




Massachusetts Comprehensive Assessment System
2016, Grade 6 Mathematics
Question 8: OpenResponse 

Reporting Category: Ratios and Proportional Relationships Standard: Mathematics.6.RP.1.03  Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 
The table below shows the amount, in pounds, of snow that Andy can remove over time using a shovel. Snow Removal Using a Shovel Time (in minutes)  1  2  3  4  5  6  Snow Removed (in pounds)  80  160  240  320   480   Based on the table, what is the amount, in pounds, of snow that Andy can remove in 5 minutes using a shovel? Show or explain how you got your answer.
On the grid in your Student Answer Booklet, copy the xaxis, the yaxis, and the labels exactly as shown below. On your grid, plot the data from the table to show the amount of snow that Andy can remove over time.
 Based on your graph, what is the amount, in pounds, of snow that Andy can remove in 10 minutes? 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 Ratios and Proportional Relationships concepts involved in making tables of equivalent ratios relating quantities with wholenumber measurements, finding missing values in the tables, and plotting pairs of values on the coordinate plane. The student completes a table and uses the data in the table to draw a graph to solve a realworld problem. 
4 
3 
The student response demonstrates a good understanding of the Ratios and Proportional Relationships concepts involved in making tables of equivalent ratios relating quantities with wholenumber measurements, finding missing values in the tables, and plotting pairs of values on the coordinate plane. 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 Ratios and Proportional Relationships concepts involved in making tables of equivalent ratios relating quantities with wholenumber measurements, finding missing values in the tables, and plotting pairs of values on the coordinate plane. 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 Ratios and Proportional Relationships concepts involved in making tables of equivalent ratios relating quantities with wholenumber measurements, finding missing values in the tables, and plotting pairs of values on the coordinate plane. 
0 
The student response contains insufficient evidence of an understanding of the Ratios and Proportional Relationships concepts involved in making tables of equivalent ratios relating quantities with wholenumber measurements, finding missing values in the tables, and plotting pairs of values on the coordinate plane to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 6 Mathematics
 Question 8: Ratios and Proportional Relationships
 Question 12: Geometry
Return to the MCAS 2016 Student Work Directory
Last Updated: September 13, 2018


