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Massachusetts Comprehensive Assessment System

2015, Grade 10 Mathematics

  Question 20: Open-Response no calculator allowed
A puzzle in the shape of a rectangle has six pieces. The puzzle and some of its dimensions are shown in the diagram below.
A rectangle that represents a puzzle is shown. The rectangle is separated into six pieces labeled R, B, P, O, G, and Y. Puzzle pieces R and B are shown in the top section of the rectangle with Piece R labeled ten inches and Piece B labeled five inches. Puzzle piece P is shown in the right section of the rectangle with Piece P labeled twelve inches.  Puzzle pieces Y, G, and O are shown in the bottom section of the rectangle with Piece Y labeled eight inches by four inches; Piece G labeled three inches; and Piece O labeled eight inches.
  1. 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.
  1. What is the area, in square inches, of piece B? Show or explain how you got your answer.
  1. What is the area, in square inches, of piece R? Show or explain how you got your answer.
  1. 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.

ScoreDescription
4 The student response demonstrates an exemplary understanding of the Geometry concepts involved in solving real-world problems involving area of two-dimensional objects composed of triangles and quadrilaterals. The student determines the perimeter of a rectangular puzzle and calculates the area of parallelogram-, trapezoid-, and triangle-shaped pieces.
4
3 The student response demonstrates a good understanding of the Geometry concepts involved in solving real-world problems involving area of two-dimensional 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 real-world problems involving area of two-dimensional 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 real-world problems involving area of two-dimensional objects composed of triangles and quadrilaterals.
0 The student response contains insufficient evidence of an understanding of the Geometry concepts involved in solving real-world problems involving area of two-dimensional 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: September 25, 2017
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