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Massachusetts Comprehensive Assessment System

2014, Grade 10 Mathematics

  Question 20: Open-Response no calculator allowed
The children’s pool and the adult pool in a recreation center are both in the shape of right rectangular prisms. In the diagram below, the two rectangles represent the children’s pool and the adult pool.
A diagram of a Children's and Adult pool composed of two rectangles. The Children's pool has a width of x and a length of y.
Define x and y as follows:
  • x = the width, in yards, of the children’s pool
  • y = the length, in yards, of the children’s pool
  1. Write an expression using x and y to represent the area of the children’s pool.
The adult pool has the following measurements:
  • The width of the adult pool is 3 times the width of the children’s pool.
  • The length of the adult pool is 2 times the length of the children’s pool.
  1. Write an expression using x and y to represent the area of the adult pool.
  2. What is the ratio of the area of the children’s pool to the area of the adult pool? Show or explain how you got your answer.
Both of the pools will be filled with water. The depth of the adult pool is 4 times the depth of the children’s pool.
  1. What is the ratio of the volume of water in the children’s pool to the volume of water in the adult pool? 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, volume, and surface area of two- and three-dimensional objects. The student writes expressions to represent the areas of rectangles, and uses ratios to compare the areas of the rectangles and the volumes of rectangular prisms.
4
3 The student response demonstrates a good understanding of the Geometry concepts involved in solving real-world problems involving area, volume, and surface area of two- and three-dimensional objects. 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, volume, and surface area of two- and three-dimensional objects. 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, volume, and surface area of two- and three-dimensional objects.
0 The student response contains insufficient evidence of an understanding of the Geometry concepts involved in solving real-world problems involving area, volume, and surface area of two- and three-dimensional objects 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: August 24, 2015
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