




Massachusetts Comprehensive Assessment System
2012, Grade 6 Mathematics
Question 18: OpenResponse 

Reporting Category: Number Sense and Operations Standard: 6.N.4  Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line.

Ms. Diaz works at a zoo. She created an exhibit with the animals listed in the table below. Animal ExhibitType of Animal  Number  elephant  8  giraffe  12  rhino  4   What fraction of the animals are giraffes? Simplify your answer to lowest terms. Show or explain how you got your answer.
Ms. Diaz plans to add more animals to the exhibit. She will add 2 more elephants.
 She will add more giraffes and rhinos so that the ratio of elephants to other animals is the same as before.
 What is the new total number of animals that will be in the exhibit? 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 Number Sense and Operation concepts involved in understanding fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. The student uses proportional reasoning to determine correct amounts based on a given ratio. 
4 
3 
The student response demonstrates a good understanding of the Number Sense and Operation concepts involved in understanding fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. 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 Number Sense and Operation concepts involved in understanding fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. 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 Number Sense and Operation concepts involved in understanding fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. 
0 
The student response contains insufficient evidence of an understanding of the Number Sense and Operation concepts involved in understanding fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line 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 28, 2016


