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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.

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.

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.

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.

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

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

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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

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'.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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.

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

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.

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

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.

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.

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.

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.

-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

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

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.

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.

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.

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

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

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.

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.

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

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.

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.

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

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.

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?

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.

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.

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.

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.

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

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

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.

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

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

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.

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.

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.

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.

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

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

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.

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

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.

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

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.

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

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.

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.

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.

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.

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.

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?

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

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.

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

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.

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

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

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

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.

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

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.

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.

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.

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

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.