Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
Massachusetts State Seal
Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board  
>
>
>
>
 
 
 
 
 
 
 
 
 
 
>
>
>
>
>
>
>

Massachusetts Comprehensive Assessment System

2015, Grade 8 Mathematics

  Question 10: Open-Response no calculator allowed
Kate is reading a 500-page book. The graph below represents the relationship between the number of hours Kate has spent reading and the number of pages she has read.
Graph titled Reading Rate. The label for the x axis is Time, in hours. The x axis goes from 0 to 6 using a scale of one third year. The label for the y axis is number of pages read. The y axis goes from 0 to 450 using a scale of 25. The graph shows a line that starts at the origin and passes through the point 5, 200.
On the grid in your Student Answer Booklet, copy the x-axis, the y-axis, and the line representing Kate’s reading rate exactly as shown. Be sure to label the line “Kate’s rate.”
  1. At what rate, in pages per hour, is Kate reading? Show or explain how you got your answer.
  1. What is the total amount of time, in hours, it will take Kate to read the entire 500-page book? Show or explain how you got your answer.
Edward is reading the same 500-page 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.
y equals fifty times x
  1. 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.”
  1. 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.

ScoreDescription
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: November 17, 2017
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search·Public Records Requests · A-Z Site Index · Policies · Site Info · Contact ESE