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206 | Use the equation 135 * 42 = 5,670 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute 1.35 * 4.2. | We know that you can ignore decimal places when you multiply until you have your product. Then count the number of decimal places in the factors and more the decimal over that many times in the product. In this case, they just need to add the 3 decimal places to the product of 5,670 to make it 5.67. | ###Write an explanation to this problem:
Use the equation 135 * 42 = 5,670 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute 1.35 * 4.2.
###Explanation:
We know that you can ignore decimal places when you multiply until you have your product. Then count the number of decimal places in the factors and more the decimal over that many times in the product. In this case, they just need to add the 3 decimal places to the product of 5,670 to make it 5.67. |
392 | The expressions below show the grams of fat in sandwiches at a popular fast food restaurant. Use these expressions and the equation to write a story. Fast Food Calories: Crispy Chicken: f Single burger with cheese: f + 11 Double burger with cheese: 2f 3f + 2f + 11 + 42f = 204 g. The Utah Middle School Math Project | The given expressions can be put into words that create a story. From the expressions, we know a crispy chicken has f fat grams. The expressions also show that a single burger with cheese has 11 more fat grams than a crispy chicken, while a double burger with cheese has two times more fat grams than a crispy chicken. The equation shows that 3 crispy chickens plus 2 single burgers with cheese plus 4 double burgers with cheese have a total of 204 fat grams. | ###Write an explanation to this problem:
The expressions below show the grams of fat in sandwiches at a popular fast food restaurant. Use these expressions and the equation to write a story. Fast Food Calories: Crispy Chicken: f Single burger with cheese: f + 11 Double burger with cheese: 2f 3f + 2f + 11 + 42f = 204 g. The Utah Middle School Math Project
###Explanation:
The given expressions can be put into words that create a story. From the expressions, we know a crispy chicken has f fat grams. The expressions also show that a single burger with cheese has 11 more fat grams than a crispy chicken, while a double burger with cheese has two times more fat grams than a crispy chicken. The equation shows that 3 crispy chickens plus 2 single burgers with cheese plus 4 double burgers with cheese have a total of 204 fat grams. |
397 | During her Tuesday shift at Sweater Barn, Fiona sells the same amount of sweaters per hour. Two hours into her shift Fiona has sold 8 sweaters. Find and describe the rate of change for this relationship. The Utah Middle School Math Project | We know that in two hours, Fiona sold 8 sweaters, but she sold the same amount each hour. This means we can divide 8/2 to find that Fiona sold 4 sweaters each hour. The rate of change for this relationship is 4 sweaters sold every hour. | ###Write an explanation to this problem:
During her Tuesday shift at Sweater Barn, Fiona sells the same amount of sweaters per hour. Two hours into her shift Fiona has sold 8 sweaters. Find and describe the rate of change for this relationship. The Utah Middle School Math Project
###Explanation:
We know that in two hours, Fiona sold 8 sweaters, but she sold the same amount each hour. This means we can divide 8/2 to find that Fiona sold 4 sweaters each hour. The rate of change for this relationship is 4 sweaters sold every hour. |
723 | Write two ratios that are equivalent to 3:11. | Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 3x2:11x2 = 6:22 3x3:11x3 = 9:33 Or any ratio that simplifies to 3:11 | ###Write an explanation to this problem:
Write two ratios that are equivalent to 3:11.
###Explanation:
Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 3x2:11x2 = 6:22 3x3:11x3 = 9:33 Or any ratio that simplifies to 3:11 |
217 | Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times. | Elena could have the computer generate 3 random integers between 1 and 100. If at least 2 of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and estimate the probability as the proportion of trials for which at least 2 of the numbers are between 1 and 15. | ###Write an explanation to this problem:
Elena is programming a video game. She needs to simulate the power-up that the player gets when they reach a certain level. The computer can run a program to return a random integer between 1 and 100. Elena wants the best power-up to be rewarded 15% of the time. Explain how Elena could use the computer to simulate the player getting the best power-up at least 2 out of 3 times.
###Explanation:
Elena could have the computer generate 3 random integers between 1 and 100. If at least 2 of the numbers are between 1 and 15, then the player got the best power-up at least twice. She could repeat this process many times and estimate the probability as the proportion of trials for which at least 2 of the numbers are between 1 and 15. |
4 | Find a value for a that makes the statement true. n / 6 is greater than 1 | Any number divided by itself =1 so 6 divided by 6 =1. Any values greater than 6 would be greater than 1 when you divide. A value that could work would be anything a>6 | ###Write an explanation to this problem:
Find a value for a that makes the statement true. n / 6 is greater than 1
###Explanation:
Any number divided by itself =1 so 6 divided by 6 =1. Any values greater than 6 would be greater than 1 when you divide. A value that could work would be anything a>6 |
642 | If you flipped the coin 100 times, how many heads would you expect to get? Explain your answer. The Utah Middle School Math Project | Sample Answer: We would expect to get a head about 1/2 of the time. So, if we flip the coin 100 times, we would expect to get 1001/2 = 50 heads. | ###Write an explanation to this problem:
If you flipped the coin 100 times, how many heads would you expect to get? Explain your answer. The Utah Middle School Math Project
###Explanation:
Sample Answer: We would expect to get a head about 1/2 of the time. So, if we flip the coin 100 times, we would expect to get 1001/2 = 50 heads. |
763 | Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market. | Since a loss of 500 in the stock market is worse than a gain of 200 in the stock market, the inequality is: -500 < 200 | ###Write an explanation to this problem:
Write an inequality that relates the rational numbers. A loss of 500 in the stock market is worse than a gain of 200 in the stock market.
###Explanation:
Since a loss of 500 in the stock market is worse than a gain of 200 in the stock market, the inequality is: -500 < 200 |
612 | The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. -3,?,0,5 The Utah Middle School Math Project | In this question, the ? falls between -3 and 0, so the integer that replaces the ? must be greater than -3 but less than 0. The only two integers where this is true are -2 and -1. | ###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in the problem. Use a number line to help you. -3,?,0,5 The Utah Middle School Math Project
###Explanation:
In this question, the ? falls between -3 and 0, so the integer that replaces the ? must be greater than -3 but less than 0. The only two integers where this is true are -2 and -1. |
546 | Here, write the first problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project | Sample Answer: Tom wants to buy a laptop that costs 800. Due to his membership, he can use a 15% discount on his purchase. How much did he pay for the laptop? Solution: whole: 800 percent: 15% = 0.15 First, we find the amount he saved, we multiply the whole by the percent: whole x percent = 800 x 0.15 = 120 Then, to find the amount he paid, we subtract the amount he saved from the original price, which is the whole: amount paid = original price - amount paid = 800 - 120 = 680 We get that Tom paid 680 for the laptop. | ###Write an explanation to this problem:
Here, write the first problem in which the percent and the whole are known, but the part is not known, and its solution. The Utah Middle School Math Project
###Explanation:
Sample Answer: Tom wants to buy a laptop that costs 800. Due to his membership, he can use a 15% discount on his purchase. How much did he pay for the laptop? Solution: whole: 800 percent: 15% = 0.15 First, we find the amount he saved, we multiply the whole by the percent: whole x percent = 800 x 0.15 = 120 Then, to find the amount he paid, we subtract the amount he saved from the original price, which is the whole: amount paid = original price - amount paid = 800 - 120 = 680 We get that Tom paid 680 for the laptop. |
683 | Create a context for the numeric representation. 5001 ndash; 5001/5 = 400 The Utah Middle School Math Project | Sample Answer: If a person has 500 apples, then loses 1/5 of the apples, this numeric expression describes how many apples they have left. | ###Write an explanation to this problem:
Create a context for the numeric representation. 5001 ndash; 5001/5 = 400 The Utah Middle School Math Project
###Explanation:
Sample Answer: If a person has 500 apples, then loses 1/5 of the apples, this numeric expression describes how many apples they have left. |
98 | Write a sentence to answer the question: How much warmer is 82 than 40? | The distance between 82 and 40 can be found by subtracting 82 -40=42 82 is 42 degrees warmer than 40. | ###Write an explanation to this problem:
Write a sentence to answer the question: How much warmer is 82 than 40?
###Explanation:
The distance between 82 and 40 can be found by subtracting 82 -40=42 82 is 42 degrees warmer than 40. |
573 | Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project | Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad. | ###Write an explanation to this problem:
Write a context to match the numeric expression given. 10 - 30.75 - 20.50 The Utah Middle School Math Project
###Explanation:
Tom has 10 dollars. He is at the store that sells books for 0.75 and cups for 0.50. He wants to buy one book for each of his 3 brothers, and one cup for his mom and one cup for his dad. |
406 | Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project | Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 | ###Write an explanation to this problem:
Make a list to find the GCF of this pair of numbers. 20 and 64 First, write the list here. The Utah Middle School Math Project
###Explanation:
Factors of 20: 1, 2, 4, 5, 10, 20Factors of 64: 1, 2, 4, 8, 16, 32, 64 |
502 | Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project | A triangular prism cut parallel to the base will always result in a traingular cross-section. | ###Write an explanation to this problem:
Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project
###Explanation:
A triangular prism cut parallel to the base will always result in a traingular cross-section. |
47 | A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches. Is the baseball's volume greater than, less than, or equal to 2.93 cubic inches? Explain how you know. Copied for free from openupresources.org | The baseball fits inside the cube, and the cube's volume is 2.93 cubic inches so the volume of the baseball would have to be less than 2.93 cubic units. | ###Write an explanation to this problem:
A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches. Is the baseball's volume greater than, less than, or equal to 2.93 cubic inches? Explain how you know. Copied for free from openupresources.org
###Explanation:
The baseball fits inside the cube, and the cube's volume is 2.93 cubic inches so the volume of the baseball would have to be less than 2.93 cubic units. |
32 | Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle. | Andre is 13, his brother is 16, his sister is 11, and his mom is 47. | ###Write an explanation to this problem:
Andre came up with the following puzzle. I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages? Try to solve the puzzle.
###Explanation:
Andre is 13, his brother is 16, his sister is 11, and his mom is 47. |
200 | A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem? | Sample Answer: You may need to know how big the bucket is, the rate of water flow, the height of the bucket, and how high the water in the bucket is after one minute. | ###Write an explanation to this problem:
A water bucket is being filled with water from a water faucet at a constant rate. When will the bucket be full? What information would you need to be able to solve the problem?
###Explanation:
Sample Answer: You may need to know how big the bucket is, the rate of water flow, the height of the bucket, and how high the water in the bucket is after one minute. |
134 | Name the parts of the expression. 30jk | 30 is the coefficient j and k are the variables 30jk is a term and is the product of 30 * j * k | ###Write an explanation to this problem:
Name the parts of the expression. 30jk
###Explanation:
30 is the coefficient j and k are the variables 30jk is a term and is the product of 30 * j * k |
27 | Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph. | I would start by plotting the y intercept 0,-1 and then from that point I would count down 4 units and to the right 1 unit and plot another point. I would then draw a line through both of these points to create the graph. | ###Write an explanation to this problem:
Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.
###Explanation:
I would start by plotting the y intercept 0,-1 and then from that point I would count down 4 units and to the right 1 unit and plot another point. I would then draw a line through both of these points to create the graph. |
749 | Fill in the blank with numbers that correctly complete the statement. Three rational numbers between 16 and 15 < < | 15.3 < 15.6 < 15.7 | ###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three rational numbers between 16 and 15 < <
###Explanation:
15.3 < 15.6 < 15.7 |
230 | 80% of x is equal to 100. Write an equation that shows the relationship of 80%, x and 100. | 0.8x=100 | ###Write an explanation to this problem:
80% of x is equal to 100. Write an equation that shows the relationship of 80%, x and 100.
###Explanation:
0.8x=100 |
489 | Give an example of an irrational number between 8 and 9. The Utah Middle School Math Project | An irrational number is a number that cannot be expressed as a fraction for any integers. So, an irrational number between 8 and 9 could be 2.8pi;, which has a value of about 8.8. | ###Write an explanation to this problem:
Give an example of an irrational number between 8 and 9. The Utah Middle School Math Project
###Explanation:
An irrational number is a number that cannot be expressed as a fraction for any integers. So, an irrational number between 8 and 9 could be 2.8pi;, which has a value of about 8.8. |
378 | How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know? copied for free from openupresources.org | If you could find the length and width of each side of the cabinet, you could find the area of each side and then add them all together. | ###Write an explanation to this problem:
How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know? copied for free from openupresources.org
###Explanation:
If you could find the length and width of each side of the cabinet, you could find the area of each side and then add them all together. |
288 | 11. Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote: 228 = 2 * 28 = 56 Elena said, No, exponents mean repeated multiplication. It should be 28 * 28, which works out to be 784. Do you agree with either of them? Explain your reasoning. copied for free from openupresources.org | Neither are correct. 228 is saying that you are multiply 2 by itself 28 times. When you multiply this out, you get 268,435,456 | ###Write an explanation to this problem:
11. Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote: 228 = 2 * 28 = 56 Elena said, No, exponents mean repeated multiplication. It should be 28 * 28, which works out to be 784. Do you agree with either of them? Explain your reasoning. copied for free from openupresources.org
###Explanation:
Neither are correct. 228 is saying that you are multiply 2 by itself 28 times. When you multiply this out, you get 268,435,456 |
418 | Dane goes to a fast food restaurant and orders some tacos t and burritos b. Write a story that matches the system of equations shown below that describes the number of items Dane ordered and how many calories he consumed. t + b = 5 170t + 370b = 1250 The Utah Middle School Math Project | Sample Answer: Dane went to a restaurant and ordered some tacos and burritos. He ordered a total of 5 items. Tacos have 170 calories each and burritos have 370 calories each. If Dane consumed 1,250 calories, how many of each item did he order? | ###Write an explanation to this problem:
Dane goes to a fast food restaurant and orders some tacos t and burritos b. Write a story that matches the system of equations shown below that describes the number of items Dane ordered and how many calories he consumed. t + b = 5 170t + 370b = 1250 The Utah Middle School Math Project
###Explanation:
Sample Answer: Dane went to a restaurant and ordered some tacos and burritos. He ordered a total of 5 items. Tacos have 170 calories each and burritos have 370 calories each. If Dane consumed 1,250 calories, how many of each item did he order? |
674 | -5 x -3 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project | This multiplication problem asks that you take the integer -5 and multiply it -3 times, so -5 x -3 can be thought of as the opposite of -5 x 3, which is -5 + -5 + -5. The opposite of -5 + -5 + -5 is 5 + 5 + 5 | ###Write an explanation to this problem:
-5 x -3 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -5 and multiply it -3 times, so -5 x -3 can be thought of as the opposite of -5 x 3, which is -5 + -5 + -5. The opposite of -5 + -5 + -5 is 5 + 5 + 5 |
391 | During the summer, Victoria plays soccer and takes swim and piano lessons. Each swim lesson is 15 minutes shorter than a soccer practice. Each piano lesson is twice as long as a soccer practice. Use this information to answer the questions that follow. The following expressions represent how long an activity is each time she goes. Write the name of the activity that matches t: The Utah Middle School Math Project | The variable t is representative of the amount of time she spends at soccer practice. | ###Write an explanation to this problem:
During the summer, Victoria plays soccer and takes swim and piano lessons. Each swim lesson is 15 minutes shorter than a soccer practice. Each piano lesson is twice as long as a soccer practice. Use this information to answer the questions that follow. The following expressions represent how long an activity is each time she goes. Write the name of the activity that matches t: The Utah Middle School Math Project
###Explanation:
The variable t is representative of the amount of time she spends at soccer practice. |
592 | Write three expressions equivalent to the expression 6 + 5. The Utah Middle School Math Project | There are many expressions that are equivalent to 6b + 5. Some examples are the expressions 23b + 2 + 3, 3b + 3b + 5, 5b + b + 10 - 5. | ###Write an explanation to this problem:
Write three expressions equivalent to the expression 6 + 5. The Utah Middle School Math Project
###Explanation:
There are many expressions that are equivalent to 6b + 5. Some examples are the expressions 23b + 2 + 3, 3b + 3b + 5, 5b + b + 10 - 5. |
498 | Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project | ð¥ + ð¦ = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1ð¥ + 2.5ð¦ = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982 | ###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. In 1982, the US Mint changed the composition of pennies from all copper to zinc with copper coating. Pennies made prior to 1982 weigh 3.1 grams. Pennies made since 1982 weigh 2.5 grams. If you have a bag of 1,254 pennies, and the bag weighs 3,508.8 grams, how many pennies from each time period are there in the bag? The Utah Middle School Math Project
###Explanation:
ð¥ + ð¦ = 1254 where x is the number of coins made prior to 1982 and y is the number of coins made since 1982 3.1ð¥ + 2.5ð¦ = 3508.8 There are 623 pennies made prior to 1982 and 631 pennies made since 1982 |
138 | Give a number between -6.1 and -6.2. The Utah Middle School Math Project | Negative numbers are the opposite of positive numbers. This means that the opposites of -6.1 and -6.2 are 6.1 and 6.2. A number that is between -6.1 and -6.2 will have its opposite between 6.1 and 6.2. There are many numbers between 6.1 and 6.2. For example: 6.11, 6.15, 6.19, and so on If we take the opposite, then these numbers are between -6.1 and -6.2. For example: -6.11, -6.15, -6.19, and so on | ###Write an explanation to this problem:
Give a number between -6.1 and -6.2. The Utah Middle School Math Project
###Explanation:
Negative numbers are the opposite of positive numbers. This means that the opposites of -6.1 and -6.2 are 6.1 and 6.2. A number that is between -6.1 and -6.2 will have its opposite between 6.1 and 6.2. There are many numbers between 6.1 and 6.2. For example: 6.11, 6.15, 6.19, and so on If we take the opposite, then these numbers are between -6.1 and -6.2. For example: -6.11, -6.15, -6.19, and so on |
62 | Here is an inequality: -2x > 10. List some values for x that would make this inequality true. | -5, -6, -7. ... | ###Write an explanation to this problem:
Here is an inequality: -2x > 10. List some values for x that would make this inequality true.
###Explanation:
-5, -6, -7. ... |
471 | The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The total number of laps run depends on the length of each workout. The Utah Middle School Math Project | Time length is the independent variable. The number of laps is the dependent on the length of the workout. Number of laps is the dependent variable. | ###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. The total number of laps run depends on the length of each workout. The Utah Middle School Math Project
###Explanation:
Time length is the independent variable. The number of laps is the dependent on the length of the workout. Number of laps is the dependent variable. |
647 | -2 x 6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project | This multiplication problem asks that you take the integer -2 and multiply it 6 times, so -2 x 6 can be thought of as -2 + -2 + -2 + -2 + -2 + -2 | ###Write an explanation to this problem:
-2 x 6 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -2 and multiply it 6 times, so -2 x 6 can be thought of as -2 + -2 + -2 + -2 + -2 + -2 |
128 | Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope m is changed to ndash;m. The Utah Middle School Math Project | The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the slope is changed from m to -m, then we know that the slopes will have the same absolute value but opposite signs. One line will be positive and the other will be negative, but they will still have the same steepness. This transformation can be described as a reflection across the y-axis. | ###Write an explanation to this problem:
Describe the transformation graph shift that occurs in the following situation. Use words like translation, reflection, and rotation. The slope m is changed to ndash;m. The Utah Middle School Math Project
###Explanation:
The slope is the rate of change of the line and determines the steepness of the line. The y-intercept is the point where the line intersects with the y-axis. If the slope is changed from m to -m, then we know that the slopes will have the same absolute value but opposite signs. One line will be positive and the other will be negative, but they will still have the same steepness. This transformation can be described as a reflection across the y-axis. |
831 | What information do you need to know to write an equation relating two quantities that have a proportional relationship? | You would need to know the number of knots per row which would be the constant of proportionality. | ###Write an explanation to this problem:
What information do you need to know to write an equation relating two quantities that have a proportional relationship?
###Explanation:
You would need to know the number of knots per row which would be the constant of proportionality. |
520 | Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project | w= 2rÂwhere w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles. | ###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project
###Explanation:
w= 2rÂwhere w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles. |
64 | Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home. Andre wrote the inequality 3x + 10 le; 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality. | x: The number of small paper cranes Andre will make 3x: The time it takes to make a small paper crane. 10: The time it take Andre to make the centerpiece 30: The amount of time Andre has to make the cranes when he gets home. | ###Write an explanation to this problem:
Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home. Andre wrote the inequality 3x + 10 le; 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.
###Explanation:
x: The number of small paper cranes Andre will make 3x: The time it takes to make a small paper crane. 10: The time it take Andre to make the centerpiece 30: The amount of time Andre has to make the cranes when he gets home. |
14 | Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1 | -0.2 is to the left of -0.1, or -0.1 is to the right of -0.2. | ###Write an explanation to this problem:
Describe the relative position of the numbers on a horizontal number line. -0.2 < -0.1
###Explanation:
-0.2 is to the left of -0.1, or -0.1 is to the right of -0.2. |
156 | Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org | 1.5b+3g=12 | ###Write an explanation to this problem:
Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org
###Explanation:
1.5b+3g=12 |
40 | Explain how to make this calculation mentally. 244 - 99 | 99 is close to 100 by 1 number. 244-100=144 but since you subtracted 100 instead of 99, there was 1 extra subtracted so you should add 1 to your answer to make up for the extra 1 subtracted. 144+1=145. This is how you would do 244-99=145 mentally. | ###Write an explanation to this problem:
Explain how to make this calculation mentally. 244 - 99
###Explanation:
99 is close to 100 by 1 number. 244-100=144 but since you subtracted 100 instead of 99, there was 1 extra subtracted so you should add 1 to your answer to make up for the extra 1 subtracted. 144+1=145. This is how you would do 244-99=145 mentally. |
492 | Write an ordered pair that would be in Quadrant III when graphed. The Utah Middle School Math Project | Any ordered pair x, y where both x and y are negative is in Quadrant III. Examples: -1, -1 -5, -3 -1/2, -3/4 | ###Write an explanation to this problem:
Write an ordered pair that would be in Quadrant III when graphed. The Utah Middle School Math Project
###Explanation:
Any ordered pair x, y where both x and y are negative is in Quadrant III. Examples: -1, -1 -5, -3 -1/2, -3/4 |
379 | 7. Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson. copied for free from openupresources.org | A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps. | ###Write an explanation to this problem:
7. Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson. copied for free from openupresources.org
###Explanation:
A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps. |
187 | Elena wants to know what proportion of people have cats as pets. Describe a process she could use to estimate an answer to her question. | She could collect a random sample of people perhaps by asking 50-100 people who come out of a store if they have a cat. She could determine the proportion of people that have cats by dividing the number of people who said yes by the number of people in her sample | ###Write an explanation to this problem:
Elena wants to know what proportion of people have cats as pets. Describe a process she could use to estimate an answer to her question.
###Explanation:
She could collect a random sample of people perhaps by asking 50-100 people who come out of a store if they have a cat. She could determine the proportion of people that have cats by dividing the number of people who said yes by the number of people in her sample |
216 | In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game. | If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day. | ###Write an explanation to this problem:
In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game.
###Explanation:
If the number is between 1 and 15, the video game should create a rainy day. If the number is between 16 and 50, the video game should not create a rainy day. |
52 | Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school? | The mean number of siblings for all the students in a school can be approximated by thinking of the number of siblings each student may have. To make the approximate value easier, all of the numbers can be rounded to whole numbers. If about 20% of the school is an only child, 40% has one sibling 20% have two siblings 10% have three siblings 10% have four or more, then the mean number of siblings should be roughly between 1 and 3. The mean number of students can change based on the students at your school. | ###Write an explanation to this problem:
Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school?
###Explanation:
The mean number of siblings for all the students in a school can be approximated by thinking of the number of siblings each student may have. To make the approximate value easier, all of the numbers can be rounded to whole numbers. If about 20% of the school is an only child, 40% has one sibling 20% have two siblings 10% have three siblings 10% have four or more, then the mean number of siblings should be roughly between 1 and 3. The mean number of students can change based on the students at your school. |
337 | Here is an equation: 4x - 4 = 4x + __. What could you write in the blank so the equation would be true for: No values of x Copied for free from openupresources.org | We have 4x on both sides of this equation. We know that if we insert a constant into this blank, then there would still only be 4x on both sides of the equation. If we subtract 4x from both sides, we get: -4 = ___ If we want this to not be true, then we would need for the constant in the blank to not equal -4. The answer is any constant not equal to -4. Example: -2, 5, 9 | ###Write an explanation to this problem:
Here is an equation: 4x - 4 = 4x + __. What could you write in the blank so the equation would be true for: No values of x Copied for free from openupresources.org
###Explanation:
We have 4x on both sides of this equation. We know that if we insert a constant into this blank, then there would still only be 4x on both sides of the equation. If we subtract 4x from both sides, we get: -4 = ___ If we want this to not be true, then we would need for the constant in the blank to not equal -4. The answer is any constant not equal to -4. Example: -2, 5, 9 |
748 | Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < < | -3 < -2 < -1 | ###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < <
###Explanation:
-3 < -2 < -1 |
719 | To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio. | Answers vary. Sample response: 12 cups of pink paint to 10 cups of blue paint and 18 cups of pink paint to 15 cups of blue paint. This is 2 batches and 3 batches, respectively, of this shade of lavender paint. | ###Write an explanation to this problem:
To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.
###Explanation:
Answers vary. Sample response: 12 cups of pink paint to 10 cups of blue paint and 18 cups of pink paint to 15 cups of blue paint. This is 2 batches and 3 batches, respectively, of this shade of lavender paint. |
724 | Write two ratios that are equivalent to 1:1. | Sample responses: 2:2, 50:50, or any ratio that simplifies to 1:1 | ###Write an explanation to this problem:
Write two ratios that are equivalent to 1:1.
###Explanation:
Sample responses: 2:2, 50:50, or any ratio that simplifies to 1:1 |
295 | Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume. | Sample Answer: Volume refers to how much of something fits inside an object. Surface area refers to how much of something is needed to cover the outside of an object. | ###Write an explanation to this problem:
Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume.
###Explanation:
Sample Answer: Volume refers to how much of something fits inside an object. Surface area refers to how much of something is needed to cover the outside of an object. |
701 | Create a context for the numeric representation. 801 + 80.40 = 801.40 = 112 The Utah Middle School Math Project | If a person has 80 apples, then gains 40% more apples than the original 80, this numeric expression describes the total number of apples. | ###Write an explanation to this problem:
Create a context for the numeric representation. 801 + 80.40 = 801.40 = 112 The Utah Middle School Math Project
###Explanation:
If a person has 80 apples, then gains 40% more apples than the original 80, this numeric expression describes the total number of apples. |
251 | List the sample space for selecting a letter a random from the word PINEAPPLE. | The sample space for a word with the same letter multiple times only needs to represent the letter once. In the word PINEAPPLE, the letters P, L and E are represented multiple times, so leave only one P, L, and E from the word. The letters for the sample space are: P, I, N, E, A, L | ###Write an explanation to this problem:
List the sample space for selecting a letter a random from the word PINEAPPLE.
###Explanation:
The sample space for a word with the same letter multiple times only needs to represent the letter once. In the word PINEAPPLE, the letters P, L and E are represented multiple times, so leave only one P, L, and E from the word. The letters for the sample space are: P, I, N, E, A, L |
726 | Write two ratios that are equivalent to 1:1. | Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 1x2:1x2 = 2:2 1x50:1x50 = 50:50 Or any ratio that simplifies to 1:1 | ###Write an explanation to this problem:
Write two ratios that are equivalent to 1:1.
###Explanation:
Sample responses: Multiply both sides of the ratio by the same number to get an equivalent ratio. 1x2:1x2 = 2:2 1x50:1x50 = 50:50 Or any ratio that simplifies to 1:1 |
461 | Given information: z = length of a side of a triangle 2z = length 2nd side of a triangle 2z + 3 = length of 3rd side of triangle Equation: z + 2z + 2z + 3 = 73 cm. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project | The length of one of the sides of a triangle is twice the length of the shortest side. The other side is 3 more than twice the length of the smallest side. The sum of the three sides is 73 cm. What is the length of the three sides? | ###Write an explanation to this problem:
Given information: z = length of a side of a triangle 2z = length 2nd side of a triangle 2z + 3 = length of 3rd side of triangle Equation: z + 2z + 2z + 3 = 73 cm. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
The length of one of the sides of a triangle is twice the length of the shortest side. The other side is 3 more than twice the length of the smallest side. The sum of the three sides is 73 cm. What is the length of the three sides? |
455 | 26% of 44 Estimate the answer. The Utah Middle School Math Project | 25% of 40 is 10, so 26% of 44 must be close to 10. | ###Write an explanation to this problem:
26% of 44 Estimate the answer. The Utah Middle School Math Project
###Explanation:
25% of 40 is 10, so 26% of 44 must be close to 10. |
850 | Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson. | A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps. | ###Write an explanation to this problem:
Write your best definition or description of a polyhedron. If possible, use the terms you learned in this lesson.
###Explanation:
A polyhedron is a three-dimensional figure. All of its faces are polygons. The faces have no gaps or overlaps. |
269 | Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality. | Sample response: In a 100 yard, Three Legged Race, distance in yards and time in minutes are proportional since each value of distance could be multiplied by 1/40 to get the time. The constant of proportionality they used was 1/40. | ###Write an explanation to this problem:
Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality.
###Explanation:
Sample response: In a 100 yard, Three Legged Race, distance in yards and time in minutes are proportional since each value of distance could be multiplied by 1/40 to get the time. The constant of proportionality they used was 1/40. |
201 | Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org | It says that Lin starts solving the equation using the distributive property, so the 7 must be multiplied by each of the terms in the parenthesis. 7x + 2 = 91 7 * x + 7 * 2 = 91 7x + 14 = 91 Now 14 must be subtracted from both sides. 7x + 14 = 91 - 14 -14 7x = 77 Finally both sides can be divided by 7. 7x = 77 /7 /7 x = 11 Noah started by dividing both sides by 7. 7x + 2 = 91 /7 /7 x + 2 = 13 Now 2 can be subtracted from both sides. x + 2 = 13 - 2 -2 x = 11 Both solution methods come up with the same value for x. | ###Write an explanation to this problem:
Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org
###Explanation:
It says that Lin starts solving the equation using the distributive property, so the 7 must be multiplied by each of the terms in the parenthesis. 7x + 2 = 91 7 * x + 7 * 2 = 91 7x + 14 = 91 Now 14 must be subtracted from both sides. 7x + 14 = 91 - 14 -14 7x = 77 Finally both sides can be divided by 7. 7x = 77 /7 /7 x = 11 Noah started by dividing both sides by 7. 7x + 2 = 91 /7 /7 x + 2 = 13 Now 2 can be subtracted from both sides. x + 2 = 13 - 2 -2 x = 11 Both solution methods come up with the same value for x. |
161 | Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3. | The slope represents that 1 muffin costs 2 and 3 represents that the delivery fee is 3. | ###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
###Explanation:
The slope represents that 1 muffin costs 2 and 3 represents that the delivery fee is 3. |
555 | Write a phrase for the following algebraic expression 2 - 15 The Utah Middle School Math Project | 2x - 15 is fifteen less than two times a number x. | ###Write an explanation to this problem:
Write a phrase for the following algebraic expression 2 - 15 The Utah Middle School Math Project
###Explanation:
2x - 15 is fifteen less than two times a number x. |
729 | Find 3 different ratios that are equivalent to 7 : 3 | Sample response: Multiply both terms of the ratio by the same value, such as 14:6, 21:9, 28:12 | ###Write an explanation to this problem:
Find 3 different ratios that are equivalent to 7 : 3
###Explanation:
Sample response: Multiply both terms of the ratio by the same value, such as 14:6, 21:9, 28:12 |
401 | Central Lewis High School has five times as many desktop computers as laptops. The school has a total of 360 computers. Write an equation to show the relationship between the amount of desktops, laptops, and the total number of computers. The Utah Middle School Math Project | The number of laptops can be represented by the variable l. There are five times as many desktops as laptops, so this can be represented by 5l. These two values together are equal to the total. The equation for this relationship is 5l+l=360. | ###Write an explanation to this problem:
Central Lewis High School has five times as many desktop computers as laptops. The school has a total of 360 computers. Write an equation to show the relationship between the amount of desktops, laptops, and the total number of computers. The Utah Middle School Math Project
###Explanation:
The number of laptops can be represented by the variable l. There are five times as many desktops as laptops, so this can be represented by 5l. These two values together are equal to the total. The equation for this relationship is 5l+l=360. |
702 | Solve the inequality. Represent the solution on a number line. 4/5xge;36 The Utah Middle School Math Project | Solve for x. The number line should be less than and equal to the solution. | ###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 4/5xge;36 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than and equal to the solution. |
476 | Your task is to design a set of stairs and a wheelchair ramp at the side. Both the stairs and the ramp will begin at the same place at ground level and end at the height of 3 feet. Answer the following questions as you develop your design. How many steps do you want or need? The Utah Middle School Math Project | The average step is at a maximum of 7 inches wide and 11 inches deep. This means that you would need | ###Write an explanation to this problem:
Your task is to design a set of stairs and a wheelchair ramp at the side. Both the stairs and the ramp will begin at the same place at ground level and end at the height of 3 feet. Answer the following questions as you develop your design. How many steps do you want or need? The Utah Middle School Math Project
###Explanation:
The average step is at a maximum of 7 inches wide and 11 inches deep. This means that you would need |
771 | Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B | I can add two to the weeks each time to get the next number. I can addððð to the money to get the next values.In the rows, we have ð: ððð, which is equal to ð: ððð. So the money is ðððtimes larger than the week. I can just multiply the week by ððð to get theamount of money in the account.The ratio used to create the table was ð: ððð. | ###Write an explanation to this problem:
Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B
###Explanation:
I can add two to the weeks each time to get the next number. I can addððð to the money to get the next values.In the rows, we have ð: ððð, which is equal to ð: ððð. So the money is ðððtimes larger than the week. I can just multiply the week by ððð to get theamount of money in the account.The ratio used to create the table was ð: ððð. |
105 | Ramon is collecting donations for a charity. He is hoping to raise 250. If he has already collected 187 in donations, how much more does he need to collect? Write an equation to solve the problem. The Utah Middle School Math Project | Ramon already has 187, and needs m more to get to 250. This means that 187+m=250 | ###Write an explanation to this problem:
Ramon is collecting donations for a charity. He is hoping to raise 250. If he has already collected 187 in donations, how much more does he need to collect? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Ramon already has 187, and needs m more to get to 250. This means that 187+m=250 |
565 | Write a context to match the numeric expression given. 40 + 625 The Utah Middle School Math Project | Angie runs a company specializing in selling rare gems. For online orders, there is a flat 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost? | ###Write an explanation to this problem:
Write a context to match the numeric expression given. 40 + 625 The Utah Middle School Math Project
###Explanation:
Angie runs a company specializing in selling rare gems. For online orders, there is a flat 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost? |
389 | Write a story that matches the expressions and equations Downloading Music of songs downloaded: s Monthly cost at bTunes: 0.99s Monthly cost at iMusic: 10 + 0.79s 0.99s = 10 + 0.79s The Utah Middle School Math Project | The monthly cost of bTunes is 0.99s, meaning you pay 0.99 per song. The monthly cost of iMusic is 10 + 0.79s, meaning you pay an 0.79 per song plus an initial fee of 10. When 0.99s = 10 + 0.79s, the cost of the two plans will be the same. Solve this equation for s to find out how many songs you have to download per month for the two plans to cost the same. | ###Write an explanation to this problem:
Write a story that matches the expressions and equations Downloading Music of songs downloaded: s Monthly cost at bTunes: 0.99s Monthly cost at iMusic: 10 + 0.79s 0.99s = 10 + 0.79s The Utah Middle School Math Project
###Explanation:
The monthly cost of bTunes is 0.99s, meaning you pay 0.99 per song. The monthly cost of iMusic is 10 + 0.79s, meaning you pay an 0.79 per song plus an initial fee of 10. When 0.99s = 10 + 0.79s, the cost of the two plans will be the same. Solve this equation for s to find out how many songs you have to download per month for the two plans to cost the same. |
1 | Was there a length measurement you did not use to find the area? If so, explain why it was not used. | The formula for the area of a parallelogram is bh=A. The base and height of a parallelogram must form a 90deg; angle. In this case, we don't need the measurement of 7.5 cm. | ###Write an explanation to this problem:
Was there a length measurement you did not use to find the area? If so, explain why it was not used.
###Explanation:
The formula for the area of a parallelogram is bh=A. The base and height of a parallelogram must form a 90deg; angle. In this case, we don't need the measurement of 7.5 cm. |
798 | Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation. | Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25. | ###Write an explanation to this problem:
Sean was at batting practice. He swung 25 times but only hit the ball 15 times. Describe and write more than one ratio related to this situation.
###Explanation:
Ratio of the number of hits to the total number of swings is 15:25. Ratio of the number hits to the number of misses is 15:10. Ratio of the number of misses to the number of hits is 10:15. Ratio of the number of misses to the total number of swings is 10:25. |
561 | Determine if the relation or situation defines a function. Justify your answer. {2, -10, 5, -25, 8, -40, -5, 25} The Utah Middle School Math Project | Yes, the data describes a function One way to determine this is to find the rule: The rule is multiply the input by -5 | ###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. {2, -10, 5, -25, 8, -40, -5, 25} The Utah Middle School Math Project
###Explanation:
Yes, the data describes a function One way to determine this is to find the rule: The rule is multiply the input by -5 |
80 | Find a number that matches the description. A 3-digit number that is divisible by 2, 3, and 6. How do you know? The Utah Middle School Math Project | There are many different correct answers to this question. We want a number that is divisible by 2, 3, and 6. We already know from our divisibility rules that any number that is divisible by both 2 and 3 is divisible by 6. We just need our number to be divisible by 2 and 3. To be divisible by 2, the last digit has to be an even number or 0. To be divisible by 3, the digits have to add up to a number that is divisible by 3. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144. | ###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 2, 3, and 6. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 2, 3, and 6. We already know from our divisibility rules that any number that is divisible by both 2 and 3 is divisible by 6. We just need our number to be divisible by 2 and 3. To be divisible by 2, the last digit has to be an even number or 0. To be divisible by 3, the digits have to add up to a number that is divisible by 3. We can pick any even number or 0, let's say 4, and put this in the ones place. _ _ 4 Now, we need the digits to add up to a number divisible by 3. This could be 9. 3 numbers that add up to 9 including 4 are 1, 4, and 4. Our number could be: 144. |
205 | For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house. | Prices for apples at all stores in our state, Prices for all fruit at these two stores. | ###Write an explanation to this problem:
For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.
###Explanation:
Prices for apples at all stores in our state, Prices for all fruit at these two stores. |
34 | Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8. | Andre subtracted 3x from each side of the equation. | ###Write an explanation to this problem:
Andre and Diego were each trying to solve 2x + 6 = 3x - 8. Describe the first step they each make to the equation. The result of Andre's first step was -x + 6 = -8.
###Explanation:
Andre subtracted 3x from each side of the equation. |
775 | The volume of Box D subtracted from the volume of Box C is 23.14 cubic centimeters. Box D has a volume of 10.115 cubic centimeters. Let C be the volume of Box C in cubic centimeters. Write an equation that could be used to determine the volume of Box C. | ðª - ðð. ððð ðð¦3 = ðð. ðð ðð¦3 | ###Write an explanation to this problem:
The volume of Box D subtracted from the volume of Box C is 23.14 cubic centimeters. Box D has a volume of 10.115 cubic centimeters. Let C be the volume of Box C in cubic centimeters. Write an equation that could be used to determine the volume of Box C.
###Explanation:
ðª - ðð. ððð ðð¦3 = ðð. ðð ðð¦3 |
508 | Use The Distributive Property to find the product. 5222 First, show your work here. The Utah Middle School Math Project | 5222 = 5200 + 20 + 2 = 5200 + 520 + 52 = 1000 + 100 + 10 = 1,110 | ###Write an explanation to this problem:
Use The Distributive Property to find the product. 5222 First, show your work here. The Utah Middle School Math Project
###Explanation:
5222 = 5200 + 20 + 2 = 5200 + 520 + 52 = 1000 + 100 + 10 = 1,110 |
427 | Peter is the event planner for a team race taking place in Park City, UT. He needs to determine how many bottles of water to have ready at the finish line of the race so that each participant in the race receives a bottle of water. There are 4 people on a team. Identify the independent variable in this situation. The Utah Middle School Math Project | The number of teams is the independent variable, because it is the one that can change. | ###Write an explanation to this problem:
Peter is the event planner for a team race taking place in Park City, UT. He needs to determine how many bottles of water to have ready at the finish line of the race so that each participant in the race receives a bottle of water. There are 4 people on a team. Identify the independent variable in this situation. The Utah Middle School Math Project
###Explanation:
The number of teams is the independent variable, because it is the one that can change. |
454 | Given information: w = width of rectangle 2w + 3 = length of rectangle Equation: w + 2w + 3 + w + 2w + 3 = 78 in. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project | The perimeter of a rectangle is 78 inches. The width of the rectangle is w and the length of the rectangle is 2w+3. Find the width and length of the rectangle. | ###Write an explanation to this problem:
Given information: w = width of rectangle 2w + 3 = length of rectangle Equation: w + 2w + 3 + w + 2w + 3 = 78 in. Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
The perimeter of a rectangle is 78 inches. The width of the rectangle is w and the length of the rectangle is 2w+3. Find the width and length of the rectangle. |
366 | The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship? | Sample Answer: There are 5,280 feet in every mile. Each additional mile that someone travels is equivalent to traveling an additional 5,280 feet. | ###Write an explanation to this problem:
The equation y=5,280x gives the number of feet, y, in x miles. What does the number 5,280 represent in this relationship?
###Explanation:
Sample Answer: There are 5,280 feet in every mile. Each additional mile that someone travels is equivalent to traveling an additional 5,280 feet. |
91 | Write a pair of numbers whose LCM is 15. The Utah Middle School Math Project | There are a few different numbers that have multiples of 15. The factors of 15 are 1, 3, 5, and 15. Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 5: 5, 10, 15, ... Multiples of 15: 15, 30, ... You could pick pairs of: 1 and 15 3 and 15 5 and 15 3 and 5 | ###Write an explanation to this problem:
Write a pair of numbers whose LCM is 15. The Utah Middle School Math Project
###Explanation:
There are a few different numbers that have multiples of 15. The factors of 15 are 1, 3, 5, and 15. Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ... Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 5: 5, 10, 15, ... Multiples of 15: 15, 30, ... You could pick pairs of: 1 and 15 3 and 15 5 and 15 3 and 5 |
339 | Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph. | This equation is in slope-intercept form: y = mx + b This means that we know the y-intercept: 0,b 0,-1 We also know the slope of the line: -4. This means that for every 1 unit we go to the right, the line goes down 4 units. Start with the intercept 0,-1, and use the slope of -4 to move down 1 and 4 to the right or up 1 and 4 to the left to find other points. Or, find two or more solutions to the equation by substituting in a number for x and solving for y. | ###Write an explanation to this problem:
Suppose you wanted to graph the equation y = -4x - 1. Describe the steps you would take to draw the graph.
###Explanation:
This equation is in slope-intercept form: y = mx + b This means that we know the y-intercept: 0,b 0,-1 We also know the slope of the line: -4. This means that for every 1 unit we go to the right, the line goes down 4 units. Start with the intercept 0,-1, and use the slope of -4 to move down 1 and 4 to the right or up 1 and 4 to the left to find other points. Or, find two or more solutions to the equation by substituting in a number for x and solving for y. |
564 | Determine if the relation or situation defines a function. Justify your answer. You know your cousin's cellular phone number is 123 456-7890 so you dial that number to call him. Is person being called a function of phone number dialed? The Utah Middle School Math Project | Yes, the data does describe a function The phone number 123 456-7890 is your cousin The phone number is the input and the only output for that phone number is your cousin | ###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. You know your cousin's cellular phone number is 123 456-7890 so you dial that number to call him. Is person being called a function of phone number dialed? The Utah Middle School Math Project
###Explanation:
Yes, the data does describe a function The phone number 123 456-7890 is your cousin The phone number is the input and the only output for that phone number is your cousin |
345 | What causes a repeating decimal in the long division algorithm? | When you are using the long division algorithm, you will know that a fraction repeats when the remainders repeat. The repetition of the remainders sets up a cyclic pattern and that pattern shows up as a repeating decimal. | ###Write an explanation to this problem:
What causes a repeating decimal in the long division algorithm?
###Explanation:
When you are using the long division algorithm, you will know that a fraction repeats when the remainders repeat. The repetition of the remainders sets up a cyclic pattern and that pattern shows up as a repeating decimal. |
776 | Write a story problem that includes both integers -8 and 12. | Example: One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat. | ###Write an explanation to this problem:
Write a story problem that includes both integers -8 and 12.
###Explanation:
Example: One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat. |
241 | For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house. | There are many correct answers for this question. Remember that a population is the group of people/things that you are interested in asking questions about. The sample is a smaller part from that population that you think could represent that population. One example of a correct answer is: Population 1: Prices for apples at all stores in our state. Population 2: Prices for all fruit at these two stores. | ###Write an explanation to this problem:
For the sample given, list two possible populations they could belong to. Sample: The prices for apples at two stores near your house.
###Explanation:
There are many correct answers for this question. Remember that a population is the group of people/things that you are interested in asking questions about. The sample is a smaller part from that population that you think could represent that population. One example of a correct answer is: Population 1: Prices for apples at all stores in our state. Population 2: Prices for all fruit at these two stores. |
13 | Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < < | -3 < -2 < -1 | ###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three integers between -4 and 0 < <
###Explanation:
-3 < -2 < -1 |
315 | Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1. | Sample Answer: Build a slope triangle. If its vertical length is greater than its horizontal length, the slope is greater than 1. If its vertical and horizontal lengths are equal, the slope is equal to 1. If the slope triangle's vertical length is less than its horizontal length, the slope is less than 1. | ###Write an explanation to this problem:
Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1.
###Explanation:
Sample Answer: Build a slope triangle. If its vertical length is greater than its horizontal length, the slope is greater than 1. If its vertical and horizontal lengths are equal, the slope is equal to 1. If the slope triangle's vertical length is less than its horizontal length, the slope is less than 1. |
600 | Replace the ? in the fraction ?/18 with a number that would make the fraction less than 1/3. The Utah Middle School Math Project | If you multiply both parts of 1/3 by 6, you get 6/18. Thus, if you want your fraction ?/18 to be less than 1/3, it needs to be less than 6/18. Any number that is less than 6 could replace the ?. Examples of correct answers are: 5, 2, -6, and so on. | ###Write an explanation to this problem:
Replace the ? in the fraction ?/18 with a number that would make the fraction less than 1/3. The Utah Middle School Math Project
###Explanation:
If you multiply both parts of 1/3 by 6, you get 6/18. Thus, if you want your fraction ?/18 to be less than 1/3, it needs to be less than 6/18. Any number that is less than 6 could replace the ?. Examples of correct answers are: 5, 2, -6, and so on. |
387 | 3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project | This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of a 3 + 3 + 3 + 3 | ###Write an explanation to this problem:
3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer 3 and multiply it 4 times, so 3 x 4 can be thought of a 3 + 3 + 3 + 3 |
273 | Five students came for after-school tutoring. Lin's teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems. 30 problems were assigned in all. Write an equation for the story. | Let x be the number of problems to complete before adding 2 more problems. We are given that 5 students are given the same number of problems. So, each student was assigned x + 2 problems to complete and there is a total of 30 problems assigned. Therefore, the equation is 5x + 2 = 30. | ###Write an explanation to this problem:
Five students came for after-school tutoring. Lin's teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems. 30 problems were assigned in all. Write an equation for the story.
###Explanation:
Let x be the number of problems to complete before adding 2 more problems. We are given that 5 students are given the same number of problems. So, each student was assigned x + 2 problems to complete and there is a total of 30 problems assigned. Therefore, the equation is 5x + 2 = 30. |
166 | A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled win and 1 labeled lose. She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games? | She needs to repeat the process many more times to get a good estimate of the probability. | ###Write an explanation to this problem:
A team has a 75% chance to win each of the 3 games they will play this week. Clare simulates the week of games by putting 4 pieces of paper in a bag, 3 labeled win and 1 labeled lose. She draws a paper, writes down the result, then replaces the paper and repeats the process two more times. Clare gets the result: win, win, lose. What can Clare do to estimate the probability the team will win at least 2 games?
###Explanation:
She needs to repeat the process many more times to get a good estimate of the probability. |
846 | Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality. | The number of legs that a group of centipedes has is proportional to the number of centipedes. The constant of proportionality would is 100 or 1/100. | ###Write an explanation to this problem:
Choose a relationship that another group found and explain why it is a proportional relationship. Make sure to include the quantities they used and any important constants of proportionality.
###Explanation:
The number of legs that a group of centipedes has is proportional to the number of centipedes. The constant of proportionality would is 100 or 1/100. |
646 | In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 6 Transformed Equation: x + 2 = 8 Action: ______ The Utah Middle School Math Project | On the left side of the equation, 2 has been added to x. 2 has also been added to 6 on the right side, to make 8. The action was: Add 2 to both sides of the equation. | ###Write an explanation to this problem:
In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 6 Transformed Equation: x + 2 = 8 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 2 has been added to x. 2 has also been added to 6 on the right side, to make 8. The action was: Add 2 to both sides of the equation. |
484 | A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project | The dependent variable is the number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students. | ###Write an explanation to this problem:
A student comes to school with the flu and infects three other students within an hour before going home. Each newly infected student passes the virus to three new students in the next hour. This pattern continues until all students in the school are infected with the virus. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The dependent variable is the number of students infected with the virus. This will depend on the time that has passed since the original student was infected and how fast the disease will spread. The dependent variable is number of students. |
835 | Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe. | Kiran's flavor would be more chocolatey than Clare's because if he double Clare's recipe correctly he would have had 4 teaspoons of chocolate syrup instead of 5 teaspoons. | ###Write an explanation to this problem:
Clare made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice. Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut putter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
###Explanation:
Kiran's flavor would be more chocolatey than Clare's because if he double Clare's recipe correctly he would have had 4 teaspoons of chocolate syrup instead of 5 teaspoons. |
504 | The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A tree grows 15 feet in 10 years. The Utah Middle School Math Project | Time is the independent variable. The growth of the tree depends on the time. Feet is dependent variable. | ###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A tree grows 15 feet in 10 years. The Utah Middle School Math Project
###Explanation:
Time is the independent variable. The growth of the tree depends on the time. Feet is dependent variable. |
243 | A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning. | If 3 out of 50 people won a small prize, that means that 3 out of 50 ducks had a red mark on them. We can scale this ratio of 3:50 by a factor of 3.2 to get the equivalent ratio of 9.6:160. This means that there are likely 9 to 10 ducks that have red marks out of 160 total ducks. As for the ducks with blue marks, there seems to be less than a 1/50 probability of getting one, since 0 out of the 50 people who played won them. If we scale the ratio 1:50 by 3.2, we get the equivalent ratio of 3.2:160. This means that there are likely 3 or less ducks with blue marks out of 160 total ducks. | ###Write an explanation to this problem:
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.
###Explanation:
If 3 out of 50 people won a small prize, that means that 3 out of 50 ducks had a red mark on them. We can scale this ratio of 3:50 by a factor of 3.2 to get the equivalent ratio of 9.6:160. This means that there are likely 9 to 10 ducks that have red marks out of 160 total ducks. As for the ducks with blue marks, there seems to be less than a 1/50 probability of getting one, since 0 out of the 50 people who played won them. If we scale the ratio 1:50 by 3.2, we get the equivalent ratio of 3.2:160. This means that there are likely 3 or less ducks with blue marks out of 160 total ducks. |
566 | Write a context to match the numeric expression given. 4 8 The Utah Middle School Math Project | Kelly wants to buy 4 eggs. Each egg is 8 dollars each. How much is she going to spend on eggs? | ###Write an explanation to this problem:
Write a context to match the numeric expression given. 4 8 The Utah Middle School Math Project
###Explanation:
Kelly wants to buy 4 eggs. Each egg is 8 dollars each. How much is she going to spend on eggs? |
562 | Imagine cutting a square based right pyramid parallel to the base. What shape is the plane section? The Utah Middle School Math Project | Cutting a square based right pyramid parallel to the base will result in a square cross-section | ###Write an explanation to this problem:
Imagine cutting a square based right pyramid parallel to the base. What shape is the plane section? The Utah Middle School Math Project
###Explanation:
Cutting a square based right pyramid parallel to the base will result in a square cross-section |
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