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525 | Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project | A triangular prism cut parallel to the base will always result in a rectangular cross-section. | ###Write an explanation to this problem:
Imagine a triangular prism: What shape is the plane section parallel to the base? The Utah Middle School Math Project
###Explanation:
A triangular prism cut parallel to the base will always result in a rectangular cross-section. |
738 | Create another possible ratio that describes the relationship between the amount of money in Pam's account and the amount of money in her brother's account. | Answers will vary. You might something like 4:10, 8:20, etc. | ###Write an explanation to this problem:
Create another possible ratio that describes the relationship between the amount of money in Pam's account and the amount of money in her brother's account.
###Explanation:
Answers will vary. You might something like 4:10, 8:20, etc. |
432 | Complete the following statements: In scientific notation, as the exponent power goes up by 1, the standard number's decimal is... The Utah Middle School Math Project | In scientific notation, as the exponent power goes up by 1, the standard number's decimal is moved one place to the right. For each exponent added, another power of 10 is added. | ###Write an explanation to this problem:
Complete the following statements: In scientific notation, as the exponent power goes up by 1, the standard number's decimal is... The Utah Middle School Math Project
###Explanation:
In scientific notation, as the exponent power goes up by 1, the standard number's decimal is moved one place to the right. For each exponent added, another power of 10 is added. |
204 | List the sample space the available options for the chance experiment given. Flipping a coin | Heads, tails | ###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
Heads, tails |
587 | Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project | Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800. | ###Write an explanation to this problem:
Here, write the first problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Tom bought a laptop for 680. Due to his membership, he used a 15% discount on his purchase. How much did the laptop cost before the discount? Solution: part: 680 percent: 15% = 0.15 We want to find the original price of the laptop. Note that with a 15% discount, the final price of 680 is 85% of the original price. 85% of the original price is 0.85 times the original price. With this information, we can write: 680 = original price x 0.85 Now, we can solve for the original price: 680 = original price x 0.85 680/0.85 = original price 800 = original price We get that the original price of the laptop Tom bought was 800. |
582 | Mr. Green is purchasing four new computers for the computer lab. Each computer costs 350. In addition, Mr. Green is purchasing a protection plan for each computer. The cost of the protection plan is 25 per computer. Use the distributive property to write two different expressions that can be used to represent the cost of the computers with the protection plans. The Utah Middle School Math Project | Since there are four computers that each cost 350 and four protection plans that each cost 25, one expression to represent the cost of the computers and protection plans is 4350 + 425 Another way to think about this is that the cost of a computer and protection plan is 350 + 25 and four computers with protection plans need to be bought, so another expression to represent the cost of the computers and protection plans is 4350 + 25 | ###Write an explanation to this problem:
Mr. Green is purchasing four new computers for the computer lab. Each computer costs 350. In addition, Mr. Green is purchasing a protection plan for each computer. The cost of the protection plan is 25 per computer. Use the distributive property to write two different expressions that can be used to represent the cost of the computers with the protection plans. The Utah Middle School Math Project
###Explanation:
Since there are four computers that each cost 350 and four protection plans that each cost 25, one expression to represent the cost of the computers and protection plans is 4350 + 425 Another way to think about this is that the cost of a computer and protection plan is 350 + 25 and four computers with protection plans need to be bought, so another expression to represent the cost of the computers and protection plans is 4350 + 25 |
306 | Jada applies two transformations to a polygon in the coordinate plane. One of the transformations is a translation and the other is a reflection. What information does Jada need to provide to communicate the transformations she has used? | For the translation, Jada needs to provide the distance and direction of the vertical displacement and the distance and direction of the horizontal displacement. For the reflection, Jada needs to give the line of reflection. It is also important for Jada to communicate the order in which the transformations are applied. | ###Write an explanation to this problem:
Jada applies two transformations to a polygon in the coordinate plane. One of the transformations is a translation and the other is a reflection. What information does Jada need to provide to communicate the transformations she has used?
###Explanation:
For the translation, Jada needs to provide the distance and direction of the vertical displacement and the distance and direction of the horizontal displacement. For the reflection, Jada needs to give the line of reflection. It is also important for Jada to communicate the order in which the transformations are applied. |
332 | The point -3,6 is on a line with a slope of 4. Find two more points on the line. | The slope is equal to the change in y over the change in x. The slope of 4 means that for every 4 units the y changes, the x changes by 1. Two more points can be found by adding 1 to x and 4 to y, or subtracting 1 from x and 4 from y. -3, 6 +1 +4 -2, 10 +1 +4 -1, 14 Two more points on the line are -2, 10 and -1, 14. | ###Write an explanation to this problem:
The point -3,6 is on a line with a slope of 4. Find two more points on the line.
###Explanation:
The slope is equal to the change in y over the change in x. The slope of 4 means that for every 4 units the y changes, the x changes by 1. Two more points can be found by adding 1 to x and 4 to y, or subtracting 1 from x and 4 from y. -3, 6 +1 +4 -2, 10 +1 +4 -1, 14 Two more points on the line are -2, 10 and -1, 14. |
425 | A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project | The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example. | ###Write an explanation to this problem:
A piece of paper is cut into two equal sections. Each new piece is cut into two additional pieces of equal size. This pattern continues until it is no longer possible to cut the paper any more. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The number of pieces of paper in this relationship will be depended on the number of cuts. Number of pieces of paper will increase with each cut. The number of pieces of paper is the dependent variables in this example. |
60 | Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org | In order to factor you need to look at the numbers and think about what is the greatest common factor that will go into those numbers. For example: 30x + 9 The common factor would be 3. 310x + 3 After you find the common factor you then need to put that number in front of the parenthesis The numbers that go inside the parenthesis are the numbers that you multiply by to equal the original expression. 12x - 4 = 43x -1 | ###Write an explanation to this problem:
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? Copied for free from openupresources.org
###Explanation:
In order to factor you need to look at the numbers and think about what is the greatest common factor that will go into those numbers. For example: 30x + 9 The common factor would be 3. 310x + 3 After you find the common factor you then need to put that number in front of the parenthesis The numbers that go inside the parenthesis are the numbers that you multiply by to equal the original expression. 12x - 4 = 43x -1 |
199 | What information do you need to know to write an equation relating two quantities that have a proportional relationship? | You would need to know the constant of proportionality and the variables for the quantities. | ###Write an explanation to this problem:
What information do you need to know to write an equation relating two quantities that have a proportional relationship?
###Explanation:
You would need to know the constant of proportionality and the variables for the quantities. |
638 | In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x - 3 = 11 Original Equation: x=14 Action: ______ The Utah Middle School Math Project | On the left side of the equation, 3 has been added to x-3. On the right side, 3 has been added to 11, which results in 14. The action was: Add 3 to both sides of the equation. | ###Write an explanation to this problem:
In the problem below, a starting transformed equation and original equation have been given. State the actions that would need to be preformed to 'deconstruct' the transformation into the original equation. In other words, how can you get the equation back to what it was at the start? Transformed Equation: x - 3 = 11 Original Equation: x=14 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 3 has been added to x-3. On the right side, 3 has been added to 11, which results in 14. The action was: Add 3 to both sides of the equation. |
685 | Create a context for the numeric representation. 1201 ndash; 1201/4 = 1203/4 = 90 The Utah Middle School Math Project | If a person has 120 apples, then loses 1/4 of the apples, this numeric expression describes how many apples they have left. | ###Write an explanation to this problem:
Create a context for the numeric representation. 1201 ndash; 1201/4 = 1203/4 = 90 The Utah Middle School Math Project
###Explanation:
If a person has 120 apples, then loses 1/4 of the apples, this numeric expression describes how many apples they have left. |
581 | Use The Distributive Property to find the product. 712 First, show your work here. The Utah Middle School Math Project | 712 = 710 + 2 = 710 + 72 = 70 + 14 = 84 | ###Write an explanation to this problem:
Use The Distributive Property to find the product. 712 First, show your work here. The Utah Middle School Math Project
###Explanation:
712 = 710 + 2 = 710 + 72 = 70 + 14 = 84 |
429 | Suppose a certain bank pays 4% interest at the end of each year on the money in an account. When Devon was born, his parents put 100 in the account and will leave it there until he goes to college. Is the relationship between time in years and the amount of money in the account in dollars linear or not? Why or why not? The Utah Middle School Math Project | This data is not linear, because the money with interest has interest added each year. | ###Write an explanation to this problem:
Suppose a certain bank pays 4% interest at the end of each year on the money in an account. When Devon was born, his parents put 100 in the account and will leave it there until he goes to college. Is the relationship between time in years and the amount of money in the account in dollars linear or not? Why or why not? The Utah Middle School Math Project
###Explanation:
This data is not linear, because the money with interest has interest added each year. |
445 | 61% of 20 Estimate the answer. The Utah Middle School Math Project | 61% = 50% + 10% + 1% 50% of 20 is 10, so the answer must be greater than 10. | ###Write an explanation to this problem:
61% of 20 Estimate the answer. The Utah Middle School Math Project
###Explanation:
61% = 50% + 10% + 1% 50% of 20 is 10, so the answer must be greater than 10. |
601 | Describe absolute value in your own words. Use examples to support your explanation. The Utah Middle School Math Project | The absolute value of a number is the number's distance from 0. Distance is always positive. You can think of it like a point on a number line. The distance from 0 is how many steps, or units, it takes to get to that point from 0. Even if that point has a negative value, it takes a positive number of steps to get to that point from 0. This distance/number of steps is the point's absolute value. | ###Write an explanation to this problem:
Describe absolute value in your own words. Use examples to support your explanation. The Utah Middle School Math Project
###Explanation:
The absolute value of a number is the number's distance from 0. Distance is always positive. You can think of it like a point on a number line. The distance from 0 is how many steps, or units, it takes to get to that point from 0. Even if that point has a negative value, it takes a positive number of steps to get to that point from 0. This distance/number of steps is the point's absolute value. |
494 | In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5x+ 4x - x 9x Explain the mistake The Utah Middle School Math Project | Notice that when combining like terms, the coefficients were added wrong. Since 5x + 4x - x = x5 + 4 - 1 =x8 does not equal 9x. | ###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. 5x+ 4x - x 9x Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that when combining like terms, the coefficients were added wrong. Since 5x + 4x - x = x5 + 4 - 1 =x8 does not equal 9x. |
791 | 9. Noah raised 54 to support the animal shelter, which is 60% of his fundraising goal. a. Write an equation to represent the situation. copied for free from openupresources.org | To set up an equation to represent this situation, I know that the unknown value is Noah's fundraising goal which will be represented by x. Also, I know that the problem says 60% of his fundraising goal and of means to multiply. 60%x=54 is how this problem could be written, but the percent needs to change to a decimal in order to solve so the final equation would be 0.6x=54 | ###Write an explanation to this problem:
9. Noah raised 54 to support the animal shelter, which is 60% of his fundraising goal. a. Write an equation to represent the situation. copied for free from openupresources.org
###Explanation:
To set up an equation to represent this situation, I know that the unknown value is Noah's fundraising goal which will be represented by x. Also, I know that the problem says 60% of his fundraising goal and of means to multiply. 60%x=54 is how this problem could be written, but the percent needs to change to a decimal in order to solve so the final equation would be 0.6x=54 |
633 | Yesterday, Ruth and Carl invited 10 friends to go out to lunch. Add one more statistical question of your own that relates to this situation. The Utah Middle School Math Project | One example of a statistical question would be: How many people were sitting at each table in the restaurant? | ###Write an explanation to this problem:
Yesterday, Ruth and Carl invited 10 friends to go out to lunch. Add one more statistical question of your own that relates to this situation. The Utah Middle School Math Project
###Explanation:
One example of a statistical question would be: How many people were sitting at each table in the restaurant? |
759 | The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero. | The temperature is 22 degrees below zero on the Celcius scale. | ###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -22 degrees Celsius below zero.
###Explanation:
The temperature is 22 degrees below zero on the Celcius scale. |
615 | Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school? | Answers will vary. | ###Write an explanation to this problem:
Think about the mean number of siblings brothers and sisters for all students at your school. What do you think is the approximate value of the mean number of siblings for the population of all students at your school?
###Explanation:
Answers will vary. |
334 | Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B. | To get a scaled copy, you have to be multiplying all of the dimensions of the original figure or shape by the same scale factor. In this case, the original figure is Rectangle B. Rectangle B measures 15 by 10. Rectangle C measures 30 by 15. We can see that Rectangle C's length is twice Rectangle B's length. BUT Rectangle C's width is not twice Rectangle B's width. This means Rectangle C cannot be a scaled copy of Rectangle B. | ###Write an explanation to this problem:
Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Explain how you know that Rectangle C is not a scaled copy of Rectangle B.
###Explanation:
To get a scaled copy, you have to be multiplying all of the dimensions of the original figure or shape by the same scale factor. In this case, the original figure is Rectangle B. Rectangle B measures 15 by 10. Rectangle C measures 30 by 15. We can see that Rectangle C's length is twice Rectangle B's length. BUT Rectangle C's width is not twice Rectangle B's width. This means Rectangle C cannot be a scaled copy of Rectangle B. |
767 | Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know. | Note that the area of a triangle is A = 1/2bh and the area of a parallelogram is A = bh. Sample response: To find the dimensions of a right triangle and a parallelogram with the same area, the base of the triangle should be double that of the parallelogram. Right Triangle: b = 10 cm h = 8 cm A = 1/2bh = 1/210 cm8cm = 40 cm2 Parallelogram: b = 5 cm h = 8 cm A = bh = 5 cm8 cm = 40 cm2 | ###Write an explanation to this problem:
Give the dimensions of a right triangle and a parallelogram with the same area. Explain how you know.
###Explanation:
Note that the area of a triangle is A = 1/2bh and the area of a parallelogram is A = bh. Sample response: To find the dimensions of a right triangle and a parallelogram with the same area, the base of the triangle should be double that of the parallelogram. Right Triangle: b = 10 cm h = 8 cm A = 1/2bh = 1/210 cm8cm = 40 cm2 Parallelogram: b = 5 cm h = 8 cm A = bh = 5 cm8 cm = 40 cm2 |
90 | The equation d=3t represents the relationship between the distance d in inches that a snail is from a certain rock and the time t in minutes. What does the number 3 represent? | The 3 is the constant in the equation which is how fast the snail can travel in 1 minute which would be 3 inches in 1 minute. | ###Write an explanation to this problem:
The equation d=3t represents the relationship between the distance d in inches that a snail is from a certain rock and the time t in minutes. What does the number 3 represent?
###Explanation:
The 3 is the constant in the equation which is how fast the snail can travel in 1 minute which would be 3 inches in 1 minute. |
800 | The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero. | The temperature is -10oF. OR The temperature is 10 degrees below zero on the Fahrenheit scale. | ###Write an explanation to this problem:
The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero.
###Explanation:
The temperature is -10oF. OR The temperature is 10 degrees below zero on the Fahrenheit scale. |
181 | Explain how you could find the difference of 1 and 0.1978. | To find the difference between 1 and 0.1978 you have to first add a decimal behind the 1. Since 0.1978 has 4 places behind the decimal, you have to add 4 zeros behind the 1 and the decimal. Then you can subtract the digits the same way you would if you were subtracting 1,978 from 10,000. Line up the decimals on top of each other and bring down a decimal in the same place of the difference. Therefore instead of getting a difference of 8,022, it is 0.8022 because of the decimal. | ###Write an explanation to this problem:
Explain how you could find the difference of 1 and 0.1978.
###Explanation:
To find the difference between 1 and 0.1978 you have to first add a decimal behind the 1. Since 0.1978 has 4 places behind the decimal, you have to add 4 zeros behind the 1 and the decimal. Then you can subtract the digits the same way you would if you were subtracting 1,978 from 10,000. Line up the decimals on top of each other and bring down a decimal in the same place of the difference. Therefore instead of getting a difference of 8,022, it is 0.8022 because of the decimal. |
456 | Given information: v = Vicki's money 5v = Wally's money Equation: 5v + v = 72 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project | Wally has five times more money than Vicki. Together they have 72. How much money do they each have? | ###Write an explanation to this problem:
Given information: v = Vicki's money 5v = Wally's money Equation: 5v + v = 72 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
Wally has five times more money than Vicki. Together they have 72. How much money do they each have? |
500 | Create a representation of an equation that defines a linear function. The Utah Middle School Math Project | There are many different equations that can be created that represent a linear function. One possible example is: y=2x+3 | ###Write an explanation to this problem:
Create a representation of an equation that defines a linear function. The Utah Middle School Math Project
###Explanation:
There are many different equations that can be created that represent a linear function. One possible example is: y=2x+3 |
744 | Write a story problem that includes both integers -8 and 12. | Answers may vary. You might write something like One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat. | ###Write an explanation to this problem:
Write a story problem that includes both integers -8 and 12.
###Explanation:
Answers may vary. You might write something like One boxer gains 12 pounds of muscle to train for a fight. Another boxer loses 8 pounds of fat. |
158 | Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0. | Slope would represent the relationship between the side length and the perimeter. Since it is equilateral, to find the perimeter you would always multiply by 3 for the 3 sides. The y- intercept is 0 because if you don't have a side length 0, you would not have a perimeter to calculate. | ###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
###Explanation:
Slope would represent the relationship between the side length and the perimeter. Since it is equilateral, to find the perimeter you would always multiply by 3 for the 3 sides. The y- intercept is 0 because if you don't have a side length 0, you would not have a perimeter to calculate. |
69 | One end point of a line segment is -3, -6. The length of the line segment is 7 units. Find four points that could serve as the other end point of the given line segment. | -10, -6 4, -6 -3, 1 -3, -13 | ###Write an explanation to this problem:
One end point of a line segment is -3, -6. The length of the line segment is 7 units. Find four points that could serve as the other end point of the given line segment.
###Explanation:
-10, -6 4, -6 -3, 1 -3, -13 |
319 | The Fabulous Fish Market orders tilapia, which costs 3 per pound, and salmon, which costs 5 per pound. The market budgets 210 to spend on this order each day. What are five different combinations of salmon and tilapia that the market can order? | 70 pounds of tilapia and 0 pounds of salmon 0 pounds of tilapia and 42 pounds of salmon 20 pounds of tilapia and 30 pounds of salmon 10 pounds of tilapia and 36 pounds of salmon 30 pounds of tilapia and 24 pounds of salmon | ###Write an explanation to this problem:
The Fabulous Fish Market orders tilapia, which costs 3 per pound, and salmon, which costs 5 per pound. The market budgets 210 to spend on this order each day. What are five different combinations of salmon and tilapia that the market can order?
###Explanation:
70 pounds of tilapia and 0 pounds of salmon 0 pounds of tilapia and 42 pounds of salmon 20 pounds of tilapia and 30 pounds of salmon 10 pounds of tilapia and 36 pounds of salmon 30 pounds of tilapia and 24 pounds of salmon |
131 | What does the expression + + + represent? | This expression represents the perimeter of the rectangle, or the sum of the four sides of a rectangle. | ###Write an explanation to this problem:
What does the expression + + + represent?
###Explanation:
This expression represents the perimeter of the rectangle, or the sum of the four sides of a rectangle. |
44 | 30 + -30 = 0. Enter another sum of two numbers that equals 0. copied for free from openupresources.org | 4 + -4 = 0 | ###Write an explanation to this problem:
30 + -30 = 0. Enter another sum of two numbers that equals 0. copied for free from openupresources.org
###Explanation:
4 + -4 = 0 |
596 | Here, write the third problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project | Sample Answer: Last night, Jeff did not read 61.54% of the targetted number of pages. He fell asleep with 40 pages unread. What was the targetted number of pages to read that night? Solution: part: 40 pages percent: 61.54% We want to find the number of pages Jeff did not read that night. Note that 61.54% of the targetted number of pages is 40 pages. 61.54% of the targetted page is 0.6154 times the targetted page. With this information, we can write: 40 pages = targetted page x 0.6154 Now, we can solve for the targetted number of pages: 40 pages = targetted page x 0.6154 40 pages/0.6154 = targetted page 65 pages = targetted page We get that Jeff planned to read 65 pages that night. | ###Write an explanation to this problem:
Here, write the third problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Last night, Jeff did not read 61.54% of the targetted number of pages. He fell asleep with 40 pages unread. What was the targetted number of pages to read that night? Solution: part: 40 pages percent: 61.54% We want to find the number of pages Jeff did not read that night. Note that 61.54% of the targetted number of pages is 40 pages. 61.54% of the targetted page is 0.6154 times the targetted page. With this information, we can write: 40 pages = targetted page x 0.6154 Now, we can solve for the targetted number of pages: 40 pages = targetted page x 0.6154 40 pages/0.6154 = targetted page 65 pages = targetted page We get that Jeff planned to read 65 pages that night. |
70 | Two of the vertices of a rectangle are 1, -6 and -8, -6. If the rectangle has a perimeter of 26 units, what are the coordinates of its other two vertices? | 1, -2 and -8, -2 or 1, -10 and -8, -10 | ###Write an explanation to this problem:
Two of the vertices of a rectangle are 1, -6 and -8, -6. If the rectangle has a perimeter of 26 units, what are the coordinates of its other two vertices?
###Explanation:
1, -2 and -8, -2 or 1, -10 and -8, -10 |
436 | The following equation is given: 0.2x + x = 240 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project | In the last year Milo's saving account has increased by 20%. If he now has 240, how much did he start with? | ###Write an explanation to this problem:
The following equation is given: 0.2x + x = 240 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
In the last year Milo's saving account has increased by 20%. If he now has 240, how much did he start with? |
806 | Write an inequality that relates the rational numbers. Three and one-half yards of fabric is less than five and one-half yards of fabric | Three and one-half yards of fabric is less than five and one-half yards of fabric | ###Write an explanation to this problem:
Write an inequality that relates the rational numbers. Three and one-half yards of fabric is less than five and one-half yards of fabric
###Explanation:
Three and one-half yards of fabric is less than five and one-half yards of fabric |
398 | On Saturday Fiona gets to work 15 minutes early and sells three sweaters before her shift even begins. She then sells 4 sweaters every hour for the rest of her shift. Find and describe the rate of change for this relationship. The Utah Middle School Math Project | The rate of change for this relationship is 4 sweaters sold for every hour worked. We do not need to include the three sweaters she sold before her shift began because she is not selling them at a constant rate during her shifts. | ###Write an explanation to this problem:
On Saturday Fiona gets to work 15 minutes early and sells three sweaters before her shift even begins. She then sells 4 sweaters every hour for the rest of her shift. Find and describe the rate of change for this relationship. The Utah Middle School Math Project
###Explanation:
The rate of change for this relationship is 4 sweaters sold for every hour worked. We do not need to include the three sweaters she sold before her shift began because she is not selling them at a constant rate during her shifts. |
351 | Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project | Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 + 2 2x + 4x - 16 + 1 | ###Write an explanation to this problem:
Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 + 2 2x + 4x - 16 + 1 |
707 | Solve the inequality. Represent the solution on a number line. r-3.5>8.25 The Utah Middle School Math Project | Solve for r. The number line should be greater than the solution, but not contain it. | ###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. r-3.5>8.25 The Utah Middle School Math Project
###Explanation:
Solve for r. The number line should be greater than the solution, but not contain it. |
239 | A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population? | A sample refers to a small portion of the entire population. In this example, in order to use the entire population, the doctor would have to test all of the blood in your body. That is probably not possible while keeping you healthy and even alive, so a smaller sample is better. | ###Write an explanation to this problem:
A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population?
###Explanation:
A sample refers to a small portion of the entire population. In this example, in order to use the entire population, the doctor would have to test all of the blood in your body. That is probably not possible while keeping you healthy and even alive, so a smaller sample is better. |
135 | Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e | 4d + 3e OR 41d + 3e | ###Write an explanation to this problem:
Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e
###Explanation:
4d + 3e OR 41d + 3e |
82 | Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project | There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240. | ###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240. |
165 | One day in Boston, MA, the high temperature was 60 degrees Fahrenheit, and the low temperature was 52 degrees. Write one or more inequalities to describe the temperatures T that are between the high and low temperatures on that day. | 60>T>52 or T52 This is saying that T is less than 60 and T is greater than 52. | ###Write an explanation to this problem:
One day in Boston, MA, the high temperature was 60 degrees Fahrenheit, and the low temperature was 52 degrees. Write one or more inequalities to describe the temperatures T that are between the high and low temperatures on that day.
###Explanation:
60>T>52 or T52 This is saying that T is less than 60 and T is greater than 52. |
164 | A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs 24. copied for free from openupresources.org | Strategy 1: Find what 25% of 24 is. 25% = 0.25 0.25*24 = 6 Subtract this value from 24 24 - 6 18 Strategy 2: You are taking away 25% from the whole. The whole is 1, or 100%. 100% - 25% = 75% Let's find what 75% of 24 is. 75% = 0.75 0.75*24 = 18 | ###Write an explanation to this problem:
A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs 24. copied for free from openupresources.org
###Explanation:
Strategy 1: Find what 25% of 24 is. 25% = 0.25 0.25*24 = 6 Subtract this value from 24 24 - 6 18 Strategy 2: You are taking away 25% from the whole. The whole is 1, or 100%. 100% - 25% = 75% Let's find what 75% of 24 is. 75% = 0.75 0.75*24 = 18 |
28 | The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them. | 0 tables for 2 and 30 tables for 4 60 tables for 2 and 0 tables for 4 10 tables for 2 and 25 tables for 4 To find combinations, I chose a number of tables for 2 and multiplied that number by 2. I then subtracted that number from 120 and divided by 4 to determine how many tables of 4 I would need. | ###Write an explanation to this problem:
The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.
###Explanation:
0 tables for 2 and 30 tables for 4 60 tables for 2 and 0 tables for 4 10 tables for 2 and 25 tables for 4 To find combinations, I chose a number of tables for 2 and multiplied that number by 2. I then subtracted that number from 120 and divided by 4 to determine how many tables of 4 I would need. |
665 | Solve the inequality. Represent the solution on a number line. x-2>7 The Utah Middle School Math Project | Solve for x. The number line should be higher than the solution, but not contain it. | ###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. x-2>7 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be higher than the solution, but not contain it. |
193 | These three points form a horizontal line: -3.5,4, 0,4, and 6.2,4. Name two additional points that fall on this line. | 2,4, -6.2, 4, and 342,4 Your answer may vary. You MUST have a 4 for the y-coordinate on the line. | ###Write an explanation to this problem:
These three points form a horizontal line: -3.5,4, 0,4, and 6.2,4. Name two additional points that fall on this line.
###Explanation:
2,4, -6.2, 4, and 342,4 Your answer may vary. You MUST have a 4 for the y-coordinate on the line. |
404 | Callie and Jeff each have a job delivering newspapers. Jeff gets paid 140 dollars for delivering 350 papers. Callie gets paid 100 for delivering 200 papers. Find the unit rate for Callie The Utah Middle School Math Project | The unit rate can be either the amount of dollars for every one newspaper or the amount of newspapers for every one dollar. Unlike just a rate, unit rates have a 1 in the denominator. To turn a rate into a unit rate, divide the numerator by the denominator. The rate that Callie was delivering papers is 100 per 200 papers or 100/200 papers. To get the unit rate divide 100 by 200 to get unit rate of 0.50/paper 0.50 is the unit rate of dollars to papers The rate that Callie delivered can also be expressed in papers per dollars. The rate would be 200 papers per 100. By simplifying the rate a unit rate of 2 papers per dollar is found. 2 is the unit rate of papers to dollars. | ###Write an explanation to this problem:
Callie and Jeff each have a job delivering newspapers. Jeff gets paid 140 dollars for delivering 350 papers. Callie gets paid 100 for delivering 200 papers. Find the unit rate for Callie The Utah Middle School Math Project
###Explanation:
The unit rate can be either the amount of dollars for every one newspaper or the amount of newspapers for every one dollar. Unlike just a rate, unit rates have a 1 in the denominator. To turn a rate into a unit rate, divide the numerator by the denominator. The rate that Callie was delivering papers is 100 per 200 papers or 100/200 papers. To get the unit rate divide 100 by 200 to get unit rate of 0.50/paper 0.50 is the unit rate of dollars to papers The rate that Callie delivered can also be expressed in papers per dollars. The rate would be 200 papers per 100. By simplifying the rate a unit rate of 2 papers per dollar is found. 2 is the unit rate of papers to dollars. |
465 | 99% of 75 Estimate the answer. The Utah Middle School Math Project | 99% is slightly less than 100%, so 99% of 75 is slightly less than 75. | ###Write an explanation to this problem:
99% of 75 Estimate the answer. The Utah Middle School Math Project
###Explanation:
99% is slightly less than 100%, so 99% of 75 is slightly less than 75. |
350 | Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project | Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 - 2 2x + 4x - 16 + 1 | ###Write an explanation to this problem:
Write three expressions that are equivalent to 2x+4x-15 The Utah Middle School Math Project
###Explanation:
Any equation that is equivalent to 2x + 4x - 15 would be a correct answer here. Some examples include: 6x - 15 6x - 17 - 2 2x + 4x - 16 + 1 |
140 | A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org | The sample space would be the numbers 1-428. | ###Write an explanation to this problem:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the sample space for this experiment? copied for free from openupresources.org
###Explanation:
The sample space would be the numbers 1-428. |
173 | Explain how to make this calculation mentally. 99 * 15 | Round the 99 to 100 so you know have: 10015 = 1500 | ###Write an explanation to this problem:
Explain how to make this calculation mentally. 99 * 15
###Explanation:
Round the 99 to 100 so you know have: 10015 = 1500 |
6 | Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1. | When a slope is greater than 1, the vertical distance between two points will always be greater than the horizontal distance. When a slope is equal to 1, the vertical distance between two points will always be the same as the horizontal distance. When a slope is less than 1, the vertical distance between two points will always be less than the horizontal distance. | ###Write an explanation to this problem:
Describe how you can tell whether a line's slope is greater than 1, equal to 1, or less than 1.
###Explanation:
When a slope is greater than 1, the vertical distance between two points will always be greater than the horizontal distance. When a slope is equal to 1, the vertical distance between two points will always be the same as the horizontal distance. When a slope is less than 1, the vertical distance between two points will always be less than the horizontal distance. |
687 | The ratio of 6th graders to 7th graders to 8th graders in a middle school is 3:1:1. If there are 180 students in total, how many of the students are in each grade? Write an equation to solve the problem. The Utah Middle School Math Project | The variable x can represent the number of students in each grade, with the ratio 1 being the base. This means that 3x+1x+1x=180 students, or 3x+x+x=180. | ###Write an explanation to this problem:
The ratio of 6th graders to 7th graders to 8th graders in a middle school is 3:1:1. If there are 180 students in total, how many of the students are in each grade? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The variable x can represent the number of students in each grade, with the ratio 1 being the base. This means that 3x+1x+1x=180 students, or 3x+x+x=180. |
342 | In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles. | If a triangle is an isosceles triangle, then two of its sides are the same length and the third side is different. This means two of the angles are the same and one is different. If A is 40, then this could be the same as one of the other angles. Angle B or Angle C could also measure 40 degrees. This means the other angle should measure 100 degrees. This is because all of the angles should add up to 180. 40 + 40 + 100 = 180 If A is 40 and is the different angle, then the other two angles together measure 140 degrees. 180 - 40 = 140 The angles must be congruent. 140/2 = 70 Angles B and C would be 70 degrees each. | ###Write an explanation to this problem:
In triangle ABC, the measure of angle A is 40deg;. Give possible measures for angles B and C if triangle ABC is isosceles.
###Explanation:
If a triangle is an isosceles triangle, then two of its sides are the same length and the third side is different. This means two of the angles are the same and one is different. If A is 40, then this could be the same as one of the other angles. Angle B or Angle C could also measure 40 degrees. This means the other angle should measure 100 degrees. This is because all of the angles should add up to 180. 40 + 40 + 100 = 180 If A is 40 and is the different angle, then the other two angles together measure 140 degrees. 180 - 40 = 140 The angles must be congruent. 140/2 = 70 Angles B and C would be 70 degrees each. |
73 | Find a number that matches the description. A 4-digit number that is not divisible by 2, 3, 5, or 10. The Utah Middle School Math Project | There are many different correct answers to this question. We want a number that is not divisible by 2, 3, 5, or 10. To be divisible by 2, the last digit must be an even number or 0. To be divisible by 3, the digits must sum to a number that is a multiple or 3. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 10, the last digit must be a 0. If we want our number to not be divisible by 2, 5, or 10, then the last digit cannot be an even number, 0, or 5. This leaves 1, 3, 7, and 9. For our example, we'll pick 7 _ _ _ 7 Finally, let's pick our other three digits so that all four digits do not add to a number divisible by 3. This could be 5447. 5 + 4 + 4 + 7 = 20, and 20 is not divisible by 3. Our number could be 5447. | ###Write an explanation to this problem:
Find a number that matches the description. A 4-digit number that is not divisible by 2, 3, 5, or 10. The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is not divisible by 2, 3, 5, or 10. To be divisible by 2, the last digit must be an even number or 0. To be divisible by 3, the digits must sum to a number that is a multiple or 3. To be divisible by 5, the last digit has to be a 0 or a 5. To be divisible by 10, the last digit must be a 0. If we want our number to not be divisible by 2, 5, or 10, then the last digit cannot be an even number, 0, or 5. This leaves 1, 3, 7, and 9. For our example, we'll pick 7 _ _ _ 7 Finally, let's pick our other three digits so that all four digits do not add to a number divisible by 3. This could be 5447. 5 + 4 + 4 + 7 = 20, and 20 is not divisible by 3. Our number could be 5447. |
591 | Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project | Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips. | ###Write an explanation to this problem:
Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips. |
602 | Use The Distributive Property to find the product. 4105 First, show your work here. The Utah Middle School Math Project | 4105 = 4100 + 45 = 400 + 20 = 420 | ###Write an explanation to this problem:
Use The Distributive Property to find the product. 4105 First, show your work here. The Utah Middle School Math Project
###Explanation:
4105 = 4100 + 45 = 400 + 20 = 420 |
734 | Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school. | There are many possible solutions. Here are some samples: The ratio of the number of male teachers to the number of female teachers is 15:35. The ratio of the number of female teachers to the number of male teachers is 35:15. The ratio of the number of female teachers to the total number of teachers in the school is 35:50. The ratio of the number of male teachers to the total number of teachers in the school is 15:50. | ###Write an explanation to this problem:
Give two different ratios with a description of the ratio relationship using the following information: There are 15 male teachers in the school. There are 35 female teachers in the school.
###Explanation:
There are many possible solutions. Here are some samples: The ratio of the number of male teachers to the number of female teachers is 15:35. The ratio of the number of female teachers to the number of male teachers is 35:15. The ratio of the number of female teachers to the total number of teachers in the school is 35:50. The ratio of the number of male teachers to the total number of teachers in the school is 15:50. |
145 | Mark the text by underlining key words. The sum of 25 and h is divided by f cubed. | The sum of 25 and h is divided by f cubed. | ###Write an explanation to this problem:
Mark the text by underlining key words. The sum of 25 and h is divided by f cubed.
###Explanation:
The sum of 25 and h is divided by f cubed. |
234 | 4. Take turns with your partner telling a story that might be represented by each equation. Then, for each equation, choose one story, state what quantity x describes, and solve the equation. If you get stuck, draw a diagram. a. 0.7 + x = 12 copied for free from openupresources.org | Here is an example, but answers may vary: First solve: 0.7 + x = 12-0.7 -0.7 --->Use inverse operation and subtract o.7 from each side to isolate xx = 11.3 Cara went to the store to buy pencils for school which cost 70 cents. She then bought some snacks to eat when she got home and her total was 12. When solving, the total Cara spent was 11.30 of her money and she used the 0.70 she found to pay the rest. | ###Write an explanation to this problem:
4. Take turns with your partner telling a story that might be represented by each equation. Then, for each equation, choose one story, state what quantity x describes, and solve the equation. If you get stuck, draw a diagram. a. 0.7 + x = 12 copied for free from openupresources.org
###Explanation:
Here is an example, but answers may vary: First solve: 0.7 + x = 12-0.7 -0.7 --->Use inverse operation and subtract o.7 from each side to isolate xx = 11.3 Cara went to the store to buy pencils for school which cost 70 cents. She then bought some snacks to eat when she got home and her total was 12. When solving, the total Cara spent was 11.30 of her money and she used the 0.70 she found to pay the rest. |
220 | A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm. She wants to test the plants at the farm, but it will ruin the crop if she tests all of them. If the farm has 5,000 spinach plants, describe a method that would produce a random sample of 10 plants. | She could put the map of the farm on a grid and number each section of the grid. She could have a computer program randomly select 10 grid numbers and choose a plant from inside the 10 grid numbers that the computer selected. | ###Write an explanation to this problem:
A public health expert is worried that a recent outbreak of a disease may be related to a batch of spinach from a certain farm. She wants to test the plants at the farm, but it will ruin the crop if she tests all of them. If the farm has 5,000 spinach plants, describe a method that would produce a random sample of 10 plants.
###Explanation:
She could put the map of the farm on a grid and number each section of the grid. She could have a computer program randomly select 10 grid numbers and choose a plant from inside the 10 grid numbers that the computer selected. |
360 | The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A child's wading pool is being inflated. The pool's size increases at a rate of 2 cubic feet per minute. The Utah Middle School Math Project | Time is the dependent variable. The size of the pool depends on the amount of time the pool has been inflating. The size is independent. | ###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. A child's wading pool is being inflated. The pool's size increases at a rate of 2 cubic feet per minute. The Utah Middle School Math Project
###Explanation:
Time is the dependent variable. The size of the pool depends on the amount of time the pool has been inflating. The size is independent. |
357 | Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org | Bananas cost 1.50 per pound. The cost for b pounds of bananas would be 1.5b. Guavas cost 3.00 per pound. The cost for g pounds of guavas would be 3g. The cost for b bananas and g guavas is 12. 12 = 1.5b + 3g | ###Write an explanation to this problem:
Bananas cost 1.50 per pound, and guavas cost 3.00 per pound. Kiran spends 12 on fruit to for a breakfast his family is hosting. Let b be the number of pounds of bananas Kiran buys and g be the number of pounds of guavas he buys. Write an equation relating the two variables. copied for free from openupresources.org
###Explanation:
Bananas cost 1.50 per pound. The cost for b pounds of bananas would be 1.5b. Guavas cost 3.00 per pound. The cost for g pounds of guavas would be 3g. The cost for b bananas and g guavas is 12. 12 = 1.5b + 3g |
132 | What does the expression represent? | The expression represents the area of a rectangle. | ###Write an explanation to this problem:
What does the expression represent?
###Explanation:
The expression represents the area of a rectangle. |
420 | Boris is setting up an exercise schedule. For five days each week, he would like to play a sport for 30 minutes, stretch for 5 minutes, and lift weights for 10 minutes. Write two different expressions that could be used to represent the total number of minutes he will exercise in five days. The Utah Middle School Math Project | To find the total number of minutes Boris exercises over the course of five days, add the number of minutes he exercises each day and multiplies the total by 5. This can be expressed in multiple ways. 1 530 + 5 + 10 2 530 + 55 + 510 | ###Write an explanation to this problem:
Boris is setting up an exercise schedule. For five days each week, he would like to play a sport for 30 minutes, stretch for 5 minutes, and lift weights for 10 minutes. Write two different expressions that could be used to represent the total number of minutes he will exercise in five days. The Utah Middle School Math Project
###Explanation:
To find the total number of minutes Boris exercises over the course of five days, add the number of minutes he exercises each day and multiplies the total by 5. This can be expressed in multiple ways. 1 530 + 5 + 10 2 530 + 55 + 510 |
626 | For what value of x does the expression 10 evaluate to 70? Write an equation to represent the problem. The Utah Middle School Math Project | To make an equation where the expression 10x evaluates to 70, we need to say that the expression equals 70. 10x=70 Any equation that simplifies to this equation is a correct answer. | ###Write an explanation to this problem:
For what value of x does the expression 10 evaluate to 70? Write an equation to represent the problem. The Utah Middle School Math Project
###Explanation:
To make an equation where the expression 10x evaluates to 70, we need to say that the expression equals 70. 10x=70 Any equation that simplifies to this equation is a correct answer. |
813 | Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data. | One question that would result in numerical data could be: How many hours did you sleep last night? This would produce numerical data because hours are a quantity that can be measured. | ###Write an explanation to this problem:
Write two questions that you could ask the students in your class that would result in numerical data. For each question, explain how you know that responses to it would produce numerical data.
###Explanation:
One question that would result in numerical data could be: How many hours did you sleep last night? This would produce numerical data because hours are a quantity that can be measured. |
41 | Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle. | In drawing a triangle with three provided side lengths, there is only one way to draw the triangle. Once one length is drawn, the other two lengths are used to draw circles with the lengths as the respective radii of each circle, centered at either end of the segment drawn first. Regardless of which order of segments is used, there is only one unique triangle that can be drawn. In drawing a triangle with two side lengths and included angle provided, there is only one way to draw the triangle. Once the angle is drawn and the two side lengths are marked off on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle. | ###Write an explanation to this problem:
Choose either the three sides condition or the two sides and included angle condition, and explain why the condition determines a unique triangle.
###Explanation:
In drawing a triangle with three provided side lengths, there is only one way to draw the triangle. Once one length is drawn, the other two lengths are used to draw circles with the lengths as the respective radii of each circle, centered at either end of the segment drawn first. Regardless of which order of segments is used, there is only one unique triangle that can be drawn. In drawing a triangle with two side lengths and included angle provided, there is only one way to draw the triangle. Once the angle is drawn and the two side lengths are marked off on the rays of the angle, there is only one possible place to position the third side of the triangle, which also determines the two remaining angle measures of the triangle. Therefore, the two sides and included angle condition determines a unique triangle. |
528 | The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Sally's track coach wants to know how far she can run based on the amount of time she runs for. The Utah Middle School Math Project | Time is the independent variable. The how far she can run is the dependent variable. | ###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. Sally's track coach wants to know how far she can run based on the amount of time she runs for. The Utah Middle School Math Project
###Explanation:
Time is the independent variable. The how far she can run is the dependent variable. |
108 | Sandy puts 6% of her income in a retirement account. If she made 1,500 in a pay period, how much of it will go into her retirement account? Write an equation to solve the problem. The Utah Middle School Math Project | Convert the percentage to a decimal. To convert a percent to a decimal, divide by 100. 6/100 = 0.06 This decimal should be multiplied by Sandy's income to reflect how much money goes into the account. The amount of money can be represented by r=0.061500. | ###Write an explanation to this problem:
Sandy puts 6% of her income in a retirement account. If she made 1,500 in a pay period, how much of it will go into her retirement account? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Convert the percentage to a decimal. To convert a percent to a decimal, divide by 100. 6/100 = 0.06 This decimal should be multiplied by Sandy's income to reflect how much money goes into the account. The amount of money can be represented by r=0.061500. |
779 | Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B | I can add two to the weeks each time to get the next number. I can add 350 to the money to get the next values. In the rows, we have 2:350, which is equal to 1:175. So the money is 175 times larger than the week. I can just multiply the week by 175 to get the amount of money in the account. The ratio used to create the table was 1:175. | ###Write an explanation to this problem:
Show more than one way you could use the structure of the table below to find the unknown value. Number of Weeks Amount of Money in Account 2 350 4 700 6 1,050 8 A 10 B
###Explanation:
I can add two to the weeks each time to get the next number. I can add 350 to the money to get the next values. In the rows, we have 2:350, which is equal to 1:175. So the money is 175 times larger than the week. I can just multiply the week by 175 to get the amount of money in the account. The ratio used to create the table was 1:175. |
56 | Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org | Lin Noah 7x+2=91 7x+14 = 91 7x = 77 x = 11 7x+2 =91 x+2 = 13 x = 11 | ###Write an explanation to this problem:
Lin and Noah are solving the equation 7x+2=91 . Lin starts by using the distributive property. Noah starts by dividing each side by 7. Show what Lin's and Noah's full solution methods might look like. copied for free from openupresources.org
###Explanation:
Lin Noah 7x+2=91 7x+14 = 91 7x = 77 x = 11 7x+2 =91 x+2 = 13 x = 11 |
291 | Zookeepers recorded the ages, weights, genders, and heights of the 10 pandas at their zoo. Write two statistical questions that could be answered using these data sets. | There are multiple correct answers to this question. These are just a couple of examples: What is the average age of the pandas in the zoo? Are male pandas typically taller than female pandas? | ###Write an explanation to this problem:
Zookeepers recorded the ages, weights, genders, and heights of the 10 pandas at their zoo. Write two statistical questions that could be answered using these data sets.
###Explanation:
There are multiple correct answers to this question. These are just a couple of examples: What is the average age of the pandas in the zoo? Are male pandas typically taller than female pandas? |
316 | In an isosceles triangle, which is not equilateral, two side lengths are equal and two angle measures are equal. Sketch three different isosceles triangles. Submit your drawing using the tools below. | Triangles should each have two sides that are the same length but not three. Answer vary. | ###Write an explanation to this problem:
In an isosceles triangle, which is not equilateral, two side lengths are equal and two angle measures are equal. Sketch three different isosceles triangles. Submit your drawing using the tools below.
###Explanation:
Triangles should each have two sides that are the same length but not three. Answer vary. |
840 | A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost 12. How much will the caterer pay for the pasta there? Write a ratio for the given information about the cost of pasta. | The ratio for the given information about the cost of pasta could be represented as 8pounds of pasta: 12 or 21 pounds of pasta: x | ###Write an explanation to this problem:
A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost 12. How much will the caterer pay for the pasta there? Write a ratio for the given information about the cost of pasta.
###Explanation:
The ratio for the given information about the cost of pasta could be represented as 8pounds of pasta: 12 or 21 pounds of pasta: x |
24 | Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9 | The subtraction rule says that subtracting a number is the same as adding its opposite. To use this rule of subtraction, we start by switching the subtraction sign to an addition sign: 5 + 9 We then change the sign of 9 to its opposite and get: 5 + -9 | ###Write an explanation to this problem:
Using the rule of subtraction, rewrite the following subtraction expression as an addition expression. 5 - 9
###Explanation:
The subtraction rule says that subtracting a number is the same as adding its opposite. To use this rule of subtraction, we start by switching the subtraction sign to an addition sign: 5 + 9 We then change the sign of 9 to its opposite and get: 5 + -9 |
750 | Fill in the blank with numbers that correctly complete the statement. Three rational numbers between -1 and -2 < < | -1.9 < -1.55 < -1.02 | ###Write an explanation to this problem:
Fill in the blank with numbers that correctly complete the statement. Three rational numbers between -1 and -2 < <
###Explanation:
-1.9 < -1.55 < -1.02 |
394 | Write a story that matches the expressions and equation shown below. Felipe's age: f Felipe's sister's age: f - 6 Felipe's mom's age: 3f - 9 f + f - 6 + 3f - 9 = 60 Hint: When writing stories like the one above, be sure to relate the unknown to its meaning in the story. Don't use the actual unknown in the story. For example, in the situation above, do not write Felipe's sister is f minus 6 years old. Think about how Felipe's sister's age is related to Felipe's age which is represented by f in the expression. Also, remember that your story needs a question. The Utah Middle School Math Project | A possible story could be: Felipe's sister is six years younger than him. His mom's age is nine less than three ties his age. Together, their ages sum to 60, How old is each person? It is important that each age is addressed in the story, along with all known parts of the story. In this case, the known part of the story is the sum of the ages, and how old each person is based on Felipe's age. | ###Write an explanation to this problem:
Write a story that matches the expressions and equation shown below. Felipe's age: f Felipe's sister's age: f - 6 Felipe's mom's age: 3f - 9 f + f - 6 + 3f - 9 = 60 Hint: When writing stories like the one above, be sure to relate the unknown to its meaning in the story. Don't use the actual unknown in the story. For example, in the situation above, do not write Felipe's sister is f minus 6 years old. Think about how Felipe's sister's age is related to Felipe's age which is represented by f in the expression. Also, remember that your story needs a question. The Utah Middle School Math Project
###Explanation:
A possible story could be: Felipe's sister is six years younger than him. His mom's age is nine less than three ties his age. Together, their ages sum to 60, How old is each person? It is important that each age is addressed in the story, along with all known parts of the story. In this case, the known part of the story is the sum of the ages, and how old each person is based on Felipe's age. |
490 | Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project | w= 2r where w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles. | ###Write an explanation to this problem:
Solve the following problem by writing and solving a system of equations. Use any method you wish to solve. Write your answer in a complete sentence. Ruby and Will are running a team relay race. Will runs twice as far as Ruby. Together they run 18 miles. How far did each person run? The Utah Middle School Math Project
###Explanation:
w= 2r where w represents Will's distance and r represents Ruby's distance r+ w= 18 Will ran 12 miles and Ruby ran 6 miles. |
51 | Write another ratio that is equivalent to the ratio 4:6. | Some ratios that could be equivalent to 4:6 are 2:3, 8:12, 12:18 and 40:60 | ###Write an explanation to this problem:
Write another ratio that is equivalent to the ratio 4:6.
###Explanation:
Some ratios that could be equivalent to 4:6 are 2:3, 8:12, 12:18 and 40:60 |
659 | Challenge: If two equal angles are supplements to each other, find the measure of each angle in terms of one variable. The Utah Middle School Math Project | The answer is x and 180-x This is because supplementary angles add to 180 so to find the angles you can do 180-x which will be one answer and x will be the other | ###Write an explanation to this problem:
Challenge: If two equal angles are supplements to each other, find the measure of each angle in terms of one variable. The Utah Middle School Math Project
###Explanation:
The answer is x and 180-x This is because supplementary angles add to 180 so to find the angles you can do 180-x which will be one answer and x will be the other |
811 | Mark the text by underlining key words. The sum of 25 and h is divided by f cubed. | The sum of 25 and h is divided by f cubed. | ###Write an explanation to this problem:
Mark the text by underlining key words. The sum of 25 and h is divided by f cubed.
###Explanation:
The sum of 25 and h is divided by f cubed. |
549 | In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. -32x-5-6x-15 Explain the mistake The Utah Middle School Math Project | Notice that -3 x -5 = 15, not -15. This means that the -3 was not distributed to the terms within the parentheses properly. | ###Write an explanation to this problem:
In the following problem, a common error has been made when simplifying the expression. Identify the mistake, explain it, and simplify the expression correctly. -32x-5-6x-15 Explain the mistake The Utah Middle School Math Project
###Explanation:
Notice that -3 x -5 = 15, not -15. This means that the -3 was not distributed to the terms within the parentheses properly. |
264 | The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100. Describe how the manager can select a fair sample of 5 packages. | There are several different correct ways the manager could select a fair sample of 5 packages. The manager should pick a method that will result in a random sample. One way is to write the numbers from 1 to 100 on slips of paper and put them in a bag. Mix them well, then select 5 slips of paper from the bag. Use the numbers on these slips to identify which packages in the shipment will be in the sample. ***Alternative: The manager might also use random digits or another type of random number generator. | ###Write an explanation to this problem:
The meat department manager at a grocery store is worried some of the packages of ground beef labeled as having one pound of meat may be under-filled. He decides to take a sample of 5 packages from a shipment containing 100 packages of ground beef. The packages were numbered as they were put in the box, so each one has a different number between 1 and 100. Describe how the manager can select a fair sample of 5 packages.
###Explanation:
There are several different correct ways the manager could select a fair sample of 5 packages. The manager should pick a method that will result in a random sample. One way is to write the numbers from 1 to 100 on slips of paper and put them in a bag. Mix them well, then select 5 slips of paper from the bag. Use the numbers on these slips to identify which packages in the shipment will be in the sample. ***Alternative: The manager might also use random digits or another type of random number generator. |
774 | A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box. | Choice One: ð ðð¦ * ð ðð¦ * ðð ðð¦ Choice Two: ð ðð¦ * ð ðð¦ * ðð ðð¦ Choice Three: ð ðð¦ * ð ðð¦ * ðð ðð¦ Choice Four: ð ðð¦ * ð ðð¦ * ð ðm | ###Write an explanation to this problem:
A company that manufactures gift boxes wants to know how many different-sized boxes having a volume of 50 cubic centimeters it can make if the dimensions must be whole centimeters. List all the possible whole number dimensions for the box.
###Explanation:
Choice One: ð ðð¦ * ð ðð¦ * ðð ðð¦ Choice Two: ð ðð¦ * ð ðð¦ * ðð ðð¦ Choice Three: ð ðð¦ * ð ðð¦ * ðð ðð¦ Choice Four: ð ðð¦ * ð ðð¦ * ð ðm |
590 | Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project | Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips. | ###Write an explanation to this problem:
Here, write the fourth problem in which the percent and the part are known, but the whole is not known. The Utah Middle School Math Project
###Explanation:
Sample Answer: Justin bought chips when he went grocery shopping. On his way back home, he ate 37.5% of the chips, which was 3 bags of chips. How many bags of chips did Justin buy? Solution: part: 3 bags percent: 37.5% = 0.375 We want to find the bags of chips that Justin bought. Note that 37.5% of the chips is 3 bags of chips. 37.5% of the chips is 0.375 times the total bags of chips. With this information, we can write: 3 bags = total bags x 0.375 Now, we can solve for the total bags of chips: 3 bags = total bags x 0.375 3 bags/0.375 = total bags 8 bags = total bags We get that Justin bought 8 bags of the chips. |
671 | -5 x 0 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project | This multiplication problem asks that you take the integer -5 and multiply it 0 times, so -5 x 0 means the opposite of five groups of 0. | ###Write an explanation to this problem:
-5 x 0 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -5 and multiply it 0 times, so -5 x 0 means the opposite of five groups of 0. |
482 | Given the graphs of two or more lines how can you determine if they are parallel? The Utah Middle School Math Project | Lines are parallel if they have the same slope. | ###Write an explanation to this problem:
Given the graphs of two or more lines how can you determine if they are parallel? The Utah Middle School Math Project
###Explanation:
Lines are parallel if they have the same slope. |
18 | Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0. | The slope shows that for every 1 unit increase in side length of the triangle, the perimeter increases by 3 units. | ###Write an explanation to this problem:
Explain what the slope and intercept mean in the situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
###Explanation:
The slope shows that for every 1 unit increase in side length of the triangle, the perimeter increases by 3 units. |
617 | Are all squares similar? Justify your answer. The Utah Middle School Math Project | The answer is yes. This is because the ratio between all sides of all squares is 1:1 | ###Write an explanation to this problem:
Are all squares similar? Justify your answer. The Utah Middle School Math Project
###Explanation:
The answer is yes. This is because the ratio between all sides of all squares is 1:1 |
833 | Why do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller? | As whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with. | ###Write an explanation to this problem:
Why do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller?
###Explanation:
As whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with. |
83 | Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project | There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240. | ###Write an explanation to this problem:
Find a number that matches the description. A 3-digit number that is divisible by 3 and 4. How do you know? The Utah Middle School Math Project
###Explanation:
There are many different correct answers to this question. We want a number that is divisible by 3 and 4. To be divisible by 3, the digits have to add up to a number that is divisible by 3. To be divisible by 4, the last two digits have to be divisible by 4. Let's pick our last two digits to be 4 and 0. 40 is divisible by 4. We have: _ 4 0 Now we need our digits to add up to a number divisible by 3. 2 + 4 + 0 = 6 6 is divisible by 3, so our number could be 240. |
61 | Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org | -7, -8, -9, -10 | ###Write an explanation to this problem:
Here is an inequality: -3x > 18. List some values for x that would make this inequality true. copied for free from openupresources.org
###Explanation:
-7, -8, -9, -10 |
272 | A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time? | Both lights will blink the same after 20 seconds. Green- 4, 8, 12, 16, 20 Yellow- 5, 10, 15, 20 | ###Write an explanation to this problem:
A green light blinks every 4 seconds and a yellow light blinks every 5 seconds. When will both lights blink at the same time?
###Explanation:
Both lights will blink the same after 20 seconds. Green- 4, 8, 12, 16, 20 Yellow- 5, 10, 15, 20 |
285 | Which data set is more likely to produce a histogram with a symmetric distribution? Explain your reasoning. Data on the number of seconds on a track of music in a pop album. Data on the number of seconds spent talking on the phone yesterday by everyone in the school. | The data on the number of seconds on a track of music in a pop album is most likely to be symmetrical because pops songs are generally about the same length. The data about talking on the phone may have a wide spread because some people may only talk for a few seconds, but others may talk on the phone for hours. | ###Write an explanation to this problem:
Which data set is more likely to produce a histogram with a symmetric distribution? Explain your reasoning. Data on the number of seconds on a track of music in a pop album. Data on the number of seconds spent talking on the phone yesterday by everyone in the school.
###Explanation:
The data on the number of seconds on a track of music in a pop album is most likely to be symmetrical because pops songs are generally about the same length. The data about talking on the phone may have a wide spread because some people may only talk for a few seconds, but others may talk on the phone for hours. |
327 | Which measurements would you need in order to draw a scale floor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specific as possible. copied for free from openupresources.org | The length and width of all the walls The measurements of doorways the measurements of all furniture in the classroom | ###Write an explanation to this problem:
Which measurements would you need in order to draw a scale floor plan of your classroom? List which parts of the classroom you would measure and include in the drawing. Be as specific as possible. copied for free from openupresources.org
###Explanation:
The length and width of all the walls The measurements of doorways the measurements of all furniture in the classroom |
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