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# Massachusetts Comprehensive Assessment System

Question 2: Constructed-Response
Jason is comparing the sizes of Earth, Saturn, and a lacrosse ball. The radius of Earth is approximately 6,378,100 meters.

#### Part A

What is the radius of Earth, in meters, written as a single-digit number multiplied by a power of 10?

#### Part B

The radius of Saturn is approximately $six times ten to the seventh power$ meters.

#### Part C

The 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 single-digit number multiplied by a power of 10.

#### Part D

Use 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.

### Scoring Guide and Sample Student WorkSelect a score point in the table below to view the sample student response.

ScoreDescription
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.