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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 180â but must all be equal. 1/3 * 180 = 60 Therefore, each measure is 60â. 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 180â but must all be equal. 1/3 * 180 = 60 Therefore, each measure is 60â. 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	null	###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 ð / ð and ð / ð. ð / ð = ð, but ð / ð = ð/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 ð / ð and ð / ð. ð / ð = ð, but ð / ð = ð/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