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Massachusetts Comprehensive Assessment System

2011, Grade 10 Mathematics

  Question 31: Open-Response calculator allowed
Nicole’s rental company has only cars and vans available to rent. The poster below shows the rental costs per day for the vehicles at her company.
A poster for a rental company titled
  1. One day last week, the total rental income for Nicole’s company was $460 for cars and vans together. Her company rented 7 cars that day. How many vans did her company rent that day? Show or explain how you got your answer.
For parts (b), (c), and (d), define c and v as follows:
  • c equals the number of cars the company owns
  • v equals the number of vans the company owns
  1. The company owns a total of 36 vehicles. Write an equation in terms of c and v that represents this fact.
  2. On a day when Nicole’s company rents all its cars and vans, the total rental income is $1700. Write an equation in terms of c and v that represents this fact.
  3. Use your equations from parts (b) and (c) to determine how many cars the company owns and how many vans the company owns. Show your work.

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 Patterns, Relations, and Algebra concepts involved in solving a real-life problem that can be modeled using systems of linear equations. The student determines the number of cars and vans owned by a rental company by solving a system of equations.
4
3 The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in solving a real-life problem that can be modeled using systems of linear equations. 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 fair understanding of the Patterns, Relations, and Algebra concepts involved in solving a real-life problem that can be modeled using systems of linear equations. 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 only minimal understanding of the Patterns, Relations, and Algebra concepts involved in solving a real-life problem that can be modeled using systems of linear equations.
0 The student response contains insufficient evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in solving a real-life problem that can be modeled using systems of linear equations.

Note: There are 2 sample student responses for Score Point 4.

Grade 10 Mathematics

Question 17: Number Sense and Operations
Question 20: Geometry
Question 21: Patterns, Relations, and Algebra
Question 31: Patterns, Relations, and Algebra
Question 41: Data Analysis, Statistics, and Probability
Question 42: Measurement

Return to the MCAS 2011 Student Work Directory



Last Updated: January 15, 2016
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