G5 U5 Constructed Response Rubric
Grade 5 Unit 5 Constructed Response Subtracting Fractions Scoring Rubric Task
Common Core State Standard for Mathematical Content (MC)
5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an 1. Subtracting Fractions equivalent sum or difference of fractions with with Unlike like denominators. Denominators Using 5.NF.2: Solve word problems involving addition Models and the Area and subtraction of fractions referring to the Model (No same whole, including cases of unlike Regrouping) denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with 2. Subtracting Fractions like denominators. with Unlike 5.NF.2: Solve word problems involving addition Denominators Using a and subtraction of fractions referring to the Number Line and an same whole, including cases of unlike Algorithm denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 3. Subtracting Fractions 5.NF.1: Add and subtract fractions with unlike with Unlike denominators (including mixed numbers) by Denominators Using: replacing given fractions with equivalent an Area Model and fractions in such a way as to produce an Algorithm (With equivalent sum or difference of fractions with Regrouping) like denominators. Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.4, MP.5, MP.6, MP.8
MP.1, MP.2, MP.3, MP.4, MP.6, MP.7, MP.8
MP.1, MP.2, MP.4, MP.6, MP.7, MP.8
Grade 5 Unit 5 Constructed Response Subtracting Fractions 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 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 5 Constructed Response Rubric, Page 2
Grade 5 Unit 5 Constructed Response Subtracting Fractions Scoring Rubric Question 8
1
1. a. Student gives correct answer: 9 − 3 = 𝑥 b. Student gives correct answer, labels estimate, and shows work by creating an accurate visual model or number line: (Check student’s visual 5 model or number line for accuracy) 9 Student gives an accurate explanation. Wording may vary. Sample explanation: 5 1 2. a. Student creates correct answer: 3 8 − 2 6 = 𝑥 b. Student gives correct answer and shows work by using an accurate area 11 model: (Check student’s model for accuracy); 𝟏 24 mile c. Student gives an accurate explanation. Response and wording may vary. Sample explanation: Using an area model helped me represent the problem and find the common denominator so I could subtract the fractions. After I drew the same number of vertical and horizontal lines 5 15 onto my 2 models, I could see 3 8 was equal to 3 24 and 1
Points 1 2
1 1
2
4
2 6 was equal to 2 24. Then it was clear to me I could subtract the fractional 15
4
pieces because the minuend, 24 ,is greater than the subtrahend, 15. I could subtract the whole numbers because 3 is greater than 1. My answer of a 11 1 24 mile difference between the bike ride the first week and the second week made sense after following this process. 7
1
5
3. a. Student gives correct answer: 10 8 − 6 4 = 4 8 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to make the number sentence true the first step I took was to look at the whole numbers given in the equation. In the equation I have some number minus 6 equals 4. The missing number here was 10 because 10 minus six equals four and this number was in the number bank. I then looked at the denominators of the fractions in the equation. The denominator in the answer portion of the equation was eight and I noticed the denominator of the fraction in the subtrahend was four, which is a factor of eight. Due to this it made sense for the denominator of the fraction in the minuend to be eight, because eight would be the Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 3
2 2
Total
Grade 5 Unit 5 Constructed Response Subtracting Fractions common denominator I would need to find to solve this equation if I had not been given the answer. My next step was to find the numerator of the fraction in the subtrahend. The last two numbers I had left were 1 and 5. Five did not make sense in this case because it would make the fraction in the subtrahend an improper fraction, so the best choice here was 1. This 1 number made sense because the fraction 4 would need to be multiplied by 2
2
2 to get the common denominator of eight in the fraction 8. Subtracting 8 7
5
from 8 would equal 8, which filled in the last value of the numerator in the answer. 4. a. Student gives correct answer and shows work by using equivalent fractions on an accurate number line: (Check student’s number line for 1 accuracy); 15 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my answer using a number line, I first had to create number lines to model each of the fractions in the expression. On the first number line, I sectioned it into three equal parts to represent the 2 denominator of thirds, and marked the location of 3. I divided the second number line into 5 parts to represent the denominator of fifths and I 3 marked the location of 5. My next step was to divide each unit fraction of one number line by the denominator of the other fraction. By doing this there was a total of 15 tick marks on each number line. On the first 2 10 number line I found 3 was equal to 15, and on the second number line I 3
9
found was equal to . Comparing these two new fractions I have to 5 15 subtract, I found they now had a common denominator. With a common 1 denominator, I could subtract them to find my answer of 15.
Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 4
1 2
Grade 5 Unit 5 Constructed Response Subtracting Fractions 5. a. Student gives correct answer and an accurate explanation. Wording may vary. Sample explanation: After analyzing their work and their answer, I determined the number of pounds of pretzels Stella and Joel found is incorrect. I know they are incorrect because their process for finding the total number of pretzels is incorrect. From their work I noticed they subtracted all three mixed numbers together without finding a common denominator. Before subtracting the fractions they should have found a common denominator. After finding the common denominator and multiplying each fraction by the number necessary to get the denominator, they could then subtract the mixed numbers together. To do this they should have subtracted the numerators together and the whole numbers together but not the denominators as they did in the problem. After doing this they could go on to simplify the fraction in their answer if necessary. b. Student gives correct answer and shows work using a standard 1 algorithm: (Check student’s work for accuracy in using strategy); 2
2
6. a. Student gives correct answers and shows accurate work using a number line or a standard algorithm: (Check student’s work for accuracy 1 1 in using the strategy.) Samantha: 20 6 minutes; Jerry: 19 12 minutes b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to figure out how to solve this problem I had to understand certain pieces of information given to me in the scenario. In this scenario I was given the time it took Ted to finish the race, but not the times for Samantha and Jerry. However, I was told each racer’s placing in the race from first to third and the time each racer came in behind the other. With this information I knew I would have to work backwards and find each racer’s time from Ted to Samantha, and then from Samantha to Jerry. First I had to subtract the minutes Ted came in after Samantha from 2 his race time of 21 3 minutes. The resulting time was Samantha’s race time. Then to find Jerry’s time I had to subtract the minutes Samantha 1 came in after Jerry from her race time of 20 6 minutes. The difference was
2
1
36
2
1
Jerry’s first place winning time of 19 12 minutes. 2
3
7. a. Student gives correct answer: 4 3 − 1 4 = 𝑥 b. Student gives correct answer and shows work by using an accurate area model: (Check student’s work for accuracy in using the strategy); 11 2 12 Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 5
1 1
Grade 5 Unit 5 Constructed Response Subtracting Fractions 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my solution I need to use addition and subtraction because this is a multistep problem. In the problem I am told 2 5 Evan and his dad have 3 5 feet of rope and then they buy an additional 2 6 feet, so to find the total they have before heading out on their trip I would need to add the quantities. I am then told when they come back home 8 they have 2 15 feet of rope left. So to find the amount of rope they have
2
8
left, I would need to subtract 2 15feet from the total feet of rope they had before they left on their trip. 2
5
8
b. Student gives correct answer: (3 5 + 2 6) − 2 15 = 𝑥 c. Student gives correct answer and shows work by using a standard 7 algorithm: (Check student’s work for accuracy in using the strategy); 3 10
1 1
9. Student gives an accurate explanation:a. Student gives correct answer 7 and shows work: 20 12 b. Student gives correct answer and shows work using an area model or 5 standard algorithm: (Check student’s work for accuracy); 9 12
1 2
Total
Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 6
30
Common Core State Standard for Mathematical Content (MC)
5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an 1. Subtracting Fractions equivalent sum or difference of fractions with with Unlike like denominators. Denominators Using 5.NF.2: Solve word problems involving addition Models and the Area and subtraction of fractions referring to the Model (No same whole, including cases of unlike Regrouping) denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with 2. Subtracting Fractions like denominators. with Unlike 5.NF.2: Solve word problems involving addition Denominators Using a and subtraction of fractions referring to the Number Line and an same whole, including cases of unlike Algorithm denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 3. Subtracting Fractions 5.NF.1: Add and subtract fractions with unlike with Unlike denominators (including mixed numbers) by Denominators Using: replacing given fractions with equivalent an Area Model and fractions in such a way as to produce an Algorithm (With equivalent sum or difference of fractions with Regrouping) like denominators. Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 1
Standards for Mathematical Practice (MP)
MP.1, MP.2, MP.4, MP.5, MP.6, MP.8
MP.1, MP.2, MP.3, MP.4, MP.6, MP.7, MP.8
MP.1, MP.2, MP.4, MP.6, MP.7, MP.8
Grade 5 Unit 5 Constructed Response Subtracting Fractions 5.NF.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. 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 5 Constructed Response Rubric, Page 2
Grade 5 Unit 5 Constructed Response Subtracting Fractions Scoring Rubric Question 8
1
1. a. Student gives correct answer: 9 − 3 = 𝑥 b. Student gives correct answer, labels estimate, and shows work by creating an accurate visual model or number line: (Check student’s visual 5 model or number line for accuracy) 9 Student gives an accurate explanation. Wording may vary. Sample explanation: 5 1 2. a. Student creates correct answer: 3 8 − 2 6 = 𝑥 b. Student gives correct answer and shows work by using an accurate area 11 model: (Check student’s model for accuracy); 𝟏 24 mile c. Student gives an accurate explanation. Response and wording may vary. Sample explanation: Using an area model helped me represent the problem and find the common denominator so I could subtract the fractions. After I drew the same number of vertical and horizontal lines 5 15 onto my 2 models, I could see 3 8 was equal to 3 24 and 1
Points 1 2
1 1
2
4
2 6 was equal to 2 24. Then it was clear to me I could subtract the fractional 15
4
pieces because the minuend, 24 ,is greater than the subtrahend, 15. I could subtract the whole numbers because 3 is greater than 1. My answer of a 11 1 24 mile difference between the bike ride the first week and the second week made sense after following this process. 7
1
5
3. a. Student gives correct answer: 10 8 − 6 4 = 4 8 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to make the number sentence true the first step I took was to look at the whole numbers given in the equation. In the equation I have some number minus 6 equals 4. The missing number here was 10 because 10 minus six equals four and this number was in the number bank. I then looked at the denominators of the fractions in the equation. The denominator in the answer portion of the equation was eight and I noticed the denominator of the fraction in the subtrahend was four, which is a factor of eight. Due to this it made sense for the denominator of the fraction in the minuend to be eight, because eight would be the Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 3
2 2
Total
Grade 5 Unit 5 Constructed Response Subtracting Fractions common denominator I would need to find to solve this equation if I had not been given the answer. My next step was to find the numerator of the fraction in the subtrahend. The last two numbers I had left were 1 and 5. Five did not make sense in this case because it would make the fraction in the subtrahend an improper fraction, so the best choice here was 1. This 1 number made sense because the fraction 4 would need to be multiplied by 2
2
2 to get the common denominator of eight in the fraction 8. Subtracting 8 7
5
from 8 would equal 8, which filled in the last value of the numerator in the answer. 4. a. Student gives correct answer and shows work by using equivalent fractions on an accurate number line: (Check student’s number line for 1 accuracy); 15 b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my answer using a number line, I first had to create number lines to model each of the fractions in the expression. On the first number line, I sectioned it into three equal parts to represent the 2 denominator of thirds, and marked the location of 3. I divided the second number line into 5 parts to represent the denominator of fifths and I 3 marked the location of 5. My next step was to divide each unit fraction of one number line by the denominator of the other fraction. By doing this there was a total of 15 tick marks on each number line. On the first 2 10 number line I found 3 was equal to 15, and on the second number line I 3
9
found was equal to . Comparing these two new fractions I have to 5 15 subtract, I found they now had a common denominator. With a common 1 denominator, I could subtract them to find my answer of 15.
Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 4
1 2
Grade 5 Unit 5 Constructed Response Subtracting Fractions 5. a. Student gives correct answer and an accurate explanation. Wording may vary. Sample explanation: After analyzing their work and their answer, I determined the number of pounds of pretzels Stella and Joel found is incorrect. I know they are incorrect because their process for finding the total number of pretzels is incorrect. From their work I noticed they subtracted all three mixed numbers together without finding a common denominator. Before subtracting the fractions they should have found a common denominator. After finding the common denominator and multiplying each fraction by the number necessary to get the denominator, they could then subtract the mixed numbers together. To do this they should have subtracted the numerators together and the whole numbers together but not the denominators as they did in the problem. After doing this they could go on to simplify the fraction in their answer if necessary. b. Student gives correct answer and shows work using a standard 1 algorithm: (Check student’s work for accuracy in using strategy); 2
2
6. a. Student gives correct answers and shows accurate work using a number line or a standard algorithm: (Check student’s work for accuracy 1 1 in using the strategy.) Samantha: 20 6 minutes; Jerry: 19 12 minutes b. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to figure out how to solve this problem I had to understand certain pieces of information given to me in the scenario. In this scenario I was given the time it took Ted to finish the race, but not the times for Samantha and Jerry. However, I was told each racer’s placing in the race from first to third and the time each racer came in behind the other. With this information I knew I would have to work backwards and find each racer’s time from Ted to Samantha, and then from Samantha to Jerry. First I had to subtract the minutes Ted came in after Samantha from 2 his race time of 21 3 minutes. The resulting time was Samantha’s race time. Then to find Jerry’s time I had to subtract the minutes Samantha 1 came in after Jerry from her race time of 20 6 minutes. The difference was
2
1
36
2
1
Jerry’s first place winning time of 19 12 minutes. 2
3
7. a. Student gives correct answer: 4 3 − 1 4 = 𝑥 b. Student gives correct answer and shows work by using an accurate area model: (Check student’s work for accuracy in using the strategy); 11 2 12 Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 5
1 1
Grade 5 Unit 5 Constructed Response Subtracting Fractions 8. a. Student gives an accurate explanation. Wording may vary. Sample explanation: In order to find my solution I need to use addition and subtraction because this is a multistep problem. In the problem I am told 2 5 Evan and his dad have 3 5 feet of rope and then they buy an additional 2 6 feet, so to find the total they have before heading out on their trip I would need to add the quantities. I am then told when they come back home 8 they have 2 15 feet of rope left. So to find the amount of rope they have
2
8
left, I would need to subtract 2 15feet from the total feet of rope they had before they left on their trip. 2
5
8
b. Student gives correct answer: (3 5 + 2 6) − 2 15 = 𝑥 c. Student gives correct answer and shows work by using a standard 7 algorithm: (Check student’s work for accuracy in using the strategy); 3 10
1 1
9. Student gives an accurate explanation:a. Student gives correct answer 7 and shows work: 20 12 b. Student gives correct answer and shows work using an area model or 5 standard algorithm: (Check student’s work for accuracy); 9 12
1 2
Total
Copyright © Swun Math Grade 5 Unit 5 Constructed Response Rubric, Page 6
30
