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# Massachusetts Comprehensive Assessment System

## 2013, Grade 4 Mathematics

 Question 7: Open-Response Reporting Category: Operations and Algebraic ThinkingStandard: 4.P.1 - Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, .... Standard: Mathematics.4.OA.3.05 - Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. The manager at a supermarket arranged 10 rows of cans. He put 2 cans in the first row, 4 cans in the second row, and 6 cans in the third row. The manager continued to add 2 cans to each new row.How many cans did the manager put in the fifth row? Show or explain how you got your answer.What is the total number of cans the manager arranged in all 10 of the rows? Show or explain how you got your answer.Describe the relationship between the row number and the number of cans in the row.

### 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 Operations and Algebraic Thinking concepts involved in generating a number pattern that follows a given rule and identifying apparent features of the pattern that were not explicit in the rule itself. Given a rule, the student extends a pattern, determines the sum of the terms in the pattern, and describes a relationship in the pattern.
4
3 The student response demonstrates a good understanding of the Operations and Algebraic Thinking concepts involved in generating a number pattern that follows a given rule and identifying apparent features of the pattern that were not explicit in the rule itself. 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 Operations and Algebraic Thinking concepts involved in generating a number pattern that follows a given rule and identifying apparent features of the pattern that were not explicit in the rule itself. 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 Operations and Algebraic Thinking concepts involved in generating a number pattern that follows a given rule and identifying apparent features of the pattern that were not explicit in the rule itself.
0 The student response contains insufficient evidence of an understanding of the Operations and Algebraic Thinking concepts involved in generating a number pattern that follows a given rule and identifying apparent features of the pattern that were not explicit in the rule itself to merit any points.

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

### Grade 4 Mathematics

Question 7:
Question 21:

Return to the MCAS 2013 Student Work Directory

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