Mass.gov
Massachusetts Department of Elementary and Secondary Education
Go to Selected Program Area
Massachusetts State Seal
Students & Families Educators & Administrators Teaching, Learning & Testing Data & Accountability Finance & Funding About the Department Education Board  
>
>
>
>
 
 
 
 
 
 
 
 
 
 
>
>
>
>
>
>
>

Massachusetts Comprehensive Assessment System

2016, Grade 6 Mathematics

  Question 12: Open-Response no calculator allowed
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.
A picture of a park. The park is in the shape of a square, with a side length of thirty yards. There is a pool in the center of the park. The diameter of the pool is ten yards.
  1. What is the radius, in yards, of the pool? Show or explain how you got your answer.
  2. What is the circumference, in yards, of the pool? Show or explain how you got your answer. (Use 3.14 for π.)
  3. 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.
  1. 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.

ScoreDescription
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 real-world 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: May 1, 2001
E-mail this page| Print View| Print Pdf  
Massachusetts Department of Elementary and Secondary Education Search·Public Records Requests · A-Z Site Index · Policies · Site Info · Contact ESE