G6 U4 Constructed Response Rubric
Grade 6 Unit 4 Constructed Response Expressions and Equations Scoring Rubric Task
1. Expressions: Properties, Parts of Expressions, and Writing Expressions
2. Equivalent Expressions, Powers and Exponents, Order of Operations
3. Evaluate Expressions
Common Core State Standard for Mathematical Content (MC) 6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.2b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. 6.EE.3: Apply the properties of operations to generate equivalent expressions. 6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them. 6.EE.1: Write and evaluate numerical expressions involving whole-number exponents. 6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them. 6.EE.2: Write, read and evaluate expressions in which letters stand for numbers.
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.3, MP.4, MP.6, MP.7
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
MP.1, MP.2, MP.3, MP.6, MP.7, MP.8
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 6 Unit 4 Constructed Response Rubric, Page 1
Grade 6 Unit 4 Constructed Response Expressions and Equations Scoring Rubric Question 1. a. Student gives correct expression: 3π + 6 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In the problem I am told Charlotte had 3 times as many oranges as strawberries. I am not told the exact number she has of each, but I know 3 times some number will equal the number of oranges she has before going to the store. So I represented this piece of information as 3s, where s equals the unknown number of strawberries. I am also told in the problem Charlotte bought an additional 6 oranges, so to represent this I wrote+6. My whole expression put together to find the total number of oranges was 3π + 6. c. Student gives an accurate explanation. Wording may vary. Sample explanation: There are two terms in my expression, β3sβ and β+6β. The variable s represents the unknown number of strawberries. The number 3 is the coefficient that will be multiplied by the variable by. The number 6 is a constant in my expression, and represents the number of additional oranges Charlotte buys. This number is the constant because it stands alone in the expression. 2. Student gives correct answers and accurate explanations. Wording may vary. Sample explanations: a.
(10π+5)
; I know this is the correct answer because I am told in the problem Mary had 10 times as many red stickers as blue stickers and then she found five more. So this matches the top portion of the fraction. She then gave stickers to her five friends so I know the number of stickers she had was to be divided by five, which is represented in the denominator of this expression. b. π + (2 Γ π) β 4 + 5 ; I know this is the correct answer because I am told in the problem Steven bought an unknown number (l) of lollipops on Monday and then he bought 2 times (2 Γ l) as many on Wednesday. I am also told he gave 4 of them to his sister, which was represented withβ4, as can be seen in the expression. The last part of the expression is +5 which represents the additional 5 lollipops Steven bought on Saturday. c. (2 Γ π) + (4 Γ π ) β 5; I know this is the correct answer because I am told in the problem Cory and Mike are combining their different sets of marbles, which is represented by(2 Γ π) + (4 Γ π ). Here c and s equal the number of marbles in each of their sets. I am told they give five of 5
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Grade 6 Unit 4 Constructed Response Expressions and Equations their marbles to Mikeβs little brother which was represented by β5 in the expression. 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: After analyzing the statement and the expression Will wrote, I found that Willβs expressions incorrect. One of the errors he made was switching the variable and the constant in the fraction. The statement says the difference between s and 9 so it should have been written as s β 9, where the constant is 9. Another error is writing the difference between s and 9 divided by 6. In the statement we are told three times the difference between s and 9 divided by 6, so this means the product of 3 and the difference between s and 9 is divided by 6. 3(π β9) b. Student gives correct answer: 6 4. a. Student gives correct answer: 7π + 63. b. Student gives an accurate explanation. Wording may vary. Sample explanation: The algebraic property I used to generate the equivalent
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expression was the Distributive Property. I used this property to distribute the 7 to the terms inside the parenthesis. First I multiplied 7 by m which gave me 7m and then I multiplied 7 by + 9 which gave me + 63. The new equivalent expression was 7π + 63.
5. a. Student gives correct answer: 4 Γ 4 Γ 4 Γ 4 Γ 4 Γ π Γ π Γ π b. Student gives correct answer: 1,024 d3 c. Student gives an accurate explanation. Wording may vary. Sample explanation: There is a relationship between the base and the exponent of each term in an expression. The exponent in the expression tells how many times the base number is used as a factor. This relationship helped me find the expanded form and standard form because the exponent told me how many times I had to multiply 4 by itself, and how many times I had to multiply the variable d by itself. So for 45 π 3 the exponent told me to multiply 4 by itself 5 times and to multiply d by itself 3 times, so4 Γ 4 Γ 4 Γ 4 Γ 4 Γ π Γ π Γ π. 6. Student correctly places parentheses and proves their correct placement by showing the steps to solve each equation. a. 42 + (12 β 5) + 7 = 30 16 + (7) + 7 = 16 + 14 = 30 b. (92 Γ· 3) β (2 Γ 3) = 21 (81 Γ· 3) β (2 Γ 3) = 21 (27) β (6) = 21 c. 59 β (72 β 15) β 10 = 15 59 β (49 β 15) β 10 = 15 59 β (34) β 10 = 15 Copyright Β© Swun Math Grade 6 Unit 4 Constructed Response Rubric, Page 3
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Grade 6 Unit 4 Constructed Response Expressions and Equations d. 25 β 10 = 15 Student gives an accurate explanation. Wording may vary. Sample explanation: Following the Order of Operations to solve equations is important because it is the way mathematicians solve problems all over the world. If I solve the problem in any order I wish, I will get an incorrect solution and will not be able to communicate mathematically with anyone else. 7. Student gives correct answers and shows work: a. 5(6 + 7) β 4(6) 5(13) β 4(6) 65 β 24 = 41 b. 5(8 + 7) β 4(8) 5(15) β 4(8) 75 β 32 = 43 c. 5(10 + 7) β 4(10) 5(17) β 4(10) 85 β 40 = 45 d. Student gives an accurate explanation. Wording may vary. Sample explanation: After analyzing the solutions I found for each value of r, I found there was a pattern in the solutions and the values of r. Each time the value of r increased by 2, the solution also increased by 2.
8. a. Student gives correct expression: $25β + $40 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to write the expression I used several important pieces of information given to me in the problem. First, Jordyn works at a rate of $25 per hour. This means she gets $25 for every hour she works, so if I wanted to find how much she makes for a certain amount of time I would multiply the rate by the number of hours she works. Based on this information, the first part of the expression is $25 times h, or $25h, where h equals the number of hours she works. I was also given that she also charges an additional $40 fee for clean-up. I knew I would add this fee to the hourly rate, so the next part of the expression was + $40. The whole expression put together with all this information is $25β + $40. c. Student gives correct answer and shows work: $25(4) + $40 $100 + $40 = $140 9. a. Student gives correct answers: EJβs Game Store: $16π β $1.00π; Game Central: $17π β $1.75π b. Student gives correct answers and shows work: EJβs Game Store: $16(9) β $1.00(9) = $144 β $9 = $135 Game Central: $17(9) β $1.75(9) = $153 β $15.75 = $137.25 Copyright Β© Swun Math Grade 6 Unit 4 Constructed Response Rubric, Page 4
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Grade 6 Unit 4 Constructed Response Expressions and Equations c. Student gives an accurate explanation. Wording may vary. Sample explanation: After finding the prices for the games at each store, I find the store that will give them the best price is EJβs Game Store. After completing the calculations I found EJβs Game Store would charge Christian and Mackenzie $135.00 versus Game Central that would charge them $137.25. They would save $2.25 by shopping at EJβs Game Store. Total
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1. Expressions: Properties, Parts of Expressions, and Writing Expressions
2. Equivalent Expressions, Powers and Exponents, Order of Operations
3. Evaluate Expressions
Common Core State Standard for Mathematical Content (MC) 6.EE.2a: Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.2b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. 6.EE.3: Apply the properties of operations to generate equivalent expressions. 6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them. 6.EE.1: Write and evaluate numerical expressions involving whole-number exponents. 6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them. 6.EE.2: Write, read and evaluate expressions in which letters stand for numbers.
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.3, MP.4, MP.6, MP.7
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
MP.1, MP.2, MP.3, MP.6, MP.7, MP.8
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 6 Unit 4 Constructed Response Rubric, Page 1
Grade 6 Unit 4 Constructed Response Expressions and Equations Scoring Rubric Question 1. a. Student gives correct expression: 3π + 6 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In the problem I am told Charlotte had 3 times as many oranges as strawberries. I am not told the exact number she has of each, but I know 3 times some number will equal the number of oranges she has before going to the store. So I represented this piece of information as 3s, where s equals the unknown number of strawberries. I am also told in the problem Charlotte bought an additional 6 oranges, so to represent this I wrote+6. My whole expression put together to find the total number of oranges was 3π + 6. c. Student gives an accurate explanation. Wording may vary. Sample explanation: There are two terms in my expression, β3sβ and β+6β. The variable s represents the unknown number of strawberries. The number 3 is the coefficient that will be multiplied by the variable by. The number 6 is a constant in my expression, and represents the number of additional oranges Charlotte buys. This number is the constant because it stands alone in the expression. 2. Student gives correct answers and accurate explanations. Wording may vary. Sample explanations: a.
(10π+5)
; I know this is the correct answer because I am told in the problem Mary had 10 times as many red stickers as blue stickers and then she found five more. So this matches the top portion of the fraction. She then gave stickers to her five friends so I know the number of stickers she had was to be divided by five, which is represented in the denominator of this expression. b. π + (2 Γ π) β 4 + 5 ; I know this is the correct answer because I am told in the problem Steven bought an unknown number (l) of lollipops on Monday and then he bought 2 times (2 Γ l) as many on Wednesday. I am also told he gave 4 of them to his sister, which was represented withβ4, as can be seen in the expression. The last part of the expression is +5 which represents the additional 5 lollipops Steven bought on Saturday. c. (2 Γ π) + (4 Γ π ) β 5; I know this is the correct answer because I am told in the problem Cory and Mike are combining their different sets of marbles, which is represented by(2 Γ π) + (4 Γ π ). Here c and s equal the number of marbles in each of their sets. I am told they give five of 5
Copyright Β© Swun Math Grade 6 Unit 4 Constructed Response Rubric, Page 2
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Grade 6 Unit 4 Constructed Response Expressions and Equations their marbles to Mikeβs little brother which was represented by β5 in the expression. 3. a. Student gives an accurate explanation. Wording may vary. Sample explanation: After analyzing the statement and the expression Will wrote, I found that Willβs expressions incorrect. One of the errors he made was switching the variable and the constant in the fraction. The statement says the difference between s and 9 so it should have been written as s β 9, where the constant is 9. Another error is writing the difference between s and 9 divided by 6. In the statement we are told three times the difference between s and 9 divided by 6, so this means the product of 3 and the difference between s and 9 is divided by 6. 3(π β9) b. Student gives correct answer: 6 4. a. Student gives correct answer: 7π + 63. b. Student gives an accurate explanation. Wording may vary. Sample explanation: The algebraic property I used to generate the equivalent
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expression was the Distributive Property. I used this property to distribute the 7 to the terms inside the parenthesis. First I multiplied 7 by m which gave me 7m and then I multiplied 7 by + 9 which gave me + 63. The new equivalent expression was 7π + 63.
5. a. Student gives correct answer: 4 Γ 4 Γ 4 Γ 4 Γ 4 Γ π Γ π Γ π b. Student gives correct answer: 1,024 d3 c. Student gives an accurate explanation. Wording may vary. Sample explanation: There is a relationship between the base and the exponent of each term in an expression. The exponent in the expression tells how many times the base number is used as a factor. This relationship helped me find the expanded form and standard form because the exponent told me how many times I had to multiply 4 by itself, and how many times I had to multiply the variable d by itself. So for 45 π 3 the exponent told me to multiply 4 by itself 5 times and to multiply d by itself 3 times, so4 Γ 4 Γ 4 Γ 4 Γ 4 Γ π Γ π Γ π. 6. Student correctly places parentheses and proves their correct placement by showing the steps to solve each equation. a. 42 + (12 β 5) + 7 = 30 16 + (7) + 7 = 16 + 14 = 30 b. (92 Γ· 3) β (2 Γ 3) = 21 (81 Γ· 3) β (2 Γ 3) = 21 (27) β (6) = 21 c. 59 β (72 β 15) β 10 = 15 59 β (49 β 15) β 10 = 15 59 β (34) β 10 = 15 Copyright Β© Swun Math Grade 6 Unit 4 Constructed Response Rubric, Page 3
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Grade 6 Unit 4 Constructed Response Expressions and Equations d. 25 β 10 = 15 Student gives an accurate explanation. Wording may vary. Sample explanation: Following the Order of Operations to solve equations is important because it is the way mathematicians solve problems all over the world. If I solve the problem in any order I wish, I will get an incorrect solution and will not be able to communicate mathematically with anyone else. 7. Student gives correct answers and shows work: a. 5(6 + 7) β 4(6) 5(13) β 4(6) 65 β 24 = 41 b. 5(8 + 7) β 4(8) 5(15) β 4(8) 75 β 32 = 43 c. 5(10 + 7) β 4(10) 5(17) β 4(10) 85 β 40 = 45 d. Student gives an accurate explanation. Wording may vary. Sample explanation: After analyzing the solutions I found for each value of r, I found there was a pattern in the solutions and the values of r. Each time the value of r increased by 2, the solution also increased by 2.
8. a. Student gives correct expression: $25β + $40 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to write the expression I used several important pieces of information given to me in the problem. First, Jordyn works at a rate of $25 per hour. This means she gets $25 for every hour she works, so if I wanted to find how much she makes for a certain amount of time I would multiply the rate by the number of hours she works. Based on this information, the first part of the expression is $25 times h, or $25h, where h equals the number of hours she works. I was also given that she also charges an additional $40 fee for clean-up. I knew I would add this fee to the hourly rate, so the next part of the expression was + $40. The whole expression put together with all this information is $25β + $40. c. Student gives correct answer and shows work: $25(4) + $40 $100 + $40 = $140 9. a. Student gives correct answers: EJβs Game Store: $16π β $1.00π; Game Central: $17π β $1.75π b. Student gives correct answers and shows work: EJβs Game Store: $16(9) β $1.00(9) = $144 β $9 = $135 Game Central: $17(9) β $1.75(9) = $153 β $15.75 = $137.25 Copyright Β© Swun Math Grade 6 Unit 4 Constructed Response Rubric, Page 4
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Grade 6 Unit 4 Constructed Response Expressions and Equations c. Student gives an accurate explanation. Wording may vary. Sample explanation: After finding the prices for the games at each store, I find the store that will give them the best price is EJβs Game Store. After completing the calculations I found EJβs Game Store would charge Christian and Mackenzie $135.00 versus Game Central that would charge them $137.25. They would save $2.25 by shopping at EJβs Game Store. Total
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