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# Massachusetts Comprehensive Assessment System

 Question 20: Open-Response Reporting Category: Number and QuantityStandard: 10.N.2 - Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(24 - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems. (AI.N.2) Standard: CCSS.Math.Content.7.EE.B.3 - Solve multi-step real-life 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.$16+{8}^{2}÷4-4$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.$\left(16+{8}^{2}\right)÷4·2-4$Talia found the value of her expression using the following steps:Step 1: $\left(16+64\right)÷4·2-4$Step 2: $80÷4·2-4$Step 3: $80÷8-4$Step 4: $10-4$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.$16+{8}^{2}÷4·2-4$What is the value of Talia's new expression? 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 Number and Quantity concepts involved in solving multi-step 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 multi-step 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 multi-step 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 multi-step 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 multi-step 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.

Question 17:
Question 20:
Question 21:
Question 36:
Question 41:
Question 42: