Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
Massachusetts State Seal
News School/District Profiles School/District Administration Educator Services Assessment/Accountability Family & Community  
 Student Assessment  Accountability, Partnership, & Assistance  Compliance/Monitoring >  
>
>
>
 
 
 
 
 
 
 
 
 
 
>
>
>
>
>
>
>
>
>
>
>

Massachusetts Comprehensive Assessment System

2013, Grade 6 Mathematics

  Question 18: Open-Response no calculator allowed
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)12345
Total Charge for Painting (c)
The painter charges $25 per hour to paint a room.
  1. 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.
  2. 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.
  1. 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.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Expressions and Equations concepts involved in using variables to represent two quantities in a real-world 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 real-world 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 real-world 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 real-world 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 real-world 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: April 17, 2009
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search · Site Index · Policies · Site Info · Contact ESE