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Massachusetts Comprehensive Assessment System

2013, Grade 7 Mathematics

  Question 7: Open-Response no calculator allowed
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
  1. 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.
  2. Based on the prices in the table, what is the price for one tennis racket? Show or explain how you got your answer.
  3. 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.
  4. 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.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Expressions and Equations concepts involved in using variables to represent quantities in a real-world 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 real-world 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 real-world 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 real-world 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 real-world 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 real-world 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: February 1, 1997
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