




Massachusetts Comprehensive Assessment System
2015, Grade 8 Mathematics
Question 10: OpenResponse 

Reporting Category: Expressions and Equations Standard: Mathematics.8.EE.2.05  Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed.

Kate is reading a 500page book. The graph below represents the relationship between the number of hours Kate has spent reading and the number of pages she has read. On the grid in your Student Answer Booklet, copy the xaxis, the yaxis, and the line representing Kate’s reading rate exactly as shown. Be sure to label the line “Kate’s rate.”  At what rate, in pages per hour, is Kate reading? Show or explain how you got your answer.
 What is the total amount of time, in hours, it will take Kate to read the entire 500page book? Show or explain how you got your answer.
Edward is reading the same 500page book. The equation below represents the relationship between y, the number of pages he has read, and x, the number of hours he has spent reading.  On your grid, graph the equation that represents the number of hours that Edward has spent reading and the number of pages he has read. Label the line “Edward’s rate.”
 Edward thinks he will finish reading the book in less time than Kate. Is he correct? 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 graphing proportional relationships and comparing two different proportional relationships represented in different ways. The student interprets the slope of a graph of a proportional relationship as a unit rate, graphs a second proportional relationship, and compares the two graphs. 
4 
3 
The student response demonstrates a good understanding of the Expressions and Equations concepts involved in graphing proportional relationships and comparing two different proportional relationships represented in different ways. 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 graphing proportional relationships and comparing two different proportional relationships represented in different ways. 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 graphing proportional relationships and comparing two different proportional relationships represented in different ways. 
0 
The student response contains insufficient evidence of an understanding of the Expressions and Equations concepts involved in graphing proportional relationships and comparing two different proportional relationships represented in different ways to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 8 Mathematics
 Question 10: Expressions and Equations
 Question 21: Geometry
Return to the MCAS 2015 Student Work Directory
Last Updated: July 30, 2018


