G3 U5 Constructed Response Rubric
Grade 3 Unit 5 Constructed Response Understanding Fractions Scoring Rubric Task
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Understanding Denominators and Numerators; Fractional Size as it Relates to the Whole
3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
MP.1, MP.4, MP.7, MP.8
2. Fractions on a Number Line
3. Fractional Parts in a Set
3.NF.2a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 3.NF.2b: Represent a fraction a/b on a number line diagram by marking off lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
MP.1, MP.3, MP.4, MP.7, MP.8
MP.1, MP.3, MP.4, MP.6, MP.7, MP.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 3 Unit 5 Constructed Response Rubric, Page 1
Grade 3 Unit 5 Constructed Response Understanding Fractions Scoring Rubric 1. a. Student partitions the rectangle into sixths correctly. Partitions may vary, but must show six equal portions. See sample answer for part b. 𝟓
b. Student shades 𝟔 of the rectangle. Any 5 of the 6 portions may be shaded. Sample answer: 1 6
1 6
1 6
1 6
1 6
1 6
c. Student gives an accurate explanation. Wording may vary. Sample explanation: A fraction represents part of a whole. It is made up of a denominator and a numerator. The numerator is the top number in a fraction, and represents the number of fractional parts that are shaded. The denominator is the bottom number in a fraction, and represents the total number of equal parts the whole is divided into. 2. a. Student creates a correct diagram: See example below. 1 8
1 8
1 8 1 8
Points 1
1
1
1
1 8 1 8
1 8
1 8
b. Student gives accurate explanations: Wording may vary. Sample explanations: Since two fewer people are coming to the office party now, she needs to cut the cookie cake into 6 equal pieces. These slices will be larger because she is cutting the cookie cake into fewer pieces than before.
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 2
2
Total
Grade 3 Unit 5 Constructed Response Understanding Fractions c. Student creates an accurate diagram: See example below. 1 1 6
1 6
1 6
1 6 1 6
1 6
d. Student provides the correct answer: 3 slices were eaten. 3. a. Student gives an accurate explanation: Wording may vary. Sample explanation: The 8 flashcards will not be the same size. I know this because Mark and Amy cut the flashcards from two differently sized pieces of paper. Even though papers were cut into fourths, the cards cut from the large construction paper will be bigger than the cards cut from the small index card. The flashcards cut from the large construction paper will be bigger than the flashcards cut from the small index card. b. Student creates accurate diagrams: See example below. Large Construction Paper: 1 4
1 4
1 4
1 4
Small Index Card: 1 4
1 4
1 4
1 4
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 3
1 1
2
Grade 3 Unit 5 Constructed Response Understanding Fractions 4. a. Student gives an accurate explanation. Wording may vary. Sample explanation: Jordan’s number line is not correct. He divided the number line into eighths correctly, but he did not label each section of the number 1 line correctly. He labeled each eighth on the number line as 8, instead of labeling in increasing order. The number line should show all the fractions, 1 2 3 least to greatest, from 0 to 1. Each section should be labeled 8, 8, 8 and so on until reaching one whole. b. Student creates an accurate number line: See example below.
1
1
0
1
2
3
4
5
6
7
8
8
8
8
8
8
8
1
5. a. Student marks the correct locations of the numbers on the number line: 3
1
4 1
0
1 4
1
2
1
1
2
2
b. Student gives accurate explanations: The number 1¼ is closer to 1 than 2 since it falls between 1 and 1½, as shown on my number line. The number ¾ is also closer to 1 than 0 since it lies between ½ and 1 on the number line. 6. a. Student creates an accurate number line:
0
2
2
1
1
2
3
4
5
6
6
6
6
6
1
b. Student creates an accurate number line: 1
0
1
2
3
4
4
4
1
c. Student gives an accurate explanation: Wording may vary. Sample explanation: A girl will run a farther distance than a boy. The girls divided their mile into four equal parts, and the boys divided their mile into six Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 4
1
Grade 3 Unit 5 Constructed Response Understanding Fractions equal parts. The girls must each run farther to get to the next girl in the relay race than the boys need to run to get to the next boy. The greater number of sections in a fraction, the smaller the value of the fraction. 7. a. Student gives an accurate explanation: Wording may vary. Sample answer: This is one set of eight equally sized stars. Six of the eight stars are shaded gray, and two are not shaded at all. 6
2
8
8
b. Student gives correct answers: Shaded stars = ; Unshaded stars = 8. a. Student gives the correct answer:
3
2 1
8 5
b. Student gives the correct answer: 9 c. Student gives an accurate explanation: Wording may vary. Sample explanation: The set I worked with in this problem was different than the set I worked with in question 7 because this set had different shapes. In question 7 all the shapes were the same and they were either shaded or unshaded. However, in this problem I was given a set that had two different shapes that were either shaded or unshaded. 9. a. Student creates accurate models for both games: Models may vary. Sample models:
Water Balloon Toss Model: Relay Race Model: 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8
1
1 1
1
1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8
Fraction of the Total Boys Water Balloon Toss:
5 8
Relay Races:
3 8
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 5
1
Grade 3 Unit 5 Constructed Response Understanding Fractions a. Student creates accurate models for both games: Models may vary. Sample models:
1
Water Balloon Toss Model: Relay Race Model: 1 1 1 1 1 1 6 6 6 6 6 6
1 1 1 1 1 1 6 6 6 6 6 6
Fraction of the Total Boys Water Balloon Toss:
3 6
Relay Races:
3 6
1
Total
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30
Common Core State Standard for Mathematical Content (MC)
Standards for Mathematical Practice (MP)
1. Understanding Denominators and Numerators; Fractional Size as it Relates to the Whole
3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
MP.1, MP.4, MP.7, MP.8
2. Fractions on a Number Line
3. Fractional Parts in a Set
3.NF.2a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 3.NF.2b: Represent a fraction a/b on a number line diagram by marking off lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
MP.1, MP.3, MP.4, MP.7, MP.8
MP.1, MP.3, MP.4, MP.6, MP.7, MP.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 3 Unit 5 Constructed Response Rubric, Page 1
Grade 3 Unit 5 Constructed Response Understanding Fractions Scoring Rubric 1. a. Student partitions the rectangle into sixths correctly. Partitions may vary, but must show six equal portions. See sample answer for part b. 𝟓
b. Student shades 𝟔 of the rectangle. Any 5 of the 6 portions may be shaded. Sample answer: 1 6
1 6
1 6
1 6
1 6
1 6
c. Student gives an accurate explanation. Wording may vary. Sample explanation: A fraction represents part of a whole. It is made up of a denominator and a numerator. The numerator is the top number in a fraction, and represents the number of fractional parts that are shaded. The denominator is the bottom number in a fraction, and represents the total number of equal parts the whole is divided into. 2. a. Student creates a correct diagram: See example below. 1 8
1 8
1 8 1 8
Points 1
1
1
1
1 8 1 8
1 8
1 8
b. Student gives accurate explanations: Wording may vary. Sample explanations: Since two fewer people are coming to the office party now, she needs to cut the cookie cake into 6 equal pieces. These slices will be larger because she is cutting the cookie cake into fewer pieces than before.
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 2
2
Total
Grade 3 Unit 5 Constructed Response Understanding Fractions c. Student creates an accurate diagram: See example below. 1 1 6
1 6
1 6
1 6 1 6
1 6
d. Student provides the correct answer: 3 slices were eaten. 3. a. Student gives an accurate explanation: Wording may vary. Sample explanation: The 8 flashcards will not be the same size. I know this because Mark and Amy cut the flashcards from two differently sized pieces of paper. Even though papers were cut into fourths, the cards cut from the large construction paper will be bigger than the cards cut from the small index card. The flashcards cut from the large construction paper will be bigger than the flashcards cut from the small index card. b. Student creates accurate diagrams: See example below. Large Construction Paper: 1 4
1 4
1 4
1 4
Small Index Card: 1 4
1 4
1 4
1 4
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 3
1 1
2
Grade 3 Unit 5 Constructed Response Understanding Fractions 4. a. Student gives an accurate explanation. Wording may vary. Sample explanation: Jordan’s number line is not correct. He divided the number line into eighths correctly, but he did not label each section of the number 1 line correctly. He labeled each eighth on the number line as 8, instead of labeling in increasing order. The number line should show all the fractions, 1 2 3 least to greatest, from 0 to 1. Each section should be labeled 8, 8, 8 and so on until reaching one whole. b. Student creates an accurate number line: See example below.
1
1
0
1
2
3
4
5
6
7
8
8
8
8
8
8
8
1
5. a. Student marks the correct locations of the numbers on the number line: 3
1
4 1
0
1 4
1
2
1
1
2
2
b. Student gives accurate explanations: The number 1¼ is closer to 1 than 2 since it falls between 1 and 1½, as shown on my number line. The number ¾ is also closer to 1 than 0 since it lies between ½ and 1 on the number line. 6. a. Student creates an accurate number line:
0
2
2
1
1
2
3
4
5
6
6
6
6
6
1
b. Student creates an accurate number line: 1
0
1
2
3
4
4
4
1
c. Student gives an accurate explanation: Wording may vary. Sample explanation: A girl will run a farther distance than a boy. The girls divided their mile into four equal parts, and the boys divided their mile into six Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 4
1
Grade 3 Unit 5 Constructed Response Understanding Fractions equal parts. The girls must each run farther to get to the next girl in the relay race than the boys need to run to get to the next boy. The greater number of sections in a fraction, the smaller the value of the fraction. 7. a. Student gives an accurate explanation: Wording may vary. Sample answer: This is one set of eight equally sized stars. Six of the eight stars are shaded gray, and two are not shaded at all. 6
2
8
8
b. Student gives correct answers: Shaded stars = ; Unshaded stars = 8. a. Student gives the correct answer:
3
2 1
8 5
b. Student gives the correct answer: 9 c. Student gives an accurate explanation: Wording may vary. Sample explanation: The set I worked with in this problem was different than the set I worked with in question 7 because this set had different shapes. In question 7 all the shapes were the same and they were either shaded or unshaded. However, in this problem I was given a set that had two different shapes that were either shaded or unshaded. 9. a. Student creates accurate models for both games: Models may vary. Sample models:
Water Balloon Toss Model: Relay Race Model: 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8
1
1 1
1
1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8
Fraction of the Total Boys Water Balloon Toss:
5 8
Relay Races:
3 8
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 5
1
Grade 3 Unit 5 Constructed Response Understanding Fractions a. Student creates accurate models for both games: Models may vary. Sample models:
1
Water Balloon Toss Model: Relay Race Model: 1 1 1 1 1 1 6 6 6 6 6 6
1 1 1 1 1 1 6 6 6 6 6 6
Fraction of the Total Boys Water Balloon Toss:
3 6
Relay Races:
3 6
1
Total
Copyright © Swun Math Grade 3 Unit 5 Constructed Response Rubric, Page 6
30
