Massachusetts Comprehensive Assessment System
2012, Grade 7 Mathematics
Question 11: OpenResponse 

Reporting Category: Patterns, Relations, and Algebra Standard: 7.P.1  Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding. This standard is intentionally the same as standard 8.P.1.
Standard: Mathematics.7.EE.2.04  Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 
The first five terms in a number pattern are shown below.7, 10, 13, 16, 19The pattern continues using the same rule. What is the next term in the pattern? Show or explain how you got your answer.
 What is the 20th term in the pattern? Show or explain how you got your answer.
 Write an expression that can be used to find the value of the nth term in the pattern.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Patterns, Relations, and Algebra concepts involved in extending and analyzing patterns. The student identifies designated terms in a pattern and then creates an expression that represents any term in the pattern. 
4 
3 
The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in extending and analyzing patterns. 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 Patterns, Relations, and Algebra concepts involved in extending and analyzing patterns. 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 Patterns, Relations, and Algebra concepts involved in extending and analyzing patterns. 
0 
The student response contains insufficient evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in extending and analyzing patterns to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
None found...
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Last Updated: September 18, 2014
