




Massachusetts Comprehensive Assessment System
2013, Grade 6 Mathematics
Question 18: OpenResponse 

Reporting Category: Expressions and Equations Standard: 6.P.6  Produce and interpret graphs that represent the relationship between two variables in everyday situations.
Standard: Mathematics.6.EE.3.09  Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

A table can be used to show the relationship between the number of hours a painter works painting and the total amount the painter charges for painting. In your Student Answer Booklet, copy the table below about the painter’s charges. Painter’s Charges Number of Hours (h)  1  2  3  4  5  Total Charge for Painting (c)       The painter charges $25 per hour to paint a room. Complete the table you copied in your Student Answer Booklet to show the relationship between h, the number of hours the painter works, and c, the total amount, in dollars, the painter charges for painting.
 Write an equation that can be used to find c, the total charge for h hours of painting.
It took the painter 13 hours to paint a room. What is the total amount, in dollars, the painter charged for painting the room? 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 two quantities in a realworld problem that change in relationship to one another; writing an equation to express one quantity in terms of the other; and analyzing the relationship between dependent and independent variables using graphs and tables, and relating these to the equation. The student completes a table about the relationship between the numbers of hours worked and the amount charged, writes an equation about the relationship, and solves the equation for a given number of hours. 
4 
3 
The student response demonstrates a good understanding of the Expressions and Equations concepts involved in using variables to represent two quantities in a realworld problem that change in relationship to one another; writing an equation to express one quantity in terms of the other; and analyzing the relationship between dependent and independent variables using graphs and tables, and relating these to the equation. 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 two quantities in a realworld problem that change in relationship to one another; writing an equation to express one quantity in terms of the other; and analyzing the relationship between dependent and independent variables using graphs and tables, and relating these to the equation. 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 two quantities in a realworld problem that change in relationship to one another; writing an equation to express one quantity in terms of the other; and analyzing the relationship between dependent and independent variables using graphs and tables, and relating these to the equation. 
0 
The student response contains insufficient evidence of an understanding of the Expressions and Equations concepts involved in using variables to represent two quantities in a realworld problem that change in relationship to one another; writing an equation to express one quantity in terms of the other; and analyzing the relationship between dependent and independent variables using graphs and tables, and relating these to the equation to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 6 Mathematics
 Question 11: Statistics and Probability
 Question 18: Expressions and Equations
Return to the MCAS 2013 Student Work Directory
Last Updated: December 24, 2015


