




Massachusetts Comprehensive Assessment System
2015, Grade 10 Mathematics
Question 20: OpenResponse 

Reporting Category: Geometry Standard: 10.M.1  Calculate perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles. Standard: Mathematics.7.G.2.06  Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 
A puzzle in the shape of a rectangle has six pieces. The puzzle and some of its dimensions are shown in the diagram below.  What is the perimeter, in inches, of the puzzle? Show or explain how you got your answer.
The shape of each piece of the puzzle is listed below.  Pieces R and O are trapezoids.
 Pieces Y and G are rectangles.
 Piece B is a parallelogram.
 Piece P is a triangle.
 What is the area, in square inches, of piece B? Show or explain how you got your answer.
 What is the area, in square inches, of piece R? Show or explain how you got your answer.
 What is the area, in square inches, of piece P? 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 Geometry concepts involved in solving realworld problems involving area of twodimensional objects composed of triangles and quadrilaterals. The student determines the perimeter of a rectangular puzzle and calculates the area of parallelogram, trapezoid, and triangleshaped pieces. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in solving realworld problems involving area of twodimensional objects composed of triangles and quadrilaterals. 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 Geometry concepts involved in solving realworld problems involving area of twodimensional objects composed of triangles and quadrilaterals. 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 Geometry concepts involved in solving realworld problems involving area of twodimensional objects composed of triangles and quadrilaterals. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in solving realworld problems involving area of twodimensional objects composed of triangles and quadrilaterals 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: Algebra and Functions
 Question 36: Statistics and Probability
 Question 41: Algebra and Functions
 Question 42: Geometry
Return to the MCAS 2015 Student Work Directory
Last Updated: October 16, 2018


