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679 | Create a data set with at least 8 data values that match each set of given conditions. A data set where the IQR is equal to the range. | There are many correct answers for this question. One example of a correct answer is: 10, 10, 10, 10, 10, 10, 10, 10 In this case, the range is 10 - 10 = 0, and the IQR must also be 10 - 10 = 0. | ###Write an explanation to this problem:
Create a data set with at least 8 data values that match each set of given conditions. A data set where the IQR is equal to the range.
###Explanation:
There are many correct answers for this question. One example of a correct answer is: 10, 10, 10, 10, 10, 10, 10, 10 In this case, the range is 10 - 10 = 0, and the IQR must also be 10 - 10 = 0. |
708 | A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project | Since the number of tables is unknown, we can use a variable, t, to represent this value. There are 8 students at each table, and the total number of students is 120. This means that: 8 students * number of tables = 120 students total 8t=120 | ###Write an explanation to this problem:
A lunch table can hold 8 students. If there are 120 students who need to eat lunch at the same time, how many tables are needed? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
Since the number of tables is unknown, we can use a variable, t, to represent this value. There are 8 students at each table, and the total number of students is 120. This means that: 8 students * number of tables = 120 students total 8t=120 |
635 | Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project | Your answer can be any statistical question, a question that asks for multiple data points that may vary. | ###Write an explanation to this problem:
Create a statistical question of your own that you could answer by surveying people in your class. Write your question here: The Utah Middle School Math Project
###Explanation:
Your answer can be any statistical question, a question that asks for multiple data points that may vary. |
703 | Solve the inequality. Represent the solution on a number line. 1.5y>9 The Utah Middle School Math Project | Solve for y. 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. 1.5y>9 The Utah Middle School Math Project
###Explanation:
Solve for y. The number line should be greater than the solution, but not contain it. |
314 | 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 shows that 2 are added for each muffin ordered. The intercept of 3 probably represents a 3 delivery fee or tip for the order. | ###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 shows that 2 are added for each muffin ordered. The intercept of 3 probably represents a 3 delivery fee or tip for the order. |
311 | In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. Submit your drawing using the tools below. | The three angle measures must add to 180â but must all be equal. Therefore, each measure is 60â, since 60 = 1/3 * 180. The answer is 60. | ###Write an explanation to this problem:
In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. Submit your drawing using the tools below.
###Explanation:
The three angle measures must add to 180â but must all be equal. Therefore, each measure is 60â, since 60 = 1/3 * 180. The answer is 60. |
522 | Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project | Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output | ###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. A car is traveling at a constant rate of 60 mph. Is the car's distance traveled a function of the number of hours the car has been driving? The Utah Middle School Math Project
###Explanation:
Yes, the data represents a function Each hour the car drives another 60 miles, giving each input a unique output |
442 | The following equation is given: -3x ndash; 5 = -2 Provide a context/word problem for the given information. The Utah Middle School Math Project | Five less than the product of -3 and a number is -2. | ###Write an explanation to this problem:
The following equation is given: -3x ndash; 5 = -2 Provide a context/word problem for the given information. The Utah Middle School Math Project
###Explanation:
Five less than the product of -3 and a number is -2. |
575 | Let's say that Mouse, Double-Dog and Triple-Threat-Tiger all have swimming pools. What would you predict about the scale factor of the volume as related to double or triple dimensions? Prove or adjust your prediction--say that Mouse has a pool which is 1 foot deep and 2 feet by 3 feet. The Utah Middle School Math Project | You would cube the scale factor of the lengths | ###Write an explanation to this problem:
Let's say that Mouse, Double-Dog and Triple-Threat-Tiger all have swimming pools. What would you predict about the scale factor of the volume as related to double or triple dimensions? Prove or adjust your prediction--say that Mouse has a pool which is 1 foot deep and 2 feet by 3 feet. The Utah Middle School Math Project
###Explanation:
You would cube the scale factor of the lengths |
411 | Suppose the cell phone company sells three different plans to its customers: Pay-as-you-go: The customer is charged per minute for each call. Unlimited minutes: The customer pays a flat fee per month and can make unlimited calls with no additional charges. Basic plan: The customer is not charged per minute unless the customer exceeds 500 minutes in the month; then, the customer is charged per minute for the extra minutes. Consider the chance experiment of selecting a customer at random and recording which plan she purchased. What outcomes are in the sample space for this chance experiment? | 1 pay-as-you-go 2 unlimited minutes 3 basic plan | ###Write an explanation to this problem:
Suppose the cell phone company sells three different plans to its customers: Pay-as-you-go: The customer is charged per minute for each call. Unlimited minutes: The customer pays a flat fee per month and can make unlimited calls with no additional charges. Basic plan: The customer is not charged per minute unless the customer exceeds 500 minutes in the month; then, the customer is charged per minute for the extra minutes. Consider the chance experiment of selecting a customer at random and recording which plan she purchased. What outcomes are in the sample space for this chance experiment?
###Explanation:
1 pay-as-you-go 2 unlimited minutes 3 basic plan |
839 | The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point. | 10, -7; as the distance between -2 and 10 is 12 units. -14, -7; as the distance between -2 and -14 is 12 units. -2, 5; as the distance between 5 and -7 is 12 units. -2, -19; as the distance between -7 and -19 is 12 units. | ###Write an explanation to this problem:
The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.
###Explanation:
10, -7; as the distance between -2 and 10 is 12 units. -14, -7; as the distance between -2 and -14 is 12 units. -2, 5; as the distance between 5 and -7 is 12 units. -2, -19; as the distance between -7 and -19 is 12 units. |
67 | It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents. | The equation shows that after h hours, the temperature has become 14 degrees. | ###Write an explanation to this problem:
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents.
###Explanation:
The equation shows that after h hours, the temperature has become 14 degrees. |
558 | The following problem is given to Miranda: 23.10*100 She states that since she is multiplying by 100 she simply must add two zeros to 23.10. Explain the error in Miranda's thinking and explain how to find the correct answer without using a calculator or long multiplication. The Utah Middle School Math Project | Multiplying by 100 indicates moving the decimal two places to the right; this will give you 2,310. | ###Write an explanation to this problem:
The following problem is given to Miranda: 23.10*100 She states that since she is multiplying by 100 she simply must add two zeros to 23.10. Explain the error in Miranda's thinking and explain how to find the correct answer without using a calculator or long multiplication. The Utah Middle School Math Project
###Explanation:
Multiplying by 100 indicates moving the decimal two places to the right; this will give you 2,310. |
275 | 1. Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice? Copied for free from openupresources.org | The angles go all the way around one point. | ###Write an explanation to this problem:
1. Draw a quadrilateral. Cut it out, tear off its angles, and line them up. What do you notice? Copied for free from openupresources.org
###Explanation:
The angles go all the way around one point. |
757 | 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. Therefore, 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. Sample response: 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. Therefore, 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. Sample response: 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 |
787 | Use tape diagrams and equations to solve the problem with visual models and algebraic methods. Alyssa is twice as old as Brittany, and Jazmyn is 15 years older than Alyssa. If Jazmyn is 35 years old, how old is Brittany? Let a represent Alyssa's age in years and b represent Brittany's age in years. Submit your work using the tools below. | According to this tape diagram, a+15=35 on Jazmyn's tape diagram. To solve for a, subtract 15 from 35. a is 20. b is half of a, so 20/2 = 10. b =10 | ###Write an explanation to this problem:
Use tape diagrams and equations to solve the problem with visual models and algebraic methods. Alyssa is twice as old as Brittany, and Jazmyn is 15 years older than Alyssa. If Jazmyn is 35 years old, how old is Brittany? Let a represent Alyssa's age in years and b represent Brittany's age in years. Submit your work using the tools below.
###Explanation:
According to this tape diagram, a+15=35 on Jazmyn's tape diagram. To solve for a, subtract 15 from 35. a is 20. b is half of a, so 20/2 = 10. b =10 |
801 | 120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78. | Change percent to a decimal of means to multiply 1.20 x= 78 | ###Write an explanation to this problem:
120% of x is equal to 78. Write an equation that shows the relationship of 120%, x, and 78.
###Explanation:
Change percent to a decimal of means to multiply 1.20 x= 78 |
768 | The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point. | ðð, -ð; as the distance between -2 and 10 is 12 units. -ðð, -ð; as the distance between -2 and -14 is 12 units. -ð, ð; as the distance between 5 and -7 is 12 units. -ð, -ðð; as the distance between -7 and -19 is 12 units. | ###Write an explanation to this problem:
The coordinates of one end point of a line segment are -2,-7. The line segment is 12 units long. Give three possible coordinates of the line segment's other end point.
###Explanation:
ðð, -ð; as the distance between -2 and 10 is 12 units. -ðð, -ð; as the distance between -2 and -14 is 12 units. -ð, ð; as the distance between 5 and -7 is 12 units. -ð, -ðð; as the distance between -7 and -19 is 12 units. |
675 | -7 x -2 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project | This multiplication problem means the opposite of seven groups of negative 2. | ###Write an explanation to this problem:
-7 x -2 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem means the opposite of seven groups of negative 2. |
326 | A map of a park says its scale is 1 to 100. What do you think that means? copied for free from openupresources.org | That the actual park is 100 times larger than the map. | ###Write an explanation to this problem:
A map of a park says its scale is 1 to 100. What do you think that means? copied for free from openupresources.org
###Explanation:
That the actual park is 100 times larger than the map. |
629 | 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: 6x = 54 Original Equation: x=9 Action: ______ The Utah Middle School Math Project | On the left side of the equation, 6x has been divided by 6. On the right side, 54 has been divided by 6, to create the result of 9. The action was: Divide both sides of the equation by 6. | ###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: 6x = 54 Original Equation: x=9 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 6x has been divided by 6. On the right side, 54 has been divided by 6, to create the result of 9. The action was: Divide both sides of the equation by 6. |
519 | 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. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project | Sarah: y= 400 - 15x Matthew: y= 50 + 20x where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250. | ###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. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project
###Explanation:
Sarah: y= 400 - 15x Matthew: y= 50 + 20x where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250. |
468 | 210% of 60 Estimate the answer. The Utah Middle School Math Project | 210% means over twice as much as the whole thing, so 210% of 60 must be over 120. | ###Write an explanation to this problem:
210% of 60 Estimate the answer. The Utah Middle School Math Project
###Explanation:
210% means over twice as much as the whole thing, so 210% of 60 must be over 120. |
412 | Mr. Cortez drove at a constant rate for 5 hours. At the end of 2 hours he had driven 90 miles. After 5 hours, he had driven 225 miles. What is the dependent variable in this relationship? The Utah Middle School Math Project | The distance that was driven depends on the amount of time that he was driving. This means distance is the dependent variable in this equation. | ###Write an explanation to this problem:
Mr. Cortez drove at a constant rate for 5 hours. At the end of 2 hours he had driven 90 miles. After 5 hours, he had driven 225 miles. What is the dependent variable in this relationship? The Utah Middle School Math Project
###Explanation:
The distance that was driven depends on the amount of time that he was driving. This means distance is the dependent variable in this equation. |
588 | Write a context to match the numeric expression given. 23 12 The Utah Middle School Math Project | Angie is making key lime pie for a bake sale. Each pie can be cut into 12 slices. If she makes 3 pies and sells each slice for 2, how much money will she make? | ###Write an explanation to this problem:
Write a context to match the numeric expression given. 23 12 The Utah Middle School Math Project
###Explanation:
Angie is making key lime pie for a bake sale. Each pie can be cut into 12 slices. If she makes 3 pies and sells each slice for 2, how much money will she make? |
526 | Determine if the relation or situation defines a function. Justify your answer. You call the post office and ask for the zip code for the city of Salt Lake City, UT. Is zip code a function of the name of the city? The Utah Middle School Math Project | No, the data does not describe a function There are several zip codes for the city of Salt Lake, and therefore several outputs or zip codes for the one input of the city of Salt Lake | ###Write an explanation to this problem:
Determine if the relation or situation defines a function. Justify your answer. You call the post office and ask for the zip code for the city of Salt Lake City, UT. Is zip code a function of the name of the city? The Utah Middle School Math Project
###Explanation:
No, the data does not describe a function There are several zip codes for the city of Salt Lake, and therefore several outputs or zip codes for the one input of the city of Salt Lake |
718 | Imagine cutting a cube, parallel to the base. What shape is the plane section? The Utah Middle School Math Project | If a cube was cut parallel to the base the resulting cross-section would have to be a square | ###Write an explanation to this problem:
Imagine cutting a cube, parallel to the base. What shape is the plane section? The Utah Middle School Math Project
###Explanation:
If a cube was cut parallel to the base the resulting cross-section would have to be a square |
213 | The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct. | The researchers might be correct because the data shows a large IQR. | ###Write an explanation to this problem:
The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.
###Explanation:
The researchers might be correct because the data shows a large IQR. |
514 | How do you read the expression --12? The Utah Middle School Math Project | The opposite of the opposite of twelve | ###Write an explanation to this problem:
How do you read the expression --12? The Utah Middle School Math Project
###Explanation:
The opposite of the opposite of twelve |
39 | 1. A balloon is floating above a lake and a sunken canoe is below the surface of the lake. The balloon's vertical position is 12 meters and the canoe's is -4.8 meters. The equation copied for free from openupresources.org | The difference in elevation between the balloon and the canoe. | ###Write an explanation to this problem:
1. A balloon is floating above a lake and a sunken canoe is below the surface of the lake. The balloon's vertical position is 12 meters and the canoe's is -4.8 meters. The equation copied for free from openupresources.org
###Explanation:
The difference in elevation between the balloon and the canoe. |
766 | Use GCF and the distributive property to write equivalent expressions in factored form for the following expression. 4d+12e | The greatest common factor of 4 and 12 is 4. 4 goes into 4 1 time, and 12/4=3. This means the coefficient of d will be 1 and the coefficient of e will be 3. Plugging this into the equation, and using the distributive property, the equation becomes 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:
The greatest common factor of 4 and 12 is 4. 4 goes into 4 1 time, and 12/4=3. This means the coefficient of d will be 1 and the coefficient of e will be 3. Plugging this into the equation, and using the distributive property, the equation becomes 41d+3e. |
168 | Write two division expressions that have the same value as 61.12 / 3.2. | There are a variety of correct answers to this problem. These are just a few examples: 6,112/320 611.2/32 0.6112/0.032 | ###Write an explanation to this problem:
Write two division expressions that have the same value as 61.12 / 3.2.
###Explanation:
There are a variety of correct answers to this problem. These are just a few examples: 6,112/320 611.2/32 0.6112/0.032 |
439 | The following equation is given: x + x+3 + x + x+3 = 34 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project | The length of a rectangle is 3 more than the width. If the perimeter is 34, what are the length and width? | ###Write an explanation to this problem:
The following equation is given: x + x+3 + x + x+3 = 34 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
The length of a rectangle is 3 more than the width. If the perimeter is 34, what are the length and width? |
467 | 150% of 16 Estimate the answer. The Utah Middle School Math Project | 150% is in between 100% and 200%, so 150% of 16 must be in between 16 and 32. | ###Write an explanation to this problem:
150% of 16 Estimate the answer. The Utah Middle School Math Project
###Explanation:
150% is in between 100% and 200%, so 150% of 16 must be in between 16 and 32. |
30 | A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle. | 6:8:10 9:12:15 | ###Write an explanation to this problem:
A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.
###Explanation:
6:8:10 9:12:15 |
338 | Graph a system of linear equations with no solutions. Submit your graph using the tools below. | The solution of a system of equations can be easily seen on a graph. It is the point where the lines intersect. To graph a system of linear equations with no solutions, graph 2 lines that are parallel. Parallel lines will never intersect, so there will not be a solution. | ###Write an explanation to this problem:
Graph a system of linear equations with no solutions. Submit your graph using the tools below.
###Explanation:
The solution of a system of equations can be easily seen on a graph. It is the point where the lines intersect. To graph a system of linear equations with no solutions, graph 2 lines that are parallel. Parallel lines will never intersect, so there will not be a solution. |
208 | List the sample space the available options for the chance experiment given. Flipping a coin | When you flip a coin, the two sides it could land on are heads or tails. | ###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
When you flip a coin, the two sides it could land on are heads or tails. |
139 | What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB | The sample space is the same for the two experiments because the words contain the same letters. Sample Space: A,B,L,M | ###Write an explanation to this problem:
What is the same about these two experiments? Selecting a letter at random from the word ALABAMA Selecting a letter at random from the word LAMB
###Explanation:
The sample space is the same for the two experiments because the words contain the same letters. Sample Space: A,B,L,M |
829 | Is there a triangle with 2 right angles? Explain your reasoning. | There is no triangle with 2 right angles. The three angles in a triangle always add up 180 degrees, since 90 + 90 = 180 there is no way to make a triangle with 2 right angles. | ###Write an explanation to this problem:
Is there a triangle with 2 right angles? Explain your reasoning.
###Explanation:
There is no triangle with 2 right angles. The three angles in a triangle always add up 180 degrees, since 90 + 90 = 180 there is no way to make a triangle with 2 right angles. |
449 | The following equation is given: 2/3x ndash; 20 = 280 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project | Paulo spent 2/3 of his savings on a new phone and then spent 20 on a new cover for it. He now has 280 left in his savings account. How much money did he start with? | ###Write an explanation to this problem:
The following equation is given: 2/3x ndash; 20 = 280 Provide a context/word problem for the given information. Write contexts that are more real life. The Utah Middle School Math Project
###Explanation:
Paulo spent 2/3 of his savings on a new phone and then spent 20 on a new cover for it. He now has 280 left in his savings account. How much money did he start with? |
586 | 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. |
479 | Create your own context or story that represents a relation that is not a function. Write your story. | To create a story that is not a function, whatever you chose to be the independent variable x must have more than one corresponding dependent variable y. | ###Write an explanation to this problem:
Create your own context or story that represents a relation that is not a function. Write your story.
###Explanation:
To create a story that is not a function, whatever you chose to be the independent variable x must have more than one corresponding dependent variable y. |
597 | The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project | In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1,2, 5, 10, and so on is a correct answer. | ###Write an explanation to this problem:
The numbers below are listed in order from least to greatest. Give two possible integer values for the ? in each problem. Use a number line to help you -2,-1,0,? The Utah Middle School Math Project
###Explanation:
In this question, the only requirement is than the number that replaces the ? is an integer that is greater than 0. Any number that is not 0 in the positive direction is greater than 0, so any number like 1,2, 5, 10, and so on is a correct answer. |
260 | 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. | Example: Elena could ask a number of people whether or not they have a cat, then record how many people said yes. She would then divide the number of people who said yes by the total number of people she asked to get the proportion of people with cats. | ###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:
Example: Elena could ask a number of people whether or not they have a cat, then record how many people said yes. She would then divide the number of people who said yes by the total number of people she asked to get the proportion of people with cats. |
745 | A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40? | Answers will vary, although it makes sense to count by 5's, since both values are multiples of 5. | ###Write an explanation to this problem:
A credit of 35 and a debit of 40 are applied to your bank account. What is an appropriate scale to graph a credit of 35 and a debit of 40?
###Explanation:
Answers will vary, although it makes sense to count by 5's, since both values are multiples of 5. |
424 | Jasper has a coin collection consisting of quarters and dimes. He has 50 coins worth 8.60. How many of each coin does he have? First define your unknowns. The Utah Middle School Math Project | Explain what your variables will represent in your problem. For example: q = number of quarter d = number of dimes | ###Write an explanation to this problem:
Jasper has a coin collection consisting of quarters and dimes. He has 50 coins worth 8.60. How many of each coin does he have? First define your unknowns. The Utah Middle School Math Project
###Explanation:
Explain what your variables will represent in your problem. For example: q = number of quarter d = number of dimes |
667 | Solve the inequality. Represent the solution on a number line. 5x<21 The Utah Middle School Math Project | Solve for x. The number line should be less than the solution, but not contain it. | ###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 5x<21 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be less than the solution, but not contain it. |
23 | Which of the numbers in problems 1-5 are not perfect squares? Explain. | The numbers 147 and 8 are not perfect squares because there is no integer x so that x2 = 147 OR x2 = 8 | ###Write an explanation to this problem:
Which of the numbers in problems 1-5 are not perfect squares? Explain.
###Explanation:
The numbers 147 and 8 are not perfect squares because there is no integer x so that x2 = 147 OR x2 = 8 |
210 | Rectangle ABCD is drawn on a coordinate plane. A = -6,9 and B = 5,9. What could be the locations of points C and D? | C could be -6,-9 and D could be 5,-9 or vice versa. This is because point A is at -6. 9 so your next point would have the same x but opposite y value. Point B is 5,9 so the new point would also have the same x but opposite y value. | ###Write an explanation to this problem:
Rectangle ABCD is drawn on a coordinate plane. A = -6,9 and B = 5,9. What could be the locations of points C and D?
###Explanation:
C could be -6,-9 and D could be 5,-9 or vice versa. This is because point A is at -6. 9 so your next point would have the same x but opposite y value. Point B is 5,9 so the new point would also have the same x but opposite y value. |
196 | For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7 | We know that subtracting a number is the same as adding its opposite. That means we can transform the equation to: 20 - 9 + 8 - 7 20 + -9 + 8 + -7 | ###Write an explanation to this problem:
For each expression, write an equivalent expression that uses only addition. 20 - 9 + 8 - 7 copied for free from openupresources.org 20-9+8-7
###Explanation:
We know that subtracting a number is the same as adding its opposite. That means we can transform the equation to: 20 - 9 + 8 - 7 20 + -9 + 8 + -7 |
732 | Choose a situation that could be described by the following ratio. Write a sentence to describe the ratio in the context of the situation you chose. 1 to 2 | Answers will vary. You might write something like For every one nose, there are two eyes. | ###Write an explanation to this problem:
Choose a situation that could be described by the following ratio. Write a sentence to describe the ratio in the context of the situation you chose. 1 to 2
###Explanation:
Answers will vary. You might write something like For every one nose, there are two eyes. |
110 | 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. |
383 | The width of a rectangle is five less than three times the length of the rectangle. The perimeter of the rectangle is 70 inches. Write an expression to find the width of the rectangle, an expression to find the length of the rectangle, and an equation to show the relationship between these expressions and the perimeter of the rectangle. The Utah Middle School Math Project | The length of the rectangle is represented by l. The width of the rectangle is is 3 times the length minus 5, so the width is 3l-5. The perimeter of a rectangle is equal to the width times 2 plus the length times 2. Therefore, the equation of the perimeter of the rectangle is 23l-5+2l=70. | ###Write an explanation to this problem:
The width of a rectangle is five less than three times the length of the rectangle. The perimeter of the rectangle is 70 inches. Write an expression to find the width of the rectangle, an expression to find the length of the rectangle, and an equation to show the relationship between these expressions and the perimeter of the rectangle. The Utah Middle School Math Project
###Explanation:
The length of the rectangle is represented by l. The width of the rectangle is is 3 times the length minus 5, so the width is 3l-5. The perimeter of a rectangle is equal to the width times 2 plus the length times 2. Therefore, the equation of the perimeter of the rectangle is 23l-5+2l=70. |
227 | Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han's sample is 59 inches. The mean height for Priya's sample is 61 inches. Does it surprise you that the two sample means are different? | Even though they both selected a random sample, their samples probably included different people from the population. This is why it would make sense that the two sample means are different. | ###Write an explanation to this problem:
Han and Priya want to know the mean height of the 30 students in their dance class. They each select a random sample of 5 students. The mean height for Han's sample is 59 inches. The mean height for Priya's sample is 61 inches. Does it surprise you that the two sample means are different?
###Explanation:
Even though they both selected a random sample, their samples probably included different people from the population. This is why it would make sense that the two sample means are different. |
513 | 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. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project | Sarah: ð¦ = 400 - 15ð¥ Matthew: ð¦ = 50 + 20ð¥ where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250. | ###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. Sarah has 400 in her savings account and she has to pay 15 each month to her parents for her cell phone. Darius has 50 and he saves 20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have? The Utah Middle School Math Project
###Explanation:
Sarah: ð¦ = 400 - 15ð¥ Matthew: ð¦ = 50 + 20ð¥ where y is amount of money and x is time in months They will have the same amount of money at 10 months. They will each have 250. |
653 | In the problem below, a starting equation and transformed equation have been given. State the action that produced the equivalent equation. Original Equation: x = 14 Transformed Equation: x - 3 = 11 Action: ______ The Utah Middle School Math Project | On the left side of the equation, 3 has been subtracted from x. On the right side, 3 has been subtracted from 14, which results in 11. The action was: Subtract 3 from 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 = 14 Transformed Equation: x - 3 = 11 Action: ______ The Utah Middle School Math Project
###Explanation:
On the left side of the equation, 3 has been subtracted from x. On the right side, 3 has been subtracted from 14, which results in 11. The action was: Subtract 3 from both sides of the equation. |
86 | Describe some similarities and differences between a situation that involves calculating surface area and a situation that involves calculating volume. | Calculating surface and calculating volume both involve measurement of 3 dimensional figures. The volume of a figure can help determine what can fit inside it. The surface area of a figure can help determine what is needed to cover the figure. | ###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:
Calculating surface and calculating volume both involve measurement of 3 dimensional figures. The volume of a figure can help determine what can fit inside it. The surface area of a figure can help determine what is needed to cover the figure. |
96 | Sam was asked to evaluate the expression 5x + 3x + 20 for x = 100. Sam's work is shown below. Sam's Work: 5x + 3x + 20 = 100 8x + 20 = 100 8x = 80 x = 10 What mistake did Sam make? Help Sam to answer the question correctly. The Utah Middle School Math Project | Sam was asked to find the value of the expression when x is equal to 100. The first step of Sam's work he sets the value of the expression equal to 100 instead of setting the value of x to 100. In order to find the actual value of the expression, the value 100 must be substituted into the expression for every instance of 'x'. 5x + 3x + 20 5100 + 3100 + 20 Now the equation can be simplified by multiplying the values in parenthesis. 5100 + 3100 + 20 500 + 300 + 20 Now the values can be added together. 500 + 300 + 20 800 + 20 820 The value of the expression when x = 100 is 820. | ###Write an explanation to this problem:
Sam was asked to evaluate the expression 5x + 3x + 20 for x = 100. Sam's work is shown below. Sam's Work: 5x + 3x + 20 = 100 8x + 20 = 100 8x = 80 x = 10 What mistake did Sam make? Help Sam to answer the question correctly. The Utah Middle School Math Project
###Explanation:
Sam was asked to find the value of the expression when x is equal to 100. The first step of Sam's work he sets the value of the expression equal to 100 instead of setting the value of x to 100. In order to find the actual value of the expression, the value 100 must be substituted into the expression for every instance of 'x'. 5x + 3x + 20 5100 + 3100 + 20 Now the equation can be simplified by multiplying the values in parenthesis. 5100 + 3100 + 20 500 + 300 + 20 Now the values can be added together. 500 + 300 + 20 800 + 20 820 The value of the expression when x = 100 is 820. |
752 | The sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation. The temperature is -10 degrees Fahrenheit below zero. | 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 10 degrees below zero on the Fahrenheit scale. |
541 | Write three expressions that are equivalent to the expression 4 + 32. The Utah Middle School Math Project | Example: 2x+2x+32; 1x+3x+216; 22x+16+16 | ###Write an explanation to this problem:
Write three expressions that are equivalent to the expression 4 + 32. The Utah Middle School Math Project
###Explanation:
Example: 2x+2x+32; 1x+3x+216; 22x+16+16 |
292 | Mai and Priya each played 10 games of bowling and recorded the scores. Mai's median score was 120, and her IQR was 5. Priya's median score was 118, and her IQR was 15. Whose scores probably had less variability? Explain how you know. | Since Mai's IQR was only 5, I believe she had less variability than Priya's IQR of 15. | ###Write an explanation to this problem:
Mai and Priya each played 10 games of bowling and recorded the scores. Mai's median score was 120, and her IQR was 5. Priya's median score was 118, and her IQR was 15. Whose scores probably had less variability? Explain how you know.
###Explanation:
Since Mai's IQR was only 5, I believe she had less variability than Priya's IQR of 15. |
136 | Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. NOW there are 78 players on the field. Write an equation whose solution is the number of players on each team. copied for free from openupresources.org | 15 6x-2 = 78 6x - 12 = 78 +12 +12 6x = 90 divide both sides by 6 x =15 | ###Write an explanation to this problem:
Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. NOW there are 78 players on the field. Write an equation whose solution is the number of players on each team. copied for free from openupresources.org
###Explanation:
15 6x-2 = 78 6x - 12 = 78 +12 +12 6x = 90 divide both sides by 6 x =15 |
109 | The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project | The equation for area of a parallelogram is area=base*height, or A=bh. Substitute the given values into this equation. 155.52=b*28.8. | ###Write an explanation to this problem:
The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The equation for area of a parallelogram is area=base*height, or A=bh. Substitute the given values into this equation. 155.52=b*28.8. |
209 | Write two division expressions that have the same value as 36.8 / 2.3. | There are multiple correct answers to this question. These are just a few examples: 3.68/0.23 368/23 3,680/230 | ###Write an explanation to this problem:
Write two division expressions that have the same value as 36.8 / 2.3.
###Explanation:
There are multiple correct answers to this question. These are just a few examples: 3.68/0.23 368/23 3,680/230 |
660 | -3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project | This multiplication problem asks that you take the integer -3 and multiply it 4 times, so -3 x 4 can be thought of as -3 + -3 + -3 + -3 | ###Write an explanation to this problem:
-3 x 4 = _____ Write the meaning of the multiplication problem. The Utah Middle School Math Project
###Explanation:
This multiplication problem asks that you take the integer -3 and multiply it 4 times, so -3 x 4 can be thought of as -3 + -3 + -3 + -3 |
691 | Consider the following equations: 3x=18 x+5=12 When you are asked to solve these equations, what are you being asked to do? The Utah Middle School Math Project | Example answer: You are asked to find the value of the unknown that makes the equation true. | ###Write an explanation to this problem:
Consider the following equations: 3x=18 x+5=12 When you are asked to solve these equations, what are you being asked to do? The Utah Middle School Math Project
###Explanation:
Example answer: You are asked to find the value of the unknown that makes the equation true. |
63 | It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents. | The equation shows that after h hours, the temperature has become 14 degrees below zero. | ###Write an explanation to this problem:
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h = -14 represents.
###Explanation:
The equation shows that after h hours, the temperature has become 14 degrees below zero. |
557 | Write a phrase for the following algebraic expression 15 - 2x The Utah Middle School Math Project | 15 - 2x is two times a number x less than fifteen. | ###Write an explanation to this problem:
Write a phrase for the following algebraic expression 15 - 2x The Utah Middle School Math Project
###Explanation:
15 - 2x is two times a number x less than fifteen. |
849 | 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. | The length of Rectangle C is double the length of Rectangle B, but the width of Rectangle C is 1.5 times the width 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:
The length of Rectangle C is double the length of Rectangle B, but the width of Rectangle C is 1.5 times the width of Rectangle B. |
328 | A rectangular parking lot is 120 feet long and 75 feet wide. Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches. Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches. Explain or show how each scale would produce an 8 inch by 5 inch drawing. copied for free from openupresources.org | For Lin's drawing, 1 in represents 15 ft, so 120 ft is 8 in 120/15=8 and 75 ft is 5 in 75/15=5. For Diego's drawing, 1 unit on the drawing represents 180 of the same unit in the actual distance, so 1 in represents 180 in. 180 in is equal to 15 ft 180/12=15. | ###Write an explanation to this problem:
A rectangular parking lot is 120 feet long and 75 feet wide. Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches. Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches. Explain or show how each scale would produce an 8 inch by 5 inch drawing. copied for free from openupresources.org
###Explanation:
For Lin's drawing, 1 in represents 15 ft, so 120 ft is 8 in 120/15=8 and 75 ft is 5 in 75/15=5. For Diego's drawing, 1 unit on the drawing represents 180 of the same unit in the actual distance, so 1 in represents 180 in. 180 in is equal to 15 ft 180/12=15. |
65 | Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ge; 500 and solved it to find the solution x ge; 55.25. Explain how you know Elena made a mistake based on her solution. | Elena's solution would mean that she has to put more than 55 movies on her hard drive. That doesn't make any sense because there should be a limit to how many movies she can put on the hard drive, it should not be unlimited. | ###Write an explanation to this problem:
Elena is trying to figure out how many movies she can download to her hard drive. The hard drive is supposed to hold 500 gigabytes of data, but 58 gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena wrote the inequality 8x + 58 ge; 500 and solved it to find the solution x ge; 55.25. Explain how you know Elena made a mistake based on her solution.
###Explanation:
Elena's solution would mean that she has to put more than 55 movies on her hard drive. That doesn't make any sense because there should be a limit to how many movies she can put on the hard drive, it should not be unlimited. |
807 | 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 |
78 | Find 3 different ratios that are equivalent to 7 : 3 | There are infinite amount of equivalent ratios to 7:3 as long as the ratio is being multiplied or divided by the same constant. Here are a couple of examples of equivalent ratios: 21:9 70:30 49:21 | ###Write an explanation to this problem:
Find 3 different ratios that are equivalent to 7 : 3
###Explanation:
There are infinite amount of equivalent ratios to 7:3 as long as the ratio is being multiplied or divided by the same constant. Here are a couple of examples of equivalent ratios: 21:9 70:30 49:21 |
300 | 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. | One way of getting a random sample would be if she could number the plants from 1 to 5,000 and have a computer select 10 random numbers between 1 and 5,000, then test the plants that correspond to the numbers the computer generated. | ###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:
One way of getting a random sample would be if she could number the plants from 1 to 5,000 and have a computer select 10 random numbers between 1 and 5,000, then test the plants that correspond to the numbers the computer generated. |
657 | Sally spent 60 on ingredients for a bake sale. She had sold 35 in baked goods. Write an inequality to represent the amount she still needs to sell to make a profit. The Utah Middle School Math Project | Sally has already sold 35 worth of baked goods, and needs 60 total. That means the inequality will be 35+s>60. | ###Write an explanation to this problem:
Sally spent 60 on ingredients for a bake sale. She had sold 35 in baked goods. Write an inequality to represent the amount she still needs to sell to make a profit. The Utah Middle School Math Project
###Explanation:
Sally has already sold 35 worth of baked goods, and needs 60 total. That means the inequality will be 35+s>60. |
689 | One angle is five times larger than another angle. Together the angles sum to 1800. What is the measure of each angle? Write an equation to solve the problem. The Utah Middle School Math Project | The measure of the smaller angle can be x, and the measure of the larger angle will be equal to 5x, because it is five times as large. Added together, these will be equal to 180. This means that: x+5x=180. | ###Write an explanation to this problem:
One angle is five times larger than another angle. Together the angles sum to 1800. What is the measure of each angle? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The measure of the smaller angle can be x, and the measure of the larger angle will be equal to 5x, because it is five times as large. Added together, these will be equal to 180. This means that: x+5x=180. |
346 | 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. |
628 | For what value of x does the expression + 6 evaluate to 8? Write an equation to represent the problem. The Utah Middle School Math Project | To make an equation where the expression x+6 evaluates to 8, we need to say that the expression equals 8. x+6=8 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 + 6 evaluate to 8? Write an equation to represent the problem. The Utah Middle School Math Project
###Explanation:
To make an equation where the expression x+6 evaluates to 8, we need to say that the expression equals 8. x+6=8 Any equation that simplifies to this equation is a correct answer. |
451 | Given information: c = cost of a shirt 0.25c = 25% of the cost of the shirt Equation: c ndash; 0.25c = 28.80 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project | A shirt is on sale for 25% off the original price. The sale price is 28.80. What was the original cost of the shirt? | ###Write an explanation to this problem:
Given information: c = cost of a shirt 0.25c = 25% of the cost of the shirt Equation: c ndash; 0.25c = 28.80 Write a word problem to go with the information and the equation given above. The Utah Middle School Math Project
###Explanation:
A shirt is on sale for 25% off the original price. The sale price is 28.80. What was the original cost of the shirt? |
547 | Ed burns 500 calories an hour running. He burns 650 calories an hour biking. Use the distributive property to write two different expressions that can be used to represent the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours. The Utah Middle School Math Project | If Ed runs for two hours, he will burn 2500 calories. If he bikes for two hours, he will burn 2650 calories. So, the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours can be represented by the following expression: 2650 - 2500 Another way to think about this problem is that the difference between the number of calories Ed burns after running for an hour and the number of calories Ed burns after biking for an hour is 650 - 500 calories. Since he runs for two hours, an appropriate representation could be 2650 - 500 | ###Write an explanation to this problem:
Ed burns 500 calories an hour running. He burns 650 calories an hour biking. Use the distributive property to write two different expressions that can be used to represent the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours. The Utah Middle School Math Project
###Explanation:
If Ed runs for two hours, he will burn 2500 calories. If he bikes for two hours, he will burn 2650 calories. So, the difference between the number of calories Ed burns after running for 2 hours and the number of calories Ed burns after biking for 2 hours can be represented by the following expression: 2650 - 2500 Another way to think about this problem is that the difference between the number of calories Ed burns after running for an hour and the number of calories Ed burns after biking for an hour is 650 - 500 calories. Since he runs for two hours, an appropriate representation could be 2650 - 500 |
576 | 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 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 40 delivery fee. Each gem is 25. If you by 6 gems, what will be the total order cost? |
49 | If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below. | The easiest way to compare recipes is to find the ratio of ingredients for multiple batches until you find a common measurement for a specific ingredient. In this case, the following tables show both recipes up to the point that they both have 2 cups of milk. First Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 2 1 2 4 2 Second Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 3 2 Since the first recipe uses more scoops of chocolate ice cream to the same amount of milk, it means it would have a stronger chocolate flavor. | ###Write an explanation to this problem:
If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why. Submit your work using the tools below.
###Explanation:
The easiest way to compare recipes is to find the ratio of ingredients for multiple batches until you find a common measurement for a specific ingredient. In this case, the following tables show both recipes up to the point that they both have 2 cups of milk. First Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 2 1 2 4 2 Second Recipe: of batches Scoops of Choc. Ice Cream Cups of Milk 1 3 2 Since the first recipe uses more scoops of chocolate ice cream to the same amount of milk, it means it would have a stronger chocolate flavor. |
120 | Lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. Explain some possible reasons why these measurements differ. | Two diameters of the same circle should have the same length. While the circle will always have the same diameter, the measured distance can change based on human error. Some errors that may have occurred when measuring the circle is: Lin not measuring across the widest part when measuring vertically the measurements could have been rounded instead of exact The thickness of the circle may have affected the measurements | ###Write an explanation to this problem:
Lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. Explain some possible reasons why these measurements differ.
###Explanation:
Two diameters of the same circle should have the same length. While the circle will always have the same diameter, the measured distance can change based on human error. Some errors that may have occurred when measuring the circle is: Lin not measuring across the widest part when measuring vertically the measurements could have been rounded instead of exact The thickness of the circle may have affected the measurements |
559 | Write a context to match the numeric expression given. 0.150 + 0.0150 + 0.0150 The Utah Middle School Math Project | Dom is a very avid magnet collector. He has found a small shop that seems to have a very cool selection of magnets. They offer large rectangular magnets for 10 cents each and small spherical magnets for 1 cent each. Since Dom's likes to have 50 of each magnet, he buys 50 rectangle and 50 sphere magnets. As he is leaving, he remembered that he owes his friend Mike 50 sphere magnets as well, and goes back to buy some more. In total, how much did Dom spend? | ###Write an explanation to this problem:
Write a context to match the numeric expression given. 0.150 + 0.0150 + 0.0150 The Utah Middle School Math Project
###Explanation:
Dom is a very avid magnet collector. He has found a small shop that seems to have a very cool selection of magnets. They offer large rectangular magnets for 10 cents each and small spherical magnets for 1 cent each. Since Dom's likes to have 50 of each magnet, he buys 50 rectangle and 50 sphere magnets. As he is leaving, he remembered that he owes his friend Mike 50 sphere magnets as well, and goes back to buy some more. In total, how much did Dom spend? |
299 | 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. | There are several ways that Elena could simulate the power up. One way to simulate getting the power-up is having the computer program pick a number between 1 and 100, if the number is between 1 and 15, then they got the best power-up. The program can be run 3 times to see if they get the best power-up 2 out of the 3 times. 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:
There are several ways that Elena could simulate the power up. One way to simulate getting the power-up is having the computer program pick a number between 1 and 100, if the number is between 1 and 15, then they got the best power-up. The program can be run 3 times to see if they get the best power-up 2 out of the 3 times. 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. |
137 | Give a number between -1 and -2. The Utah Middle School Math Project | Negative numbers are the opposite of positive numbers. This means that the opposites of -1 and -2 are 1 and 2. A number that is between -1 and -2 will have its opposite between 1 and 2. There are many numbers between 1 and 2. For example: 1.5, 1.76, 1 2/3, and so on If we take the opposite, then these numbers are between -1 and -2. For example: -1.5, -1.76, -1 2/3, and so on | ###Write an explanation to this problem:
Give a number between -1 and -2. The Utah Middle School Math Project
###Explanation:
Negative numbers are the opposite of positive numbers. This means that the opposites of -1 and -2 are 1 and 2. A number that is between -1 and -2 will have its opposite between 1 and 2. There are many numbers between 1 and 2. For example: 1.5, 1.76, 1 2/3, and so on If we take the opposite, then these numbers are between -1 and -2. For example: -1.5, -1.76, -1 2/3, and so on |
265 | The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct. | In this case, we are using the median as our measure of center. This means that our middle point of our data that our data tends to cluster up around is the median. When the median is used in this way, then we use the interquartile range IQR as the measure of variability. This is how much our data varies from each other. If the medians are less than 2 IQR's apart, then they would not have a meaningful difference. The medians are 14,000 apart. If the IQR is 7,000 or more, then the medians would be less than 2 IQR's apart. | ###Write an explanation to this problem:
The median income for a sample of people from Chicago is about 60,000 and the median income for a sample of people from Kansas City is about 46,000, but researchers have determined there is not a meaningful difference in the medians. Explain why the researchers might be correct.
###Explanation:
In this case, we are using the median as our measure of center. This means that our middle point of our data that our data tends to cluster up around is the median. When the median is used in this way, then we use the interquartile range IQR as the measure of variability. This is how much our data varies from each other. If the medians are less than 2 IQR's apart, then they would not have a meaningful difference. The medians are 14,000 apart. If the IQR is 7,000 or more, then the medians would be less than 2 IQR's apart. |
848 | List the sample space the available options for the chance experiment given. Flipping a coin | The sample space for flipping a coin is heads or tails. You have a 1/2 chance of either flipping a coin on tales or flipping a coin on heads. This works out to be a 50% of each outcome occurring. | ###Write an explanation to this problem:
List the sample space the available options for the chance experiment given. Flipping a coin
###Explanation:
The sample space for flipping a coin is heads or tails. You have a 1/2 chance of either flipping a coin on tales or flipping a coin on heads. This works out to be a 50% of each outcome occurring. |
440 | The following equation is given: 4x + 2 = 30 Provide a context/word problem for the given information. The Utah Middle School Math Project | Four times a number increased by 2 is 30. What is the number? | ###Write an explanation to this problem:
The following equation is given: 4x + 2 = 30 Provide a context/word problem for the given information. The Utah Middle School Math Project
###Explanation:
Four times a number increased by 2 is 30. What is the number? |
777 | What is the difference between 6z and z6? | 6z is z+z+z+z+z+z, and z^6 is z*z*z*z*z*z. | ###Write an explanation to this problem:
What is the difference between 6z and z6?
###Explanation:
6z is z+z+z+z+z+z, and z^6 is z*z*z*z*z*z. |
33 | In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe. | There are multiple answers to this question. These are just a couple of examples. The ratio of cups of sparkling water to cups of grape juice concentrate is 6 to 2. The ratio of cups of sparkling water to cups of grape juice concentrate is 30 to 10. | ###Write an explanation to this problem:
In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1. Find two more ratios of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
###Explanation:
There are multiple answers to this question. These are just a couple of examples. The ratio of cups of sparkling water to cups of grape juice concentrate is 6 to 2. The ratio of cups of sparkling water to cups of grape juice concentrate is 30 to 10. |
31 | A fisherman weighs an ahi tuna a very large fish on a scale and gets a reading of 135 pounds. The reading on the scale may have an error of up to 5%. What are two possible values for the actual weight of the fish? | If there is a 1% error, the actual weight of the fish would be 133.65 pounds because 0.99135 = 133.65 or 136.35 pounds because 1.01135 = 136.35. | ###Write an explanation to this problem:
A fisherman weighs an ahi tuna a very large fish on a scale and gets a reading of 135 pounds. The reading on the scale may have an error of up to 5%. What are two possible values for the actual weight of the fish?
###Explanation:
If there is a 1% error, the actual weight of the fish would be 133.65 pounds because 0.99135 = 133.65 or 136.35 pounds because 1.01135 = 136.35. |
696 | The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project | The equation for area of a parallelogram is area=base*height, or A=bh. Plug the given values into this equation. 155.52=b*28.8. | ###Write an explanation to this problem:
The height of a parallelogram is 28.8 inches. If the area of the parallelogram is 155.52 in2, what is the length of the base of the parallelogram? Write an equation to solve the problem. The Utah Middle School Math Project
###Explanation:
The equation for area of a parallelogram is area=base*height, or A=bh. Plug the given values into this equation. 155.52=b*28.8. |
712 | Solve the inequality. Represent the solution on a number line. 8xge;2 The Utah Middle School Math Project | Solve for x. The number line should be greater than and equal to the solution. | ###Write an explanation to this problem:
Solve the inequality. Represent the solution on a number line. 8xge;2 The Utah Middle School Math Project
###Explanation:
Solve for x. The number line should be greater than and equal to the solution. |
367 | Write each expression as a multiple of a power of 10: 42,300 copied for free from openupresources.org | Sample Answer: 423*10^2, 4.23*10^4 | ###Write an explanation to this problem:
Write each expression as a multiple of a power of 10: 42,300 copied for free from openupresources.org
###Explanation:
Sample Answer: 423*10^2, 4.23*10^4 |
76 | 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. |
247 | Explain how to make this calculation mentally. 99 * 15 | I would add 1 to 99 to get 100 x 15=1,500 and then subtract the extra group of 15 that we added and get 1,500-15=1,485. | ###Write an explanation to this problem:
Explain how to make this calculation mentally. 99 * 15
###Explanation:
I would add 1 to 99 to get 100 x 15=1,500 and then subtract the extra group of 15 that we added and get 1,500-15=1,485. |
477 | 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 dependent. | ###Write an explanation to this problem:
The following situation represents a functional relationship between two quantities. Identify the independent variable and the dependent variable. 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 dependent. |
235 | 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 | Pages 1 through 428 are the sample space for this experiment. | ###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:
Pages 1 through 428 are the sample space for this experiment. |
72 | A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour. Name two quantities in this situation that are in a functional relationship. Copied for free from openupresources.org | The amount of yeast and the amount of flour. | ###Write an explanation to this problem:
A recipe for bread calls for 1 teaspoon of yeast for every 2 cups of flour. Name two quantities in this situation that are in a functional relationship. Copied for free from openupresources.org
###Explanation:
The amount of yeast and the amount of flour. |
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