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# Massachusetts Comprehensive Assessment System

## 2013, Grade 5 Mathematics

 Question 19: Open-Response Reporting Category: Number and Operations-FractionsStandard: 5.N.13 - Accurately and efficiently add and subtract positive fractions and mixed numbers with like denominators and with unlike denominators (2, 4, 5, 10 only); multiply positive fractions with whole numbers. Simplify fractions in cases when both the numerator and the denominator have 2, 3, 4, 5, or 10 as a common factor.Standard: Mathematics.5.NF.1.01 - 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 like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Brenda is making tree costumes for a play. The list below shows the amounts of the different colors of cloth Brenda will use to make one tree costume. yards brown cloth yards orange cloth yard yellow clothWhat is the difference, in yards, between the amount of orange cloth and the amount of brown cloth that Brenda will use to make one tree costume? Show or explain how you got your answer.Brenda plans to use brown cloth for the trunk and branches of the tree, and orange and yellow cloth for the leaves.What is the total amount of cloth, in yards, Brenda will use to make the leaves of one tree costume? Show or explain how you got your answer.Brenda wants to make two tree costumes.What is the total amount of cloth, in yards, Brenda will use to make two tree costumes? Show or explain how you got your answer.

### Scoring Guide and Sample Student WorkSelect a score point in the table below to view the sample student response.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Number and Operations-Fractions concepts involved in adding and subtracting 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 like denominators.
4
3
The student response demonstrates a good understanding of the Number and Operations-Fractions concepts involved in adding and subtracting 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 like denominators. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result, the response merits 3 points.
2
The student response demonstrates a fair understanding of the Number and Operations-Fractions concepts involved in adding and subtracting 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 like denominators. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points.
1
The student response demonstrates a minimal understanding of the Number and Operations-Fractions concepts involved in adding and subtracting 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 like denominators.
0
The student response contains insufficient evidence of an understanding of the Number and Operations-Fractions concepts involved in adding and subtracting 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 like denominators to merit any points.

Note: There are 2 sample student responses for Score Point 4.

### Grade 5 Mathematics

Question 5:
Question 19:

Return to the MCAS 2013 Student Work Directory

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