




Massachusetts Comprehensive Assessment System
2013, Grade 7 Mathematics
Question 7: OpenResponse 

Reporting Category: Expressions and Equations Standard: 7.P.3  Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations. 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. 
Gerald wants to purchase a tennis racket and some cans of tennis balls. The table below shows the total prices he would pay at a discount store to buy one tennis racket and 1 to 4 cans of tennis balls. Total Prices for Tennis Racket and Cans of Tennis Balls Number of Cans of Tennis Balls  Total Price with Racket  1  $43  2  $46  3  $49  4  $52   Based on the prices in the table, what is the total price for one tennis racket and 6 cans of tennis balls? Show or explain how you got your answer.
 Based on the prices in the table, what is the price for one tennis racket? Show or explain how you got your answer.
 Write an expression that can be used to find the total price for one tennis racket and b cans of tennis balls. Explain your reasoning.
 Gerald purchased one tennis racket and b cans of tennis balls. The total price of his purchase was $70. How many cans of tennis balls did Gerald purchase? Show or explain how you got your answer.

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 Expressions and Equations concepts involved in using variables to represent quantities in a realworld or mathematical problem and constructing simple equations and inequalities to solve problems by reasoning about quantities. The student reasons about the quantities in a table, writes an expression, and then uses the expression in an equation to solve a realworld problem. 
4 
3 
The student response demonstrates a good understanding of the Expressions and Equations concepts involved in using variables to represent quantities in a realworld or mathematical problem and constructing simple equations and inequalities to solve problems by reasoning about quantities. 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 Expressions and Equations concepts involved in using variables to represent quantities in a realworld or mathematical problem and constructing simple equations and inequalities to solve problems by reasoning about quantities. 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 Expressions and Equations concepts involved in using variables to represent quantities in a realworld or mathematical problem and constructing simple equations and inequalities to solve problems by reasoning about quantities. 
0 
The student response contains insufficient evidence of an understanding of the Expressions and Equations concepts involved in using variables to represent quantities in a realworld or mathematical problem and constructing simple equations and inequalities to solve problems by reasoning about quantities to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 7 Mathematics
 Question 7: Expressions and Equations
 Question 21: Ratios and Proportional Relationships
Return to the MCAS 2013 Student Work Directory
Last Updated: June 7, 2011


