G5 U2 Constructed Response Rubric
Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers Scoring Rubric Task
1. Interpreting and Evaluating Expressions
2. Multiplication of Whole Numbers
3. Division of Whole Numbers
Common Core State Standard 5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 5.NBT.5: Fluently multiply multi-digit whole
numbers using the standard algorithm. 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6: Find whole-number quotients with up to four-digit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.3, SMP.6, SMP.7, SMP.8
SMP.1, SMP.2, SMP.3, SMP.4, SMP.7
SMP.1, SMP.3, SMP.4, SMP.5, SMP.7, SMP.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 ques tion 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 © Swun Math Grade 5 Unit 2 Constructed Response Rubric, Page 1
Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers Scoring Rubric Question 1. a. Student completes table: Step 1: E Explanation: This is the correct step because it is the un-simplified expression that is being worked with. Step 2: A Explanation: This is the correct step because the numbers in the parentheses were solved first, (3-3)=0. Step 3: C Explanation: This is the correct step because the values in the bracket were solved for, [2 – 0]=2. Step 4: B Explanation: This is the correct step because the values in the braces were solved for: {44-14} = 30. Step 5: F Explanation: This is the correct step because according to the order of operations we first multiply and divide from left to right. Then we add and subtract. Step 6: D Explanation: This is the correct step because subtraction is the last operation to be performed on the expression due to the order of operations rule. 2. a. Student gives correct answer: (3 + 5) × $4 b. Student gives correct answer and shows work: $60 c. Student gives explanation: A rule that was very useful when solving the expression was the Order of Operations Rule. This rule was useful because it told me which parts of the equation needed to be solved for first. In this case the operation in the parentheses was solved first and then multiplication as stated in the Order of Operations rule. 3. a. Student gives correct answer: Expression A: 2; Expression B: 10 b. Student gives explanation: After analyzing and solving the expression I observed that the relationship between the two expressions is that Expression B is 5 times as large as Expression A. This is apparent in the answers for each expression. Expression A (16 – 6) ÷ 5 is equal to 2, whereas Expression B 16 − 6 is equal to 10. The answer for Expression B is five times larger than the answer for Expression A. Copyright © Swun Math Grade 5 Unit 2 Constructed Response Rubric, Page 2
Points Total 2
0.5 0.5 1
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Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers 4. a. Student gives correct answer and shows work: 312; check students’ area models and standard algorithms for accuracy. b. Student gives explanation: The area model relates to concepts I have learned about finding the area of a rectangle. The area of a rectangle is found by multiplying the length or vertical side by the width or horizontal side of the rectangle. In the area model we are doing the same thing; only that in this model the rectangle is divided up into sections for each part of the expanded form of the multi-digit number in the expression. Each horizontal section is multiplied by the digit along the vertical side. 5. a. Student gives correct answer and shows work: 15,408; Check students’ work for accuracy. b. Student gives explanation: Understanding the Distributive Property can help me understand what is going on in the standard algorithm because when I am solving an expression using the Distributive Property I am breaking down each number to its expanded form and distributing the values through multiplication. As the name says, you can see were the place value in numbers get distributed when you are multiplying. 6. a. Student provides explanation: After analyzing Sofia’s work I was able to determine that both her process and her answer for the expression are incorrect. I know that she is incorrect because after she finished multiplying the 4 in 14 by all the numbers in 312, she did not place a zero on the far right of the next row underneath the 8. She proceeded with the multiplication correctly but because of her placement of the numbers in the second row her answer was also incorrect. b. Student gives correct answer and shows work: 7,488 7. a. Student gives correct answer and shows work: 24 marbles b. Student gives explanation: The strategy of dividing by decomposing was helpful in finding this solution because the numbers that I was working with were simple numbers that I was able to divide easily. Each part of the dividend broken down into expanded notation was easily divided by 20, which gave me quotients with no remainders. This made it simpler to add the quotients when I was finding my final answer.
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Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers 8. a. Student gives correct answer and shows work: 81 strawberry boxes. check students’ work for accuracy. b. Student gives correct answer: In order to prove that my answer is correct I would need multiply my answer from part A by the number of markets the farmer needs to distribute to. If this number is equal to the total number of strawberry boxes the farmer has then I know my answer in part A is correct. c. Student shows process of proving answer:
1 0.5
0.5
25 × 81 = 2,025
9. a. Student gives explanation: The statement which is incorrect is statement C. The reason why it is incorrect is because four crates cannot hold 45 boxes of rocks according to the quantity we are told each crate can hold. b. Student gives correct answer: Four crates can hold 40 boxes of rocks. Test Total
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1. Interpreting and Evaluating Expressions
2. Multiplication of Whole Numbers
3. Division of Whole Numbers
Common Core State Standard 5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 5.NBT.5: Fluently multiply multi-digit whole
numbers using the standard algorithm. 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6: Find whole-number quotients with up to four-digit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.3, SMP.6, SMP.7, SMP.8
SMP.1, SMP.2, SMP.3, SMP.4, SMP.7
SMP.1, SMP.3, SMP.4, SMP.5, SMP.7, SMP.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 ques tion 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 © Swun Math Grade 5 Unit 2 Constructed Response Rubric, Page 1
Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers Scoring Rubric Question 1. a. Student completes table: Step 1: E Explanation: This is the correct step because it is the un-simplified expression that is being worked with. Step 2: A Explanation: This is the correct step because the numbers in the parentheses were solved first, (3-3)=0. Step 3: C Explanation: This is the correct step because the values in the bracket were solved for, [2 – 0]=2. Step 4: B Explanation: This is the correct step because the values in the braces were solved for: {44-14} = 30. Step 5: F Explanation: This is the correct step because according to the order of operations we first multiply and divide from left to right. Then we add and subtract. Step 6: D Explanation: This is the correct step because subtraction is the last operation to be performed on the expression due to the order of operations rule. 2. a. Student gives correct answer: (3 + 5) × $4 b. Student gives correct answer and shows work: $60 c. Student gives explanation: A rule that was very useful when solving the expression was the Order of Operations Rule. This rule was useful because it told me which parts of the equation needed to be solved for first. In this case the operation in the parentheses was solved first and then multiplication as stated in the Order of Operations rule. 3. a. Student gives correct answer: Expression A: 2; Expression B: 10 b. Student gives explanation: After analyzing and solving the expression I observed that the relationship between the two expressions is that Expression B is 5 times as large as Expression A. This is apparent in the answers for each expression. Expression A (16 – 6) ÷ 5 is equal to 2, whereas Expression B 16 − 6 is equal to 10. The answer for Expression B is five times larger than the answer for Expression A. Copyright © Swun Math Grade 5 Unit 2 Constructed Response Rubric, Page 2
Points Total 2
0.5 0.5 1
1 1
Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers 4. a. Student gives correct answer and shows work: 312; check students’ area models and standard algorithms for accuracy. b. Student gives explanation: The area model relates to concepts I have learned about finding the area of a rectangle. The area of a rectangle is found by multiplying the length or vertical side by the width or horizontal side of the rectangle. In the area model we are doing the same thing; only that in this model the rectangle is divided up into sections for each part of the expanded form of the multi-digit number in the expression. Each horizontal section is multiplied by the digit along the vertical side. 5. a. Student gives correct answer and shows work: 15,408; Check students’ work for accuracy. b. Student gives explanation: Understanding the Distributive Property can help me understand what is going on in the standard algorithm because when I am solving an expression using the Distributive Property I am breaking down each number to its expanded form and distributing the values through multiplication. As the name says, you can see were the place value in numbers get distributed when you are multiplying. 6. a. Student provides explanation: After analyzing Sofia’s work I was able to determine that both her process and her answer for the expression are incorrect. I know that she is incorrect because after she finished multiplying the 4 in 14 by all the numbers in 312, she did not place a zero on the far right of the next row underneath the 8. She proceeded with the multiplication correctly but because of her placement of the numbers in the second row her answer was also incorrect. b. Student gives correct answer and shows work: 7,488 7. a. Student gives correct answer and shows work: 24 marbles b. Student gives explanation: The strategy of dividing by decomposing was helpful in finding this solution because the numbers that I was working with were simple numbers that I was able to divide easily. Each part of the dividend broken down into expanded notation was easily divided by 20, which gave me quotients with no remainders. This made it simpler to add the quotients when I was finding my final answer.
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Grade 5 Unit 2 Constructed Response Multiplication and Division of Whole Numbers 8. a. Student gives correct answer and shows work: 81 strawberry boxes. check students’ work for accuracy. b. Student gives correct answer: In order to prove that my answer is correct I would need multiply my answer from part A by the number of markets the farmer needs to distribute to. If this number is equal to the total number of strawberry boxes the farmer has then I know my answer in part A is correct. c. Student shows process of proving answer:
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0.5
25 × 81 = 2,025
9. a. Student gives explanation: The statement which is incorrect is statement C. The reason why it is incorrect is because four crates cannot hold 45 boxes of rocks according to the quantity we are told each crate can hold. b. Student gives correct answer: Four crates can hold 40 boxes of rocks. Test Total
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