G3 U2 Constructed Response Rubric
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication Scoring Rubric Task 1. Repeated Addition and Arrays 2. Associative and Commutative Properties of Multiplication 3. Distributive Property of Multiplication
Common Core State Standard
Standards for Mathematical Practice
3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
SMP.1, SMP.4, SMP.7
3.OA.5: Apply properties of operations as strategies to multiply and divide.
SMP.2, SMP.3, SMP.4, SMP.7, SMP.8,
3.OA.5: Apply properties of operations as
SMP.1, SMP.2, SMP.4, SMP.7, SMP.8
strategies to multiply and divide.
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 © Swun Math Grade 3 Unit 2 Constructed Response Rubric, Page 1
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication Scoring Rubric Question 1. a. Student gives explanation: In order to solve this problem by using repeated addition I first need to identify the number of groups present and the number of objects per group. In this case the number of groups is represented by the 9 canoes and the number of objects per group is the 3 people that can fit in the group, so there are 9 groups of 3. With this information I can do repeated addition by adding 3 by itself 9 times. b. Student gives correct answer using repeated addition: 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27 people c. Student gives correct answer: 9 × 3 = 27
2. a. Student draws an array: o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o b. Student gives correct answers: 56 cookies; 7 × 8 = 56 c. Student gives explanation: An array is a good model to use when solving this type of problem because it allows you to visualize the number of groups and the number of items per group that you are trying to multiply. It also gives you a better understanding of the total product that is resulting from multiplying these two numbers. 3. Student gives correct answers: (Arrays should be drawn for each arrangement) 1 row of 18 seeds, 6 rows of 3 seeds, 3 rows of 6 seeds, 9 rows of 2 seeds, 2 rows of 9 seeds. There are five possible arrangements for the seeds. 4. Student creates Venn Diagram: Associative Property: The product is the same regardless of the grouping of the factors. Ex.; (2 × 3)×4=24 2 × (3×4)=24
Commutative Property: Products remain the same when using either property
The product is the same regardless of the order of the factors. Ex.: 4 × 8 = 32 8 × 4 = 32
Copyright © Swun Math Grade 3 Unit 2 Constructed Response Rubric, Page 2
Points 0.5
0.25 0.25 0.5
0.5 1
2
1
Total
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication 5. a. Student gives correct answers: 6 × 9 = 54; 9 × 6 = 54 b. Student draws two arrays:
9 × 6 = 54 6 × 9 = 54 c. Student gives explanation: In order to solve this problem I had to use the Commutative Property of Multiplication. I used this property because I was being asked to create two multiplication sentences with the same answer but with factors being placed in a different order. 6. a. Student completes equation: ( 5 × 3) × 7= 5 × (3 × 7) b. Student gives explanation: In order to solve this problem I had to use the Associative Property of Multiplication. I used this property because when I was analyzing both sides of the equation I noticed that parentheses representing the grouping of the numbers changed positions but the numbers themselves did not change. c. Student gives explanation: Some similarities that I noticed in both sides of the equation are that both sides had the same numbers and operations. Even though the grouping on each side was different, the answer was the same - 105. 7. Student gives explanation: The Distributive Property of Multiplication can be used to simplify multiplication equations because this property involves breaking down one of the factors into smaller numbers. These smaller factors are then multiplied in two new number sentences. Then the products of these two sentences are added. This sum is equal to the product of the original equation. 8. a. Student gives correct answers: Possible answer: Decomposition of 11= 5 + 6; Two new number sentences= 5 × 2 = 10 and 6 × 2 = 12. b. Student gives explanation: In order to check that my answers are correct I need to add the products of the two new number sentences I wrote. If their sum is equal to the product of the original equation then I know my work is correct. c. Student shows work and should confirm that their answers are correct.
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0.5 0.5
1
0.5 0.5
1
0.25
0.25 0.50 1 0.5
0.5
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication 9. a. Student gives explanation: After reading this problem I was able to get some pieces of information that were important towards solving the problem. I am told that there are three teams with nine players each, and that each player will be getting two jerseys, one for practice and the other for games. This information can help me to write an equation to solve the problem. b. Student gives correct answer and shows work: Answers will vary; Associative property: 3 × (9 × 2) = 54 jerseys Test Total
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1 15
Common Core State Standard
Standards for Mathematical Practice
3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
SMP.1, SMP.4, SMP.7
3.OA.5: Apply properties of operations as strategies to multiply and divide.
SMP.2, SMP.3, SMP.4, SMP.7, SMP.8,
3.OA.5: Apply properties of operations as
SMP.1, SMP.2, SMP.4, SMP.7, SMP.8
strategies to multiply and divide.
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 © Swun Math Grade 3 Unit 2 Constructed Response Rubric, Page 1
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication Scoring Rubric Question 1. a. Student gives explanation: In order to solve this problem by using repeated addition I first need to identify the number of groups present and the number of objects per group. In this case the number of groups is represented by the 9 canoes and the number of objects per group is the 3 people that can fit in the group, so there are 9 groups of 3. With this information I can do repeated addition by adding 3 by itself 9 times. b. Student gives correct answer using repeated addition: 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27 people c. Student gives correct answer: 9 × 3 = 27
2. a. Student draws an array: o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o b. Student gives correct answers: 56 cookies; 7 × 8 = 56 c. Student gives explanation: An array is a good model to use when solving this type of problem because it allows you to visualize the number of groups and the number of items per group that you are trying to multiply. It also gives you a better understanding of the total product that is resulting from multiplying these two numbers. 3. Student gives correct answers: (Arrays should be drawn for each arrangement) 1 row of 18 seeds, 6 rows of 3 seeds, 3 rows of 6 seeds, 9 rows of 2 seeds, 2 rows of 9 seeds. There are five possible arrangements for the seeds. 4. Student creates Venn Diagram: Associative Property: The product is the same regardless of the grouping of the factors. Ex.; (2 × 3)×4=24 2 × (3×4)=24
Commutative Property: Products remain the same when using either property
The product is the same regardless of the order of the factors. Ex.: 4 × 8 = 32 8 × 4 = 32
Copyright © Swun Math Grade 3 Unit 2 Constructed Response Rubric, Page 2
Points 0.5
0.25 0.25 0.5
0.5 1
2
1
Total
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication 5. a. Student gives correct answers: 6 × 9 = 54; 9 × 6 = 54 b. Student draws two arrays:
9 × 6 = 54 6 × 9 = 54 c. Student gives explanation: In order to solve this problem I had to use the Commutative Property of Multiplication. I used this property because I was being asked to create two multiplication sentences with the same answer but with factors being placed in a different order. 6. a. Student completes equation: ( 5 × 3) × 7= 5 × (3 × 7) b. Student gives explanation: In order to solve this problem I had to use the Associative Property of Multiplication. I used this property because when I was analyzing both sides of the equation I noticed that parentheses representing the grouping of the numbers changed positions but the numbers themselves did not change. c. Student gives explanation: Some similarities that I noticed in both sides of the equation are that both sides had the same numbers and operations. Even though the grouping on each side was different, the answer was the same - 105. 7. Student gives explanation: The Distributive Property of Multiplication can be used to simplify multiplication equations because this property involves breaking down one of the factors into smaller numbers. These smaller factors are then multiplied in two new number sentences. Then the products of these two sentences are added. This sum is equal to the product of the original equation. 8. a. Student gives correct answers: Possible answer: Decomposition of 11= 5 + 6; Two new number sentences= 5 × 2 = 10 and 6 × 2 = 12. b. Student gives explanation: In order to check that my answers are correct I need to add the products of the two new number sentences I wrote. If their sum is equal to the product of the original equation then I know my work is correct. c. Student shows work and should confirm that their answers are correct.
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0.5 0.5
1
0.5 0.5
1
0.25
0.25 0.50 1 0.5
0.5
Grade 3 Unit 2 Constructed Response Understanding the Meaning of Multiplication 9. a. Student gives explanation: After reading this problem I was able to get some pieces of information that were important towards solving the problem. I am told that there are three teams with nine players each, and that each player will be getting two jerseys, one for practice and the other for games. This information can help me to write an equation to solve the problem. b. Student gives correct answer and shows work: Answers will vary; Associative property: 3 × (9 × 2) = 54 jerseys Test Total
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