




Massachusetts Comprehensive Assessment System
2016, Grade 6 Mathematics
Question 12: OpenResponse 

Reporting Category: Geometry Standard: Mathematics.6.G.1.01  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems.

A circular pool is located in the center of a square park. The park, the pool, and some of their dimensions are shown in the diagram below.  What is the radius, in yards, of the pool? Show or explain how you got your answer.
 What is the circumference, in yards, of the pool? Show or explain how you got your answer. (Use 3.14 for π.)
 What is the area, in square yards, of the pool? Show or explain how you got your answer. (Use 3.14 for π.)
The ground in the park surrounding the pool is covered with grass.  What is the total area, in square yards, of the ground in the park that is covered with grass? 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 Geometry concepts involved in using the relationships among radius, diameter, and center of a circle to find its circumference and area. The student finds the area and circumference of a circle and uses the measurements to solve a realworld problem. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in using the relationships among radius, diameter, and center of a circle to find its circumference and area. 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 Geometry concepts involved in using the relationships among radius, diameter, and center of a circle to find its circumference and area. 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 Geometry concepts involved in using the relationships among radius, diameter, and center of a circle to find its circumference and area. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in using the relationships among radius, diameter, and center of a circle to find its circumference and area 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: January 26, 2018


