G4 U5 Constructed Response Rubric
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions Scoring Rubric Task
Common Core State Standard
4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring 1. Decompose Fractions, to the same whole. Add Fractions by 4.NF.3b: Decompose a fraction into a sum of Joining Parts, fractions with the same denominator in more Subtract Fractions by than one way, recording each decomposition by Separating Parts an equation. Justify decompositions, e.g., by using a visual fraction model. 2. Addition and 4.NF.3c: Add and subtract mixed numbers with Subtraction of Mixed like denominators, e.g., by replacing each mixed Numbers Using number with an equivalent fraction, and/or by Equivalent Fractions using properties of operations and the and Properties of relationship between addition and subtraction. Operations 4.NF.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the 3. Addition and relationship between addition and subtraction. Subtraction Word 4.NF.3d: Solve word problems involving addition Problems and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6, 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 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 4 Unit 5 Constructed Response Rubric, Page 1
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions Scoring Rubric Question 1. a. Student gives correct answer and shows work by creating a model: 11 (Answers may vary. Check student work for accuracy in decomposing 15) 1
1
1
1
1
1
1
1
1
1
1
Possible answer: 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 b. Student gives correct answer and shows work by creating a model: 11 (Answers may vary. Check student work for accuracy in decomposing 15) 3
2
Points 1
1
6
Possible answer: 15 + 15 + 15 1
5
2. a. Student creates correct answer: 8 + 18 b. Student gives correct answer and shows work by creating a visual 6 model: (Check students model for accuracy); 8 c. Student gives explanation: Answers may vary depending on the model the student created to find the solution. Example: To find my solution I chose to use two circles divided into 8 partitions because I felt it was the best model to show how much of each pie Brad had left over. This allowed me to visualize the quantities he had on each plate and how much pie he would have if he combined the two plates of left over pie together. 3. a. Student gives explanation: After reading through the problem I know that to solve this problem I need to use subtraction to find my solution. I am not told the measurement of the length of ribbon they buy, but I am 7 3 told they use 15 to make one bow and 15 to make the second bow. Looking at these two fractions I noticed they have the same denominator of 15. So 15 represents the whole length of ribbon they have. To find the amount of 15 7
1 1
2
3
15
ribbon they have left over I would need to first subtract 15 from 15 (1 3
whole) and then subtract 15 from the difference. The fraction I get is the amount of ribbon they have left over. b. Student gives correct answer and shows work by creating a number 5 line: (Check students number line for accuracy); 15 4. a. Student gives correct answer and shows work by using equivalent 7 fractions on a number line: (Check students number line for accuracy);3 8 b. Student gives explanation: Using a number line helped me to visualize the location of the equivalent fractions because the number line was divided up into whole ones from zero to seven and each of those wholes Copyright © Swun Math Grade 4 Unit 5 Constructed Response Rubric, Page 2
1
1 3
Total
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions was broken up into eight equal segments. These segments were labeled 1 along the line starting from 8. The equivalent fraction could be seen clearly by the location of the mixed number on the number line. Since the number line gave me the equivalent fractions of the mixed numbers it was then easy to combine these two equivalent fractions on a new number 18 13 31 line. First I located 8 and then I added 8 which was equal to 8 . Based on 7
this location I knew this was the equivalent fraction of 3 8 , which was my final answer. 5. a. Student gives correct answer and shows work using properties of operations and an illustration: (Check students work for accuracy in using 2 the strategy); 2 5 b. Student gives explanation: Answers may vary. Example: Creating an illustration helps me make sense of the problem because when I create the model to represent the mixed numbers it helps me see what parts of the whole number and the fraction are being taken away as I am subtracting. The illustration helps me visualize my answer from using the Property of operations and check that it makes sense. 6. a. Student gives explanation: In the problem I am told Alice is training for a race and she has been training for two weeks. I am given the total miles she runs during the second week but not the distance she ran during her first week of training. However, I am given the increase in miles she ran from the first week to the second week. This mixed number is important because it is the difference in miles between the two weeks. So I can use this to find the miles she ran the first week, by subtracting it from the miles she ran the second week. 5 1 b. Student gives correct answer: 7 7 − 2 7 c. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s work for 4 accuracy in using the strategy); 5 7 7. a. Student gives explanation: In order to find my solution I need to use addition and subtraction because this is a multistep problem. In the 5 problem I am told they first make 20 6 gallons of ice cream and then they 3
make an additional 8 6 gallons, so to find the total they made during the
1
month I need to add the quantities. At the end of the month they have 5 6 gallons left in their inventory, so to find the amount of ice cream they sold Copyright © Swun Math Grade 4 Unit 5 Constructed Response Rubric, Page 3
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2
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Grade 4 Unit 5 Constructed Response Add and Subtract Fractions I would need to subtract what they have left from the total ice cream they made during June. 5 3 1 b. Student gives correct answer: 20 6 + 8 6 − 5 6 c. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s work for 1 accuracy in using the strategy); 24 6
1 1
8. a. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s work for 8 accuracy in using the strategy); 268 12 b. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s 6 work for accuracy in using the strategy); 94 12
1
Test Total
30
Copyright © Swun Math Grade 4 Unit 5 Constructed Response Rubric, Page 4
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Common Core State Standard
4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring 1. Decompose Fractions, to the same whole. Add Fractions by 4.NF.3b: Decompose a fraction into a sum of Joining Parts, fractions with the same denominator in more Subtract Fractions by than one way, recording each decomposition by Separating Parts an equation. Justify decompositions, e.g., by using a visual fraction model. 2. Addition and 4.NF.3c: Add and subtract mixed numbers with Subtraction of Mixed like denominators, e.g., by replacing each mixed Numbers Using number with an equivalent fraction, and/or by Equivalent Fractions using properties of operations and the and Properties of relationship between addition and subtraction. Operations 4.NF.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the 3. Addition and relationship between addition and subtraction. Subtraction Word 4.NF.3d: Solve word problems involving addition Problems and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Standards for Mathematical Practice
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
SMP.1, SMP.2, SMP.4, SMP.5, SMP.6, 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 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 4 Unit 5 Constructed Response Rubric, Page 1
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions Scoring Rubric Question 1. a. Student gives correct answer and shows work by creating a model: 11 (Answers may vary. Check student work for accuracy in decomposing 15) 1
1
1
1
1
1
1
1
1
1
1
Possible answer: 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 b. Student gives correct answer and shows work by creating a model: 11 (Answers may vary. Check student work for accuracy in decomposing 15) 3
2
Points 1
1
6
Possible answer: 15 + 15 + 15 1
5
2. a. Student creates correct answer: 8 + 18 b. Student gives correct answer and shows work by creating a visual 6 model: (Check students model for accuracy); 8 c. Student gives explanation: Answers may vary depending on the model the student created to find the solution. Example: To find my solution I chose to use two circles divided into 8 partitions because I felt it was the best model to show how much of each pie Brad had left over. This allowed me to visualize the quantities he had on each plate and how much pie he would have if he combined the two plates of left over pie together. 3. a. Student gives explanation: After reading through the problem I know that to solve this problem I need to use subtraction to find my solution. I am not told the measurement of the length of ribbon they buy, but I am 7 3 told they use 15 to make one bow and 15 to make the second bow. Looking at these two fractions I noticed they have the same denominator of 15. So 15 represents the whole length of ribbon they have. To find the amount of 15 7
1 1
2
3
15
ribbon they have left over I would need to first subtract 15 from 15 (1 3
whole) and then subtract 15 from the difference. The fraction I get is the amount of ribbon they have left over. b. Student gives correct answer and shows work by creating a number 5 line: (Check students number line for accuracy); 15 4. a. Student gives correct answer and shows work by using equivalent 7 fractions on a number line: (Check students number line for accuracy);3 8 b. Student gives explanation: Using a number line helped me to visualize the location of the equivalent fractions because the number line was divided up into whole ones from zero to seven and each of those wholes Copyright © Swun Math Grade 4 Unit 5 Constructed Response Rubric, Page 2
1
1 3
Total
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions was broken up into eight equal segments. These segments were labeled 1 along the line starting from 8. The equivalent fraction could be seen clearly by the location of the mixed number on the number line. Since the number line gave me the equivalent fractions of the mixed numbers it was then easy to combine these two equivalent fractions on a new number 18 13 31 line. First I located 8 and then I added 8 which was equal to 8 . Based on 7
this location I knew this was the equivalent fraction of 3 8 , which was my final answer. 5. a. Student gives correct answer and shows work using properties of operations and an illustration: (Check students work for accuracy in using 2 the strategy); 2 5 b. Student gives explanation: Answers may vary. Example: Creating an illustration helps me make sense of the problem because when I create the model to represent the mixed numbers it helps me see what parts of the whole number and the fraction are being taken away as I am subtracting. The illustration helps me visualize my answer from using the Property of operations and check that it makes sense. 6. a. Student gives explanation: In the problem I am told Alice is training for a race and she has been training for two weeks. I am given the total miles she runs during the second week but not the distance she ran during her first week of training. However, I am given the increase in miles she ran from the first week to the second week. This mixed number is important because it is the difference in miles between the two weeks. So I can use this to find the miles she ran the first week, by subtracting it from the miles she ran the second week. 5 1 b. Student gives correct answer: 7 7 − 2 7 c. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s work for 4 accuracy in using the strategy); 5 7 7. a. Student gives explanation: In order to find my solution I need to use addition and subtraction because this is a multistep problem. In the 5 problem I am told they first make 20 6 gallons of ice cream and then they 3
make an additional 8 6 gallons, so to find the total they made during the
1
month I need to add the quantities. At the end of the month they have 5 6 gallons left in their inventory, so to find the amount of ice cream they sold Copyright © Swun Math Grade 4 Unit 5 Constructed Response Rubric, Page 3
1
2
3
1 1 3
Grade 4 Unit 5 Constructed Response Add and Subtract Fractions I would need to subtract what they have left from the total ice cream they made during June. 5 3 1 b. Student gives correct answer: 20 6 + 8 6 − 5 6 c. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s work for 1 accuracy in using the strategy); 24 6
1 1
8. a. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s work for 8 accuracy in using the strategy); 268 12 b. Student gives correct answer and shows work by either using a number line, area model, or properties of operations: (Check student’s 6 work for accuracy in using the strategy); 94 12
1
Test Total
30
Copyright © Swun Math Grade 4 Unit 5 Constructed Response Rubric, Page 4
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