




Massachusetts Comprehensive Assessment System
2016, Grade 7 Mathematics
Question 21: OpenResponse 

Reporting Category: Expressions and Equations 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. 
Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee of $15 plus $17 per hour to clean a house.  Write an equation that can be used to determine c, the total amount in dollars that the cleaning company charges to clean a house in h hours.
 The cleaning company charged a total of $83 to clean Peter's house. How many hours did it take to clean Peter's house? Show or explain how you got your answer.
A second cleaning company charges $20 per hour to clean a house. The second company does not charge a fixed fee in addition to their hourly rate.  For what number of hours is the total amount charged for cleaning a house the same for both companies? 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 mathematical problem, and constructing simple equations to solve problems by reasoning about the quantities. The student represents a realworld situation with an equation, uses the equation to solve a problem, and then uses the equation to solve a pair of simultaneous equations. 
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 mathematical problem, and constructing simple equations to solve problems by reasoning about the 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 mathematical problem, and constructing simple equations to solve problems by reasoning about the 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 mathematical problem, and constructing simple equations to solve problems by reasoning about the 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 mathematical problem, and constructing simple equations to solve problems by reasoning about the quantities to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 7 Mathematics
 Question 10: Statistics and Probability
 Question 21: Expressions and Equations
Return to the MCAS 2016 Student Work Directory
Last Updated: July 27, 2016


