Massachusetts Comprehensive Assessment System
2012, Grade 10 Mathematics
Question 42: OpenResponse 

Reporting Category: Measurement Standard: 10.M.2  Given the formula, find the lateral area, surface area, and volume of prisms, pyramids, spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface area. 
A monument in the shape of a right square pyramid is located in a park. The park is in the shape of a rectangle. The measurements of the monument and the park are shown in the diagram below.  What is the area, in square meters, of the base of the monument? Show or explain how you got your answer.
 What is the area, in square meters, of the park, not including the base of the monument? Show or explain how you got your answer.
 What is the lateral surface area, in square meters, of the monument? Show or explain how you got your answer.
The height of the monument is 24 meters. What is the volume, in cubic meters, of the monument? 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 Measurement concepts involved in finding the lateral area, surface area, and volume of pyramids. 
4 
3 
The student response demonstrates a good understanding of the Measurement concepts involved in finding the lateral area, surface area, and volume of pyramids. 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 fair understanding of the Measurement concepts involved in finding the lateral area, surface area, and volume of pyramids. 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 only minimal understanding of the Measurement concepts involved in finding the lateral area, surface area, and volume of pyramids. 
0 
The student response contains insufficient evidence of an understanding of the Measurement concepts involved in finding the lateral area, surface area, and volume of pyramids to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Patterns, Relations, and Algebra
 Question 20: Data Analysis, Statistics, and Probability
 Question 21: Number Sense and Operations
 Question 31: Data Analysis, Statistics, and Probability
 Question 41: Patterns, Relations, and Algebra
 Question 42: Measurement
Return to the MCAS 2012 Student Work Directory
Last Updated: August 8, 2017
