G3 U3 Constructed Response Rubric
Grade 3 Unit 3 Constructed Response Understanding Division Scoring Rubric Task
1. Relating Multiplication and Division
Common Core State Standard
Standards for Mathematical Practice
3.OA.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
SMP.1, SMP.7
3.OA.2: Interpret whole-number quotients 2. Division as Sharing
of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
SMP.1, SMP.4, SMP.7
3.OA.2: Interpret whole-number quotients 3. Division as Grouping
of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
SMP.1, SMP.4, SMP.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 © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 1
Grade 3 Unit 3 Constructed Response Understanding Division Scoring Rubric Question 1. a. Student gives explanation: In order to solve this problem I could use an array to find the unknown number the problem is asking for. This tool would be useful in this situation because division is the inverse of multiplication. b. Student gives correct answer and draws array: 9 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
×
7
=
21
7
×
3
=
21
21
÷
7
=
3
21
÷
3
=
7
0.5
o o o o o o o
2. a. Student gives correct answers: The missing number from the fact family is 7. 3
Points 0.5
b. Student creates an array:
0.5
0.5 1
o o o o o o o o o o o o o o o o o o o o o c. Student provides explanation: The array proves that my answer is correct because it shows that 3 × 7 = 21, and 21 divided into 3 groups as shown in the table is equal to 7. 3. Student gives correct answers: 6 orange trees in each row. 8 × 6 = 48 6 × 7 = 48 48 ÷ 6 = 8 48 ÷ 8 = 6
Copyright © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 2
2
Total
Grade 3 Unit 3 Constructed Response Understanding Division 4. Student gives explanation: After reading through the problem I underlined pieces of information which helped me to understand what the problem is asking me to find. I am told that Marley sold 63 muffins last week, and there are 7 days in a week so she sold 63 muffins in 7 days. The question asks for how many muffins she sold on average per day, so I know that to find this I need to divide the total muffins she sold by 7 days. b. Student gives correct answer: 63 ÷ 7 = ? c. Student gives correct answer: 9 muffins sold per day d. Student provides illustration: Illustrations may vary; looking for students understanding of 7 groups of 9 in their illustration. 5. a. Student gives correct answer: 20 ÷ 5 = ? b. Student gives correct answer and shows work: 4 boxes of markers per table. c. Student gives explanation: This type of question relates to division as sharing because Ryan is passing out markers to each of the 4 tables until they are gone.
0.25
6. a. Student gives correct answer, equation, and illustration: 3 cookies, 3 leftover. 18 ÷ 5 = ?, Students should draw an array, picture, or number line. b. Student gives correct answer, equation, and illustration: 3 crayons, 3 leftover. 18 ÷ 5 = ?, Students should draw an array, picture, or number line. c. Student gives correct answer, equation, and illustration: 3 pennies, 3 leftover. 18 ÷ 5 = ?, Students should draw an array, picture, or number line. 7. a. Student gives correct answer: 36 ÷ 6 = ? b. Student gives explanation: In the equation I wrote, the 36 represents the total number of items that are needed or the dividend, and the 6 represents the size of the group that those items are placed into. c. Student gives correct answer and creates number line: 6 packs of cups
2
0
6
12
18
24
30
36
Copyright © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 3
0.25 0.25 0.25 0.5 0.5 1
0.25 0.75
1
Grade 3 Unit 3 Constructed Response Understanding Division 8. a. Student underlines information in sentence: A toy boat travels 8 inches across the water in 1 second. How long will it take for the toy boat to travel 40 inches? b. Student draws number line: 5 minutes
0
8
16
24
32
0.5
1
40
c. Student gives correct answer: 40 ÷ 8 = 5 9. a. Student gives correct answer and shows work: 3 rows b. Student gives correct answer and shows work: 2 groups c. Student gives correct answer and shows work: 4 groups with 2 leftovers; or 4 groups of 4 players and 1 group of 2 players d. Student gives correct answer and shows work: 9 groups Test Total
Copyright © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 4
0.5 0.5 0.5 0.5 0.5 15
1. Relating Multiplication and Division
Common Core State Standard
Standards for Mathematical Practice
3.OA.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
SMP.1, SMP.7
3.OA.2: Interpret whole-number quotients 2. Division as Sharing
of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
SMP.1, SMP.4, SMP.7
3.OA.2: Interpret whole-number quotients 3. Division as Grouping
of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.
SMP.1, SMP.4, SMP.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 © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 1
Grade 3 Unit 3 Constructed Response Understanding Division Scoring Rubric Question 1. a. Student gives explanation: In order to solve this problem I could use an array to find the unknown number the problem is asking for. This tool would be useful in this situation because division is the inverse of multiplication. b. Student gives correct answer and draws array: 9 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
×
7
=
21
7
×
3
=
21
21
÷
7
=
3
21
÷
3
=
7
0.5
o o o o o o o
2. a. Student gives correct answers: The missing number from the fact family is 7. 3
Points 0.5
b. Student creates an array:
0.5
0.5 1
o o o o o o o o o o o o o o o o o o o o o c. Student provides explanation: The array proves that my answer is correct because it shows that 3 × 7 = 21, and 21 divided into 3 groups as shown in the table is equal to 7. 3. Student gives correct answers: 6 orange trees in each row. 8 × 6 = 48 6 × 7 = 48 48 ÷ 6 = 8 48 ÷ 8 = 6
Copyright © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 2
2
Total
Grade 3 Unit 3 Constructed Response Understanding Division 4. Student gives explanation: After reading through the problem I underlined pieces of information which helped me to understand what the problem is asking me to find. I am told that Marley sold 63 muffins last week, and there are 7 days in a week so she sold 63 muffins in 7 days. The question asks for how many muffins she sold on average per day, so I know that to find this I need to divide the total muffins she sold by 7 days. b. Student gives correct answer: 63 ÷ 7 = ? c. Student gives correct answer: 9 muffins sold per day d. Student provides illustration: Illustrations may vary; looking for students understanding of 7 groups of 9 in their illustration. 5. a. Student gives correct answer: 20 ÷ 5 = ? b. Student gives correct answer and shows work: 4 boxes of markers per table. c. Student gives explanation: This type of question relates to division as sharing because Ryan is passing out markers to each of the 4 tables until they are gone.
0.25
6. a. Student gives correct answer, equation, and illustration: 3 cookies, 3 leftover. 18 ÷ 5 = ?, Students should draw an array, picture, or number line. b. Student gives correct answer, equation, and illustration: 3 crayons, 3 leftover. 18 ÷ 5 = ?, Students should draw an array, picture, or number line. c. Student gives correct answer, equation, and illustration: 3 pennies, 3 leftover. 18 ÷ 5 = ?, Students should draw an array, picture, or number line. 7. a. Student gives correct answer: 36 ÷ 6 = ? b. Student gives explanation: In the equation I wrote, the 36 represents the total number of items that are needed or the dividend, and the 6 represents the size of the group that those items are placed into. c. Student gives correct answer and creates number line: 6 packs of cups
2
0
6
12
18
24
30
36
Copyright © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 3
0.25 0.25 0.25 0.5 0.5 1
0.25 0.75
1
Grade 3 Unit 3 Constructed Response Understanding Division 8. a. Student underlines information in sentence: A toy boat travels 8 inches across the water in 1 second. How long will it take for the toy boat to travel 40 inches? b. Student draws number line: 5 minutes
0
8
16
24
32
0.5
1
40
c. Student gives correct answer: 40 ÷ 8 = 5 9. a. Student gives correct answer and shows work: 3 rows b. Student gives correct answer and shows work: 2 groups c. Student gives correct answer and shows work: 4 groups with 2 leftovers; or 4 groups of 4 players and 1 group of 2 players d. Student gives correct answer and shows work: 9 groups Test Total
Copyright © Swun Math Grade 3 Unit 3 Constructed Response Rubric, Page 4
0.5 0.5 0.5 0.5 0.5 15
