




Massachusetts Comprehensive Assessment System
2017, Grade 10 Mathematics
Question 20: OpenResponse 

Reporting Category: Number and Quantity 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)
Standard: CCSS.Math.Content.7.EE.B.3  Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Stuart wrote the expression shown below.
$16+{8}^{2}\xf744$  What is the value of Stuart's expression? Show or explain how you got your answer.
 In your Student Answer Booklet, insert one set of parentheses into Stuart's expression so that the value of the expression is undefined. Show or explain how you got your answer.
Talia wrote the expression shown below.
$\left(16+{8}^{2}\right)\xf74\xb724$ Talia found the value of her expression using the following steps:
Step 1: $\left(16+64\right)\xf74\xb724$ Step 2: $80\xf74\xb724$ Step 3: $80\xf784$ Step 4: $104$ Step 5: $6$  Is the value that Talia found for her expression correct? Explain your reasoning.
Talia removed the set of parentheses from her expression to create the new expression shown below.
$16+{8}^{2}\xf74\xb724$  What is the value of Talia's new expression? 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 and Quantity concepts involved in solving multistep mathematical problems and applying properties of operations to calculate with numbers in any form. The student assesses the evaluation of a given expression. 
4 
3 
The student response demonstrates a good understanding of the Number and Quantity concepts involved in solving multistep mathematical problems and applying properties of operations to calculate with numbers in any form. 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 Number and Quantity concepts involved in solving multistep mathematical problems and applying properties of operations to calculate with numbers in any form. 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 Number and Quantity concepts involved in solving multistep mathematical problems and applying properties of operations to calculate with numbers in any form. 
0 
The student response contains insufficient evidence of an understanding of the Number and Quantity concepts involved in solving multistep mathematical problems and applying properties of operations to calculate with numbers in any form to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Geometry
 Question 20: Number and Quantity
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2017 Student Work Directory
Last Updated: August 28, 2018


