and used this information to write the equation of the line in slope-intercept form. In the next lesson, you will be given 2 points and asked to write the equation in slope-intercept form. Write down your thoughts on how you might do this. The Utah Middle School Math Project
###Explanation:
First find the slope and then plug in the slope and one of the points to find b. Now you have the slope and y-intercept needed to create the equation in slope-intercept form."
754,Write an inequality that relates the rational numbers. Sixteen degrees Celsius is warmer than zero degrees Celsius.,Since sixteen degrees Celsius is warmer than zero degrees Celsius the inequality is: 16>0,"###Write an explanation to this problem:
Write an inequality that relates the rational numbers. Sixteen degrees Celsius is warmer than zero degrees Celsius.
###Explanation:
Since sixteen degrees Celsius is warmer than zero degrees Celsius the inequality is: 16>0"
129,"Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The y-intercept is increased while the slope is held constant. The Utah Middle School Math Project","The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the y-intercept is increased while the slope is held constant, then we know that the line is being moved up. This can be described as a vertical translation up.","###Write an explanation to this problem:
Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The y-intercept is increased while the slope is held constant. The Utah Middle School Math Project
###Explanation:
The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the y-intercept is increased while the slope is held constant, then we know that the line is being moved up. This can be described as a vertical translation up."
402,"At Discovery Preschool, parents who have two students enrolled get a discount on the second child. The second child's tuition is 10 dollars less per day than the first child's. If Tess has her two children enrolled for 5 days and her total bill for both children is 200, how much does she pay each day for her second child to attend daycare? Write an equation to solve the question. The Utah Middle School Math Project","The tuition for one day for the first child is t and the tuition for one day for the second child is t-10. Both prices must be multiplied by 5, for the 5 days the children are in attendance. Then these values must be added together, and set equal to the total bill. This equation will be 5t+5t-10=200.","###Write an explanation to this problem:
At Discovery Preschool, parents who have two students enrolled get a discount on the second child. The second child's tuition is 10 dollars less per day than the first child's. If Tess has her two children enrolled for 5 days and her total bill for both children is 200, how much does she pay each day for her second child to attend daycare? Write an equation to solve the question. The Utah Middle School Math Project
###Explanation:
The tuition for one day for the first child is t and the tuition for one day for the second child is t-10. Both prices must be multiplied by 5, for the 5 days the children are in attendance. Then these values must be added together, and set equal to the total bill. This equation will be 5t+5t-10=200."
672,Solve the inequality. Represent the solution on a number line. 7/8tge;56 The Utah Middle School Math Project,Solve for t. The number line should be greater than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 7/8tge;56 The Utah Middle School Math Project
###Explanation:
Solve for t. The number line should be greater than and equal to the solution."
834,"A steel beam can be cut to different lengths for a project. Assuming the weight of a steel beam is proportional to its length, what information would you need to know to write an equation that represents this relationship?",The weight and length of at least one beam.,"###Write an explanation to this problem:
A steel beam can be cut to different lengths for a project. Assuming the weight of a steel beam is proportional to its length, what information would you need to know to write an equation that represents this relationship?
###Explanation:
The weight and length of at least one beam."
793,What does the expression + + + represent?,"This is the perimeter, because the perimeter is the length twice plus the width twice.","###Write an explanation to this problem:
What does the expression + + + represent?
###Explanation:
This is the perimeter, because the perimeter is the length twice plus the width twice."
219,Lin wants to know how many games teenagers in the United States have on their phones. What is the population for Lin's question?,All 13 to 19 year olds in the United States who have a phone.,"###Write an explanation to this problem:
Lin wants to know how many games teenagers in the United States have on their phones. What is the population for Lin's question?
###Explanation:
All 13 to 19 year olds in the United States who have a phone."
641,"If you flipped the coin 100 times, how many heads would you expect to get? Explain your answer. The Utah Middle School Math Project","Sample Answer: We would expect to get a head about 1/2 of the time. So, if we flip the coin 100 times, we would expect to get 1001/2 = 50 heads.","###Write an explanation to this problem:
If you flipped the coin 100 times, how many heads would you expect to get? Explain your answer. The Utah Middle School Math Project
###Explanation:
Sample Answer: We would expect to get a head about 1/2 of the time. So, if we flip the coin 100 times, we would expect to get 1001/2 = 50 heads."
778,Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.,Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number of hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25.,"###Write an explanation to this problem:
Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.
###Explanation:
Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number of hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25."
742,The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.,"We don't say that a negative temperature is also below zero. In this case, we can either say the temperature is -10deg;F or we can say the temperature is 10 degrees below zero Fahrenheit.","###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.
###Explanation:
We don't say that a negative temperature is also below zero. In this case, we can either say the temperature is -10deg;F or we can say the temperature is 10 degrees below zero Fahrenheit."
781,"How are the ordered pairs 4, 9 and 4,-9 similar?",The x-coordinates are the same.,"###Write an explanation to this problem:
How are the ordered pairs 4, 9 and 4,-9 similar?
###Explanation:
The x-coordinates are the same."
624,Give a number between -6.1 and -6.2. The Utah Middle School Math Project,"Your answer can be any negative number that is less than -6.1 and greater than -6.2. Possible answers: -6.11, -6.19, -6 1/2","###Write an explanation to this problem:
Give a number between -6.1 and -6.2. The Utah Middle School Math Project
###Explanation:
Your answer can be any negative number that is less than -6.1 and greater than -6.2. Possible answers: -6.11, -6.19, -6 1/2"
717,"Imagine cutting a cube, parallel to the base. What shape is the plane section? The Utah Middle School Math Project",If a cube was cut parallel to the base the resulting cross-section would have to be a square,"###Write an explanation to this problem:
Imagine cutting a cube, parallel to the base. What shape is the plane section? The Utah Middle School Math Project
###Explanation:
If a cube was cut parallel to the base the resulting cross-section would have to be a square"
655,3 x -6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer 3 and multiply it -6 times, so 3 x -6 can be thought of as -3 + -3 + -3 + -3 + -3 + -3","###Write an explanation to this problem:
3 x -6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer 3 and multiply it -6 times, so 3 x -6 can be thought of as -3 + -3 + -3 + -3 + -3 + -3"
386,"Based on your current preparation, summarize the four steps you are expected to complete as part of presenting a statistical study.","Step 1: State my statistical question. My question is based on collecting data that will vary. Step 2: Devise a plan to collect data. I prepared a question to ask the students in my class. Step 3: Summarize my data. I prepared a dot plot of the responses to the question. My dot plot indicated that the responses to my question were skewed to the left; therefore, I used the median of the data distribution to describe my center and the IQR to describe the variability. Step 4: Based on my graphs and numerical summaries, I answered my question.","###Write an explanation to this problem:
Based on your current preparation, summarize the four steps you are expected to complete as part of presenting a statistical study.
###Explanation:
Step 1: State my statistical question. My question is based on collecting data that will vary. Step 2: Devise a plan to collect data. I prepared a question to ask the students in my class. Step 3: Summarize my data. I prepared a dot plot of the responses to the question. My dot plot indicated that the responses to my question were skewed to the left; therefore, I used the median of the data distribution to describe my center and the IQR to describe the variability. Step 4: Based on my graphs and numerical summaries, I answered my question."
827,List two different possibilities for the angle measures of an isosceles triangle.,"One possibility could be 40deg;, 40deg;, 100deg; because 40 + 40 + 100 = 180 and two of the angle measurements are the same. A second possibility could be 20deg;, 20deg;, 140deg; because 20 + 20 + 140 = 180 and two of the angle measurements are the same.","###Write an explanation to this problem:
List two different possibilities for the angle measures of an isosceles triangle.
###Explanation:
One possibility could be 40deg;, 40deg;, 100deg; because 40 + 40 + 100 = 180 and two of the angle measurements are the same. A second possibility could be 20deg;, 20deg;, 140deg; because 20 + 20 + 140 = 180 and two of the angle measurements are the same."
509,Write a situation that can be represented by the rational number. 0 The Utah Middle School Math Project,"Any situation that involves the base level of something, like having no net profit or being at boiling temperature in degrees Fahrenheit, could be represented by 0. One example of a correct situation would be: At sea level.","###Write an explanation to this problem:
Write a situation that can be represented by the rational number. 0 The Utah Middle School Math Project
###Explanation:
Any situation that involves the base level of something, like having no net profit or being at boiling temperature in degrees Fahrenheit, could be represented by 0. One example of a correct situation would be: At sea level."
267,Five students came for after-school tutoring. Priya's teacher assigned each of them the same number of problems to complete. Then she assigned 2 more problems to one of the students. 27 problems were assigned in all. Write an equation for the story.,"Let x be the number of problems the teacher assigned to all of the five students. An additional two problems are assigned to one of the students. So, an expression for the number of problems assigned would be 5x + 2. Also, we are given the total number of problems assigned, which is 27 problems. Now, we can set the expression equal to 27. Therefore, the equation is 5x + 2 = 27","###Write an explanation to this problem:
Five students came for after-school tutoring. Priya's teacher assigned each of them the same number of problems to complete. Then she assigned 2 more problems to one of the students. 27 problems were assigned in all. Write an equation for the story.
###Explanation:
Let x be the number of problems the teacher assigned to all of the five students. An additional two problems are assigned to one of the students. So, an expression for the number of problems assigned would be 5x + 2. Also, we are given the total number of problems assigned, which is 27 problems. Now, we can set the expression equal to 27. Therefore, the equation is 5x + 2 = 27"
772,"Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B","I can add two to the weeks each time to get the next number. I can add 350 to the money to get the next values. In the rows, we have 2:350, which is equal to 1:175. So the money is 175 times larger than the week. I can just multiply the week by 175 to get the amount of money in the account. The ratio used to create the table was 1:175.","###Write an explanation to this problem:
Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B
###Explanation:
I can add two to the weeks each time to get the next number. I can add 350 to the money to get the next values. In the rows, we have 2:350, which is equal to 1:175. So the money is 175 times larger than the week. I can just multiply the week by 175 to get the amount of money in the account. The ratio used to create the table was 1:175."
441,Given information: e = Elisabeth's age now e ndash; 7 = Zack's age now e + 4 = Gail's age now 2e = Bob's age now Equation: e + e - 7 + e + 4 + 2e = 82 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,"Zack is 7 years younger than Elizabeth, Gail is 4 years older than Elizabeth, and Bob is 2 times the age of Elizabeth. The sum of their ages is 82. How old are Elizabeth, Zack, Gail and Bob?","###Write an explanation to this problem:
Given information: e = Elisabeth's age now e ndash; 7 = Zack's age now e + 4 = Gail's age now 2e = Bob's age now Equation: e + e - 7 + e + 4 + 2e = 82 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Zack is 7 years younger than Elizabeth, Gail is 4 years older than Elizabeth, and Bob is 2 times the age of Elizabeth. The sum of their ages is 82. How old are Elizabeth, Zack, Gail and Bob?"
496,Create a representation of a context story that can be modeled by a nonlinear function. The Utah Middle School Math Project,"There are many different stories that can be created that represent a nonlinear function. One possible example is: Kelly hears a rumor about the class receiving extra recess time. She tells two of her friends, who each tell two more of their friends. Each person that hears the rumor tells two more people. How many people have heard the rumor in 4 hours if it is shared every 30 minutes?","###Write an explanation to this problem:
Create a representation of a context story that can be modeled by a nonlinear function. The Utah Middle School Math Project
###Explanation:
There are many different stories that can be created that represent a nonlinear function. One possible example is: Kelly hears a rumor about the class receiving extra recess time. She tells two of her friends, who each tell two more of their friends. Each person that hears the rumor tells two more people. How many people have heard the rumor in 4 hours if it is shared every 30 minutes?"
112,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project","In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1, 2, 5, 10, and so on is a correct answer.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project
###Explanation:
In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1, 2, 5, 10, and so on is a correct answer."
232,"There is a bag of 50 marbles. Andre takes out a marble, records its color, and puts it back in. In 4 trials, he gets a green marble 1 time. Jada takes out a marble, records its color, and puts it back in. In 12 trials, she gets a green marble 5 times. Noah takes out a marble, records its color, and puts it back in. In 9 trials, he gets a green marble 3 times. Estimate the probability of getting a green marble from this bag.","Sample Answer: A good estimate of the probability of getting a green marble comes from combining Andre, Jada, and Noah's trials. They took a marble out of the bag a total of 25 times and got a green marble 9 of those times. So, the probability of getting a green marble appears to be close to 9/25=0.36. Since there are 50 marbles in the bag, it is a reasonable estimate that 18 of the 50 marbles are green, though this is not guaranteed.","###Write an explanation to this problem:
There is a bag of 50 marbles. Andre takes out a marble, records its color, and puts it back in. In 4 trials, he gets a green marble 1 time. Jada takes out a marble, records its color, and puts it back in. In 12 trials, she gets a green marble 5 times. Noah takes out a marble, records its color, and puts it back in. In 9 trials, he gets a green marble 3 times. Estimate the probability of getting a green marble from this bag.
###Explanation:
Sample Answer: A good estimate of the probability of getting a green marble comes from combining Andre, Jada, and Noah's trials. They took a marble out of the bag a total of 25 times and got a green marble 9 of those times. So, the probability of getting a green marble appears to be close to 9/25=0.36. Since there are 50 marbles in the bag, it is a reasonable estimate that 18 of the 50 marbles are green, though this is not guaranteed."
741,"Write an inequality that relates the rational numbers. In December, the total snowfall was 13.2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6.15 inches, respectively.","Since in December, the total snowfall was 13.2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6.15 inches, respectively, the inequality is: 13.2 > 6.15 > 3.7","###Write an explanation to this problem:
Write an inequality that relates the rational numbers. In December, the total snowfall was 13.2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6.15 inches, respectively.
###Explanation:
Since in December, the total snowfall was 13.2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6.15 inches, respectively, the inequality is: 13.2 > 6.15 > 3.7"
607,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. ?,-10,3,8 The Utah Middle School Math Project","In this question, the only requirement is than the number that replaces the ? is an integer that is less than -10. Any number that is farther from 0 than -10 is less than -10. Possible answers include: -11, -12, -25, and so on.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. ?,-10,3,8 The Utah Middle School Math Project
###Explanation:
In this question, the only requirement is than the number that replaces the ? is an integer that is less than -10. Any number that is farther from 0 than -10 is less than -10. Possible answers include: -11, -12, -25, and so on."
373,"To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.","To find more ratios of cups of pink paint to cups of blue paint, you will have to apply a scale factor. For example, 6 to 5 is equivalent to 12 to 10 6*2 = 12 and 5 *2=10 when we apply a scale factor of 2. Here is another example: 6 to 5 is equivalent to 18 to 15 6*3=18 and 5*3=15 Here is one more example: 6 to 5 is equivalent to 3 to 2.5 6 * 1/2 = 3 and 5 * 1/2 = 2.5","###Write an explanation to this problem:
To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.
###Explanation:
To find more ratios of cups of pink paint to cups of blue paint, you will have to apply a scale factor. For example, 6 to 5 is equivalent to 12 to 10 6*2 = 12 and 5 *2=10 when we apply a scale factor of 2. Here is another example: 6 to 5 is equivalent to 18 to 15 6*3=18 and 5*3=15 Here is one more example: 6 to 5 is equivalent to 3 to 2.5 6 * 1/2 = 3 and 5 * 1/2 = 2.5"
233,Explain why zero is considered its own opposite.,"Numbers have an opposite because the number line has a line of symmetry on 0. Since 0 is the mid-point, it's also its own opposite. The distance from 0 to 0 is 0.","###Write an explanation to this problem:
Explain why zero is considered its own opposite.
###Explanation:
Numbers have an opposite because the number line has a line of symmetry on 0. Since 0 is the mid-point, it's also its own opposite. The distance from 0 to 0 is 0."
673,-7 x -2 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer -7 and multiply it -2 times, so -7 x -2 can be thought of as the opposite of -7 x 2, which is -7 + -7. The opposite of -7 + -7 is 7 + 7","###Write an explanation to this problem:
-7 x -2 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -7 and multiply it -2 times, so -7 x -2 can be thought of as the opposite of -7 x 2, which is -7 + -7. The opposite of -7 + -7 is 7 + 7"
317,Draw two polygons that are similar but could be mistaken for not being similar. Submit your drawing using the tools below.,"There are many correct answers to this question. To be similar, the two polygons must be the same shape, but can involve some sorts of transformations to turn one into the other. For example, you could: start with two triangles that are exactly the same and rotate one of them by however many degrees you want. You can then multiply all of the side lengths in the rotated triangle by a certain factor. start with two triangles that are exactly the same and reflect one of them over a horizontal line. You can then multiply all of the side lengths in the reflected triangle by a certain factor.","###Write an explanation to this problem:
Draw two polygons that are similar but could be mistaken for not being similar. Submit your drawing using the tools below.
###Explanation:
There are many correct answers to this question. To be similar, the two polygons must be the same shape, but can involve some sorts of transformations to turn one into the other. For example, you could: start with two triangles that are exactly the same and rotate one of them by however many degrees you want. You can then multiply all of the side lengths in the rotated triangle by a certain factor. start with two triangles that are exactly the same and reflect one of them over a horizontal line. You can then multiply all of the side lengths in the reflected triangle by a certain factor."
648,Create a statistical question that could be answered by collecting numerical data. The Utah Middle School Math Project,"A statistical question is one that can be answered by collecting a data set of varying answers. If the data is numerical, each piece of data is a number that represents a count or measure of something. One example of a statistical question that can be answered with numerical data: How many hours does each person in your class spend on the internet on a given day?","###Write an explanation to this problem:
Create a statistical question that could be answered by collecting numerical data. The Utah Middle School Math Project
###Explanation:
A statistical question is one that can be answered by collecting a data set of varying answers. If the data is numerical, each piece of data is a number that represents a count or measure of something. One example of a statistical question that can be answered with numerical data: How many hours does each person in your class spend on the internet on a given day?"
410,The Utah Middle School Math Project,"Choose four arbitrary values for x such as 0,1,2,3 and solve for y for each of these values, and put these four points in the chart. Then plot these points on the graph, and connect the points in a line.","###Write an explanation to this problem:
The Utah Middle School Math Project
###Explanation:
Choose four arbitrary values for x such as 0,1,2,3 and solve for y for each of these values, and put these four points in the chart. Then plot these points on the graph, and connect the points in a line."
764,Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1,"-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2","###Write an explanation to this problem:
Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1
###Explanation:
-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2"
358,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The greater the distance a sprinter has to run the more time it takes to finish the race The Utah Middle School Math Project,"Distance is independent variable, because the sprinter can go any reasonable distance within any time. The Time is the dependent variable.","###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The greater the distance a sprinter has to run the more time it takes to finish the race The Utah Middle School Math Project
###Explanation:
Distance is independent variable, because the sprinter can go any reasonable distance within any time. The Time is the dependent variable."
258,The weather forecast says there is a 75% chance it will rain later today. Draw a spinner you could use to simulate this probability. Submit your drawing using the tools below.,There are different ways to represent the given information on a spinner. One possible answer is shown below. It is a circle spinner with 3/4 colored in blue and labeled rain. The other 1/4 is yellow and labeled no rain.,"###Write an explanation to this problem:
The weather forecast says there is a 75% chance it will rain later today. Draw a spinner you could use to simulate this probability. Submit your drawing using the tools below.
###Explanation:
There are different ways to represent the given information on a spinner. One possible answer is shown below. It is a circle spinner with 3/4 colored in blue and labeled rain. The other 1/4 is yellow and labeled no rain."
627,Write three numbers that are less than -1. The Utah Middle School Math Project,"Possible answers: -2, -10, -4/3, -5.75","###Write an explanation to this problem:
Write three numbers that are less than -1. The Utah Middle School Math Project
###Explanation:
Possible answers: -2, -10, -4/3, -5.75"
632,Create a statistical question that could be answered by collecting categorical data. The Utah Middle School Math Project,"A statistical question is one that can be answered by collecting a data set of varying answers. If the data is categorical, each piece of data is a word or category. One example of a statistical question that can be answered with categorical data: What color are the eyes of each person in your class?","###Write an explanation to this problem:
Create a statistical question that could be answered by collecting categorical data. The Utah Middle School Math Project
###Explanation:
A statistical question is one that can be answered by collecting a data set of varying answers. If the data is categorical, each piece of data is a word or category. One example of a statistical question that can be answered with categorical data: What color are the eyes of each person in your class?"
282,"Think about your work today, and write your best definition of area.",Area is the amount of space inside a shape or polygon. It is measured in square units.,"###Write an explanation to this problem:
Think about your work today, and write your best definition of area.
###Explanation:
Area is the amount of space inside a shape or polygon. It is measured in square units."
376,"Using circles and squares, create pictures that represent the ratio given. The ratio of circles to squares is 3:5. Draw your pictures on paper, take a picture, and upload it using the image upload icon If you do not have the ability to upload an image of your work type Picture is on paper. The Utah Middle School Math Project",DO NOT DO THIS ON SEPARATE PAPER. TYPE C for CIRCLE and S for SQUARE into the box making the correct ratio.,"###Write an explanation to this problem:
Using circles and squares, create pictures that represent the ratio given. The ratio of circles to squares is 3:5. Draw your pictures on paper, take a picture, and upload it using the image upload icon If you do not have the ability to upload an image of your work type Picture is on paper. The Utah Middle School Math Project
###Explanation:
DO NOT DO THIS ON SEPARATE PAPER. TYPE C for CIRCLE and S for SQUARE into the box making the correct ratio."
384,Write a story that matches the expressions and equations. World Languages Number of years: t of students in French: 160 - 9t of students in Spanish: 85 + 6t 160 - 9t = 85 + 6t The Utah Middle School Math Project,"Initially at t = 0 years, there must be 160 students in French and 85 students in Spanish. Each year, the number of students in French will decrease by 9 and the number of students in Spanish will increase by 6. So 160 - 9t is the number of students in French after t years and 85 + 6t is the number of students in Spanish after t years. When 160 - 9t = 85 + 6t, there will be the same number f students in French class as there are in Spanish class. After how many years will the number of students in French class be the same as the number of students in Spanish class?","###Write an explanation to this problem:
Write a story that matches the expressions and equations. World Languages Number of years: t of students in French: 160 - 9t of students in Spanish: 85 + 6t 160 - 9t = 85 + 6t The Utah Middle School Math Project
###Explanation:
Initially at t = 0 years, there must be 160 students in French and 85 students in Spanish. Each year, the number of students in French will decrease by 9 and the number of students in Spanish will increase by 6. So 160 - 9t is the number of students in French after t years and 85 + 6t is the number of students in Spanish after t years. When 160 - 9t = 85 + 6t, there will be the same number f students in French class as there are in Spanish class. After how many years will the number of students in French class be the same as the number of students in Spanish class?"
224,"Decide which measure of center makes the most sense to use based on the distribution of your sample. Discuss your thinking with your partner. If you disagree, work to reach an agreement. copied for free from openupresources.org",I think the mean would be the best measure because there were no outliers in the data.,"###Write an explanation to this problem:
Decide which measure of center makes the most sense to use based on the distribution of your sample. Discuss your thinking with your partner. If you disagree, work to reach an agreement. copied for free from openupresources.org
###Explanation:
I think the mean would be the best measure because there were no outliers in the data."
810,Invent a data set with five numbers that has a mean of 10 and a median of 12.,"There are several data sets that could work for this scenario but here is an example of one that would work: 3, 11, 12, 12, 12 12 is the median because it is the middle number. 10 is the mean because the average add up all the values and divide by 5 you would get 10.","###Write an explanation to this problem:
Invent a data set with five numbers that has a mean of 10 and a median of 12.
###Explanation:
There are several data sets that could work for this scenario but here is an example of one that would work: 3, 11, 12, 12, 12 12 is the median because it is the middle number. 10 is the mean because the average add up all the values and divide by 5 you would get 10."
698,"Ramon is collecting donations for a charity. He is hoping to raise 250. If he has already collected 187 in donations, how much more does he need to collect? Write an equation to solve the problem. The Utah Middle School Math Project","Ramon already has 187, and needs m more to get to 250. This means that 187+m=250","###Write an explanation to this problem:
Ramon is collecting donations for a charity. He is hoping to raise 250. If he has already collected 187 in donations, how much more does he need to collect? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Ramon already has 187, and needs m more to get to 250. This means that 187+m=250"
472,Create your own context or story that represents a relation that is a function. Write your story.,"To be a function, whatever you chose to be the independent variable x must have only one corresponding dependent variable y.","###Write an explanation to this problem:
Create your own context or story that represents a relation that is a function. Write your story.
###Explanation:
To be a function, whatever you chose to be the independent variable x must have only one corresponding dependent variable y."
347,A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour. Name two quantities in this situation that are in a functional relationship. Copied for free from openupresources.org,"The amount of yeast and the amount of flour are in a functional relationship. This means that if we know the amount of flour, then we can find the corresponding amount of yeast using a function, or the reverse.","###Write an explanation to this problem:
A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour. Name two quantities in this situation that are in a functional relationship. Copied for free from openupresources.org
###Explanation:
The amount of yeast and the amount of flour are in a functional relationship. This means that if we know the amount of flour, then we can find the corresponding amount of yeast using a function, or the reverse."
505,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Write your own relationship that contains an independent and dependent variable. The Utah Middle School Math Project,"Possible Example, The size of a balloon depends on how long you are inflating it.","###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Write your own relationship that contains an independent and dependent variable. The Utah Middle School Math Project
###Explanation:
Possible Example, The size of a balloon depends on how long you are inflating it."
639,You are starting a small business mowing lawns in your neighborhood for the summer. Create two statistical questions that will help make your lawn mowing business a success. The Utah Middle School Math Project,"One example of an important question to ask would be: How many times in a summer does each house like to mow their lawn? How much is each person willing to pay someone to mow their lawn? You can collect data which will vary from house to house in order to answer these questions. They will help make the lawn mowing business a success by helping you figure out how many lawns you can mow, and if you know the amount of money you can make per lawn, you can estimate how much money you will make and make a budget from that.","###Write an explanation to this problem:
You are starting a small business mowing lawns in your neighborhood for the summer. Create two statistical questions that will help make your lawn mowing business a success. The Utah Middle School Math Project
###Explanation:
One example of an important question to ask would be: How many times in a summer does each house like to mow their lawn? How much is each person willing to pay someone to mow their lawn? You can collect data which will vary from house to house in order to answer these questions. They will help make the lawn mowing business a success by helping you figure out how many lawns you can mow, and if you know the amount of money you can make per lawn, you can estimate how much money you will make and make a budget from that."
841,"The equation c=2.95g shows how much it costs to buy gas at a gas station on a certain day. In the equation, c represents the cost in dollars, and g represents how many gallons of gas were purchased. Write down at least four gallons of gas, cost pairs that fit this relationship.","1, 2.95 2,5.80 4, 10.60 0,0","###Write an explanation to this problem:
The equation c=2.95g shows how much it costs to buy gas at a gas station on a certain day. In the equation, c represents the cost in dollars, and g represents how many gallons of gas were purchased. Write down at least four gallons of gas, cost pairs that fit this relationship.
###Explanation:
1, 2.95 2,5.80 4, 10.60 0,0"
790,What is a net? Describe it in your own words.,Example: A net is a two-dimensional figure that can be folded to create a three-dimensional solid.,"###Write an explanation to this problem:
What is a net? Describe it in your own words.
###Explanation:
Example: A net is a two-dimensional figure that can be folded to create a three-dimensional solid."
832,Represent 56 / 8 = 7 using subtraction. Explain your reasoning.,56 - 7 - 7 - 7 - 7 - 7 - 7 - 7 - 7 = 0 because 56 - 7 = 49; 49 - 7 = 42; 42 - 7 = 35; 35 - 7 = 28; 28 - 7 = 21; 21 - 7 = 14; 14 - 7 = 7; 7 - 7 = 0 OR 56 - 8 - 8 - 8 - 8 - 8 - 8 - 8 = 0 because 56 - 8 = 48; 48 - 8 = 40; 40 - 8 = 32; 32 - 8 = 24; 24 - 8 = 16; 16 - 8 = 8; 8 - 8 = 0,"###Write an explanation to this problem:
Represent 56 / 8 = 7 using subtraction. Explain your reasoning.
###Explanation:
56 - 7 - 7 - 7 - 7 - 7 - 7 - 7 - 7 = 0 because 56 - 7 = 49; 49 - 7 = 42; 42 - 7 = 35; 35 - 7 = 28; 28 - 7 = 21; 21 - 7 = 14; 14 - 7 = 7; 7 - 7 = 0 OR 56 - 8 - 8 - 8 - 8 - 8 - 8 - 8 = 0 because 56 - 8 = 48; 48 - 8 = 40; 40 - 8 = 32; 32 - 8 = 24; 24 - 8 = 16; 16 - 8 = 8; 8 - 8 = 0"
619,Write a situation that can be represented by the rational number. 3.25 The Utah Middle School Math Project,"Any situation that could be represented by the rational number 3.25 just needs to involve words like deposit, increase, profit, and so on that would indicate a positive number. One example of a correct situation would be: 3.25 feet ahead","###Write an explanation to this problem:
Write a situation that can be represented by the rational number. 3.25 The Utah Middle School Math Project
###Explanation:
Any situation that could be represented by the rational number 3.25 just needs to involve words like deposit, increase, profit, and so on that would indicate a positive number. One example of a correct situation would be: 3.25 feet ahead"
728,Describe some things you could notice in two polygons that would help you decide that they were not scaled copies.,"If they were not the same shape for example, if one was a triangle and one was a square, they could not be scaled copies. I could find an angle measure in one that was not an angle measure of the other. I could find that a different scale factor would have to be used on one part of the pair than on another.","###Write an explanation to this problem:
Describe some things you could notice in two polygons that would help you decide that they were not scaled copies.
###Explanation:
If they were not the same shape for example, if one was a triangle and one was a square, they could not be scaled copies. I could find an angle measure in one that was not an angle measure of the other. I could find that a different scale factor would have to be used on one part of the pair than on another."
645,"In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 6 Transformed Equation: x + 2 = 8 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 2 has been added to x. 2 has also been added to 6 on the right side, to make 8. The action was: Add 2 to both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 6 Transformed Equation: x + 2 = 8 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 2 has been added to x. 2 has also been added to 6 on the right side, to make 8. The action was: Add 2 to both sides of the equation."
721,Choose a situation that could be described by the following ratio. Write a sentence to describe the ratio in the context of the situation you chose. 1 to 2,A sample could be for every one person there are 2 eyes.,"###Write an explanation to this problem:
Choose a situation that could be described by the following ratio. Write a sentence to describe the ratio in the context of the situation you chose. 1 to 2
###Explanation:
A sample could be for every one person there are 2 eyes."
556,Write a phrase for the following algebraic expression 15 - 2x The Utah Middle School Math Project,15 - 2x is 2 times a number x less than 15.,"###Write an explanation to this problem:
Write a phrase for the following algebraic expression 15 - 2x The Utah Middle School Math Project
###Explanation:
15 - 2x is 2 times a number x less than 15."
814,"Sixth-grade students were asked, What grade are you in? Explain why this is not a statistical question.",This is NOT a statistical question because every answer would be 6th grade which will not produce a variety of answers. There would be no data to interpret with this question.,"###Write an explanation to this problem:
Sixth-grade students were asked, What grade are you in? Explain why this is not a statistical question.
###Explanation:
This is NOT a statistical question because every answer would be 6th grade which will not produce a variety of answers. There would be no data to interpret with this question."
577,"Simplify the following expressions using two different methods. Three multiplied by the difference of fifty and one First, show your work for each method. The Utah Middle School Math Project","The difference of fifty and one is 50 - 1, so three multiplied by the difference of fifty and one 350 - 1 One method is to first distribute the 3 to the terms within the parentheses: 350 - 1 = 350 - 31 = 150 - 3 = 147 Another method is to first combine the terms in the parentheses and then distribute the 3: 350 - 1 = 349 = 147","###Write an explanation to this problem:
Simplify the following expressions using two different methods. Three multiplied by the difference of fifty and one First, show your work for each method. The Utah Middle School Math Project
###Explanation:
The difference of fifty and one is 50 - 1, so three multiplied by the difference of fifty and one 350 - 1 One method is to first distribute the 3 to the terms within the parentheses: 350 - 1 = 350 - 31 = 150 - 3 = 147 Another method is to first combine the terms in the parentheses and then distribute the 3: 350 - 1 = 349 = 147"
85,"The height of the water in a tank decreases by 3.5 cm each day. When the tank is full, the water is 10 m deep. The water tank needs to be refilled when the water height drops below 4 m. Write a question that could be answered by solving the equation 10 - 0.035d = 4.",How many days will pass before the water tank needs to be refilled?,"###Write an explanation to this problem:
The height of the water in a tank decreases by 3.5 cm each day. When the tank is full, the water is 10 m deep. The water tank needs to be refilled when the water height drops below 4 m. Write a question that could be answered by solving the equation 10 - 0.035d = 4.
###Explanation:
How many days will pass before the water tank needs to be refilled?"
242,"A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.","If 3 out of 50 people won a small prize, that means that 3 out of 50 ducks had a red mark on them. We can scale this ratio of 3:50 by a factor of 3.2 to get the equivalent ratio of 9.6:160. This means that there are likely 9 to 10 ducks that have red marks out of 160 total ducks.","###Write an explanation to this problem:
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.
###Explanation:
If 3 out of 50 people won a small prize, that means that 3 out of 50 ducks had a red mark on them. We can scale this ratio of 3:50 by a factor of 3.2 to get the equivalent ratio of 9.6:160. This means that there are likely 9 to 10 ducks that have red marks out of 160 total ducks."
159,30 + -30 = 0. Enter another sum of two numbers that equals 0. copied for free from openupresources.org,Any two numbers that have the same absolute value but opposite signs will equal 0 when added together. Sample Answer: 45+-45 = 0,"###Write an explanation to this problem:
30 + -30 = 0. Enter another sum of two numbers that equals 0. copied for free from openupresources.org
###Explanation:
Any two numbers that have the same absolute value but opposite signs will equal 0 when added together. Sample Answer: 45+-45 = 0"
524,Describe in your own words what it means for two figures to be similar. The Utah Middle School Math Project,Example; Two figures are said to be similar if there is a sequence of rigid motions and dilations that take one figure onto the other. Corresponding angles are congruent and corresponding sides are proportional the ratios of corresponding sides are all the same and are equal to the scale factor.,"###Write an explanation to this problem:
Describe in your own words what it means for two figures to be similar. The Utah Middle School Math Project
###Explanation:
Example; Two figures are said to be similar if there is a sequence of rigid motions and dilations that take one figure onto the other. Corresponding angles are congruent and corresponding sides are proportional the ratios of corresponding sides are all the same and are equal to the scale factor."
35,Priya has completed 9 exam questions. This is 60% of the questions on the exam. Write an equation representing this situation. Explain the meaning of any variables you use.,0.6x=9 Change 60% to a decimal 0.6 of means to multiply,"###Write an explanation to this problem:
Priya has completed 9 exam questions. This is 60% of the questions on the exam. Write an equation representing this situation. Explain the meaning of any variables you use.
###Explanation:
0.6x=9 Change 60% to a decimal 0.6 of means to multiply"
540,"Create an algebraic expression that has four terms and meets the following requirements: the expression has no like terms, the expression contains a constant, one of the coefficients is 3. The Utah Middle School Math Project",Example: x+2y+3z+4,"###Write an explanation to this problem:
Create an algebraic expression that has four terms and meets the following requirements: the expression has no like terms, the expression contains a constant, one of the coefficients is 3. The Utah Middle School Math Project
###Explanation:
Example: x+2y+3z+4"
170,Explain why zero is considered its own opposite.,0 is a neutral number. The opposite of 0 is already 0.,"###Write an explanation to this problem:
Explain why zero is considered its own opposite.
###Explanation:
0 is a neutral number. The opposite of 0 is already 0."
654,"In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: 5 = x Transformed Equation: 0 = x - 5 Action: ______ The Utah Middle School Math Project","On the right side of the equation, 5 has been subtracted from x. On the left side, 5 has been subtracted from 5, which results in 0. The action was: Subtract 5 from both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: 5 = x Transformed Equation: 0 = x - 5 Action: ______ The Utah Middle School Math Project
###Explanation:
On the right side of the equation, 5 has been subtracted from x. On the left side, 5 has been subtracted from 5, which results in 0. The action was: Subtract 5 from both sides of the equation."
730,Find 3 different ratios that are equivalent to 7 : 3,"Sample response: Multiply both terms of the ratio, 7 and 3, by the same value, such as 14:6, 21:9, 28:12","###Write an explanation to this problem:
Find 3 different ratios that are equivalent to 7 : 3
###Explanation:
Sample response: Multiply both terms of the ratio, 7 and 3, by the same value, such as 14:6, 21:9, 28:12"
722,Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.,Ratio of the number of hits to the total number of swings is 𝟏𝟓: 𝟐𝟓. Ratio of the number hits to the number of misses is 𝟏𝟓: 𝟏𝟎. Ratio of the number of misses to the number of hits is 𝟏𝟎: 𝟏𝟓. Ratio of the number of misses to the total number of swings is 𝟏𝟎: 𝟐5,"###Write an explanation to this problem:
Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.
###Explanation:
Ratio of the number of hits to the total number of swings is 𝟏𝟓: 𝟐𝟓. Ratio of the number hits to the number of misses is 𝟏𝟓: 𝟏𝟎. Ratio of the number of misses to the number of hits is 𝟏𝟎: 𝟏𝟓. Ratio of the number of misses to the total number of swings is 𝟏𝟎: 𝟐5"
803,"5. 60% of x is equal to 87. a. Write an equation that expresses the relationship between 60%, x, and 87. copied for free from openupresources.org","60% of x means to multiply 60% and x. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.6x=87 would be the equation that expresses the relationship between 60%, x, and 87.","###Write an explanation to this problem:
5. 60% of x is equal to 87. a. Write an equation that expresses the relationship between 60%, x, and 87. copied for free from openupresources.org
###Explanation:
60% of x means to multiply 60% and x. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.6x=87 would be the equation that expresses the relationship between 60%, x, and 87."
95,What causes a repeating decimal in the long division algorithm?,"When following the long division algorithm, you basically divide, multiply, subtract and bring down. Many times, after you subtract, there is a remainder. If, after you subtract, you end up with the same remainder as the time before, and you are bringing down the same number as before, you will find that the algorithm will just keep producing the same digit in the quotient over and over again because you are dividing the same number over and over again. This causes a repeating decimal. As soon as you recognize this pattern, you can stop dividing because you will know that the digits in the quotient will continue to repeat on and on and on.","###Write an explanation to this problem:
What causes a repeating decimal in the long division algorithm?
###Explanation:
When following the long division algorithm, you basically divide, multiply, subtract and bring down. Many times, after you subtract, there is a remainder. If, after you subtract, you end up with the same remainder as the time before, and you are bringing down the same number as before, you will find that the algorithm will just keep producing the same digit in the quotient over and over again because you are dividing the same number over and over again. This causes a repeating decimal. As soon as you recognize this pattern, you can stop dividing because you will know that the digits in the quotient will continue to repeat on and on and on."
563,Determine if the relation or situation defines a function. Justify your answer. You know your cousin lives at the zip code 12345 so you type it in Google to find your cousin's full address. Is address a function of zip code? The Utah Middle School Math Project,"No, the data does not describe a function More than one address relates to a zip code The zip code is the input and there is more than one address or output for each zip code","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. You know your cousin lives at the zip code 12345 so you type it in Google to find your cousin's full address. Is address a function of zip code? The Utah Middle School Math Project
###Explanation:
No, the data does not describe a function More than one address relates to a zip code The zip code is the input and there is more than one address or output for each zip code"
240,"For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.",There are many correct answers for this question. Remember that a population is the group of people/things that you are interested in asking questions about. The sample is a smaller part from that population that you think could represent that population. One example of a correct answer is: Population 1: Prices for apples at all stores in our state. Population 2: Prices for all fruit at these two stores.,"###Write an explanation to this problem:
For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.
###Explanation:
There are many correct answers for this question. Remember that a population is the group of people/things that you are interested in asking questions about. The sample is a smaller part from that population that you think could represent that population. One example of a correct answer is: Population 1: Prices for apples at all stores in our state. Population 2: Prices for all fruit at these two stores."
574,Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project,"Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad. How much money will he have left?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project
###Explanation:
Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad. How much money will he have left?"
690,"A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project","Since the number of tables is unknown, we can use a variable, t, to represent this value. There are 8 students at each table, and the total number of students is 120. This means that: 8 students * number of tables = 120 students total 8t=120","###Write an explanation to this problem:
A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Since the number of tables is unknown, we can use a variable, t, to represent this value. There are 8 students at each table, and the total number of students is 120. This means that: 8 students * number of tables = 120 students total 8t=120"
460,Given information: x = Amount of money Jaime earned 1/5x = one-fifth of the money Jaime spent on clothes 2/5x = two-fifths of the money Jaime spent on shoes Equation: 1/5x + 2/5x = 165 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,"Jaime earned some money. She spent 1/5 of that money on clothes and 2/5 of it on shoes. If she spent a total of 165, how much money did she earn?","###Write an explanation to this problem:
Given information: x = Amount of money Jaime earned 1/5x = one-fifth of the money Jaime spent on clothes 2/5x = two-fifths of the money Jaime spent on shoes Equation: 1/5x + 2/5x = 165 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Jaime earned some money. She spent 1/5 of that money on clothes and 2/5 of it on shoes. If she spent a total of 165, how much money did she earn?"
553,Write a phrase for the following algebraic expression - 7 The Utah Middle School Math Project,x - 7 is seven less than a number x.,"###Write an explanation to this problem:
Write a phrase for the following algebraic expression - 7 The Utah Middle School Math Project
###Explanation:
x - 7 is seven less than a number x."
819,A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.,Choice One: 1 cm * 1 cm * 50 cm Choice Two: 1 cm * 2 cm * 25 cm Choice Three: 1 cm * 5 cm * 10 cm Choice Four: 2 cm * 5 cm * 5 cm,"###Write an explanation to this problem:
A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.
###Explanation:
Choice One: 1 cm * 1 cm * 50 cm Choice Two: 1 cm * 2 cm * 25 cm Choice Three: 1 cm * 5 cm * 10 cm Choice Four: 2 cm * 5 cm * 5 cm"
206,"Use the equation 135 * 42 = 5,670 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute 1.35 * 4.2.","We know that you can ignore decimal places when you multiply until you have your product. Then count the number of decimal places in the factors and more the decimal over that many times in the product. In this case, they just need to add the 3 decimal places to the product of 5,670 to make it 5.67.","###Write an explanation to this problem:
Use the equation 135 * 42 = 5,670 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute 1.35 * 4.2.
###Explanation:
We know that you can ignore decimal places when you multiply until you have your product. Then count the number of decimal places in the factors and more the decimal over that many times in the product. In this case, they just need to add the 3 decimal places to the product of 5,670 to make it 5.67."
392,The expressions below show the grams of fat in sandwiches at a popular fast food restaurant. Use these expressions and the equation to write a story. Fast Food Calories: Crispy Chicken: f Single burger with cheese: f + 11 Double burger with cheese: 2f 3f + 2f + 11 + 42f = 204 g. The Utah Middle School Math Project,"The given expressions can be put into words that create a story. From the expressions, we know a crispy chicken has f fat grams. The expressions also show that a single burger with cheese has 11 more fat grams than a crispy chicken, while a double burger with cheese has two times more fat grams than a crispy chicken. The equation shows that 3 crispy chickens plus 2 single burgers with cheese plus 4 double burgers with cheese have a total of 204 fat grams.","###Write an explanation to this problem:
The expressions below show the grams of fat in sandwiches at a popular fast food restaurant. Use these expressions and the equation to write a story. Fast Food Calories: Crispy Chicken: f Single burger with cheese: f + 11 Double burger with cheese: 2f 3f + 2f + 11 + 42f = 204 g. The Utah Middle School Math Project
###Explanation:
The given expressions can be put into words that create a story. From the expressions, we know a crispy chicken has f fat grams. The expressions also show that a single burger with cheese has 11 more fat grams than a crispy chicken, while a double burger with cheese has two times more fat grams than a crispy chicken. The equation shows that 3 crispy chickens plus 2 single burgers with cheese plus 4 double burgers with cheese have a total of 204 fat grams."
397,"During her Tuesday shift at Sweater Barn, Fiona sells the same amount of sweaters per hour. Two hours into her shift Fiona has sold 8 sweaters. Find and describe the rate of change for this relationship. The Utah Middle School Math Project","We know that in two hours, Fiona sold 8 sweaters, but she sold the same amount each hour. This means we can divide 8/2 to find that Fiona sold 4 sweaters each hour. The rate of change for this relationship is 4 sweaters sold every hour.","###Write an explanation to this problem:
During her Tuesday shift at Sweater Barn, Fiona sells the same amount of sweaters per hour. Two hours into her shift Fiona has sold 8 sweaters. Find and describe the rate of change for this relationship. The Utah Middle School Math Project
###Explanation:
We know that in two hours, Fiona sold 8 sweaters, but she sold the same amount each hour. This means we can divide 8/2 to find that Fiona sold 4 sweaters each hour. The rate of change for this relationship is 4 sweaters sold every hour."
723,Write two ratios that are equivalent to 3:11.,Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 3x2:11x2 = 6:22 3x3:11x3 = 9:33 Or any ratio that simplifies to 3:11,"###Write an explanation to this problem:
Write two ratios that are equivalent to 3:11.
###Explanation:
Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 3x2:11x2 = 6:22 3x3:11x3 = 9:33 Or any ratio that simplifies to 3:11"
217,Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.,"Elena could have the computer generate 3 random integers between 1 and 100. If at least 2 of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and estimate the probability as the proportion of trials for which at least 2 of the numbers are between 1 and 15.","###Write an explanation to this problem:
Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.
###Explanation:
Elena could have the computer generate 3 random integers between 1 and 100. If at least 2 of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and estimate the probability as the proportion of trials for which at least 2 of the numbers are between 1 and 15."
4,Find a value for a that makes the statement true. n / 6 is greater than 1,Any number divided by itself =1 so 6 divided by 6 =1. Any values greater than 6 would be greater than 1 when you divide. A value that could work would be anything a>6,"###Write an explanation to this problem:
Find a value for a that makes the statement true. n / 6 is greater than 1
###Explanation:
Any number divided by itself =1 so 6 divided by 6 =1. Any values greater than 6 would be greater than 1 when you divide. A value that could work would be anything a>6"
642,"If you flipped the coin 100 times, how many heads would you expect to get? Explain your answer. The Utah Middle School Math Project","Sample Answer: We would expect to get a head about 1/2 of the time. So, if we flip the coin 100 times, we would expect to get 1001/2 = 50 heads.","###Write an explanation to this problem:
If you flipped the coin 100 times, how many heads would you expect to get? Explain your answer. The Utah Middle School Math Project
###Explanation:
Sample Answer: We would expect to get a head about 1/2 of the time. So, if we flip the coin 100 times, we would expect to get 1001/2 = 50 heads."
763,Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.,"Since a loss of 500 in the stock market is worse than a gain of 200 in the stock market, the inequality is: -500 < 200","###Write an explanation to this problem:
Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.
###Explanation:
Since a loss of 500 in the stock market is worse than a gain of 200 in the stock market, the inequality is: -500 < 200"
612,"The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. -3,?,0,5 The Utah Middle School Math Project","In this question, the ? falls between -3 and 0, so the integer that replaces the ? must be greater than -3 but less than 0. The only two integers where this is true are -2 and -1.","###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. -3,?,0,5 The Utah Middle School Math Project
###Explanation:
In this question, the ? falls between -3 and 0, so the integer that replaces the ? must be greater than -3 but less than 0. The only two integers where this is true are -2 and -1."
546,"Here, write the first problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project","Sample Answer: Tom wants to buy a laptop that costs 800. Due to his membership, he can use a 15% discount on his purchase. How much did he pay for the laptop? Solution: whole: 800 percent: 15% = 0.15 First, we find the amount he saved, we multiply the whole by the percent: whole x percent = 800 x 0.15 = 120 Then, to find the amount he paid, we subtract the amount he saved from the original price, which is the whole: amount paid = original price - amount paid = 800 - 120 = 680 We get that Tom paid 680 for the laptop.","###Write an explanation to this problem:
Here, write the first problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Tom wants to buy a laptop that costs 800. Due to his membership, he can use a 15% discount on his purchase. How much did he pay for the laptop? Solution: whole: 800 percent: 15% = 0.15 First, we find the amount he saved, we multiply the whole by the percent: whole x percent = 800 x 0.15 = 120 Then, to find the amount he paid, we subtract the amount he saved from the original price, which is the whole: amount paid = original price - amount paid = 800 - 120 = 680 We get that Tom paid 680 for the laptop."
683,Create a context for the numeric representation. 5001 ndash; 5001/5 = 400 The Utah Middle School Math Project,"Sample Answer: If a person has 500 apples, then loses 1/5 of the apples, this numeric expression describes how many apples they have left.","###Write an explanation to this problem:
Create a context for the numeric representation. 5001 ndash; 5001/5 = 400 The Utah Middle School Math Project
###Explanation:
Sample Answer: If a person has 500 apples, then loses 1/5 of the apples, this numeric expression describes how many apples they have left."
98,Write a sentence to answer the question: How much warmer is 82 than 40?,The distance between 82 and 40 can be found by subtracting 82 -40=42 82 is 42 degrees warmer than 40.,"###Write an explanation to this problem:
Write a sentence to answer the question: How much warmer is 82 than 40?
###Explanation:
The distance between 82 and 40 can be found by subtracting 82 -40=42 82 is 42 degrees warmer than 40."
573,Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project,"Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad.","###Write an explanation to this problem:
Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project
###Explanation:
Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad."
406,"Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project","Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64","###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64"
502,Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project,A triangular prism cut parallel to the base will always result in a traingular cross-section.,"###Write an explanation to this problem:
Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project
###Explanation:
A triangular prism cut parallel to the base will always result in a traingular cross-section."
47,"A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches. Is the baseball's volume greater than, less than, or equal to 2.93 cubic inches? Explain how you know. Copied for free from openupresources.org","The baseball fits inside the cube, and the cube's volume is 2.93 cubic inches so the volume of the baseball would have to be less than 2.93 cubic units.","###Write an explanation to this problem:
A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches. Is the baseball's volume greater than, less than, or equal to 2.93 cubic inches? Explain how you know. Copied for free from openupresources.org
###Explanation:
The baseball fits inside the cube, and the cube's volume is 2.93 cubic inches so the volume of the baseball would have to be less than 2.93 cubic units."
32,"Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.","Andre is 13, his brother is 16, his sister is 11, and his mom is 47.","###Write an explanation to this problem:
Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.
###Explanation:
Andre is 13, his brother is 16, his sister is 11, and his mom is 47."
200,A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?,"Sample Answer: You may need to know how big the bucket is, the rate of water flow, the height of the bucket, and how high the water in the bucket is after one minute.","###Write an explanation to this problem:
A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?
###Explanation:
Sample Answer: You may need to know how big the bucket is, the rate of water flow, the height of the bucket, and how high the water in the bucket is after one minute."
134,Name the parts of the expression. 30jk,30 is the coefficient j and k are the variables 30jk is a term and is the product of 30 * j * k,"###Write an explanation to this problem:
Name the parts of the expression. 30jk
###Explanation:
30 is the coefficient j and k are the variables 30jk is a term and is the product of 30 * j * k"
27,Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.,"I would start by plotting the y intercept 0,-1 and then from that point I would count down 4 units and to the right 1 unit and plot another point. I would then draw a line through both of these points to create the graph.","###Write an explanation to this problem:
Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.
###Explanation:
I would start by plotting the y intercept 0,-1 and then from that point I would count down 4 units and to the right 1 unit and plot another point. I would then draw a line through both of these points to create the graph."
749,Fill in the blank with numbers that correctly complete the statement. Three rational numbers between 16 and 15 < <,15.3 < 15.6 < 15.7,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three rational numbers between 16 and 15 < <
###Explanation:
15.3 < 15.6 < 15.7"
230,"80% of x is equal to 100. Write an equation that shows the relationship of 80%, x and 100.",0.8x=100,"###Write an explanation to this problem:
80% of x is equal to 100. Write an equation that shows the relationship of 80%, x and 100.
###Explanation:
0.8x=100"
489,Give an example of an irrational number between 8 and 9. The Utah Middle School Math Project,"An irrational number is a number that cannot be expressed as a fraction for any integers. So, an irrational number between 8 and 9 could be 2.8pi;, which has a value of about 8.8.","###Write an explanation to this problem:
Give an example of an irrational number between 8 and 9. The Utah Middle School Math Project
###Explanation:
An irrational number is a number that cannot be expressed as a fraction for any integers. So, an irrational number between 8 and 9 could be 2.8pi;, which has a value of about 8.8."
378,"How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know? copied for free from openupresources.org","If you could find the length and width of each side of the cabinet, you could find the area of each side and then add them all together.","###Write an explanation to this problem:
How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know? copied for free from openupresources.org
###Explanation:
If you could find the length and width of each side of the cabinet, you could find the area of each side and then add them all together."
288,"11. Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote: 228 = 2 * 28 = 56 Elena said, No, exponents mean repeated multiplication. It should be 28 * 28, which works out to be 784. Do you agree with either of them? Explain your reasoning. copied for free from openupresources.org","Neither are correct. 228 is saying that you are multiply 2 by itself 28 times. When you multiply this out, you get 268,435,456","###Write an explanation to this problem:
11. Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote: 228 = 2 * 28 = 56 Elena said, No, exponents mean repeated multiplication. It should be 28 * 28, which works out to be 784. Do you agree with either of them? Explain your reasoning. copied for free from openupresources.org
###Explanation:
Neither are correct. 228 is saying that you are multiply 2 by itself 28 times. When you multiply this out, you get 268,435,456"
418,Dane goes to a fast food restaurant and orders some tacos t and burritos b. Write a story that matches the system of equations shown below that describes the number of items Dane ordered and how many calories he consumed. t + b = 5 170t + 370b = 1250 The Utah Middle School Math Project,"Sample Answer: Dane went to a restaurant and ordered some tacos and burritos. He ordered a total of 5 items. Tacos have 170 calories each and burritos have 370 calories each. If Dane consumed 1,250 calories, how many of each item did he order?","###Write an explanation to this problem:
Dane goes to a fast food restaurant and orders some tacos t and burritos b. Write a story that matches the system of equations shown below that describes the number of items Dane ordered and how many calories he consumed. t + b = 5 170t + 370b = 1250 The Utah Middle School Math Project
###Explanation:
Sample Answer: Dane went to a restaurant and ordered some tacos and burritos. He ordered a total of 5 items. Tacos have 170 calories each and burritos have 370 calories each. If Dane consumed 1,250 calories, how many of each item did he order?"
674,-5 x -3 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer -5 and multiply it -3 times, so -5 x -3 can be thought of as the opposite of -5 x 3, which is -5 + -5 + -5. The opposite of -5 + -5 + -5 is 5 + 5 + 5","###Write an explanation to this problem:
-5 x -3 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -5 and multiply it -3 times, so -5 x -3 can be thought of as the opposite of -5 x 3, which is -5 + -5 + -5. The opposite of -5 + -5 + -5 is 5 + 5 + 5"
391,"During the summer, Victoria plays soccer and takes swim and piano lessons. Each swim lesson is 15 minutes shorter than a soccer practice. Each piano lesson is twice as long as a soccer practice. Use this information to answer the questions that follow. The following expressions represent how long an activity is each time she goes. Write the name of the activity that matches t: The Utah Middle School Math Project",The variable t is representative of the amount of time she spends at soccer practice.,"###Write an explanation to this problem:
During the summer, Victoria plays soccer and takes swim and piano lessons. Each swim lesson is 15 minutes shorter than a soccer practice. Each piano lesson is twice as long as a soccer practice. Use this information to answer the questions that follow. The following expressions represent how long an activity is each time she goes. Write the name of the activity that matches t: The Utah Middle School Math Project
###Explanation:
The variable t is representative of the amount of time she spends at soccer practice."
592,Write three expressions equivalent to the expression 6 + 5. The Utah Middle School Math Project,"There are many expressions that are equivalent to 6b + 5. Some examples are the expressions 23b + 2 + 3, 3b + 3b + 5, 5b + b + 10 - 5.","###Write an explanation to this problem:
Write three expressions equivalent to the expression 6 + 5. The Utah Middle School Math Project
###Explanation:
There are many expressions that are equivalent to 6b + 5. Some examples are the expressions 23b + 2 + 3, 3b + 3b + 5, 5b + b + 10 - 5."
498,"Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project",𝑥 + 𝑦 = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1𝑥 + 2.5𝑦 = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project
###Explanation:
𝑥 + 𝑦 = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1𝑥 + 2.5𝑦 = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982"
138,Give a number between -6.1 and -6.2. The Utah Middle School Math Project,"Negative numbers are the opposite of positive numbers. This means that the opposites of -6.1 and -6.2 are 6.1 and 6.2. A number that is between -6.1 and -6.2 will have its opposite between 6.1 and 6.2. There are many numbers between 6.1 and 6.2. For example: 6.11, 6.15, 6.19, and so on If we take the opposite, then these numbers are between -6.1 and -6.2. For example: -6.11, -6.15, -6.19, and so on","###Write an explanation to this problem:
Give a number between -6.1 and -6.2. The Utah Middle School Math Project
###Explanation:
Negative numbers are the opposite of positive numbers. This means that the opposites of -6.1 and -6.2 are 6.1 and 6.2. A number that is between -6.1 and -6.2 will have its opposite between 6.1 and 6.2. There are many numbers between 6.1 and 6.2. For example: 6.11, 6.15, 6.19, and so on If we take the opposite, then these numbers are between -6.1 and -6.2. For example: -6.11, -6.15, -6.19, and so on"
62,Here is an inequality: -2x > 10. List some values for x that would make this inequality true.,"-5, -6, -7. ...","###Write an explanation to this problem:
Here is an inequality: -2x > 10. List some values for x that would make this inequality true.
###Explanation:
-5, -6, -7. ..."
471,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The total number of laps run depends on the length of each workout. The Utah Middle School Math Project,Time length is the independent variable. The number of laps is the dependent on the length of the workout. Number of laps is the dependent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The total number of laps run depends on the length of each workout. The Utah Middle School Math Project
###Explanation:
Time length is the independent variable. The number of laps is the dependent on the length of the workout. Number of laps is the dependent variable."
647,-2 x 6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer -2 and multiply it 6 times, so -2 x 6 can be thought of as -2 + -2 + -2 + -2 + -2 + -2","###Write an explanation to this problem:
-2 x 6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -2 and multiply it 6 times, so -2 x 6 can be thought of as -2 + -2 + -2 + -2 + -2 + -2"
128,"Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope m is changed to ndash;m. The Utah Middle School Math Project","The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the slope is changed from m to -m, then we know that the slopes will have the same absolute value but opposite signs. One line will be positive and the other will be negative, but they will still have the same steepness. This transformation can be described as a reflection across the y-axis.","###Write an explanation to this problem:
Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope m is changed to ndash;m. The Utah Middle School Math Project
###Explanation:
The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the slope is changed from m to -m, then we know that the slopes will have the same absolute value but opposite signs. One line will be positive and the other will be negative, but they will still have the same steepness. This transformation can be described as a reflection across the y-axis."
831,What information do you need to know to write an equation relating two quantities that have a proportional relationship?,You would need to know the number of knots per row which would be the constant of proportionality.,"###Write an explanation to this problem:
What information do you need to know to write an equation relating two quantities that have a proportional relationship?
###Explanation:
You would need to know the number of knots per row which would be the constant of proportionality."
520,Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project,w= 2rwhere w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles.,"###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project
###Explanation:
w= 2rwhere w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles."
64,"Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home. ​Andre wrote the inequality 3x + 10 le; 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.",x: The number of small paper cranes Andre will make 3x: The time it takes to make a small paper crane. 10: The time it take Andre to make the centerpiece 30: The amount of time Andre has to make the cranes when he gets home.,"###Write an explanation to this problem:
Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home. ​Andre wrote the inequality 3x + 10 le; 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.
###Explanation:
x: The number of small paper cranes Andre will make 3x: The time it takes to make a small paper crane. 10: The time it take Andre to make the centerpiece 30: The amount of time Andre has to make the cranes when he gets home."
14,Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1,"-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2.","###Write an explanation to this problem:
Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1
###Explanation:
-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2."
156,"Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org",1.5b+3g=12,"###Write an explanation to this problem:
Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org
###Explanation:
1.5b+3g=12"
40,Explain how to make this calculation mentally. 244 - 99,"99 is close to 100 by 1 number. 244-100=144 but since you subtracted 100 instead of 99, there was 1 extra subtracted so you should add 1 to your answer to make up for the extra 1 subtracted. 144+1=145. This is how you would do 244-99=145 mentally.","###Write an explanation to this problem:
Explain how to make this calculation mentally. 244 - 99
###Explanation:
99 is close to 100 by 1 number. 244-100=144 but since you subtracted 100 instead of 99, there was 1 extra subtracted so you should add 1 to your answer to make up for the extra 1 subtracted. 144+1=145. This is how you would do 244-99=145 mentally."
492,Write an ordered pair that would be in Quadrant III when graphed. The Utah Middle School Math Project,"Any ordered pair x, y where both x and y are negative is in Quadrant III. Examples: -1, -1 -5, -3 -1/2, -3/4","###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant III when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair x, y where both x and y are negative is in Quadrant III. Examples: -1, -1 -5, -3 -1/2, -3/4"
379,"7. Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson. copied for free from openupresources.org",A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps.,"###Write an explanation to this problem:
7. Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson. copied for free from openupresources.org
###Explanation:
A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps."
187,Elena wants to know what proportion of people have cats as pets. Describe a process she could use to estimate an answer to her question.,She could collect a random sample of people perhaps by asking 50-100 people who come out of a store if they have a cat. She could determine the proportion of people that have cats by dividing the number of people who said yes by the number of people in her sample,"###Write an explanation to this problem:
Elena wants to know what proportion of people have cats as pets. Describe a process she could use to estimate an answer to her question.
###Explanation:
She could collect a random sample of people perhaps by asking 50-100 people who come out of a store if they have a cat. She could determine the proportion of people that have cats by dividing the number of people who said yes by the number of people in her sample"
216,"In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.","If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day.","###Write an explanation to this problem:
In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.
###Explanation:
If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day."
52,Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school?,"The mean number of siblings for all the students in a school can be approximated by thinking of the number of siblings each student may have. To make the approximate value easier, all of the numbers can be rounded to whole numbers. If about 20% of the school is an only child, 40% has one sibling 20% have two siblings 10% have three siblings 10% have four or more, then the mean number of siblings should be roughly between 1 and 3. The mean number of students can change based on the students at your school.","###Write an explanation to this problem:
Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school?
###Explanation:
The mean number of siblings for all the students in a school can be approximated by thinking of the number of siblings each student may have. To make the approximate value easier, all of the numbers can be rounded to whole numbers. If about 20% of the school is an only child, 40% has one sibling 20% have two siblings 10% have three siblings 10% have four or more, then the mean number of siblings should be roughly between 1 and 3. The mean number of students can change based on the students at your school."
337,Here is an equation: 4x - 4 = 4x + __. What could you write in the blank so the equation would be true for: No values of x Copied for free from openupresources.org,"We have 4x on both sides of this equation. We know that if we insert a constant into this blank, then there would still only be 4x on both sides of the equation. If we subtract 4x from both sides, we get: -4 = ___ If we want this to not be true, then we would need for the constant in the blank to not equal -4. The answer is any constant not equal to -4. Example: -2, 5, 9","###Write an explanation to this problem:
Here is an equation: 4x - 4 = 4x + __. What could you write in the blank so the equation would be true for: No values of x Copied for free from openupresources.org
###Explanation:
We have 4x on both sides of this equation. We know that if we insert a constant into this blank, then there would still only be 4x on both sides of the equation. If we subtract 4x from both sides, we get: -4 = ___ If we want this to not be true, then we would need for the constant in the blank to not equal -4. The answer is any constant not equal to -4. Example: -2, 5, 9"
748,Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < <,-3 < -2 < -1,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < <
###Explanation:
-3 < -2 < -1"
719,"To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.","Answers vary. Sample response: 12 cups of pink paint to 10 cups of blue paint and 18 cups of pink paint to 15 cups of blue paint. This is 2 batches and 3 batches, respectively, of this shade of lavender paint.","###Write an explanation to this problem:
To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.
###Explanation:
Answers vary. Sample response: 12 cups of pink paint to 10 cups of blue paint and 18 cups of pink paint to 15 cups of blue paint. This is 2 batches and 3 batches, respectively, of this shade of lavender paint."
724,Write two ratios that are equivalent to 1:1.,"Sample responses: 2:2, 50:50, or any ratio that simplifies to 1:1","###Write an explanation to this problem:
Write two ratios that are equivalent to 1:1.
###Explanation:
Sample responses: 2:2, 50:50, or any ratio that simplifies to 1:1"
295,Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume.,Sample Answer: Volume refers to how much of something fits inside an object. Surface area refers to how much of something is needed to cover the outside of an object.,"###Write an explanation to this problem:
Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume.
###Explanation:
Sample Answer: Volume refers to how much of something fits inside an object. Surface area refers to how much of something is needed to cover the outside of an object."
701,Create a context for the numeric representation. 801 + 80.40 = 801.40 = 112 The Utah Middle School Math Project,"If a person has 80 apples, then gains 40% more apples than the original 80, this numeric expression describes the total number of apples.","###Write an explanation to this problem:
Create a context for the numeric representation. 801 + 80.40 = 801.40 = 112 The Utah Middle School Math Project
###Explanation:
If a person has 80 apples, then gains 40% more apples than the original 80, this numeric expression describes the total number of apples."
251,List the sample space for selecting a letter a random from the word PINEAPPLE.,"The sample space for a word with the same letter multiple times only needs to represent the letter once. In the word PINEAPPLE, the letters P, L and E are represented multiple times, so leave only one P, L, and E from the word. The letters for the sample space are: P, I, N, E, A, L","###Write an explanation to this problem:
List the sample space for selecting a letter a random from the word PINEAPPLE.
###Explanation:
The sample space for a word with the same letter multiple times only needs to represent the letter once. In the word PINEAPPLE, the letters P, L and E are represented multiple times, so leave only one P, L, and E from the word. The letters for the sample space are: P, I, N, E, A, L"
726,Write two ratios that are equivalent to 1:1.,Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 1x2:1x2 = 2:2 1x50:1x50 = 50:50 Or any ratio that simplifies to 1:1,"###Write an explanation to this problem:
Write two ratios that are equivalent to 1:1.
###Explanation:
Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 1x2:1x2 = 2:2 1x50:1x50 = 50:50 Or any ratio that simplifies to 1:1"
461,Given information: z = length of a side of a triangle 2z = length 2nd side of a triangle 2z + 3 = length of 3rd side of triangle Equation: z + 2z + 2z + 3 = 73 cm. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,The length of one of the sides of a triangle is twice the length of the shortest side. The other side is 3 more than twice the length of the smallest side. The sum of the three sides is 73 cm. What is the length of the three sides?,"###Write an explanation to this problem:
Given information: z = length of a side of a triangle 2z = length 2nd side of a triangle 2z + 3 = length of 3rd side of triangle Equation: z + 2z + 2z + 3 = 73 cm. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
The length of one of the sides of a triangle is twice the length of the shortest side. The other side is 3 more than twice the length of the smallest side. The sum of the three sides is 73 cm. What is the length of the three sides?"
455,26% of 44 Estimate the answer. The Utah Middle School Math Project,"25% of 40 is 10, so 26% of 44 must be close to 10.","###Write an explanation to this problem:
26% of 44 Estimate the answer. The Utah Middle School Math Project
###Explanation:
25% of 40 is 10, so 26% of 44 must be close to 10."
850,"Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson.",A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps.,"###Write an explanation to this problem:
Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson.
###Explanation:
A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps."
269,Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality.,"Sample response: In a 100 yard, Three Legged Race, distance in yards and time in minutes are proportional since each value of distance could be multiplied by 1/40 to get the time. The constant of proportionality they used was 1/40.","###Write an explanation to this problem:
Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality.
###Explanation:
Sample response: In a 100 yard, Three Legged Race, distance in yards and time in minutes are proportional since each value of distance could be multiplied by 1/40 to get the time. The constant of proportionality they used was 1/40."
201,Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org,"It says that Lin starts solving the equation using the distributive property, so the 7 must be multiplied by each of the terms in the parenthesis. 7x + 2 = 91 7 * x + 7 * 2 = 91 7x + 14 = 91 Now 14 must be subtracted from both sides. 7x + 14 = 91 - 14 -14 7x = 77 Finally both sides can be divided by 7. 7x = 77 /7 /7 x = 11 Noah started by dividing both sides by 7. 7x + 2 = 91 /7 /7 x + 2 = 13 Now 2 can be subtracted from both sides. x + 2 = 13 - 2 -2 x = 11 Both solution methods come up with the same value for x.","###Write an explanation to this problem:
Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org
###Explanation:
It says that Lin starts solving the equation using the distributive property, so the 7 must be multiplied by each of the terms in the parenthesis. 7x + 2 = 91 7 * x + 7 * 2 = 91 7x + 14 = 91 Now 14 must be subtracted from both sides. 7x + 14 = 91 - 14 -14 7x = 77 Finally both sides can be divided by 7. 7x = 77 /7 /7 x = 11 Noah started by dividing both sides by 7. 7x + 2 = 91 /7 /7 x + 2 = 13 Now 2 can be subtracted from both sides. x + 2 = 13 - 2 -2 x = 11 Both solution methods come up with the same value for x."
161,"Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.",The slope represents that 1 muffin costs 2 and 3 represents that the delivery fee is 3.,"###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
###Explanation:
The slope represents that 1 muffin costs 2 and 3 represents that the delivery fee is 3."
555,Write a phrase for the following algebraic expression 2 - 15 The Utah Middle School Math Project,2x - 15 is fifteen less than two times a number x.,"###Write an explanation to this problem:
Write a phrase for the following algebraic expression 2 - 15 The Utah Middle School Math Project
###Explanation:
2x - 15 is fifteen less than two times a number x."
729,Find 3 different ratios that are equivalent to 7 : 3,"Sample response: Multiply both terms of the ratio by the same value, such as 14:6, 21:9, 28:12","###Write an explanation to this problem:
Find 3 different ratios that are equivalent to 7 : 3
###Explanation:
Sample response: Multiply both terms of the ratio by the same value, such as 14:6, 21:9, 28:12"
401,"Central Lewis High School has five times as many desktop computers as laptops. The school has a total of 360 computers. Write an equation to show the relationship between the amount of desktops, laptops, and the total number of computers. The Utah Middle School Math Project","The number of laptops can be represented by the variable l. There are five times as many desktops as laptops, so this can be represented by 5l. These two values together are equal to the total. The equation for this relationship is 5l+l=360.","###Write an explanation to this problem:
Central Lewis High School has five times as many desktop computers as laptops. The school has a total of 360 computers. Write an equation to show the relationship between the amount of desktops, laptops, and the total number of computers. The Utah Middle School Math Project
###Explanation:
The number of laptops can be represented by the variable l. There are five times as many desktops as laptops, so this can be represented by 5l. These two values together are equal to the total. The equation for this relationship is 5l+l=360."
702,Solve the inequality. Represent the solution on a number line. 4/5xge;36 The Utah Middle School Math Project,Solve for x. The number line should be less than and equal to the solution.,"###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 4/5xge;36 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than and equal to the solution."
476,Your task is to design a set of stairs and a wheelchair ramp at the side. Both the stairs and the ramp will begin at the same place at ground level and end at the height of 3 feet. Answer the following questions as you develop your design. How many steps do you want or need? The Utah Middle School Math Project,The average step is at a maximum of 7 inches wide and 11 inches deep. This means that you would need,"###Write an explanation to this problem:
Your task is to design a set of stairs and a wheelchair ramp at the side. Both the stairs and the ramp will begin at the same place at ground level and end at the height of 3 feet. Answer the following questions as you develop your design. How many steps do you want or need? The Utah Middle School Math Project
###Explanation:
The average step is at a maximum of 7 inches wide and 11 inches deep. This means that you would need"
771,"Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B","I can add two to the weeks each time to get the next number. I can add𝟑𝟓𝟎 to the money to get the next values.In the rows, we have 𝟐: 𝟑𝟓𝟎, which is equal to 𝟏: 𝟏𝟕𝟓. So the money is 𝟏𝟕𝟓times larger than the week. I can just multiply the week by 𝟏𝟕𝟓 to get theamount of money in the account.The ratio used to create the table was 𝟏: 𝟏𝟕𝟓.","###Write an explanation to this problem:
Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B
###Explanation:
I can add two to the weeks each time to get the next number. I can add𝟑𝟓𝟎 to the money to get the next values.In the rows, we have 𝟐: 𝟑𝟓𝟎, which is equal to 𝟏: 𝟏𝟕𝟓. So the money is 𝟏𝟕𝟓times larger than the week. I can just multiply the week by 𝟏𝟕𝟓 to get theamount of money in the account.The ratio used to create the table was 𝟏: 𝟏𝟕𝟓."
105,"Ramon is collecting donations for a charity. He is hoping to raise 250. If he has already collected 187 in donations, how much more does he need to collect? Write an equation to solve the problem. The Utah Middle School Math Project","Ramon already has 187, and needs m more to get to 250. This means that 187+m=250","###Write an explanation to this problem:
Ramon is collecting donations for a charity. He is hoping to raise 250. If he has already collected 187 in donations, how much more does he need to collect? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Ramon already has 187, and needs m more to get to 250. This means that 187+m=250"
565,Write a context to match the numeric expression given. 40 + 625 The Utah Middle School Math Project,"Angie runs a company specializing in selling rare gems. For online orders, there is a flat 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 40 + 625 The Utah Middle School Math Project
###Explanation:
Angie runs a company specializing in selling rare gems. For online orders, there is a flat 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost?"
389,Write a story that matches the expressions and equations Downloading Music of songs downloaded: s Monthly cost at bTunes: 0.99s Monthly cost at iMusic: 10 + 0.79s 0.99s = 10 + 0.79s The Utah Middle School Math Project,"The monthly cost of bTunes is 0.99s, meaning you pay 0.99 per song. The monthly cost of iMusic is 10 + 0.79s, meaning you pay an 0.79 per song plus an initial fee of 10. When 0.99s = 10 + 0.79s, the cost of the two plans will be the same. Solve this equation for s to find out how many songs you have to download per month for the two plans to cost the same.","###Write an explanation to this problem:
Write a story that matches the expressions and equations Downloading Music of songs downloaded: s Monthly cost at bTunes: 0.99s Monthly cost at iMusic: 10 + 0.79s 0.99s = 10 + 0.79s The Utah Middle School Math Project
###Explanation:
The monthly cost of bTunes is 0.99s, meaning you pay 0.99 per song. The monthly cost of iMusic is 10 + 0.79s, meaning you pay an 0.79 per song plus an initial fee of 10. When 0.99s = 10 + 0.79s, the cost of the two plans will be the same. Solve this equation for s to find out how many songs you have to download per month for the two plans to cost the same."
1,"Was there a length measurement you did not use to find the area? If so, explain why it was not used.","The formula for the area of a parallelogram is bh=A. The base and height of a parallelogram must form a 90deg; angle. In this case, we don't need the measurement of 7.5 cm.","###Write an explanation to this problem:
Was there a length measurement you did not use to find the area? If so, explain why it was not used.
###Explanation:
The formula for the area of a parallelogram is bh=A. The base and height of a parallelogram must form a 90deg; angle. In this case, we don't need the measurement of 7.5 cm."
798,Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.,Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25.,"###Write an explanation to this problem:
Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.
###Explanation:
Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25."
561,"Determine if the relation or situation defines a function. Justify your answer. {2, -10, 5, -25, 8, -40, -5, 25} The Utah Middle School Math Project","Yes, the data describes a function One way to determine this is to find the rule: The rule is multiply the input by -5","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. {2, -10, 5, -25, 8, -40, -5, 25} The Utah Middle School Math Project
###Explanation:
Yes, the data describes a function One way to determine this is to find the rule: The rule is multiply the input by -5"
80,"Find a number that matches the description. A 3-digit number that is divisible by 2, 3, and 6. How do you know? The Utah Middle School Math Project","There are many different correct answers to this question. We want a number that is divisible by 2, 3, and 6. We already know from our divisibility rules that any number that is divisible by both 2 and 3 is divisible by 6. We just need our number to be divisible by 2 and 3. To be divisible by 2, the last digit has to be an even number or 0. To be divisible by 3, the digits have to add up to a number that is divisible by 3. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144.","###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 2, 3, and 6. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 2, 3, and 6. We already know from our divisibility rules that any number that is divisible by both 2 and 3 is divisible by 6. We just need our number to be divisible by 2 and 3. To be divisible by 2, the last digit has to be an even number or 0. To be divisible by 3, the digits have to add up to a number that is divisible by 3. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144."
205,"For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.","Prices for apples at all stores in our state, Prices for all fruit at these two stores.","###Write an explanation to this problem:
For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.
###Explanation:
Prices for apples at all stores in our state, Prices for all fruit at these two stores."
34,Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8.,Andre subtracted 3x from each side of the equation.,"###Write an explanation to this problem:
Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8.
###Explanation:
Andre subtracted 3x from each side of the equation."
775,The volume of Box D subtracted from the volume of Box C is 23.14 cubic centimeters. Box D has a volume of 10.115 cubic centimeters. Let C be the volume of Box C in cubic centimeters. Write an equation that could be used to determine the volume of Box C.,𝑪 - 𝟏𝟎. 𝟏𝟏𝟓 𝐜𝐦3 = 𝟐𝟑. 𝟏𝟒 𝐜𝐦3,"###Write an explanation to this problem:
The volume of Box D subtracted from the volume of Box C is 23.14 cubic centimeters. Box D has a volume of 10.115 cubic centimeters. Let C be the volume of Box C in cubic centimeters. Write an equation that could be used to determine the volume of Box C.
###Explanation:
𝑪 - 𝟏𝟎. 𝟏𝟏𝟓 𝐜𝐦3 = 𝟐𝟑. 𝟏𝟒 𝐜𝐦3"
508,"Use The Distributive Property to find the product. 5222 First, show your work here. The Utah Middle School Math Project","5222 = 5200 + 20 + 2 = 5200 + 520 + 52 = 1000 + 100 + 10 = 1,110","###Write an explanation to this problem:
Use The Distributive Property to find the product. 5222 First, show your work here. The Utah Middle School Math Project
###Explanation:
5222 = 5200 + 20 + 2 = 5200 + 520 + 52 = 1000 + 100 + 10 = 1,110"
427,"Peter is the event planner for a team race taking place in Park City, UT. He needs to determine how many bottles of water to have ready at the finish line of the race so that each participant in the race receives a bottle of water. There are 4 people on a team. Identify the independent variable in this situation. The Utah Middle School Math Project","The number of teams is the independent variable, because it is the one that can change.","###Write an explanation to this problem:
Peter is the event planner for a team race taking place in Park City, UT. He needs to determine how many bottles of water to have ready at the finish line of the race so that each participant in the race receives a bottle of water. There are 4 people on a team. Identify the independent variable in this situation. The Utah Middle School Math Project
###Explanation:
The number of teams is the independent variable, because it is the one that can change."
454,Given information: w = width of rectangle 2w + 3 = length of rectangle Equation: w + 2w + 3 + w + 2w + 3 = 78 in. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,The perimeter of a rectangle is 78 inches. The width of the rectangle is w and the length of the rectangle is 2w+3. Find the width and length of the rectangle.,"###Write an explanation to this problem:
Given information: w = width of rectangle 2w + 3 = length of rectangle Equation: w + 2w + 3 + w + 2w + 3 = 78 in. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
The perimeter of a rectangle is 78 inches. The width of the rectangle is w and the length of the rectangle is 2w+3. Find the width and length of the rectangle."
366,"The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?","Sample Answer: There are 5,280 feet in every mile. Each additional mile that someone travels is equivalent to traveling an additional 5,280 feet.","###Write an explanation to this problem:
The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?
###Explanation:
Sample Answer: There are 5,280 feet in every mile. Each additional mile that someone travels is equivalent to traveling an additional 5,280 feet."
91,Write a pair of numbers whose LCM is 15. The Utah Middle School Math Project,"There are a few different numbers that have multiples of 15. The factors of 15 are 1, 3, 5, and 15. Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 5: 5, 10, 15, ... Multiples of 15: 15, 30, ... You could pick pairs of: 1 and 15 3 and 15 5 and 15 3 and 5","###Write an explanation to this problem:
Write a pair of numbers whose LCM is 15. The Utah Middle School Math Project
###Explanation:
There are a few different numbers that have multiples of 15. The factors of 15 are 1, 3, 5, and 15. Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 5: 5, 10, 15, ... Multiples of 15: 15, 30, ... You could pick pairs of: 1 and 15 3 and 15 5 and 15 3 and 5"
339,Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.,"This equation is in slope-intercept form: y = mx + b This means that we know the y-intercept: 0,b 0,-1 We also know the slope of the line: -4. This means that for every 1 unit we go to the right, the line goes down 4 units. Start with the intercept 0,-1, and use the slope of -4 to move down 1 and 4 to the right or up 1 and 4 to the left to find other points. Or, find two or more solutions to the equation by substituting in a number for x and solving for y.","###Write an explanation to this problem:
Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.
###Explanation:
This equation is in slope-intercept form: y = mx + b This means that we know the y-intercept: 0,b 0,-1 We also know the slope of the line: -4. This means that for every 1 unit we go to the right, the line goes down 4 units. Start with the intercept 0,-1, and use the slope of -4 to move down 1 and 4 to the right or up 1 and 4 to the left to find other points. Or, find two or more solutions to the equation by substituting in a number for x and solving for y."
564,Determine if the relation or situation defines a function. Justify your answer. You know your cousin's cellular phone number is 123 456-7890 so you dial that number to call him. Is person being called a function of phone number dialed? The Utah Middle School Math Project,"Yes, the data does describe a function The phone number 123 456-7890 is your cousin The phone number is the input and the only output for that phone number is your cousin","###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. You know your cousin's cellular phone number is 123 456-7890 so you dial that number to call him. Is person being called a function of phone number dialed? The Utah Middle School Math Project
###Explanation:
Yes, the data does describe a function The phone number 123 456-7890 is your cousin The phone number is the input and the only output for that phone number is your cousin"
345,What causes a repeating decimal in the long division algorithm?,"When you are using the long division algorithm, you will know that a fraction repeats when the remainders repeat. The repetition of the remainders sets up a cyclic pattern and that pattern shows up as a repeating decimal.","###Write an explanation to this problem:
What causes a repeating decimal in the long division algorithm?
###Explanation:
When you are using the long division algorithm, you will know that a fraction repeats when the remainders repeat. The repetition of the remainders sets up a cyclic pattern and that pattern shows up as a repeating decimal."
776,Write a story problem that includes both integers -8 and 12.,Example: One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat.,"###Write an explanation to this problem:
Write a story problem that includes both integers -8 and 12.
###Explanation:
Example: One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat."
241,"For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.",There are many correct answers for this question. Remember that a population is the group of people/things that you are interested in asking questions about. The sample is a smaller part from that population that you think could represent that population. One example of a correct answer is: Population 1: Prices for apples at all stores in our state. Population 2: Prices for all fruit at these two stores.,"###Write an explanation to this problem:
For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.
###Explanation:
There are many correct answers for this question. Remember that a population is the group of people/things that you are interested in asking questions about. The sample is a smaller part from that population that you think could represent that population. One example of a correct answer is: Population 1: Prices for apples at all stores in our state. Population 2: Prices for all fruit at these two stores."
13,Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < <,-3 < -2 < -1,"###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < <
###Explanation:
-3 < -2 < -1"
315,"Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1.","Sample Answer: Build a slope triangle. If its vertical length is greater than its horizontal length, the slope is greater than 1. If its vertical and horizontal lengths are equal, the slope is equal to 1. If the slope triangle's vertical length is less than its horizontal length, the slope is less than 1.","###Write an explanation to this problem:
Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1.
###Explanation:
Sample Answer: Build a slope triangle. If its vertical length is greater than its horizontal length, the slope is greater than 1. If its vertical and horizontal lengths are equal, the slope is equal to 1. If the slope triangle's vertical length is less than its horizontal length, the slope is less than 1."
600,Replace the ? in the fraction ?/18 with a number that would make the fraction less than 1/3. The Utah Middle School Math Project,"If you multiply both parts of 1/3 by 6, you get 6/18. Thus, if you want your fraction ?/18 to be less than 1/3, it needs to be less than 6/18. Any number that is less than 6 could replace the ?. Examples of correct answers are: 5, 2, -6, and so on.","###Write an explanation to this problem:
Replace the ? in the fraction ?/18 with a number that would make the fraction less than 1/3. The Utah Middle School Math Project
###Explanation:
If you multiply both parts of 1/3 by 6, you get 6/18. Thus, if you want your fraction ?/18 to be less than 1/3, it needs to be less than 6/18. Any number that is less than 6 could replace the ?. Examples of correct answers are: 5, 2, -6, and so on."
387,3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,"This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of a 3 + 3 + 3 + 3","###Write an explanation to this problem:
3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of a 3 + 3 + 3 + 3"
273,Five students came for after-school tutoring. Lin's teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems. 30 problems were assigned in all. Write an equation for the story.,"Let x be the number of problems to complete before adding 2 more problems. We are given that 5 students are given the same number of problems. So, each student was assigned x + 2 problems to complete and there is a total of 30 problems assigned. Therefore, the equation is 5x + 2 = 30.","###Write an explanation to this problem:
Five students came for after-school tutoring. Lin's teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems. 30 problems were assigned in all. Write an equation for the story.
###Explanation:
Let x be the number of problems to complete before adding 2 more problems. We are given that 5 students are given the same number of problems. So, each student was assigned x + 2 problems to complete and there is a total of 30 problems assigned. Therefore, the equation is 5x + 2 = 30."
166,"A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled win and 1 labeled lose. She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?",She needs to repeat the process many more times to get a good estimate of the probability.,"###Write an explanation to this problem:
A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled win and 1 labeled lose. She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?
###Explanation:
She needs to repeat the process many more times to get a good estimate of the probability."
846,Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality.,The number of legs that a group of centipedes has is proportional to the number of centipedes. The constant of proportionality would is 100 or 1/100.,"###Write an explanation to this problem:
Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality.
###Explanation:
The number of legs that a group of centipedes has is proportional to the number of centipedes. The constant of proportionality would is 100 or 1/100."
646,"In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 6 Transformed Equation: x + 2 = 8 Action: ______ The Utah Middle School Math Project","On the left side of the equation, 2 has been added to x. 2 has also been added to 6 on the right side, to make 8. The action was: Add 2 to both sides of the equation.","###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 6 Transformed Equation: x + 2 = 8 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 2 has been added to x. 2 has also been added to 6 on the right side, to make 8. The action was: Add 2 to both sides of the equation."
484,A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project,The dependent variable is the number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students.,"###Write an explanation to this problem:
A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The dependent variable is the number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students."
835,"Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.",Kiran's flavor would be more chocolatey than Clare's because if he double Clare's recipe correctly he would have had 4 teaspoons of chocolate syrup instead of 5 teaspoons.,"###Write an explanation to this problem:
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
###Explanation:
Kiran's flavor would be more chocolatey than Clare's because if he double Clare's recipe correctly he would have had 4 teaspoons of chocolate syrup instead of 5 teaspoons."
504,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A tree grows 15 feet in 10 years. The Utah Middle School Math Project,Time is the independent variable. The growth of the tree depends on the time. Feet is dependent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A tree grows 15 feet in 10 years. The Utah Middle School Math Project
###Explanation:
Time is the independent variable. The growth of the tree depends on the time. Feet is dependent variable."
243,"A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.","If 3 out of 50 people won a small prize, that means that 3 out of 50 ducks had a red mark on them. We can scale this ratio of 3:50 by a factor of 3.2 to get the equivalent ratio of 9.6:160. This means that there are likely 9 to 10 ducks that have red marks out of 160 total ducks. As for the ducks with blue marks, there seems to be less than a 1/50 probability of getting one, since 0 out of the 50 people who played won them. If we scale the ratio 1:50 by 3.2, we get the equivalent ratio of 3.2:160. This means that there are likely 3 or less ducks with blue marks out of 160 total ducks.","###Write an explanation to this problem:
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.
###Explanation:
If 3 out of 50 people won a small prize, that means that 3 out of 50 ducks had a red mark on them. We can scale this ratio of 3:50 by a factor of 3.2 to get the equivalent ratio of 9.6:160. This means that there are likely 9 to 10 ducks that have red marks out of 160 total ducks. As for the ducks with blue marks, there seems to be less than a 1/50 probability of getting one, since 0 out of the 50 people who played won them. If we scale the ratio 1:50 by 3.2, we get the equivalent ratio of 3.2:160. This means that there are likely 3 or less ducks with blue marks out of 160 total ducks."
566,Write a context to match the numeric expression given. 4 8 The Utah Middle School Math Project,Kelly wants to buy 4 eggs. Each egg is 8 dollars each. How much is she going to spend on eggs?,"###Write an explanation to this problem:
Write a context to match the numeric expression given. 4 8 The Utah Middle School Math Project
###Explanation:
Kelly wants to buy 4 eggs. Each egg is 8 dollars each. How much is she going to spend on eggs?"
562,Imagine cutting a square based right pyramid parallel to the base. What shape is the plane section? The Utah Middle School Math Project,Cutting a square based right pyramid parallel to the base will result in a square cross-section,"###Write an explanation to this problem:
Imagine cutting a square based right pyramid parallel to the base. What shape is the plane section? The Utah Middle School Math Project
###Explanation:
Cutting a square based right pyramid parallel to the base will result in a square cross-section"
686,Explain what you know about the lengths of the sides of a triangle the triangle inequality theorem. The Utah Middle School Math Project,"By the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.","###Write an explanation to this problem:
Explain what you know about the lengths of the sides of a triangle the triangle inequality theorem. The Utah Middle School Math Project
###Explanation:
By the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side."
189,"Graph these points in a coordinate plane: -2,3, 2,3, -2,-3, 2,-3. Submit your graph using the tools below.","-2,3 ---> Start at 0,0 and go 2 units to the left and 3 units up2,3 ---> Start at 0,0 and go 2 units to the right and 3 units up -2,-3 ---> Start at 0,0 and go two units to the left and 3 units down2, -3 ---> Start at 0,0 and go two units to the right and 3 units down.","###Write an explanation to this problem:
Graph these points in a coordinate plane: -2,3, 2,3, -2,-3, 2,-3. Submit your graph using the tools below.
###Explanation:
-2,3 ---> Start at 0,0 and go 2 units to the left and 3 units up2,3 ---> Start at 0,0 and go 2 units to the right and 3 units up -2,-3 ---> Start at 0,0 and go two units to the left and 3 units down2, -3 ---> Start at 0,0 and go two units to the right and 3 units down."
782,Represent 56 / 8 = 7 using subtraction. Explain your reasoning.,56 - 7 - 7 - 7 - 7 - 7 - 7 - 7 = 0 because 56 - 7 = 49 49 - 7 = 42 42 - 7 = 35 35 - 7 = 28 28 - 7 = 21 21 - 7 = 14 14 - 7 = 7 7 - 7 = 0 OR 56 - 8 - 8 - 8 - 8 - 8 - 8 - 8 = 0 because 56 - 8 = 48 48 - 8 = 40 40 - 8 = 32 32 - 8 = 24 24 - 8 = 16 16 - 8 = 8 8 - 8 = 0,"###Write an explanation to this problem:
Represent 56 / 8 = 7 using subtraction. Explain your reasoning.
###Explanation:
56 - 7 - 7 - 7 - 7 - 7 - 7 - 7 = 0 because 56 - 7 = 49 49 - 7 = 42 42 - 7 = 35 35 - 7 = 28 28 - 7 = 21 21 - 7 = 14 14 - 7 = 7 7 - 7 = 0 OR 56 - 8 - 8 - 8 - 8 - 8 - 8 - 8 = 0 because 56 - 8 = 48 48 - 8 = 40 40 - 8 = 32 32 - 8 = 24 24 - 8 = 16 16 - 8 = 8 8 - 8 = 0"
699,"Gavin is out shopping. After he buys 2 pairs of pants for 27 each, he has 60. How much money did he have before he bought the 2 pairs of pants? Write an equation to solve the problem. The Utah Middle School Math Project","Gavin has already spent 27 twice, and has 60 left. This means that m-227=60","###Write an explanation to this problem:
Gavin is out shopping. After he buys 2 pairs of pants for 27 each, he has 60. How much money did he have before he bought the 2 pairs of pants? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Gavin has already spent 27 twice, and has 60 left. This means that m-227=60"
475,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. There are 5 inches of water in a bucket after a 2 frac12; hour rain storm. The Utah Middle School Math Project,The time of the rain storm is the independent variable. The inches of water is the dependent variable.,"###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. There are 5 inches of water in a bucket after a 2 frac12; hour rain storm. The Utah Middle School Math Project
###Explanation:
The time of the rain storm is the independent variable. The inches of water is the dependent variable."
681,"Sandy puts 6% of her income in a retirement account. If she made 1,500 in a pay period, how much of it will go into her retirement account? Write an equation to solve the problem. The Utah Middle School Math Project",Convert the percentage to a decimal. This decimal should be multiplied by Sandy's income to reflect how much money goes into the account. The amount of money can be represented by r=0.061500.,"###Write an explanation to this problem:
Sandy puts 6% of her income in a retirement account. If she made 1,500 in a pay period, how much of it will go into her retirement account? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Convert the percentage to a decimal. This decimal should be multiplied by Sandy's income to reflect how much money goes into the account. The amount of money can be represented by r=0.061500."
510,The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The greater the distance a sprinter has to run the more time it takes to finish the race The Utah Middle School Math Project,"Distance is independent variable, as it will depend on the time that is left in the race. The Time is the dependent variable.","###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The greater the distance a sprinter has to run the more time it takes to finish the race The Utah Middle School Math Project
###Explanation:
Distance is independent variable, as it will depend on the time that is left in the race. The Time is the dependent variable."
58,"Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org",Factoring is sort of the opposite of using the distributive property. Kiran should tell Lin to look for a factor that she can pull out of each term in the expression.,"###Write an explanation to this problem:
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org
###Explanation:
Factoring is sort of the opposite of using the distributive property. Kiran should tell Lin to look for a factor that she can pull out of each term in the expression."
474,What is the relationship between 7 and -7 on the number line? The Utah Middle School Math Project,"Possible explanations: They are opposites. They are the same distance from zero, but -7 is to the left of zero and 7 is to the right.","###Write an explanation to this problem:
What is the relationship between 7 and -7 on the number line? The Utah Middle School Math Project
###Explanation:
Possible explanations: They are opposites. They are the same distance from zero, but -7 is to the left of zero and 7 is to the right."
560,Write a context to match the numeric expression given. 0.150 + 0.0150 + 0.0150 The Utah Middle School Math Project,"Dom is a very avid magnet collector. He has found a small shop that seems to have a very cool selection of magnets. They offer large rectangular magnets for 10 cents each and small spherical magnets for 1 cent each. Since Dom likes to have 50 of each magnet, he buys 50 rectangle and 50 sphere magnets. As he is leaving, he remembered that he owes his friend Mike 50 sphere magnets as well, and goes back to buy some more. In total, how much did Dom spend?","###Write an explanation to this problem:
Write a context to match the numeric expression given. 0.150 + 0.0150 + 0.0150 The Utah Middle School Math Project
###Explanation:
Dom is a very avid magnet collector. He has found a small shop that seems to have a very cool selection of magnets. They offer large rectangular magnets for 10 cents each and small spherical magnets for 1 cent each. Since Dom likes to have 50 of each magnet, he buys 50 rectangle and 50 sphere magnets. As he is leaving, he remembered that he owes his friend Mike 50 sphere magnets as well, and goes back to buy some more. In total, how much did Dom spend?"
747,"If two rational numbers, a and b, are ordered such that a is less than b, then what must be true about the order for their opposites: -a and -b?","The order will be reversed for the opposites, which means -a is greater than -b.","###Write an explanation to this problem:
If two rational numbers, a and b, are ordered such that a is less than b, then what must be true about the order for their opposites: -a and -b?
###Explanation:
The order will be reversed for the opposites, which means -a is greater than -b."
252,"Are you ready for more? Sometimes two transformations, one performed after the other, have a nice description as a single transformation. For example, instead of translating 2 units up followed by translating 3 units up, we could simply translate 5 units up. Instead of rotating 20 degrees counterclockwise around the origin followed by rotating 80 degrees clockwise around the origin, we could simply rotate 60 degrees clockwise around the origin. Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis? Copied for free from openupresources.org",a 180 degree rotation.,"###Write an explanation to this problem:
Are you ready for more? Sometimes two transformations, one performed after the other, have a nice description as a single transformation. For example, instead of translating 2 units up followed by translating 3 units up, we could simply translate 5 units up. Instead of rotating 20 degrees counterclockwise around the origin followed by rotating 80 degrees clockwise around the origin, we could simply rotate 60 degrees clockwise around the origin. Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis? Copied for free from openupresources.org
###Explanation:
a 180 degree rotation."
21,"Triangle A has side lengths 3, 4, and 5. Triangle B has side lengths 6, 7, and 8. Explain how you know that Triangle B is not similar to Triangle A.","The smallest side in the first triangle is 1/2 the size of the smallest side in the second triangle. The largest side in the first triangle is 5/8 the size of the largest side in the second triangle. If these triangles were similar, these ratios would have to be equivalent.","###Write an explanation to this problem:
Triangle A has side lengths 3, 4, and 5. Triangle B has side lengths 6, 7, and 8. Explain how you know that Triangle B is not similar to Triangle A.
###Explanation:
The smallest side in the first triangle is 1/2 the size of the smallest side in the second triangle. The largest side in the first triangle is 5/8 the size of the largest side in the second triangle. If these triangles were similar, these ratios would have to be equivalent."
313,"In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. Submit your drawing using the tools below.","The three angle measures must add to 180∘ but must all be equal. 1/3 * 180 = 60 Therefore, each measure is 60∘. The answer is 60.","###Write an explanation to this problem:
In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. Submit your drawing using the tools below.
###Explanation:
The three angle measures must add to 180∘ but must all be equal. 1/3 * 180 = 60 Therefore, each measure is 60∘. The answer is 60."
459,Given information: x = length of blue ribbon 2x + 3 = length of red ribbon 3x ndash; 1 = length of green ribbon Equation: x + 2x +3 + 3x ndash; 1 = 92 inches Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,"There is a blue, red, and green ribbon. The red ribbon is 3 inches more than twice the length of the blue ribbon. The green ribbon is one inch less than 3 times the length of the blue ribbon. What is the length of each ribbon?","###Write an explanation to this problem:
Given information: x = length of blue ribbon 2x + 3 = length of red ribbon 3x ndash; 1 = length of green ribbon Equation: x + 2x +3 + 3x ndash; 1 = 92 inches Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
There is a blue, red, and green ribbon. The red ribbon is 3 inches more than twice the length of the blue ribbon. The green ribbon is one inch less than 3 times the length of the blue ribbon. What is the length of each ribbon?"
160,A number line can represent positions that are north and south of a truck stop on a highway. Decide whether you want positive positions to be north or south of the truck stop. Then plot the following positions on a number line. The truck stop 5 miles north of the truck stop 3.5 miles south of the truck stop Submit your number line using the tools below.,"Sample Answer: Generally the truck stop would be at point zero, and the north is regarded as positive. Therefore, 5 miles north will be positive, and 3.5 miles south would be negative.","###Write an explanation to this problem:
A number line can represent positions that are north and south of a truck stop on a highway. Decide whether you want positive positions to be north or south of the truck stop. Then plot the following positions on a number line. The truck stop 5 miles north of the truck stop 3.5 miles south of the truck stop Submit your number line using the tools below.
###Explanation:
Sample Answer: Generally the truck stop would be at point zero, and the north is regarded as positive. Therefore, 5 miles north will be positive, and 3.5 miles south would be negative."
276,"Sixth-grade students were asked, What grade are you in? Explain why this is not a statistical question.","All 6th grade students would have the same answer, they are in 6th grade. This does not differ the data nor is it random. So your data would be biased.","###Write an explanation to this problem:
Sixth-grade students were asked, What grade are you in? Explain why this is not a statistical question.
###Explanation:
All 6th grade students would have the same answer, they are in 6th grade. This does not differ the data nor is it random. So your data would be biased."
191,An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?,A standard number cube only has 6 possible outcomes.,"###Write an explanation to this problem:
An experiment will produce one of ten different outcomes with equal probability for each. Why would using a standard number cube to simulate the experiment be a bad choice?
###Explanation:
A standard number cube only has 6 possible outcomes."
385,3 x -6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project,,"###Write an explanation to this problem:
3 x -6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
nan"
805,Why is there no commutative property for subtraction or division? Show examples.,"Sample response: The commutative property does not work for subtraction and division. An example would be 8 / 2 and 2 / 8. 8 / 2 = 4, but 2 / 8 = 1/4.","###Write an explanation to this problem:
Why is there no commutative property for subtraction or division? Show examples.
###Explanation:
Sample response: The commutative property does not work for subtraction and division. An example would be 8 / 2 and 2 / 8. 8 / 2 = 4, but 2 / 8 = 1/4."
413,The expression 25x ndash; 3 can be written as 10x ndash; 6 OR 10x + ndash;6. Write the following expressions in two different ways as the example shows: 43x ndash; 5 The Utah Middle School Math Project,"43x - 5 means five groups of 3x - 5 3x - 5 + 3x - 5 + 3x - 5 + 3x - 5 Then, combine like terms: 3x + 3x + 3x + 3x = 12x -5 + -5 + -5 + -5 = -20 The answer is 12x - 20 = 12x + -20","###Write an explanation to this problem:
The expression 25x ndash; 3 can be written as 10x ndash; 6 OR 10x + ndash;6. Write the following expressions in two different ways as the example shows: 43x ndash; 5 The Utah Middle School Math Project
###Explanation:
43x - 5 means five groups of 3x - 5 3x - 5 + 3x - 5 + 3x - 5 + 3x - 5 Then, combine like terms: 3x + 3x + 3x + 3x = 12x -5 + -5 + -5 + -5 = -20 The answer is 12x - 20 = 12x + -20"
491,"In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. x+3x+6x 10x2 Explain the mistake The Utah Middle School Math Project","Notice that no x terms are being multiplied together in this expression, so there should not be an x2 term in the simplified expression.","###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. x+3x+6x 10x2 Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that no x terms are being multiplied together in this expression, so there should not be an x2 term in the simplified expression."
343,How do you get from one number to the next using multiplication or division? From 100 to 106. copied for free from openupresources.org,From 100 to 106 you would use multiplication. Going from 100 to 106 is an increase from one number to the next. To find out what number to multiply by you could also use division to do this. 106/100 = 1.06 100 times 1.06 = 106 With this Math you can always check to make sure that the numbers and Math make sense.,"###Write an explanation to this problem:
How do you get from one number to the next using multiplication or division? From 100 to 106. copied for free from openupresources.org
###Explanation:
From 100 to 106 you would use multiplication. Going from 100 to 106 is an increase from one number to the next. To find out what number to multiply by you could also use division to do this. 106/100 = 1.06 100 times 1.06 = 106 With this Math you can always check to make sure that the numbers and Math make sense."
769,Why is there no commutative property for subtraction or division? Show examples.,"The commutative property does not work for subtraction and division. An example is 𝟖 / 𝟐 and 𝟐 / 𝟖. 𝟖 / 𝟐 = 𝟒, but 𝟐 / 𝟖 = 𝟏/4 .","###Write an explanation to this problem:
Why is there no commutative property for subtraction or division? Show examples.
###Explanation:
The commutative property does not work for subtraction and division. An example is 𝟖 / 𝟐 and 𝟐 / 𝟖. 𝟖 / 𝟐 = 𝟒, but 𝟐 / 𝟖 = 𝟏/4 ."
308,"In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.","If a triangle is isosceles, then two of its sides are the same length and the third side is different. This means two of the angles are the same and one is different. If A is 40, then this could be the same as one of the other angles. Angle B or Angle C could also measure 40 degrees. This means the other angle should measure 100 degrees. This is because all of the angles should add up to 180. 40 + 40 + 100 = 180 If A is 40 and is the different angle, then the other two angles together measure 140 degrees. 180 - 40 = 140 The angles must be congruent. 140/2 = 70 Angles B and C would be 70 degrees each.","###Write an explanation to this problem:
In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.
###Explanation:
If a triangle is isosceles, then two of its sides are the same length and the third side is different. This means two of the angles are the same and one is different. If A is 40, then this could be the same as one of the other angles. Angle B or Angle C could also measure 40 degrees. This means the other angle should measure 100 degrees. This is because all of the angles should add up to 180. 40 + 40 + 100 = 180 If A is 40 and is the different angle, then the other two angles together measure 140 degrees. 180 - 40 = 140 The angles must be congruent. 140/2 = 70 Angles B and C would be 70 degrees each."
661,Describe the similarities and differences between an equation and an inequality. Use examples to support your ideas. The Utah Middle School Math Project,Sample Answer: You solve equations and inequalities using the same process. The solution to an equation is one number while the solution to an inequality is infinitely many numbers that meet a requirement or set of requirements.,"###Write an explanation to this problem:
Describe the similarities and differences between an equation and an inequality. Use examples to support your ideas. The Utah Middle School Math Project
###Explanation:
Sample Answer: You solve equations and inequalities using the same process. The solution to an equation is one number while the solution to an inequality is infinitely many numbers that meet a requirement or set of requirements."
130,Describe absolute value in your own words. Use examples to support your explanation. The Utah Middle School Math Project,"The absolute value of a number is the number's distance from 0. Distance is always positive. You can think of it like a point on a number line. The distance from 0 is how many steps, or units, it takes to get to that point from 0. Even if that point has a negative value, it takes a positive number of steps to get to that point from 0. This distance/number of steps is the point's absolute value.","###Write an explanation to this problem:
Describe absolute value in your own words. Use examples to support your explanation. The Utah Middle School Math Project
###Explanation:
The absolute value of a number is the number's distance from 0. Distance is always positive. You can think of it like a point on a number line. The distance from 0 is how many steps, or units, it takes to get to that point from 0. Even if that point has a negative value, it takes a positive number of steps to get to that point from 0. This distance/number of steps is the point's absolute value."
663,One angle is five times larger than another angle. Together the angles sum to 1800. What is the measure of each angle? Write an equation to solve the problem. The Utah Middle School Math Project,"The measure of the smaller angle can be x, and the measure of the larger angle will be equal to 5x, because it is five times as large. Added together, these will be equal to 180. This means that x+5x=180.","###Write an explanation to this problem:
One angle is five times larger than another angle. Together the angles sum to 1800. What is the measure of each angle? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The measure of the smaller angle can be x, and the measure of the larger angle will be equal to 5x, because it is five times as large. Added together, these will be equal to 180. This means that x+5x=180."
99,Is there an association between the weight of a candle and the amount of time it burns? Make a prediction. The Utah Middle School Math Project,The candle weight will decrease as the time burned increases,"###Write an explanation to this problem:
Is there an association between the weight of a candle and the amount of time it burns? Make a prediction. The Utah Middle School Math Project
###Explanation:
The candle weight will decrease as the time burned increases"
372,Your task is to design a set of stairs and a wheelchair ramp at the side. Both the stairs and the ramp will begin at the same place at ground level and end at the height of 3 feet. Answer the following questions as you develop your design. How many steps do you want or need? The Utah Middle School Math Project,The average step is at a maximum of 7 inches wide and 11 inches deep. This means that you would need to base your steps on these measurements.,"###Write an explanation to this problem:
Your task is to design a set of stairs and a wheelchair ramp at the side. Both the stairs and the ramp will begin at the same place at ground level and end at the height of 3 feet. Answer the following questions as you develop your design. How many steps do you want or need? The Utah Middle School Math Project
###Explanation:
The average step is at a maximum of 7 inches wide and 11 inches deep. This means that you would need to base your steps on these measurements."
87,"Kiran wrote the expression x - 10 for this number puzzle: Pick a number, add -2, and multiply by 5. Lin thinks Kiran made a mistake. How can she convince Kiran he made a mistake?",Kiran made a mistake because he only wrote x -10. He forgot to account for the multiplying by 5 part. For this you would think of a number .... x +-2 and the whole thing needs to be multiplied by 5. So it would look like this 5x - 2 and then if you distribute the 5 through the parenthesis it would look like 5 x - 10. So he should have really written 5x-10 instead of x - 10.,"###Write an explanation to this problem:
Kiran wrote the expression x - 10 for this number puzzle: Pick a number, add -2, and multiply by 5. Lin thinks Kiran made a mistake. How can she convince Kiran he made a mistake?
###Explanation:
Kiran made a mistake because he only wrote x -10. He forgot to account for the multiplying by 5 part. For this you would think of a number .... x +-2 and the whole thing needs to be multiplied by 5. So it would look like this 5x - 2 and then if you distribute the 5 through the parenthesis it would look like 5 x - 10. So he should have really written 5x-10 instead of x - 10."
458,Given information: g = Gordon's allowance 2g ndash; 1= Chris's allowance 0.5g = Drew's allowance Equation: g + 2g ndash; 1 + 0.5g = 51.50 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project,Chris's allowance is one dollar less than twice of Gordon's allowance. Drew's allowance is only half of Gordon's allowance. All three friends together have 51.50. How much does each one get for allowance?,"###Write an explanation to this problem:
Given information: g = Gordon's allowance 2g ndash; 1= Chris's allowance 0.5g = Drew's allowance Equation: g + 2g ndash; 1 + 0.5g = 51.50 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Chris's allowance is one dollar less than twice of Gordon's allowance. Drew's allowance is only half of Gordon's allowance. All three friends together have 51.50. How much does each one get for allowance?"
330,"Your teacher will give you some cards with a scale on each card. Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards. Trade places with another group and check each other's work. If you disagree about how the scales should be sorted, work to reach an agreement. copied for free from openupresources.org","1 centimeter to 1 meter, and 1 to 100 1 centimeter to 1 kilometer, 12 cm to 500 m, and 1 to 100,000 1 inch to 8 feet, 18 inch to 1 foot, and 1 to 96 1 centimeter to 10 meters, 1 inch to 1,000 inches, and 1 millimeter to 1 meter 1 foot to 1 mile, and 1 to 5,280 1 inch to 1 mile, and 1 to 63,360","###Write an explanation to this problem:
Your teacher will give you some cards with a scale on each card. Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards. Trade places with another group and check each other's work. If you disagree about how the scales should be sorted, work to reach an agreement. copied for free from openupresources.org
###Explanation:
1 centimeter to 1 meter, and 1 to 100 1 centimeter to 1 kilometer, 12 cm to 500 m, and 1 to 100,000 1 inch to 8 feet, 18 inch to 1 foot, and 1 to 96 1 centimeter to 10 meters, 1 inch to 1,000 inches, and 1 millimeter to 1 meter 1 foot to 1 mile, and 1 to 5,280 1 inch to 1 mile, and 1 to 63,360"
214,The mean weight for a sample of a certain kind of ring made from platinum is 8.21 grams. The mean weight for a sample of a certain kind of ring made from gold is 8.61 grams. Is there a meaningful difference in the weights of the two types of rings? Explain your reasoning.,"There is not enough information to say for sure if there is a meaningful distance. In order to determine if the difference is meaningful, you would need to know the MAD.","###Write an explanation to this problem:
The mean weight for a sample of a certain kind of ring made from platinum is 8.21 grams. The mean weight for a sample of a certain kind of ring made from gold is 8.61 grams. Is there a meaningful difference in the weights of the two types of rings? Explain your reasoning.
###Explanation:
There is not enough information to say for sure if there is a meaningful distance. In order to determine if the difference is meaningful, you would need to know the MAD."
466,99% of 75 Estimate the answer. The Utah Middle School Math Project,"99% is slightly less than 100%, so 99% of 75 must be slightly less than 75.","###Write an explanation to this problem:
99% of 75 Estimate the answer. The Utah Middle School Math Project
###Explanation:
99% is slightly less than 100%, so 99% of 75 must be slightly less than 75."
121,Kiran drinks 6.4 oz of milk each morning. How many days does it take him to finish a 32 oz container of milk? Write and solve an equation for the situation.,6.4d=32 6.4 oz is the constant that will be multiplied by the amount of days d to equal a total of 32 oz of milk.,"###Write an explanation to this problem:
Kiran drinks 6.4 oz of milk each morning. How many days does it take him to finish a 32 oz container of milk? Write and solve an equation for the situation.
###Explanation:
6.4d=32 6.4 oz is the constant that will be multiplied by the amount of days d to equal a total of 32 oz of milk."
614,What does it mean to simplify an algebraic expression? Use examples to support your ideas. The Utah Middle School Math Project,Simplifying algebraic expressions is when you apply the rules of arithmetic to distribute and combine like terms.,"###Write an explanation to this problem:
What does it mean to simplify an algebraic expression? Use examples to support your ideas. The Utah Middle School Math Project
###Explanation:
Simplifying algebraic expressions is when you apply the rules of arithmetic to distribute and combine like terms."
20,"Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.",The slope means that each muffin costs 2. The y intercept means that there is some kind of 3 charge per order. It could be a tip or a delivery fee.,"###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
###Explanation:
The slope means that each muffin costs 2. The y intercept means that there is some kind of 3 charge per order. It could be a tip or a delivery fee."
700,Create a context for the numeric representation. 601 + 60.75 = 601.75 = 105 The Utah Middle School Math Project,"If a person has 60 apples, then gains 75% more apples than the original 60, this numeric expression describes the total number of apples.","###Write an explanation to this problem:
Create a context for the numeric representation. 601 + 60.75 = 601.75 = 105 The Utah Middle School Math Project
###Explanation:
If a person has 60 apples, then gains 75% more apples than the original 60, this numeric expression describes the total number of apples."
71,"The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.","10, -7 -14, -7 -2, 5 -2, -19","###Write an explanation to this problem:
The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.
###Explanation:
10, -7 -14, -7 -2, 5 -2, -19"
106,"Gavin is out shopping. After he buys 2 pairs of pants for 27 each, he has 60. How much money did he have before he bought the 2 pairs of pants? Write an equation to solve the problem. The Utah Middle School Math Project","Gavin has already spent 27 twice, and has 60 left. This means that m-227=60","###Write an explanation to this problem:
Gavin is out shopping. After he buys 2 pairs of pants for 27 each, he has 60. How much money did he have before he bought the 2 pairs of pants? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Gavin has already spent 27 twice, and has 60 left. This means that m-227=60"
270,7. Write three expressions containing exponents so that each expression equals 81. copied for free from openupresources.org,92 = 81because 9 x 9 = 81 34 = 81because 3 x 3 x 3 x = 81 811because 81 x 1 = 81,"###Write an explanation to this problem:
7. Write three expressions containing exponents so that each expression equals 81. copied for free from openupresources.org
###Explanation:
92 = 81because 9 x 9 = 81 34 = 81because 3 x 3 x 3 x = 81 811because 81 x 1 = 81"
435,"In Mr. Johnson's third and fourth period classes, 30% of the students scored a 95% or higher on a quiz. Let n be the the total number of students in Mr. Johnson's classes. If 15 students scored a 95% or higher, write an equation involving n that relates the number of students who scored a 95% or higher to the total number of students in Mr. Johnsons's third and fourth period classes.",0.3n = 15,"###Write an explanation to this problem:
In Mr. Johnson's third and fourth period classes, 30% of the students scored a 95% or higher on a quiz. Let n be the the total number of students in Mr. Johnson's classes. If 15 students scored a 95% or higher, write an equation involving n that relates the number of students who scored a 95% or higher to the total number of students in Mr. Johnsons's third and fourth period classes.
###Explanation:
0.3n = 15"
102,Is there an association between the weight of a candle and the amount of time it burns? Make a prediction. The Utah Middle School Math Project,The candle weight will decrease as the time burned increases,"###Write an explanation to this problem:
Is there an association between the weight of a candle and the amount of time it burns? Make a prediction. The Utah Middle School Math Project
###Explanation:
The candle weight will decrease as the time burned increases"