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# Massachusetts Comprehensive Assessment System

## 2014, Grade 10 Mathematics

 Question 20: Open-Response Reporting Category: GeometryStandard: 10.M.3 - Relate changes in the measurement of one attribute of an object to changes in other attributes, e.g., how changing the radius or height of a cylinder affects its surface area or volume.Standard: Mathematics.7.G.2.06 - Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 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.Define x and y as follows:x = the width, in yards, of the children’s pooly = the length, in yards, of the children’s poolWrite 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.Write an expression using x and y to represent the area of the adult pool.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.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 WorkSelect 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:
Question 20:
Question 21:
Question 36:
Question 41:
Question 42:

Return to the MCAS 2014 Student Work Directory

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