G7 U5 Constructed Response
Name: ________________________________________ Date:_______________
Grade 7 Unit 5 Constructed Response Expressions TASK 1: Adding and Subtracting Expressions (CCSS ο 7.EE.1; SMP ο 1, 2, 6, 7)
1. Analyze the expression: β3 + 4π₯ + π₯ + 5 + β8 a. In the table below write an equivalent expression. Show your work in detailed and organized steps.
Answer: _________________ b. After finding the solution, write an explanation in which you discuss how you found the equivalent expression.
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Grade 7 Unit 5 Constructed Response Expressions 2. Analyze the expression: (10π β 7) β (β6π + 8) a. In the table below simplify the expression using both the horizontal and vertical method. Show your work in detailed and organized steps. Horizontal Method:
Vertical Method:
Answer: __________________
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Grade 7 Unit 5 Constructed Response Expressions b. After finding the solution, compare the two strategies you used. Which strategy was the most effective in helping you find your solution? Why was this strategy more efficient?
3. Find the difference between the perimeters of the two rectangles: π₯+8 π₯+4
π₯+6 π₯
a. Before solving the problem, write a discussion in which you describe a possible strategy for finding the solution. What mathematical properties or formulas you have learned would be useful in finding the solution?
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Grade 7 Unit 5 Constructed Response Expressions b. Using the strategy you explained, find the difference between the perimeters of the two rectangles. In the table below, show your work in detailed and organized steps.
Answer: _________________
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Grade 7 Unit 5 Constructed Response Expressions TASK 2: Expanding and Factoring Expressions (CCSS: 7.EE.1; SMP: 1, 2, 3, 4, 5, 6, 7)
4. Analyze the expression: 4(π₯ + 2) + 6(π₯ β 3) a. In the table below, create a model that best represents the expression. Model:
b. Simplify the expression in the table below. Show your work in detailed and organized steps.
Answer: _________________________
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Grade 7 Unit 5 Constructed Response Expressions c. Identify the property you used to find your solution. How did you use this property?
5. Mary is asked to factor the expression below on a test. She does the following work to find her solution: 27π¦ + 63 27(π¦ + 63) a. After analyzing Maryβs work, determine if her work and her answer are correct or incorrect. Explain how you know whether her answer is correct. If Mary is incorrect, identify her error(s) and correct them.
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Grade 7 Unit 5 Constructed Response Expressions b. If Mary is incorrect, find the correct answer for the problem she solved. Show your work in detailed and organized steps.
Answer: __________________ 6. Robin wants to build a square garden that has a perimeter of 36π₯ + 40 feet. How long will each side of Robinβs garden be? a. In the table below, find the length of each side of the square. Show your work in detailed and organized steps.
Answer: __________________ Copyright Β© Swun Math Grade 7 Unit 5 Constructed Response, Page 7
Grade 7 Unit 5 Constructed Response Expressions b. After finding your solution, create an illustration to visually represent the garden. Include the length of the sides in your illustration. Model:
c. Explain the strategy you used to find the solution to the problem. What information given to you in the problem was important to find your solution?
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Grade 7 Unit 5 Constructed Response Expressions TASK 3: Working with the Distributive Property and Writing Equivalent Expressions (CCSS: 7.EE.1; SMP: 1, 2, 4, 5, 6, 7)
7. In the table below, create a square and a rectangle that each have a perimeter of 24π₯ + 28 units. Label your illustrations with the length and width of each side. a. Square:
b. Rectangle:
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Grade 7 Unit 5 Constructed Response Expressions c. Based on the measurements you found for the square and the rectangle, prove they each have a perimeter of 24π₯ + 28 units. In the table below, show your work in detailed and organized steps. Square:
Rectangle:
8. Brandon wants to buy a new gaming system from an electronics store. The gaming system he wants to buy costs $299. He is a rewards member at the store and receives a coupon for 25% off his purchase. a. Write two expressions that best represent the final price Brandon will pay for the gaming system. Answer: ________________________________________ ________________________________________
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Grade 7 Unit 5 Constructed Response Expressions b. Write an explanation in which you discuss how your expressions represent the information given to you in the scenario.
9. Georgina and her mom want to put fencing around their rectangular vegetable garden. The length of their garden is 45 feet long and the width is 2π + 5 feet long. a. Write two expressions that represent the perimeter of their garden. Answer: ___________________________ ___________________________
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Grade 7 Unit 5 Constructed Response Expressions b. In the table below, find how much fencing they will need to buy if f is equal to 14. Show your work in detailed and organized steps.
Answer: __________________ c. Using your answer from question 9b, find how much it will cost for Georgina and her mom to put up a new fence around their garden if the price per foot of fencing costs $2.75. In the table below, show your work in detailed and organized steps.
Answer: __________________
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Grade 7 Unit 5 Constructed Response Expressions TASK 1: Adding and Subtracting Expressions (CCSS ο 7.EE.1; SMP ο 1, 2, 6, 7)
1. Analyze the expression: β3 + 4π₯ + π₯ + 5 + β8 a. In the table below write an equivalent expression. Show your work in detailed and organized steps.
Answer: _________________ b. After finding the solution, write an explanation in which you discuss how you found the equivalent expression.
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Grade 7 Unit 5 Constructed Response Expressions 2. Analyze the expression: (10π β 7) β (β6π + 8) a. In the table below simplify the expression using both the horizontal and vertical method. Show your work in detailed and organized steps. Horizontal Method:
Vertical Method:
Answer: __________________
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Grade 7 Unit 5 Constructed Response Expressions b. After finding the solution, compare the two strategies you used. Which strategy was the most effective in helping you find your solution? Why was this strategy more efficient?
3. Find the difference between the perimeters of the two rectangles: π₯+8 π₯+4
π₯+6 π₯
a. Before solving the problem, write a discussion in which you describe a possible strategy for finding the solution. What mathematical properties or formulas you have learned would be useful in finding the solution?
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Grade 7 Unit 5 Constructed Response Expressions b. Using the strategy you explained, find the difference between the perimeters of the two rectangles. In the table below, show your work in detailed and organized steps.
Answer: _________________
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Grade 7 Unit 5 Constructed Response Expressions TASK 2: Expanding and Factoring Expressions (CCSS: 7.EE.1; SMP: 1, 2, 3, 4, 5, 6, 7)
4. Analyze the expression: 4(π₯ + 2) + 6(π₯ β 3) a. In the table below, create a model that best represents the expression. Model:
b. Simplify the expression in the table below. Show your work in detailed and organized steps.
Answer: _________________________
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Grade 7 Unit 5 Constructed Response Expressions c. Identify the property you used to find your solution. How did you use this property?
5. Mary is asked to factor the expression below on a test. She does the following work to find her solution: 27π¦ + 63 27(π¦ + 63) a. After analyzing Maryβs work, determine if her work and her answer are correct or incorrect. Explain how you know whether her answer is correct. If Mary is incorrect, identify her error(s) and correct them.
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Grade 7 Unit 5 Constructed Response Expressions b. If Mary is incorrect, find the correct answer for the problem she solved. Show your work in detailed and organized steps.
Answer: __________________ 6. Robin wants to build a square garden that has a perimeter of 36π₯ + 40 feet. How long will each side of Robinβs garden be? a. In the table below, find the length of each side of the square. Show your work in detailed and organized steps.
Answer: __________________ Copyright Β© Swun Math Grade 7 Unit 5 Constructed Response, Page 7
Grade 7 Unit 5 Constructed Response Expressions b. After finding your solution, create an illustration to visually represent the garden. Include the length of the sides in your illustration. Model:
c. Explain the strategy you used to find the solution to the problem. What information given to you in the problem was important to find your solution?
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Grade 7 Unit 5 Constructed Response Expressions TASK 3: Working with the Distributive Property and Writing Equivalent Expressions (CCSS: 7.EE.1; SMP: 1, 2, 4, 5, 6, 7)
7. In the table below, create a square and a rectangle that each have a perimeter of 24π₯ + 28 units. Label your illustrations with the length and width of each side. a. Square:
b. Rectangle:
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Grade 7 Unit 5 Constructed Response Expressions c. Based on the measurements you found for the square and the rectangle, prove they each have a perimeter of 24π₯ + 28 units. In the table below, show your work in detailed and organized steps. Square:
Rectangle:
8. Brandon wants to buy a new gaming system from an electronics store. The gaming system he wants to buy costs $299. He is a rewards member at the store and receives a coupon for 25% off his purchase. a. Write two expressions that best represent the final price Brandon will pay for the gaming system. Answer: ________________________________________ ________________________________________
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Grade 7 Unit 5 Constructed Response Expressions b. Write an explanation in which you discuss how your expressions represent the information given to you in the scenario.
9. Georgina and her mom want to put fencing around their rectangular vegetable garden. The length of their garden is 45 feet long and the width is 2π + 5 feet long. a. Write two expressions that represent the perimeter of their garden. Answer: ___________________________ ___________________________
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Grade 7 Unit 5 Constructed Response Expressions b. In the table below, find how much fencing they will need to buy if f is equal to 14. Show your work in detailed and organized steps.
Answer: __________________ c. Using your answer from question 9b, find how much it will cost for Georgina and her mom to put up a new fence around their garden if the price per foot of fencing costs $2.75. In the table below, show your work in detailed and organized steps.
Answer: __________________
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