




Massachusetts Comprehensive Assessment System
2012, Grade 6 Mathematics
Question 12: OpenResponse 

Reporting Category: Measurement Standard: 6.M.3  Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed.
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. 
Jan is using a map to plan a twoday hiking trip. The scale for the map she is using is shown below. Scale  1 inch : mile 
 The distance that Jan will hike on the first day is equal to 12 inches on the map. What is the actual distance, in miles, that Jan will hike on the first day? Show or explain how you got your answer.
 The actual distance that Jan will hike on the second day is miles. What distance on the map, in inches, represents miles? Show or explain how you got your answer.
 Based on the scale Jan used, how many feet are represented by 1 inch on the map? Show or explain how you got your answer. (1 mile = 5280 feet)

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 Measurement concepts involved in solving problems involving proportional relationships and units of measurement in scale models. The student uses the scale on a map to solve problems. 
4 
3 
The student response demonstrates a good understanding of the Measurement concepts involved in solving problems involving proportional relationships and units of measurement in scale models. 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 Measurement concepts involved in solving problems involving proportional relationships and units of measurement in scale models. 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 Measurement concepts involved in solving problems involving proportional relationships and units of measurement in scale models. 
0 
The student response contains insufficient evidence of an understanding of the Measurement concepts involved in solving problems involving proportional relationships and units of measurement in scale models to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 6 Mathematics
 Question 12: Measurement
 Question 18: Number Sense and Operations
Return to the MCAS 2012 Student Work Directory
Last Updated: September 18, 2006


