




Massachusetts Comprehensive Assessment System
2012, Grade 5 Mathematics
Question 21: OpenResponse 

Reporting Category: Patterns, Relations, and Algebra Standard: 5.P.4  Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., inputoutput tables. This standard is intentionally the same as standard 6.P.4. 
Abe stacked boxes onto a truck. Each box he stacked had the same weight. The table below shows the total weight for different numbers of boxes. Total Weight of BoxesNumber of Boxes  Total Weight (in pounds)  2  50  4  100  6  150   What is the total weight, in pounds, of 8 boxes? Show or explain how you got your answer.
 Based on the table, write or describe a rule that can be used to find the weight of n boxes, where n is any number of boxes.
 Is it possible for the total weight of the boxes Abe stacked onto the truck to be exactly 520 pounds? 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 Patterns, Relations, and Algebra concepts involved in representing real situations and mathematical relationships with tables and with rules using words and symbols. The student determines if a scenario is possible based on a model of a real situation. 
4 
3 
The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in representing real situations and mathematical relationships with tables and with rules using words and symbols. 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 Patterns, Relations, and Algebra concepts involved in representing real situations and mathematical relationships with tables and with rules using words and symbols. 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 Patterns, Relations, and Algebra concepts involved in representing real situations and mathematical relationships with tables and with rules using words and symbols. 
0 
The student response contains insufficient evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in representing real situations and mathematical relationships with tables and with rules using words and symbols to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 5 Mathematics
 Question 5: Number Sense and Operations
 Question 21: Patterns, Relations, and Algebra
Return to the MCAS 2012 Student Work Directory
Last Updated: July 13, 2011


