G5 U7 Constructed Response Rubric
Grade 5 Unit 7 Constructed Response Dividing Fractions Scoring Rubric Task
1. Division of a Unit Fraction by a Whole Number
2. Division of a Whole Number by a Unit Fraction
3. Word Problems Involving Mixed Numbers and Whole Numbers
Common Core State Standard for Mathematical Content (MC) 5.NF.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. 5.NF.7b: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. 5.NF.7c: Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.3, MP.4, MP.5, MP.6,
MP.1, MP.2, MP.4, MP.5, MP.6
MP.1, MP.2, MP.4, 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 © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 1
Grade 5 Unit 7 Constructed Response Dividing Fractions Scoring Rubric Question 7
1. a. Student gives correct answer: ÷ 4 = 𝑥 8 b. Student gives correct answer and shows work using an accurate model: 7 (Check student’s model for accuracy in using this strategy); 32 of a pound c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to check that my anwer is correct I can use the inverse operation of division which is multiplication. To check my answer I 7 need to multiply 32 by 4. If my answer is equal to the original fraction in my equation then I know my answer is correct. d. Student checks answer using the strategy described above. 2. a. Student creates word problem: (Check that the student represents the equation in their word problem correctly, and includes all elements of a division word problem learned); 5 Sample answer: Jerry has 6 pounds of trail mix. He wants to store it equally into 7 snack bags for the week. How much trail mix should Jerry put into each snack bag? Student gives an accurate explanation. Wording may vary. Sample explanation: Sampleb. Student gives correct answer and shows work using an accurate model: (Check the student’s model for accuracy in using this strategy; Units may vary for the answer depending on the student’s 5 word problem); 42 of a pound of trail mix 1
3. a. Student gives correct answer: 10 ÷ 5 = 𝑥 b. Student gives correct answer and shows work using an accurate number line: (Check student’s number line for accuracy in using the 1 strategy); 50 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my answer using a number line, I first had to 1 create a number line to represent the dividend in the problem, 10. To do this I numbered from zero to one and divided my number line into ten equal 1 parts. To represent the fraction I shaded the area from zero to 10 on the number line. Since the divisor in the problem is 5 equal pieces, I divided 1 each 10 on my number line into 5 equal parts. In total the number line was Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 2
Points 1 1 1
1 1
1
1 1
2
Total
Grade 5 Unit 7 Constructed Response Dividing Fractions divided into 50 equal parts and the shaded area on my line still represented 1 the 10 of a yard Brianna has. So looking at the number line the length of 1
each piece of ribbon is 50 of a yard.
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4. a. Student gives correct answer: 4 ÷ 3 = 𝑥 b. Student gives correct answer and shows work using an accurate model: 12 batches of cookies c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve my problem using a model I drew four squares to represent the cups of sugar Teresa has and I divided each of these cups into thirds. Based on my drawing there would be 3 batches of cookies made per cup of chocolate chips. So for 4 cups of chocolate chips, 4 × 3 = 12 batches of cookies can be made. Based on my model I was 1 also able to determine that 4 ÷ 3 = 12 could also be solved by multiplying 4 × 3. 5. a. Student creates an accurate word problem: (Check that the student represents the equation in their word problem correctly, and includes all elements of a division word problem learned); Sample answer: Evelyn baked 6 loaves of homemade banana bread for a party. To make sure there was enough for everyone, she gave each person 1 of the banana bread. How many people did she give banana bread to at 5 the party? b. Student gives an accurate explanation. Wording may vary. Sample 1 explanation: : I am representing the expression 6 ÷ 5 in my word problem because I included certain elements of division word problems. The first element in my word problem is identifying a person doing an action. In this case it is Teresa making the banana bread. The next element is identifying the dividend, by giving the amount and label of the items being divided. In this case it is the number 6 from the expression. In my word problem I made this 6 be the quantity of loaves of banana bread she made. The next element I included in my word problem was identifying the divisor. In my 1 word problem I represented the 5 as the equal portion each person got of banana bread. The last element of my word problem was the question asking for the answer of the expression. In this case it was how many people Teresa gave banana bread to at the party. c. Student gives correct answer and shows work using an accurate model: (Check student’s model for accuracy in using this strategy; Units may vary for the answer depending on the student’s word problem); 30 people Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 3
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Grade 5 Unit 7 Constructed Response Dividing Fractions 1
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6. a. Student gives correct answer: (2 ÷ 8) + (2 ÷ 6) = 𝑥 Student gives an accurate explanation. Wording may vary. Sample explanation: b. Student gives correct answer and shows work: 28 slices of pie 5
7. a. Student gives correct answer: 1 6 ÷ 7 = 𝑥 b. Student gives correct answer and shows work using an accurate 11 number line: (Check student’s work for accuracy in using the strategy); 42 of a pound 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: The problem tells me Ted initially purchased 9 yards of rope, 1 and for the project he needs to cut the rope into pieces that measure 1 2 yards long. So he is dividing his original amount into smaller equal pieces. Based on this I know my answer is going to represent the number of equal pieces he can cut the rope into. 1 b. Student gives correct answer: 9 ÷ 1 2 = 𝑥 c. Student gives correct answer and shows work using an accurate model: 6 pieces of rope Student gives an accurate explanation. Wording may vary. Sample explanation: 1
1 1
1 1
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1 1
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9. a. Student gives correct answer: (10 − 2) ÷ 12 = 𝑥 19
b. Student gives correct answer and shows work: 24 of a pound c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the solution for this problem I had to use several pieces of information given to me in the scenario. I knew 1 Christopher and his dad picked 7 pounds of peaches and kept 2 of a pound for themselves. I am then told they distributed the remaining amount among their 12 friends. Since the question is asking me to find the fraction of the pounds of peaches they each got, the first step I had to take was to 1 subtract 2 from 10 to find the actual amount of peaches distributed. This 1
1 2
1
number was 9 2 pounds. After finding this quantity I then had to divide 9 2 19
by 12 which is the number of friends. My answer, 24, represented the fraction of the total pounds of peaches each friend received. Total
Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 4
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Grade 5 Unit 7 Constructed Response Dividing Fractions
Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 5
1. Division of a Unit Fraction by a Whole Number
2. Division of a Whole Number by a Unit Fraction
3. Word Problems Involving Mixed Numbers and Whole Numbers
Common Core State Standard for Mathematical Content (MC) 5.NF.7a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. 5.NF.7b: Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. 5.NF.7c: Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.3, MP.4, MP.5, MP.6,
MP.1, MP.2, MP.4, MP.5, MP.6
MP.1, MP.2, MP.4, 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 © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 1
Grade 5 Unit 7 Constructed Response Dividing Fractions Scoring Rubric Question 7
1. a. Student gives correct answer: ÷ 4 = 𝑥 8 b. Student gives correct answer and shows work using an accurate model: 7 (Check student’s model for accuracy in using this strategy); 32 of a pound c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to check that my anwer is correct I can use the inverse operation of division which is multiplication. To check my answer I 7 need to multiply 32 by 4. If my answer is equal to the original fraction in my equation then I know my answer is correct. d. Student checks answer using the strategy described above. 2. a. Student creates word problem: (Check that the student represents the equation in their word problem correctly, and includes all elements of a division word problem learned); 5 Sample answer: Jerry has 6 pounds of trail mix. He wants to store it equally into 7 snack bags for the week. How much trail mix should Jerry put into each snack bag? Student gives an accurate explanation. Wording may vary. Sample explanation: Sampleb. Student gives correct answer and shows work using an accurate model: (Check the student’s model for accuracy in using this strategy; Units may vary for the answer depending on the student’s 5 word problem); 42 of a pound of trail mix 1
3. a. Student gives correct answer: 10 ÷ 5 = 𝑥 b. Student gives correct answer and shows work using an accurate number line: (Check student’s number line for accuracy in using the 1 strategy); 50 c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my answer using a number line, I first had to 1 create a number line to represent the dividend in the problem, 10. To do this I numbered from zero to one and divided my number line into ten equal 1 parts. To represent the fraction I shaded the area from zero to 10 on the number line. Since the divisor in the problem is 5 equal pieces, I divided 1 each 10 on my number line into 5 equal parts. In total the number line was Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 2
Points 1 1 1
1 1
1
1 1
2
Total
Grade 5 Unit 7 Constructed Response Dividing Fractions divided into 50 equal parts and the shaded area on my line still represented 1 the 10 of a yard Brianna has. So looking at the number line the length of 1
each piece of ribbon is 50 of a yard.
1
4. a. Student gives correct answer: 4 ÷ 3 = 𝑥 b. Student gives correct answer and shows work using an accurate model: 12 batches of cookies c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to solve my problem using a model I drew four squares to represent the cups of sugar Teresa has and I divided each of these cups into thirds. Based on my drawing there would be 3 batches of cookies made per cup of chocolate chips. So for 4 cups of chocolate chips, 4 × 3 = 12 batches of cookies can be made. Based on my model I was 1 also able to determine that 4 ÷ 3 = 12 could also be solved by multiplying 4 × 3. 5. a. Student creates an accurate word problem: (Check that the student represents the equation in their word problem correctly, and includes all elements of a division word problem learned); Sample answer: Evelyn baked 6 loaves of homemade banana bread for a party. To make sure there was enough for everyone, she gave each person 1 of the banana bread. How many people did she give banana bread to at 5 the party? b. Student gives an accurate explanation. Wording may vary. Sample 1 explanation: : I am representing the expression 6 ÷ 5 in my word problem because I included certain elements of division word problems. The first element in my word problem is identifying a person doing an action. In this case it is Teresa making the banana bread. The next element is identifying the dividend, by giving the amount and label of the items being divided. In this case it is the number 6 from the expression. In my word problem I made this 6 be the quantity of loaves of banana bread she made. The next element I included in my word problem was identifying the divisor. In my 1 word problem I represented the 5 as the equal portion each person got of banana bread. The last element of my word problem was the question asking for the answer of the expression. In this case it was how many people Teresa gave banana bread to at the party. c. Student gives correct answer and shows work using an accurate model: (Check student’s model for accuracy in using this strategy; Units may vary for the answer depending on the student’s word problem); 30 people Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 3
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Grade 5 Unit 7 Constructed Response Dividing Fractions 1
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6. a. Student gives correct answer: (2 ÷ 8) + (2 ÷ 6) = 𝑥 Student gives an accurate explanation. Wording may vary. Sample explanation: b. Student gives correct answer and shows work: 28 slices of pie 5
7. a. Student gives correct answer: 1 6 ÷ 7 = 𝑥 b. Student gives correct answer and shows work using an accurate 11 number line: (Check student’s work for accuracy in using the strategy); 42 of a pound 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: The problem tells me Ted initially purchased 9 yards of rope, 1 and for the project he needs to cut the rope into pieces that measure 1 2 yards long. So he is dividing his original amount into smaller equal pieces. Based on this I know my answer is going to represent the number of equal pieces he can cut the rope into. 1 b. Student gives correct answer: 9 ÷ 1 2 = 𝑥 c. Student gives correct answer and shows work using an accurate model: 6 pieces of rope Student gives an accurate explanation. Wording may vary. Sample explanation: 1
1 1
1 1
2
1 1
1
9. a. Student gives correct answer: (10 − 2) ÷ 12 = 𝑥 19
b. Student gives correct answer and shows work: 24 of a pound c. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find the solution for this problem I had to use several pieces of information given to me in the scenario. I knew 1 Christopher and his dad picked 7 pounds of peaches and kept 2 of a pound for themselves. I am then told they distributed the remaining amount among their 12 friends. Since the question is asking me to find the fraction of the pounds of peaches they each got, the first step I had to take was to 1 subtract 2 from 10 to find the actual amount of peaches distributed. This 1
1 2
1
number was 9 2 pounds. After finding this quantity I then had to divide 9 2 19
by 12 which is the number of friends. My answer, 24, represented the fraction of the total pounds of peaches each friend received. Total
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Grade 5 Unit 7 Constructed Response Dividing Fractions
Copyright © Swun Math Grade 5 Unit 7 Constructed Response Rubric, Page 5
