




Massachusetts Comprehensive Assessment System
2017, Grade 8 Mathematics
Question 2: ConstructedResponse 

Reporting Category: Expressions and Equations Standard: CCSS.Math.Content.8.EE.A.3  Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^{8} and the population of the world as 7 x 10^{9}, and determine that the world population is more than 20 times larger.
Item Description: Solve a multistep realworld problem involving singledigit numbers multiplied by powers of 10 and the relationships among them. 
Jason is comparing the sizes of Earth, Saturn, and a lacrosse ball. The radius of Earth is approximately 6,378,100 meters.
Part AWhat is the radius of Earth, in meters, written as a singledigit number multiplied by a power of 10?
Enter your answer in the space provided. Enter only your answer.
Part BThe radius of Saturn is approximately $6\times {10}^{7}$ meters.
Use your answer from Part A to estimate how many times greater the radius of Saturn is than the radius of Earth. Show or explain how you got your answer.
Enter your answer and your work or explanation in the space provided.
Part CThe radius of a lacrosse ball is approximately 0.032 meter.
Estimate the radius of a lacrosse ball, in meters, by expressing the radius as a singledigit number multiplied by a power of 10.
Enter your answer in the space provided. Enter only your answer.
Part DUse your answers from Parts A and C to estimate how many times greater the radius of Earth is than the radius of a lacrosse ball. Show or explain how you got your answer.
Enter your answer and your work or explanation in the space provided.

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 Expressions and Equations concepts involved in using numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. The student estimates quantities as a single digit times a power of 10 using either positive or negative exponents, and expresses how many times greater one quantity is than the other. 
4 
3 
The student response demonstrates a good understanding of the Expressions and Equations concepts involved in using numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 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 Expressions and Equations concepts involved in using numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 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 Expressions and Equations concepts involved in using numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. 
0 
The student response contains insufficient evidence of an understanding of the Expressions and Equations concepts involved in using numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 8 Mathematics
 Question 2: Expressions and Equations
Return to the MCAS 2017 Student Work Directory
Last Updated: May 22, 2015


