




Massachusetts Comprehensive Assessment System
2012, Grade 10 Mathematics
Question 21: OpenResponse 

Reporting Category: Number Sense and Operations Standard: 10.N.2  Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(2^{4}  1) = 45, 43  5 + 6 = 14; apply such simplifications in the solution of problems. (AI.N.2)

Kim and Sean are playing a mathematics card game for extra credit. Each card in the game has an expression written on it. Kim’s first card is shown below.  What is the value of the expression on Kim’s first card? Show or explain how you got your answer.
Sean’s first card is shown below. What is the value of the expression on Sean’s first card? Show or explain how you got your answer.
For Kim to earn extra credit from the game, she must select a second card that has an expression with a value that is exactly twice the value of the expression on her first card. Which of the following cards shows an expression with a value that is exactly twice the value of the expression on Kim’s card? Show or explain how you got your answer.
Sean’s second card is shown below. For Sean to earn extra credit from the game, he must insert one set of absolute value bars in the expression so that the value of the expression is a negative integer. If Sean inserts the set of absolute value bars correctly, what is one possible value of the expression on Sean’s second card? 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 Number Sense and Operations concepts involved in simplifying numerical expressions involving absolute value and applying such simplifications in the solution of problems. 
4 
3 
The student response demonstrates a good understanding of the Number Sense and Operations concepts involved in simplifying numerical expressions involving absolute value and applying such simplifications in the solution of problems. 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 Number Sense and Operations concepts involved in simplifying numerical expressions involving absolute value and applying such simplifications in the solution of problems. 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 Number Sense and Operations concepts involved in simplifying numerical expressions involving absolute value and applying such simplifications in the solution of problems. 
0 
The student response contains insufficient evidence of an understanding of the Number Sense and Operations concepts involved in simplifying numerical expressions involving absolute value and applying such simplifications in the solution of problems 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 17, 2016


