G7 U5 Constructed Reponse Rubric
Grade 7 Unit 5 Constructed Response Expressions Scoring Rubric Task
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Adding and Subtracting Expressions
7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
MP.1, MP.2, MP.6, MP.7,
2. Expanding and Factoring Expressions
7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7
3. Working with the 7.EE.1: Apply properties of operations as Distributive Property strategies to add, subtract, factor, and expand and Writing Equivalent linear expressions with rational coefficients. Expressions
MP.1, MP.2, MP.4, MP.5, MP.6, MP.7
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
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Grade 7 Unit 5 Constructed Response Expressions Scoring Rubric Question
Points
1. a. Student gives correct answer and shows work: 5π₯ β 6 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the equivalent expression I first rewrote the original expression to group the like terms together. This helped me to combine the like terms later. So I took β3 + 4π₯ + π₯ + 5 + β8, and rewrote it as (4π₯ + π₯) + (β3 + 5 β 8). From here I combined like terms and combined constants and got 5π₯ β 6. 2. a. Student gives correct answer and shows work using both the vertical method and the horizontal method: (Check studentβs work for accuracy in using the strategy); 16π β 15 b. Student gives an accurate explanation. Answers may vary depending on the studentβs ability to use either strategy more effectively. Wording may vary. Sample explanation: In order to solve an expression using the vertical method you need to line up like terms and like constants vertically and add or subtract. In the horizontal method on the other hand, you leave the expression as is but still group like terms and constants to solve. Of the two methods the one that was the most efficient for me to simplify the expression was β¦. 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve this problem I have to use the formula for the perimeter of a rectangle, π = 2π + 2π€. I first need to find the perimeter of each rectangle using this formula. To find the perimeter I need to plug in the length and width of each rectangle into the formula and solve using either the vertical or horizontal method. Since the lengths and widths of the rectangle involve a variable, I will need to combine like terms and combine constants to solve. Once I have the simplified expression representing each perimeter, I then need to subtract the perimeter of the smaller rectangle from the larger rectangle. Again to simplify this new expression I will need to combine like terms and combine constants to solve. b. Student gives correct answer and shows work: 12 units 4. Student creates an accurate model:
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Grade 7 Unit 5 Constructed Response Expressions x x x x x x x x x x
1 1 1 1 -1 -1 -1 -1 -1 -1
1 1 1 1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1
b. Student gives correct answer and shows work: 10π₯ β 10 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my solution I used the distributive property. I first used this property to distribute the four in the first part of the expression to (π₯ + 2), which gave me 4x + 8. I then used it again to distribute the six in the second part of the expression to (π₯ β 3), which gave me 6x β 18. 5. a. Student gives correct answer and an accurate explanation: After analyzing Maryβs work and answer I was able to determine she is incorrect. I know she is incorrect because she did not factor the expression correctly. She factored out 27 but that is not the GCF of 27 and 63. Based on her final answer, the expression would equal 27y β 1,701 if solved. What she should have done was factor out a 9 because that is the GCF of 27 and 63. b. Student gives correct answer and shows work: 9(3π¦ + 7) 6. a. Student gives correct answer and shows work: 9π₯ + 10 feet long b. Student creates an accurate visual model:
1 1
2
1 1 1
9π₯ + 10 feet 9π₯ + 10 feet
9π₯ + 10 feet
9π₯ + 10 feet c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the solution to the problem, I had to use several pieces of information. In the problem I am told the perimeter of the garden is 36π₯ + 42 feet, and the garden is in the shape of a square. Since a square has four sides, I used 4 as the greatest common factor. When I factored out a 4 my equation became 4(9π₯ + 10). In this Copyright Β© Swun Math Grade 7 Unit 5 Constructed Response Rubric, Page 3
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Grade 7 Unit 5 Constructed Response Expressions expression the four represents the number of sides and the (9π₯ + 10) represents the length of each side. 7. a.-b. Student creates a rectangle and square with the given perimeter: (Check studentβs answers for accuracy.) Possible answers:
2
6π₯ + 7 feet 6π₯ + 7 feet
6π₯ + 7 feet
6π₯ + 7 feet 8π₯ + 9 feet 4π₯ + 5 feet
4π₯ + 5 feet
8π₯ + 9 feet b. Student checks accuracy of measurements finding the perimeter of each shape. Should equal πππ + ππ units.
1
8. a. Student gives correct answers: cost of gaming system β25% = sale price of gaming system; π β 0.25π =sale price of gaming system. b. Student gives an accurate explanation. Wording may vary. Sample explanation: My two expressions represent the final price Brandon will pay for the gaming system because each part of my expressions represents a piece of information given to me in the problem. For example, the cost of the gaming system, $299, is represented as the first constant in my equation. Since he receives a coupon for a discount I know I need to subtract the quantity of the discount from the original cost of the gaming system. The discount is represented in my equation as a decimal times g, because the percent needs to be converted to a decimal and multiplied by the original cost of the gaming system g. 9. a. Student gives correct answers: 2(45) + 2(2π + 5) ; 2(45 + 2π + 5) b. Student gives correct answer and shows work: 156 feet
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Grade 7 Unit 5 Constructed Response Expressions c. Student gives correct answer and shows work: $429 Total
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Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Adding and Subtracting Expressions
7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
MP.1, MP.2, MP.6, MP.7,
2. Expanding and Factoring Expressions
7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
MP.1, MP.2, MP.3, MP.4, MP.5, MP.6, MP.7
3. Working with the 7.EE.1: Apply properties of operations as Distributive Property strategies to add, subtract, factor, and expand and Writing Equivalent linear expressions with rational coefficients. Expressions
MP.1, MP.2, MP.4, MP.5, MP.6, MP.7
Note to Teacher: The following scoring rubric should be used as a guide to determine points given to students for each question answered. Students are required to show the process through which they arrived at their answers for every question involving problem solving. For questions involving a written answer, full points should be given to answers that are written in complete sentences which address each component of the questions being asked.
Copyright Β© Swun Math Grade 7 Unit 5 Constructed Response Rubric, Page 1
Grade 7 Unit 5 Constructed Response Expressions Scoring Rubric Question
Points
1. a. Student gives correct answer and shows work: 5π₯ β 6 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the equivalent expression I first rewrote the original expression to group the like terms together. This helped me to combine the like terms later. So I took β3 + 4π₯ + π₯ + 5 + β8, and rewrote it as (4π₯ + π₯) + (β3 + 5 β 8). From here I combined like terms and combined constants and got 5π₯ β 6. 2. a. Student gives correct answer and shows work using both the vertical method and the horizontal method: (Check studentβs work for accuracy in using the strategy); 16π β 15 b. Student gives an accurate explanation. Answers may vary depending on the studentβs ability to use either strategy more effectively. Wording may vary. Sample explanation: In order to solve an expression using the vertical method you need to line up like terms and like constants vertically and add or subtract. In the horizontal method on the other hand, you leave the expression as is but still group like terms and constants to solve. Of the two methods the one that was the most efficient for me to simplify the expression was β¦. 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve this problem I have to use the formula for the perimeter of a rectangle, π = 2π + 2π€. I first need to find the perimeter of each rectangle using this formula. To find the perimeter I need to plug in the length and width of each rectangle into the formula and solve using either the vertical or horizontal method. Since the lengths and widths of the rectangle involve a variable, I will need to combine like terms and combine constants to solve. Once I have the simplified expression representing each perimeter, I then need to subtract the perimeter of the smaller rectangle from the larger rectangle. Again to simplify this new expression I will need to combine like terms and combine constants to solve. b. Student gives correct answer and shows work: 12 units 4. Student creates an accurate model:
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Grade 7 Unit 5 Constructed Response Expressions x x x x x x x x x x
1 1 1 1 -1 -1 -1 -1 -1 -1
1 1 1 1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1
b. Student gives correct answer and shows work: 10π₯ β 10 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my solution I used the distributive property. I first used this property to distribute the four in the first part of the expression to (π₯ + 2), which gave me 4x + 8. I then used it again to distribute the six in the second part of the expression to (π₯ β 3), which gave me 6x β 18. 5. a. Student gives correct answer and an accurate explanation: After analyzing Maryβs work and answer I was able to determine she is incorrect. I know she is incorrect because she did not factor the expression correctly. She factored out 27 but that is not the GCF of 27 and 63. Based on her final answer, the expression would equal 27y β 1,701 if solved. What she should have done was factor out a 9 because that is the GCF of 27 and 63. b. Student gives correct answer and shows work: 9(3π¦ + 7) 6. a. Student gives correct answer and shows work: 9π₯ + 10 feet long b. Student creates an accurate visual model:
1 1
2
1 1 1
9π₯ + 10 feet 9π₯ + 10 feet
9π₯ + 10 feet
9π₯ + 10 feet c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the solution to the problem, I had to use several pieces of information. In the problem I am told the perimeter of the garden is 36π₯ + 42 feet, and the garden is in the shape of a square. Since a square has four sides, I used 4 as the greatest common factor. When I factored out a 4 my equation became 4(9π₯ + 10). In this Copyright Β© Swun Math Grade 7 Unit 5 Constructed Response Rubric, Page 3
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Grade 7 Unit 5 Constructed Response Expressions expression the four represents the number of sides and the (9π₯ + 10) represents the length of each side. 7. a.-b. Student creates a rectangle and square with the given perimeter: (Check studentβs answers for accuracy.) Possible answers:
2
6π₯ + 7 feet 6π₯ + 7 feet
6π₯ + 7 feet
6π₯ + 7 feet 8π₯ + 9 feet 4π₯ + 5 feet
4π₯ + 5 feet
8π₯ + 9 feet b. Student checks accuracy of measurements finding the perimeter of each shape. Should equal πππ + ππ units.
1
8. a. Student gives correct answers: cost of gaming system β25% = sale price of gaming system; π β 0.25π =sale price of gaming system. b. Student gives an accurate explanation. Wording may vary. Sample explanation: My two expressions represent the final price Brandon will pay for the gaming system because each part of my expressions represents a piece of information given to me in the problem. For example, the cost of the gaming system, $299, is represented as the first constant in my equation. Since he receives a coupon for a discount I know I need to subtract the quantity of the discount from the original cost of the gaming system. The discount is represented in my equation as a decimal times g, because the percent needs to be converted to a decimal and multiplied by the original cost of the gaming system g. 9. a. Student gives correct answers: 2(45) + 2(2π + 5) ; 2(45 + 2π + 5) b. Student gives correct answer and shows work: 156 feet
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Grade 7 Unit 5 Constructed Response Expressions c. Student gives correct answer and shows work: $429 Total
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