




Massachusetts Comprehensive Assessment System
2014, Grade 10 Mathematics
Question 17: 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: Mathematics.7.EE.2.03  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.

Ms. Culjak is giving her students their scores on the last math test. She provides each student with an expression that has a value equal to the number of points the student scored on the test.
Leo must score a minimum of 80 points on the test to maintain a B in the class. The expression below represents the number of points Leo scored on the test.  Did Leo score enough points to maintain a B in the class? Show your work or explain how you got your answer.
Gerard estimates that he scored 90 points on the test. The expression below represents the actual number of points Gerard scored on the test. What is the difference between Gerard’s estimate and the actual number of points he scored on the test? Show your work or explain how you got your answer.
Tia was given the expression below to represent the number of points she scored on the test. Tia claims that the expression cannot represent the number of points she scored on the test. Explain why Tia’s claim is correct.
Ms. Culjak confirms that Tia’s claim is correct. She says Tia’s expression is missing one set of parentheses. Ms. Culjak also says that Tia scored 76 points on the test. In your Student Answer Booklet, copy Tia’s expression and insert one set of parentheses in the expression so that the value of the expression is 76.

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 reallife and mathematical problems and assessing the reasonableness of answers. The student finds the values of given expressions, and inserts a set of parentheses into a numerical expression so that the expression simplifies to a given value. 
4 
3 
The student response demonstrates a good understanding of the Number and Quantity concepts involved in solving multistep reallife and mathematical problems and assessing the reasonableness of answers. 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 reallife and mathematical problems and assessing the reasonableness of answers. 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 reallife and mathematical problems and assessing the reasonableness of answers. 
0 
The student response contains insufficient evidence of an understanding of the Number and Quantity concepts involved in solving multistep reallife and mathematical problems and assessing the reasonableness of answers to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Number and Quantity
 Question 20: Geometry
 Question 21: Statistics and Probability
 Question 36: Algebra and Functions
 Question 41: Geometry
 Question 42: Algebra and Functions
Return to the MCAS 2014 Student Work Directory
Last Updated: December 1, 2015


