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# Massachusetts Comprehensive Assessment System

 Question 7: Open-Response Reporting Category: Number Sense and OperationsStandard: 4.N.4 - Select, use, and explain models to relate common fractions  (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12) and mixed numbers, find equivalent fractions, mixed numbers, and decimals, and order fractions.  Standard: Mathematics.4.NF.1.01 - Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [Note: Grade 4 expectations in this domain are limited to fractions with denominators 2,3,4,5,6,8,10, 12, and 100.] Chet shaded part of the two large rectangles shown below.Write a fraction that represents the shaded part of the two large rectangles.Write a different number that is equivalent to the fraction you wrote in part (a). Show or explain how you got your answer.In your Student Answer Booklet, draw and shade a picture of rectangles that represents the number . 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 Sense and Operations concepts involved in using models to represent mixed numbers and find equivalent fractions.
4
3 The student response demonstrates a good understanding of the Number Sense and Operations concepts involved in using models to represent mixed numbers and find equivalent fractions.  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 Sense and Operations concepts involved in using models to represent mixed numbers and find equivalent fractions. 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 Sense and Operations concepts involved in using models to represent mixed numbers and find equivalent fractions.
0 The student response contains insufficient evidence of an understanding of the Number Sense and Operations concepts involved in using models to represent mixed numbers and find equivalent fractions to merit any points.

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