Massachusetts Comprehensive Assessment System

2018, Grade 10 Mathematics

Question 17: Open-Response

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(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.

Stacey will paint the four walls of a room. Two walls each have a length of 20 feet, and the other two walls each have a length of 16 feet.

The expression below represents the total perimeter, in feet, of the room.

$2 (20 + 16)$

What is the total perimeter, in feet, of the room? Show or explain how you got your answer.

The room has 2 windows and 3 doors. Each window is 4 feet high and 3 feet wide, and each door is 7 feet high and 3 feet wide.

The expression below represents the total area, in square feet, of the windows and doors in the room.

$2 (4 \cdot 3) + 3 (7 \cdot 3)$

What is the total area, in square feet, of the windows and doors in the room? Show or explain how you got your answer.

The height of each of the walls in the room is 8 feet. Stacey will not paint the windows or doors.

The expression below represents the total area, in square feet, that Stacey will paint.

$2 (20 \cdot 8 + 16 \cdot 8) - [2 (4 \cdot 3) + 3 (7 \cdot 3)]$

What is the total area, in square feet, that Stacey will paint? Show or explain how you got your answer.

Each gallon of paint covers a total area of 300 square feet. Stacey will cover the walls with 2 layers of paint.

The expression below represents the total number of gallons of paint Stacey will need to paint the room with 2 layers of paint.

$\frac{2 \{2 (20 \cdot 8 + 16 \cdot 8) - [2 (4 \cdot 3) + 3 (7 \cdot 3)]\}}{300}$

Each gallon of paint costs $26. Stacey must purchase full gallons of paint.

What is the total cost, in dollars, of the gallons of paint Stacey will need to purchase to paint the room? 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 mathematical problems involving the four operations. The student evaluates numerical expressions that represent quantities in a real-life situation.
4
3	The student response demonstrates a good understanding of the Number and Quantity concepts involved in solving mathematical problems involving the four operations. 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 mathematical problems involving the four operations. 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 mathematical problems involving the four operations.
0	The student response contains insufficient evidence of an understanding of the Number and Quantity concepts involved in solving mathematical problems involving the four operations 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: Algebra and Functions

Question 21: Algebra and Functions

Question 36: Geometry

Question 41: Statistics and Probability

Question 42: Geometry

Return to the MCAS 2018 Student Work Directory

Last Updated: March 11, 2024