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For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7

20 + - 9 + 8 +-7 A subtraction sign is the same thing as adding the opposite. This expression could be combined to equal 12

###Write an explanation to this problem: For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7 ###Explanation: 20 + - 9 + 8 +-7 A subtraction sign is the same thing as adding the opposite. This expression could be combined to equal 12

Jane paid 40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was 48. How do you think Jane's friend arrived at this amount?

Jane's friend found that 20% of 40 is 8. Then, she added 8 to the sale price: 40 + 8 = 48. That is how she determined that the original amount was 48.

###Write an explanation to this problem: Jane paid 40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was 48. How do you think Jane's friend arrived at this amount? ###Explanation: Jane's friend found that 20% of 40 is 8. Then, she added 8 to the sale price: 40 + 8 = 48. That is how she determined that the original amount was 48.

Write an ordered pair that would be on the y-axis when graphed. The Utah Middle School Math Project

Any ordered pair x, y where x = 0 is on the y-axis. Examples: 0, 7 0, -7 0, 0

###Write an explanation to this problem: Write an ordered pair that would be on the y-axis when graphed. The Utah Middle School Math Project ###Explanation: Any ordered pair x, y where x = 0 is on the y-axis. Examples: 0, 7 0, -7 0, 0

Make a list to find the GCF of this pair of numbers. 45 and 60 First, write the list here. The Utah Middle School Math Project

Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

###Write an explanation to this problem: Make a list to find the GCF of this pair of numbers. 45 and 60 First, write the list here. The Utah Middle School Math Project ###Explanation: Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Decide if the data set below might produce one or more gaps when represented by a histogram. If you think the data set might produce gaps, briefly describe or give an example of how the values in the data set might do so. The ages of students in a sixth-grade class.

This would not have any gaps.

###Write an explanation to this problem: Decide if the data set below might produce one or more gaps when represented by a histogram. If you think the data set might produce gaps, briefly describe or give an example of how the values in the data set might do so. The ages of students in a sixth-grade class. ###Explanation: This would not have any gaps.

Over several months, the weight of a baby measured in pounds doubles. Does its weight measure in kilograms also double? Explain

Yes, the weight is doubled. Whatever measurement you are using, if one unit of measurement doubles, then all units of measurement will double. The weights will just be different since 1lb is equal to about 0.45 kilograms.

###Write an explanation to this problem: Over several months, the weight of a baby measured in pounds doubles. Does its weight measure in kilograms also double? Explain ###Explanation: Yes, the weight is doubled. Whatever measurement you are using, if one unit of measurement doubles, then all units of measurement will double. The weights will just be different since 1lb is equal to about 0.45 kilograms.

Augusto tips 20% on his meals. If he tipped 4.80 on a meal, how much was the meal? Write an equation to solve the problem. The Utah Middle School Math Project

The percent tipped in decimal form times the original order is the amount tipped. This means 0.2*m=4.80

###Write an explanation to this problem: Augusto tips 20% on his meals. If he tipped 4.80 on a meal, how much was the meal? Write an equation to solve the problem. The Utah Middle School Math Project ###Explanation: The percent tipped in decimal form times the original order is the amount tipped. This means 0.2*m=4.80

A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org

The sample space for this experiment is the pages in the book. You have an opportunity to land at any page in the book equally.

###Write an explanation to this problem: A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org ###Explanation: The sample space for this experiment is the pages in the book. You have an opportunity to land at any page in the book equally.

Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.

There are multiple answers to this question, this is just an example: How many followers do you have on Twitter? It will produce numerical data because all of the answers we receive will be in number form.

###Write an explanation to this problem: Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data. ###Explanation: There are multiple answers to this question, this is just an example: How many followers do you have on Twitter? It will produce numerical data because all of the answers we receive will be in number form.

Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9

5 - 9 = 5 + -9

###Write an explanation to this problem: Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9 ###Explanation: 5 - 9 = 5 + -9

Create a representation of a table of data that represents a linear function. The Utah Middle School Math Project

There are many different tables that can be created that represent a linear function. One possible example is: x 1 2 3 4 5 6 y 2 4 6 8 10 12

###Write an explanation to this problem: Create a representation of a table of data that represents a linear function. The Utah Middle School Math Project ###Explanation: There are many different tables that can be created that represent a linear function. One possible example is: x 1 2 3 4 5 6 y 2 4 6 8 10 12

Solve the inequality. Represent the solution on a number line. x/0.5le;18 The Utah Middle School Math Project

Solve for x. The number line should be less than and equal to the solution.

###Write an explanation to this problem: Solve the inequality. Represent the solution on a number line. x/0.5le;18 The Utah Middle School Math Project ###Explanation: Solve for x. The number line should be less than and equal to the solution.

Give a number between -1 and -2. The Utah Middle School Math Project

Your answer can be any negative number that is less than -1 and greater than -2. Possible answers: -1.01, -1.99, -1 1/4, -3/2

###Write an explanation to this problem: Give a number between -1 and -2. The Utah Middle School Math Project ###Explanation: Your answer can be any negative number that is less than -1 and greater than -2. Possible answers: -1.01, -1.99, -1 1/4, -3/2

In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: 0 = x - 5 Original Equation: 5=x Action: ______ The Utah Middle School Math Project

On the right side of the equation, 5 has been added to x-5. On the left side, 5 has been added to 0, which results in 5. The action was: Add 5 to both sides of the equation.

###Write an explanation to this problem: In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: 0 = x - 5 Original Equation: 5=x Action: ______ The Utah Middle School Math Project ###Explanation: On the right side of the equation, 5 has been added to x-5. On the left side, 5 has been added to 0, which results in 5. The action was: Add 5 to both sides of the equation.

The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org

The first expression represents the volume of liquid in one of the containers. The second expression represents the volume of liquid in the other container. If you set the two expressions equal to each other, this means that the volume of liquid in both of the containers is equal. You are trying to solve for t to find how much time, t, must pass before the two containers have the same amount of liquid in them.

###Write an explanation to this problem: The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org ###Explanation: The first expression represents the volume of liquid in one of the containers. The second expression represents the volume of liquid in the other container. If you set the two expressions equal to each other, this means that the volume of liquid in both of the containers is equal. You are trying to solve for t to find how much time, t, must pass before the two containers have the same amount of liquid in them.

Invent a data set with five numbers that has a mean of 10 and a median of 12.

There are a variety of correct answers to this question.

###Write an explanation to this problem: Invent a data set with five numbers that has a mean of 10 and a median of 12. ###Explanation: There are a variety of correct answers to this question.

Explain ratio in your own words. Give several examples of ratios. The Utah Middle School Math Project

Sample: A ratio expresses a relationship between two quantities.

###Write an explanation to this problem: Explain ratio in your own words. Give several examples of ratios. The Utah Middle School Math Project ###Explanation: Sample: A ratio expresses a relationship between two quantities.

Priya has completed 9 exam questions. This is 60% of the questions on the exam. Write an equation representing this situation. Explain the meaning of any variables you use.

0.6x=9 x represents the total number of exam questions

###Write an explanation to this problem: Priya has completed 9 exam questions. This is 60% of the questions on the exam. Write an equation representing this situation. Explain the meaning of any variables you use. ###Explanation: 0.6x=9 x represents the total number of exam questions

Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.

Subtracting a negative number is the same as adding the positive version of that number. For example, 3 - -2 = 3 + 2. So -9.5 - -8 - 6.5 = -9.5 + 8 - 6.5.

###Write an explanation to this problem: Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. ###Explanation: Subtracting a negative number is the same as adding the positive version of that number. For example, 3 - -2 = 3 + 2. So -9.5 - -8 - 6.5 = -9.5 + 8 - 6.5.

The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org

The two sides of the equation represent the volume in the two containers.

###Write an explanation to this problem: The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t +1250 = 50t + 250 mean in this situation? copied for free from openupresources.org ###Explanation: The two sides of the equation represent the volume in the two containers.

Justine and her family are floating down a river. After 1 hour, they have floated 1.25 miles, after 4 hours they have floated 5 miles, and after 6 hours they have floated 7.5 miles. Is the relationship between time in hours and distance in miles linear? Why or why not? The Utah Middle School Math Project

This data is linear, because the relationship between the number of hours that have passed, and the distance they have floated is constant.

###Write an explanation to this problem: Justine and her family are floating down a river. After 1 hour, they have floated 1.25 miles, after 4 hours they have floated 5 miles, and after 6 hours they have floated 7.5 miles. Is the relationship between time in hours and distance in miles linear? Why or why not? The Utah Middle School Math Project ###Explanation: This data is linear, because the relationship between the number of hours that have passed, and the distance they have floated is constant.

Use the expressions and equation below about the cost of clothes to answer the questions that follow Cost of a shirt: c Cost of a pair of jeans: + 12 3 + 2 + 12 = 164 Write a story that matches the expressions and equation in the space provided. The Utah Middle School Math Project

A pair of jeans costs 12 dollars more than the cost of a shirt. Because of what these expressions are divided by in the final equation, we can see that 3 shirts were bought, and 2 pairs of jeans were bought.

###Write an explanation to this problem: Use the expressions and equation below about the cost of clothes to answer the questions that follow Cost of a shirt: c Cost of a pair of jeans: + 12 3 + 2 + 12 = 164 Write a story that matches the expressions and equation in the space provided. The Utah Middle School Math Project ###Explanation: A pair of jeans costs 12 dollars more than the cost of a shirt. Because of what these expressions are divided by in the final equation, we can see that 3 shirts were bought, and 2 pairs of jeans were bought.

Explain how to make this calculation mentally. 244 - 99

I would add 1 to 99 to make it 244 - 100= 144 and since you took one more away than you needed to, you add that one back to get 144+1=145.

###Write an explanation to this problem: Explain how to make this calculation mentally. 244 - 99 ###Explanation: I would add 1 to 99 to make it 244 - 100= 144 and since you took one more away than you needed to, you add that one back to get 144+1=145.

Make up your own pattern that is not linear. Prove that your pattern is not linear with at least 2 pieces of evidence. The Utah Middle School Math Project

A pattern is determined to be linear if the same amount of objects is being added each time. The problem asks you to create a pattern that is not linear. In order to prove that your pattern is not linear, you could draw a graph or a diagram, show math work to back up your answer, and explain in text why the pattern is not linear.

###Write an explanation to this problem: Make up your own pattern that is not linear. Prove that your pattern is not linear with at least 2 pieces of evidence. The Utah Middle School Math Project ###Explanation: A pattern is determined to be linear if the same amount of objects is being added each time. The problem asks you to create a pattern that is not linear. In order to prove that your pattern is not linear, you could draw a graph or a diagram, show math work to back up your answer, and explain in text why the pattern is not linear.

Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project

Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad.

###Write an explanation to this problem: Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project ###Explanation: Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad.

In your own words, what is the least common multiple of two whole numbers? How can you find it?

The least common multiple of two whole numbers is the lowest number that is a multiple of both of the two whole numbers. For example, the lowest common multiple of 2 and 5 is 10, because the first few multiples for 2 are 2, 4, 6, 8, 10 and the first few multiples of 5 is 5 and 10. 10 is a number that is a multiple of both, but it is also the lowest multiple they have in common.

###Write an explanation to this problem: In your own words, what is the least common multiple of two whole numbers? How can you find it? ###Explanation: The least common multiple of two whole numbers is the lowest number that is a multiple of both of the two whole numbers. For example, the lowest common multiple of 2 and 5 is 10, because the first few multiples for 2 are 2, 4, 6, 8, 10 and the first few multiples of 5 is 5 and 10. 10 is a number that is a multiple of both, but it is also the lowest multiple they have in common.

Write a story that matches the expressions and equations. Fixing Your Car Time hours: h Cost of Mike's Mechanics dollars: 15h + 75 Cost of Bubba's Body Shop dollars: 25h 15h + 75 = 25h The Utah Middle School Math Project

The cost of Mike's Mechanics is 15h + 75, meaning there must be an initial fee of 75 and for every hour you will pay an additional 15. The cost of Bubba's Body Shop is 25h, meaning you will pay 25 dollars per hour. So, when 15h +75 = 25h, the cost of Mike's Mechanics will be equal to the cost of Bubba's Body Shop. Solve for h to find out after how many hours will both shops charge the same rate to fix your car.

###Write an explanation to this problem: Write a story that matches the expressions and equations. Fixing Your Car Time hours: h Cost of Mike's Mechanics dollars: 15h + 75 Cost of Bubba's Body Shop dollars: 25h 15h + 75 = 25h The Utah Middle School Math Project ###Explanation: The cost of Mike's Mechanics is 15h + 75, meaning there must be an initial fee of 75 and for every hour you will pay an additional 15. The cost of Bubba's Body Shop is 25h, meaning you will pay 25 dollars per hour. So, when 15h +75 = 25h, the cost of Mike's Mechanics will be equal to the cost of Bubba's Body Shop. Solve for h to find out after how many hours will both shops charge the same rate to fix your car.

A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered? Explain your answer, and how you got it.

Sample response: An even number of tiles fit on the30 foot length of the room 20 tiles, but the width requires 13 1/3 tiles. This accounts for a 20 tile by 13 tile array. 20 * 13 = 260 260 tiles need to be ordered. The remaining area is 30 ft. * 0.5 ft. 20 * 1/3 tile Since 20 of the 1/3 tiles are needed, 7 additional tiles must be cut to form 21/3. 20 of these will be used with 1/3 of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles.

###Write an explanation to this problem: A classroom has a length of 30 ft. and a width of 20 ft. The flooring is to be replaced by tiles. If the tiles are square, 18 in. on a side. If these are to be installed, how many must be ordered? Explain your answer, and how you got it. ###Explanation: Sample response: An even number of tiles fit on the30 foot length of the room 20 tiles, but the width requires 13 1/3 tiles. This accounts for a 20 tile by 13 tile array. 20 * 13 = 260 260 tiles need to be ordered. The remaining area is 30 ft. * 0.5 ft. 20 * 1/3 tile Since 20 of the 1/3 tiles are needed, 7 additional tiles must be cut to form 21/3. 20 of these will be used with 1/3 of 1 tile left over. Using the same logic as above, some students may correctly say they will need 280 tiles.

Find 3 different ratios that are equivalent to 7 : 3

14:6 21:9 70:30

###Write an explanation to this problem: Find 3 different ratios that are equivalent to 7 : 3 ###Explanation: 14:6 21:9 70:30

Find a number that matches the description. A 4-digit number that is divisible by 5 and 9 but not divisible by 10. How do you know? The Utah Middle School Math Project

There are many different correct answers to this question. We want a number that is divisible by 5 and 9, but not by 10. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 9, the digits must sum to a number that is divisible by 9. To be divisible by 10, the last digit must be a 0. If we want our number to be divisible by 5 but not 10, then the last digit must be a 5. _ _ _ 5 Finally, let's pick our other three digits so that all four digits add to a number divisible by 9. This could be 5445. 5 + 4 + 4 + 5 = 18, and 18 is divisible by 9. Our number could be 5445.

###Write an explanation to this problem: Find a number that matches the description. A 4-digit number that is divisible by 5 and 9 but not divisible by 10. How do you know? The Utah Middle School Math Project ###Explanation: There are many different correct answers to this question. We want a number that is divisible by 5 and 9, but not by 10. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 9, the digits must sum to a number that is divisible by 9. To be divisible by 10, the last digit must be a 0. If we want our number to be divisible by 5 but not 10, then the last digit must be a 5. _ _ _ 5 Finally, let's pick our other three digits so that all four digits add to a number divisible by 9. This could be 5445. 5 + 4 + 4 + 5 = 18, and 18 is divisible by 9. Our number could be 5445.

Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < <

-1 < 0 < 1

###Write an explanation to this problem: Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < < ###Explanation: -1 < 0 < 1

Solve the inequality. Represent the solution on a number line. y/11<66 The Utah Middle School Math Project

Solve for y. The number line should be less than the solution, but not contain it.

###Write an explanation to this problem: Solve the inequality. Represent the solution on a number line. y/11<66 The Utah Middle School Math Project ###Explanation: Solve for y. The number line should be less than the solution, but not contain it.

Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.

This is the original problem: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 Now we can see how this problem, which began as subtraction, can be rewritten as an addition problem.

###Write an explanation to this problem: Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. ###Explanation: This is the original problem: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 Now we can see how this problem, which began as subtraction, can be rewritten as an addition problem.

Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. -14 - -2

-14 - -2 = -14 + 2

###Write an explanation to this problem: Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. -14 - -2 ###Explanation: -14 - -2 = -14 + 2

120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.

120% is equivalent to the decimal 1.2. 1.2 * x = 78 ---> The word of means to multiply

###Write an explanation to this problem: 120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78. ###Explanation: 120% is equivalent to the decimal 1.2. 1.2 * x = 78 ---> The word of means to multiply

Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org

From 8:00 am to 9:20 am, the phone lost 10% battery. This is 80 minutes time, so every 8 minutes, she will lost 1% battery. After 800 total minutes from 8:00 am, she would lose all of her battery. 8 min/1%*100% = 800 minutes 800 minutes is 13 hours and 20 minutes. 13 hours and 20 minutes from 8:00 am is 9:20 pm. We can estimate her phone will die at around 9:20 pm.

###Write an explanation to this problem: Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org ###Explanation: From 8:00 am to 9:20 am, the phone lost 10% battery. This is 80 minutes time, so every 8 minutes, she will lost 1% battery. After 800 total minutes from 8:00 am, she would lose all of her battery. 8 min/1%*100% = 800 minutes 800 minutes is 13 hours and 20 minutes. 13 hours and 20 minutes from 8:00 am is 9:20 pm. We can estimate her phone will die at around 9:20 pm.

Suppose EF and GH are line segments of the same length. Describe a sequence of transformations that moves EF to GH . Copied for free from openupresources.org

A translation of EF that moves E to G ,and then rotate EF with center G until the image of F lines up with H.

###Write an explanation to this problem: Suppose EF and GH are line segments of the same length. Describe a sequence of transformations that moves EF to GH . Copied for free from openupresources.org ###Explanation: A translation of EF that moves E to G ,and then rotate EF with center G until the image of F lines up with H.

Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true. Copied for free from openupresources.org

40,100 20,140 10,160

###Write an explanation to this problem: Triangle A is an isosceles triangle with two angles of measure x degrees and one angle of measure y degrees. Find three combinations of x and y that make this sentence true. Copied for free from openupresources.org ###Explanation: 40,100 20,140 10,160

Solve the inequality. Represent the solution on a number line. 32ge;8x The Utah Middle School Math Project

Solve for x. The number line should be less than and equal to the solution.

###Write an explanation to this problem: Solve the inequality. Represent the solution on a number line. 32ge;8x The Utah Middle School Math Project ###Explanation: Solve for x. The number line should be less than and equal to the solution.

Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < <

-1 < 0 < 1

###Write an explanation to this problem: Fill in the blank with numbers that correctly complete the statement. Three integers between 2 and -2 < < ###Explanation: -1 < 0 < 1

A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M. What letters are possible to teach using this method? There are 15

List the days of the week and highlight each of the letters only once. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY These letters are M, O, N, D, A, Y, T, U, E, S, W, H, R, F, I. Put these in order. A,D,E,F,H,I,M,N,O,R,S,T,U,W,Y

###Write an explanation to this problem: A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M. What letters are possible to teach using this method? There are 15 ###Explanation: List the days of the week and highlight each of the letters only once. MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY These letters are M, O, N, D, A, Y, T, U, E, S, W, H, R, F, I. Put these in order. A,D,E,F,H,I,M,N,O,R,S,T,U,W,Y

Here is an equation that is true for all values of x: 5x + 2 = 5x + 10. Elena saw this equation and says she can tell 20x + 2 + 31 = 45x + 10 + 31 is also true for any value of x. How can she tell? Explain your reasoning.

Elena can tell that the equation, 20x + 2 + 31 = 45x + 10 + 31, is true for any value of x, because both sides of the equation are equal and will cancel out. While the two sides do not look equal at first, the equation can be rearranged using the distributive property. First the equation can be simplified to make it easier to compare both sides. 20x + 2 + 31 = 45x + 10 + 31 Both sides have 31 being added to them so that term cancels out after subtracting 31 from both sides. 20x + 2 = 45x + 10 Within the parenthesis on the right both terms are multiples of 5, so using the distributive property, a 5 can be taken out of the parenthesis. 20x + 2 = 4*5x + 2 20x + 2 = 20x + 2 Since both sides are the same, each term will cancel out and the equation will eventually simplify to 0 = 0, making all values of x true.

###Write an explanation to this problem: Here is an equation that is true for all values of x: 5x + 2 = 5x + 10. Elena saw this equation and says she can tell 20x + 2 + 31 = 45x + 10 + 31 is also true for any value of x. How can she tell? Explain your reasoning. ###Explanation: Elena can tell that the equation, 20x + 2 + 31 = 45x + 10 + 31, is true for any value of x, because both sides of the equation are equal and will cancel out. While the two sides do not look equal at first, the equation can be rearranged using the distributive property. First the equation can be simplified to make it easier to compare both sides. 20x + 2 + 31 = 45x + 10 + 31 Both sides have 31 being added to them so that term cancels out after subtracting 31 from both sides. 20x + 2 = 45x + 10 Within the parenthesis on the right both terms are multiples of 5, so using the distributive property, a 5 can be taken out of the parenthesis. 20x + 2 = 4*5x + 2 20x + 2 = 20x + 2 Since both sides are the same, each term will cancel out and the equation will eventually simplify to 0 = 0, making all values of x true.

Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project

There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 4 + 0 = 4, so to get to the next number that is divisible by 3, 6, we have to add 2. 2 4 0 240 is divisible by 3 and 4. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144.

###Write an explanation to this problem: Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project ###Explanation: There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 4 + 0 = 4, so to get to the next number that is divisible by 3, 6, we have to add 2. 2 4 0 240 is divisible by 3 and 4. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144.

In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x + 5 = 12 Original Equation: x=7 Action: ______ The Utah Middle School Math Project

On the left side of the equation, 5 has been subtracted from x+5. On the right side, 5 has been subtracted from 12, which results in 7. The action was: Subtract 5 from both sides of the equation.

###Write an explanation to this problem: In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x + 5 = 12 Original Equation: x=7 Action: ______ The Utah Middle School Math Project ###Explanation: On the left side of the equation, 5 has been subtracted from x+5. On the right side, 5 has been subtracted from 12, which results in 7. The action was: Subtract 5 from both sides of the equation.

3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project

This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of as 3 + 3 + 3 + 3

###Write an explanation to this problem: 3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project ###Explanation: This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of as 3 + 3 + 3 + 3

In your own words, describe what it means for two figures to be congruent. The Utah Middle School Math Project

Two figures are congruent if the second can be obtained from the first by a rigid motion rotation, reflection, or translation or a sequence of rigid motions. If you can move one of the figures using one of these transformations or a series of these transformations so that it fits exactly on the other one, the two figures are congruent.

###Write an explanation to this problem: In your own words, describe what it means for two figures to be congruent. The Utah Middle School Math Project ###Explanation: Two figures are congruent if the second can be obtained from the first by a rigid motion rotation, reflection, or translation or a sequence of rigid motions. If you can move one of the figures using one of these transformations or a series of these transformations so that it fits exactly on the other one, the two figures are congruent.

Make a mapping of a relation that is a function. Explain how you know. The Utah Middle School Math Project

There are many different mappings that represent functions, so answers will vary Each input should have exactly one output

###Write an explanation to this problem: Make a mapping of a relation that is a function. Explain how you know. The Utah Middle School Math Project ###Explanation: There are many different mappings that represent functions, so answers will vary Each input should have exactly one output

Write a word problem whose solution is |20| = 20.

Kelli flew a kite 𝟐𝟎 feet above the ground. Determine the distance between the kite and the ground.

###Write an explanation to this problem: Write a word problem whose solution is |20| = 20. ###Explanation: Kelli flew a kite 𝟐𝟎 feet above the ground. Determine the distance between the kite and the ground.

Problem 7 Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 5:1 and 15:3 copied for free from openupresources.org

In order to find equivalent ratios, we multiply or divide the numbers in a ratio by the same number. So we can take one set of ratio numbers and see if we can find a number that we could multiply or divide to equal the other set of ratio numbers. If we use the 5:1 ratio, and multiply each of those by 3 we will get the 15:3 ratio. We could also take the 15:3 ratio and divide each of those by 3 to get the 5:1 ratio.

###Write an explanation to this problem: Problem 7 Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. 5:1 and 15:3 copied for free from openupresources.org ###Explanation: In order to find equivalent ratios, we multiply or divide the numbers in a ratio by the same number. So we can take one set of ratio numbers and see if we can find a number that we could multiply or divide to equal the other set of ratio numbers. If we use the 5:1 ratio, and multiply each of those by 3 we will get the 15:3 ratio. We could also take the 15:3 ratio and divide each of those by 3 to get the 5:1 ratio.

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

Describe a situation that could be modeled with the ratio 4:1.

For every four customers at a restaurant, one orders dessert.

###Write an explanation to this problem: Describe a situation that could be modeled with the ratio 4:1. ###Explanation: For every four customers at a restaurant, one orders dessert.

61% of 20 Estimate the answer. The Utah Middle School Math Project

50% of 20 is 10, so 61% of 20 must be greater than 10.

###Write an explanation to this problem: 61% of 20 Estimate the answer. The Utah Middle School Math Project ###Explanation: 50% of 20 is 10, so 61% of 20 must be greater than 10.

Create a context for the numeric representation. 601 + 60.75 = 601.75 = 105 The Utah Middle School Math Project

Sample Answer: If a person has 60 apples, then gains 75% more apples than the original 60, this numeric expression describes the total number of apples.

###Write an explanation to this problem: Create a context for the numeric representation. 601 + 60.75 = 601.75 = 105 The Utah Middle School Math Project ###Explanation: Sample Answer: If a person has 60 apples, then gains 75% more apples than the original 60, this numeric expression describes the total number of apples.

Given information: m = height of a maple tree 0.15m = 15% of the height of the maple tree Equation: m + 0.15m = 97.75 feet Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project

Since January, the maple tree in front of my house has grown by15% of its original height. It's now 97.75 feet. How tall was my tree in January?

###Write an explanation to this problem: Given information: m = height of a maple tree 0.15m = 15% of the height of the maple tree Equation: m + 0.15m = 97.75 feet Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project ###Explanation: Since January, the maple tree in front of my house has grown by15% of its original height. It's now 97.75 feet. How tall was my tree in January?

The inequalities h > 42 and h < 60 represent the height requirements for an amusement park ride, where h represents a person's height in inches. Write a sentence or draw a sign that describes these rules as clearly as possible.

You have to be at least 42 inches tall to ride, but you can not ride if you are taller than 60 inches.

###Write an explanation to this problem: The inequalities h > 42 and h < 60 represent the height requirements for an amusement park ride, where h represents a person's height in inches. Write a sentence or draw a sign that describes these rules as clearly as possible. ###Explanation: You have to be at least 42 inches tall to ride, but you can not ride if you are taller than 60 inches.

Andre would like to estimate the mean number of books the students at his school read over the summer break. He has a list of the names of all the students at the school, but he doesn't have time to ask every student how many books they read. What should Andre do to estimate the mean number of books?

There are many things that Andre could do to estimate the mean number of books. Andre could estimate the mean by using the list he has to select a random sample of the students, then asking the students in the sample how many books they read over the summer. He could choose a sample size, but it would be better to take a larger sample if he can, because this probably gives him a more accurate estimate.

###Write an explanation to this problem: Andre would like to estimate the mean number of books the students at his school read over the summer break. He has a list of the names of all the students at the school, but he doesn't have time to ask every student how many books they read. What should Andre do to estimate the mean number of books? ###Explanation: There are many things that Andre could do to estimate the mean number of books. Andre could estimate the mean by using the list he has to select a random sample of the students, then asking the students in the sample how many books they read over the summer. He could choose a sample size, but it would be better to take a larger sample if he can, because this probably gives him a more accurate estimate.

Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8.

The original equation and Andre's equation look like: 2x + 6 = 3x - 8 -x + 6 = -8 We can see that the constants 6 and -8 did not change, only the x's on both sides did. There is no longer 3x on the right hand side. Andre must have subtracted 3x from both sides of the equation. Remember that subtracting 3x is the same as adding -3x.

###Write an explanation to this problem: Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8. ###Explanation: The original equation and Andre's equation look like: 2x + 6 = 3x - 8 -x + 6 = -8 We can see that the constants 6 and -8 did not change, only the x's on both sides did. There is no longer 3x on the right hand side. Andre must have subtracted 3x from both sides of the equation. Remember that subtracting 3x is the same as adding -3x.

Find a value for x that makes -x less than 2x. copied for free from openupresources.org

If x is any positive number, -x will be less than 2x.

###Write an explanation to this problem: Find a value for x that makes -x less than 2x. copied for free from openupresources.org ###Explanation: If x is any positive number, -x will be less than 2x.

Make up a situation where a quantity is changing. Explain what it means to have a negative change.

A negative change can be a loss or expenditure.

###Write an explanation to this problem: Make up a situation where a quantity is changing. Explain what it means to have a negative change. ###Explanation: A negative change can be a loss or expenditure.

Nathan is your school's star soccer player. When he takes a shot on goal, he typically scores half of the time. Suppose that he takes six shots in a game. To estimate the probability of the number of goals Nathan makes, use simulation with a number cube. One roll of a number cube represents one shot. For this problem, what represents a trial of taking six shots?

To simulate taking six shots, we will roll the number cube six times.

###Write an explanation to this problem: Nathan is your school's star soccer player. When he takes a shot on goal, he typically scores half of the time. Suppose that he takes six shots in a game. To estimate the probability of the number of goals Nathan makes, use simulation with a number cube. One roll of a number cube represents one shot. For this problem, what represents a trial of taking six shots? ###Explanation: To simulate taking six shots, we will roll the number cube six times.

Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data.

There are multiple answers to this question, this is just an example: Are you on Instagram? Answers: Yes or No

###Write an explanation to this problem: Write two questions that you could ask the students in your class that would result in categorical data. For each question, explain how you know that responses to it would produce categorical data. ###Explanation: There are multiple answers to this question, this is just an example: Are you on Instagram? Answers: Yes or No

A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.

Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue.

###Write an explanation to this problem: A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount. ###Explanation: Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue.

Explain why 6:4 and 18:8 are not equivalent ratios.

6:4 and 18:8 are not equivalent because 6 x 3= 18, but 4 x 3= 12, not 8. In order for two ratios to be equivalent, both numbers have to be multiplied or divided by the same number. 6 4 12 8 18 12

###Write an explanation to this problem: Explain why 6:4 and 18:8 are not equivalent ratios. ###Explanation: 6:4 and 18:8 are not equivalent because 6 x 3= 18, but 4 x 3= 12, not 8. In order for two ratios to be equivalent, both numbers have to be multiplied or divided by the same number. 6 4 12 8 18 12

Solve the inequality. Represent the solution on a number line. 2ge;0.4b The Utah Middle School Math Project

Solve for b. Divide both sides of the inequality by 0.4, because this is the inverse of multiplying b by 0.4. 2/0.4 = 5 b<5 The number line should be less than and equal to the solution.

###Write an explanation to this problem: Solve the inequality. Represent the solution on a number line. 2ge;0.4b The Utah Middle School Math Project ###Explanation: Solve for b. Divide both sides of the inequality by 0.4, because this is the inverse of multiplying b by 0.4. 2/0.4 = 5 b<5 The number line should be less than and equal to the solution.

Choose an integer between -5 and -10. Label it R on a number line created and complete the following tasks. What is the opposite of R? Label it Q.

Sample response: Let R be -6, then the opposite of R is 6. Therefore, Q is 6.

###Write an explanation to this problem: Choose an integer between -5 and -10. Label it R on a number line created and complete the following tasks. What is the opposite of R? Label it Q. ###Explanation: Sample response: Let R be -6, then the opposite of R is 6. Therefore, Q is 6.

Write an ordered pair that would be in Quadrant I when graphed. The Utah Middle School Math Project

Any ordered pair x, y where both x and y are positive is in Quadrant I. Examples: 1, 1 5, 3 1/2, 3/4

###Write an explanation to this problem: Write an ordered pair that would be in Quadrant I when graphed. The Utah Middle School Math Project ###Explanation: Any ordered pair x, y where both x and y are positive is in Quadrant I. Examples: 1, 1 5, 3 1/2, 3/4

A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project

The dependent variable is number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students.

###Write an explanation to this problem: A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project ###Explanation: The dependent variable is number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students.

50% of 21 Estimate the answer. The Utah Middle School Math Project

50% of 20 is 10, so 50% of 21 must be greater than 10.

###Write an explanation to this problem: 50% of 21 Estimate the answer. The Utah Middle School Math Project ###Explanation: 50% of 20 is 10, so 50% of 21 must be greater than 10.

How can you find 50% of a number quickly in your head?

50% is half of 100%, so finding 50% of a number quickly in your head would be the same thing as dividing by 2 half.

###Write an explanation to this problem: How can you find 50% of a number quickly in your head? ###Explanation: 50% is half of 100%, so finding 50% of a number quickly in your head would be the same thing as dividing by 2 half.

An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor?

This simulation gives every flavor of ice cream a random chance of being selected. This would not accurately show the likelihood of each flavor being chose because people choose their ice cream flavor based on what they like.

###Write an explanation to this problem: An ice cream shop offers 40 different flavors. To simulate the most commonly chosen flavor, you could write the name of each flavor on a piece of paper and put it in a bag. Draw from the bag 100 times, and see which flavor is chosen the most. Why is this simulation a bad way to figure out the most commonly chosen flavor? ###Explanation: This simulation gives every flavor of ice cream a random chance of being selected. This would not accurately show the likelihood of each flavor being chose because people choose their ice cream flavor based on what they like.

Given information: s = the price of a pair of socks 5s ndash; 1 = the price of a pair of shoes Equation: 3s + 25s ndash; 1 = 56.50 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project

Sally bought 3 pairs of socks and 2 pairs of shoes. A pair of shoes costs one dollar less than 5 times the price of a pair of socks. She spent 56.50. How much does a pair of socks cost and how much does a pair of shoes cost?

###Write an explanation to this problem: Given information: s = the price of a pair of socks 5s ndash; 1 = the price of a pair of shoes Equation: 3s + 25s ndash; 1 = 56.50 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project ###Explanation: Sally bought 3 pairs of socks and 2 pairs of shoes. A pair of shoes costs one dollar less than 5 times the price of a pair of socks. She spent 56.50. How much does a pair of socks cost and how much does a pair of shoes cost?

The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Whitney is training for a half marathon. She wants to know how long it will take her to run based on how far she has to run for. The Utah Middle School Math Project

How long it will take is the dependent variable The how far she has to run for is the independent variable.

###Write an explanation to this problem: The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Whitney is training for a half marathon. She wants to know how long it will take her to run based on how far she has to run for. The Utah Middle School Math Project ###Explanation: How long it will take is the dependent variable The how far she has to run for is the independent variable.

Jayden's soccer team wins 24 of the 30 games they play in a season. Find two equivalent ratios that are smaller than the one given in the problem. Explain how you found your smaller equivalent ratios. The Utah Middle School Math Project

Ratios equivalent to 24:30 12:15 Divide each side by 2 to get this. 4:5 Divide each side by 6 to get this.

###Write an explanation to this problem: Jayden's soccer team wins 24 of the 30 games they play in a season. Find two equivalent ratios that are smaller than the one given in the problem. Explain how you found your smaller equivalent ratios. The Utah Middle School Math Project ###Explanation: Ratios equivalent to 24:30 12:15 Divide each side by 2 to get this. 4:5 Divide each side by 6 to get this.

A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?

Sample response: I would count by 5's

###Write an explanation to this problem: A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40? ###Explanation: Sample response: I would count by 5's

A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project

The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example.

###Write an explanation to this problem: A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project ###Explanation: The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example.

If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.

You would get a stronger chocolate flavor in the milkshake with 2 scoops of chocolate ice cream and 1 cup of milk because in the second milkshake they doubled the amount milk but only added 1 1/2 times the amount of chocolate ice cream. Therefore, the chocolate flavor would not be as strong as the first milkshake. If you doubled the recipe you would have 4 scoops/2 cups but instead the ratio is 3 scoops/2 cups which would be less ice cream therefore less chocolate flavor.

###Write an explanation to this problem: If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below. ###Explanation: You would get a stronger chocolate flavor in the milkshake with 2 scoops of chocolate ice cream and 1 cup of milk because in the second milkshake they doubled the amount milk but only added 1 1/2 times the amount of chocolate ice cream. Therefore, the chocolate flavor would not be as strong as the first milkshake. If you doubled the recipe you would have 4 scoops/2 cups but instead the ratio is 3 scoops/2 cups which would be less ice cream therefore less chocolate flavor.

List 4 ordered pairs that when graphed would fall on the same vertical line. The Utah Middle School Math Project

Any four ordered pairs that have the same x-value would fall on the same vertical line. Examples: 3, 0 3, 5 3, -2 These all fall on the vertical line at x = 3.

###Write an explanation to this problem: List 4 ordered pairs that when graphed would fall on the same vertical line. The Utah Middle School Math Project ###Explanation: Any four ordered pairs that have the same x-value would fall on the same vertical line. Examples: 3, 0 3, 5 3, -2 These all fall on the vertical line at x = 3.

Your teacher will give you some cards with a scale on each card. Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards. Trade places with another group and check each other's work. If you disagree about how the scales should be sorted, work to reach an agreement. copied for free from openupresources.org

1 centimeter to 1 meter, and 1 to 100 1 centimeter to 1 kilometer, 1/2 cm to 500 m, and 1 to 100,000 1 inch to 8 feet, 1/8 inch to 1 foot, and 1 to 96 1 centimeter to 10 meters, 1 inch to 1,000 inches, and 1 millimeter to 1 meter 1 foot to 1 mile, and 1 to 5,280 1 inch to 1 mile, and 1 to 63,360

###Write an explanation to this problem: Your teacher will give you some cards with a scale on each card. Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards. Trade places with another group and check each other's work. If you disagree about how the scales should be sorted, work to reach an agreement. copied for free from openupresources.org ###Explanation: 1 centimeter to 1 meter, and 1 to 100 1 centimeter to 1 kilometer, 1/2 cm to 500 m, and 1 to 100,000 1 inch to 8 feet, 1/8 inch to 1 foot, and 1 to 96 1 centimeter to 10 meters, 1 inch to 1,000 inches, and 1 millimeter to 1 meter 1 foot to 1 mile, and 1 to 5,280 1 inch to 1 mile, and 1 to 63,360

Create a representation of an equation that defines a nonlinear function. The Utah Middle School Math Project

There are many different equations that can be created that represent a nonlinear function. One possible example is: y=x2+5

###Write an explanation to this problem: Create a representation of an equation that defines a nonlinear function. The Utah Middle School Math Project ###Explanation: There are many different equations that can be created that represent a nonlinear function. One possible example is: y=x2+5

Here, write the fourth problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project

Sample Answer: Justin bought 8 bags of chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips. How many bags of chips did Justin eat? Solution: whole: 8 bags percent: 37.5% = 0.375 To find the number of bags of chips Justin ate on his way home, we multiply the whole by the percent: whole x percent = 8 bags x 0.375 = 3 bags We get that Justin ate 3 bags of the chips on his way home.

###Write an explanation to this problem: Here, write the fourth problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project ###Explanation: Sample Answer: Justin bought 8 bags of chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips. How many bags of chips did Justin eat? Solution: whole: 8 bags percent: 37.5% = 0.375 To find the number of bags of chips Justin ate on his way home, we multiply the whole by the percent: whole x percent = 8 bags x 0.375 = 3 bags We get that Justin ate 3 bags of the chips on his way home.

Write three expressions that are equivalent to 3x + 15 The Utah Middle School Math Project

Any equation that is equivalent to 3x + 15 would be a correct answer here. Some examples include 3x + 15 3x + 17 - 2 x + 2x + 15

###Write an explanation to this problem: Write three expressions that are equivalent to 3x + 15 The Utah Middle School Math Project ###Explanation: Any equation that is equivalent to 3x + 15 would be a correct answer here. Some examples include 3x + 15 3x + 17 - 2 x + 2x + 15

The following equation is given: 3x + 2x = 85 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project

The ratio of girls to boys on the track team is 3 to 2. If there are 85 people on the team, how many girls and boys are there?

###Write an explanation to this problem: The following equation is given: 3x + 2x = 85 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project ###Explanation: The ratio of girls to boys on the track team is 3 to 2. If there are 85 people on the team, how many girls and boys are there?

Each statement contains a quantity. Rewrite each quantity using a power of 10. There are about 37 trillion cells in an average human body. copied for free from openupresources.org

Sample Answer: 37*10^12

###Write an explanation to this problem: Each statement contains a quantity. Rewrite each quantity using a power of 10. There are about 37 trillion cells in an average human body. copied for free from openupresources.org ###Explanation: Sample Answer: 37*10^12

Write the expression 6 + 42 as the product of two factors. The Utah Middle School Math Project

Example: 23x+21

###Write an explanation to this problem: Write the expression 6 + 42 as the product of two factors. The Utah Middle School Math Project ###Explanation: Example: 23x+21

Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org

-7, -8 , -9 -3x > 18 x < -6 x needs to be a number that is less than -6

###Write an explanation to this problem: Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org ###Explanation: -7, -8 , -9 -3x > 18 x < -6 x needs to be a number that is less than -6

A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount.

Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue.

###Write an explanation to this problem: A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the same shade of green but a smaller amount. ###Explanation: Example mixture: 1 yellow, 1.75 blue To get the same shade of green, we need the same ratio of yellow to blue. The green paint is made with 2 cups of yellow and 3.5 cups of blue, so the ratio is 2:3.5. We can divide both sides of the ratio by 2 and get the equivalent ratio of 1:1.75, meaning that for every 1 cup of yellow we use 1.75 cups of blue.

Write a story that matches the expressions and equations. World Languages Number of years: t of students in French: 160 - 9t of students in Spanish: 85 + 6t 160 - 9t = 85 + 6t The Utah Middle School Math Project

Initially at t = 0 years, there must be 160 students in French and 85 students in Spanish. Each year, the number of students in French will decrease by 9 and the number of students in Spanish will increase by 6. So 160 - 9t is the number of students in French after t years and 85 + 6t is the number of students in Spanish after t years. When 160 - 9t = 85 + 6t, there will be the same number of students will be in French class as there are in Spanish class. After how many years will the number of students in French class be the same as the number of students in Spanish class?

###Write an explanation to this problem: Write a story that matches the expressions and equations. World Languages Number of years: t of students in French: 160 - 9t of students in Spanish: 85 + 6t 160 - 9t = 85 + 6t The Utah Middle School Math Project ###Explanation: Initially at t = 0 years, there must be 160 students in French and 85 students in Spanish. Each year, the number of students in French will decrease by 9 and the number of students in Spanish will increase by 6. So 160 - 9t is the number of students in French after t years and 85 + 6t is the number of students in Spanish after t years. When 160 - 9t = 85 + 6t, there will be the same number of students will be in French class as there are in Spanish class. After how many years will the number of students in French class be the same as the number of students in Spanish class?

Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.

Elena could have the computer pick any 3 integers from 1 to 100. If either 2 or three of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and use the data to estimate the probability by finding the proportion of the trials that had a successful outcome.

###Write an explanation to this problem: Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times. ###Explanation: Elena could have the computer pick any 3 integers from 1 to 100. If either 2 or three of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and use the data to estimate the probability by finding the proportion of the trials that had a successful outcome.

6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org

60% of c means to multiply 60% and c. Is means equal to. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.6c=43.2

###Write an explanation to this problem: 6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org ###Explanation: 60% of c means to multiply 60% and c. Is means equal to. In order to multiply by a percent, you will need to change the percent to a decimal first. 0.6c=43.2

When is it better to use a table? When is it better to use a scatter plot? Copied for free from openupresources.org

Sample Answer: Scatter plots are best when looking for an overall pattern or lack of one. Tables are best when looking for the precise details of the data.

###Write an explanation to this problem: When is it better to use a table? When is it better to use a scatter plot? Copied for free from openupresources.org ###Explanation: Sample Answer: Scatter plots are best when looking for an overall pattern or lack of one. Tables are best when looking for the precise details of the data.

Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain.

-9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 When we add two negative terms, the signs are both negative. Will the sum be negative or positive? Will we add or subtract the absolute values? We will add the absolute values and put the common sign, so our new equation is as follows: -9.5+ -6.5 + 8 -16 + 8 -16 has a greater absolute value than 8. -16 is negative. Will the final answer be negative or positive?

###Write an explanation to this problem: Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. -9.5 - -8- 6.5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. ###Explanation: -9.5 - -8 - 6.5 This problem has subtraction in it, so we will begin by rewriting subtraction by adding the opposite: -9.5 - -8 - 6.5 -9.5 + +8 + ndash;6.5 -9.5 + 8 + -6.5 We might begin by regrouping the terms so the negative terms are together: -9.5+ -6.5 + 8 When we add two negative terms, the signs are both negative. Will the sum be negative or positive? Will we add or subtract the absolute values? We will add the absolute values and put the common sign, so our new equation is as follows: -9.5+ -6.5 + 8 -16 + 8 -16 has a greater absolute value than 8. -16 is negative. Will the final answer be negative or positive?

Four families are renting a house together on vacation. If each family pays 75 per night to rent the house, what is the total cost of the house each night? Write an equation to solve the problem. The Utah Middle School Math Project

Each family spends 75 a night, and the total cost is split 4 ways, so the cost of the house is h/4=75

###Write an explanation to this problem: Four families are renting a house together on vacation. If each family pays 75 per night to rent the house, what is the total cost of the house each night? Write an equation to solve the problem. The Utah Middle School Math Project ###Explanation: Each family spends 75 a night, and the total cost is split 4 ways, so the cost of the house is h/4=75

In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC is an acute triangle.

Sample response: To make an acute triangle, the other two angles must measure less than 90 degrees for example: 60, 70.

###Write an explanation to this problem: In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC is an acute triangle. ###Explanation: Sample response: To make an acute triangle, the other two angles must measure less than 90 degrees for example: 60, 70.

Name the parts of the expression. 14b

14 is the coefficient b is the variable 14b is a term and is the product of 14 and b

###Write an explanation to this problem: Name the parts of the expression. 14b ###Explanation: 14 is the coefficient b is the variable 14b is a term and is the product of 14 and b

You and your friends go to a BMX dirt-biking race. For one of the events, the competitors are going off a jump. The winner of the event is the competitor that gets the most air or jumps the highest. Do you think the relationship between the weight of the bike and the height of the jump can be modeled by a linear relationship? Why or why not? The Utah Middle School Math Project

Logically, it makes sense that as the weight of the bike increases, the height of the jump may decrease. This is linear, because - for example - for each 1 pound increase in weight, a biker jumps 1 cm lower or 0.5 cm lower.

###Write an explanation to this problem: You and your friends go to a BMX dirt-biking race. For one of the events, the competitors are going off a jump. The winner of the event is the competitor that gets the most air or jumps the highest. Do you think the relationship between the weight of the bike and the height of the jump can be modeled by a linear relationship? Why or why not? The Utah Middle School Math Project ###Explanation: Logically, it makes sense that as the weight of the bike increases, the height of the jump may decrease. This is linear, because - for example - for each 1 pound increase in weight, a biker jumps 1 cm lower or 0.5 cm lower.

6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org

0.60c = 43.2 First, you need to change 60% to a decimal in order to be able to use it with an operation. 60% is equal to 0.60. Next, 60% of c means that you are multiplying because of implies multiplication. Lastly is implies what the expression is equal to.

###Write an explanation to this problem: 6. 60% of c is 43.2. a. Write an equation to help you find the value of each variable. copied for free from openupresources.org ###Explanation: 0.60c = 43.2 First, you need to change 60% to a decimal in order to be able to use it with an operation. 60% is equal to 0.60. Next, 60% of c means that you are multiplying because of implies multiplication. Lastly is implies what the expression is equal to.

Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project

Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output To better visualize this, try creating a table, graph, or equation that could represent the data given

###Write an explanation to this problem: Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project ###Explanation: Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output To better visualize this, try creating a table, graph, or equation that could represent the data given

Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org

9:20 pm

###Write an explanation to this problem: Lin's smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will die? Copied for free from openupresources.org ###Explanation: 9:20 pm

Use The Distributive Property to find the product. 719 First, show your work here. The Utah Middle School Math Project

719 = 720 - 1 = 720 - 71 = 140 - 7 = 133

###Write an explanation to this problem: Use The Distributive Property to find the product. 719 First, show your work here. The Utah Middle School Math Project ###Explanation: 719 = 720 - 1 = 720 - 71 = 140 - 7 = 133

Beckham is interested in the hand span, the length from the tip of the pinky finger to the tip of the thumb, for people in his class. He asks the statistical question, How long is the hand span for people in my class? He decides to conduct a survey to answer his question. His data is shown below. Length of hand span in inches: 6, 6.5, 9, 7.5, 7.5, 7, 6.5, 7, 7, 9.5, 6, 8, 5.5, 7, 6.5 What is the attribute that is being measured?

The attribute being measured is the lengths of hand span.

###Write an explanation to this problem: Beckham is interested in the hand span, the length from the tip of the pinky finger to the tip of the thumb, for people in his class. He asks the statistical question, How long is the hand span for people in my class? He decides to conduct a survey to answer his question. His data is shown below. Length of hand span in inches: 6, 6.5, 9, 7.5, 7.5, 7, 6.5, 7, 7, 9.5, 6, 8, 5.5, 7, 6.5 What is the attribute that is being measured? ###Explanation: The attribute being measured is the lengths of hand span.