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# Massachusetts Comprehensive Assessment System

 Question 36: Open-Response Reporting Category: Algebra and FunctionsStandard: 10.P.8 - Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems. (AI.P.12) Standard: Mathematics.A.CED.1.03 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* A construction contractor received two deliveries of building supplies from a lumberyard. The two deliveries included 10 boxes of nails, which cost a total of \$110.Write and solve an equation to determine n, the cost in dollars of one box of nails.The table below shows the numbers of sheets of plywood, trim boards, and boxes of nails delivered, and the total cost of each delivery.Using your answer from part (a) and the information from the table, create a system of equations that can be used to determine x, the cost in dollars of one sheet of plywood, and y, the cost in dollars of one trim board.Determine the cost in dollars of one sheet of plywood and the cost in dollars of one trim board. Show or explain how you got your answer.The contractor has an additional \$200 to spend. She tells her assistant to order at least 5 trim boards and as many sheets of plywood as possible with this money.What is the maximum number of sheets of plywood that the assistant could order following the contractor's instructions? 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 Algebra and Functions concepts involved in representing constraints by systems of equations and/or inequalities, and interpreting solutions as viable or non-viable options in a modeling context. The student writes and solves a system of equations and then solves a system of inequalities based on given constraints.
4
3 The student response demonstrates a good understanding of the Algebra and Functions concepts involved in representing constraints by systems of equations and/or inequalities, and interpreting solutions as viable or non-viable options in a modeling context. 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 Algebra and Functions concepts involved in representing constraints by systems of equations and/or inequalities, and interpreting solutions as viable or non-viable options in a modeling context. 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 Algebra and Functions concepts involved in representing constraints by systems of equations and/or inequalities, and interpreting solutions as viable or non-viable options in a modeling context.
0 The student response contains insufficient evidence of an understanding of the Algebra and Functions concepts involved in representing constraints by systems of equations and/or inequalities, and interpreting solutions as viable or non-viable options in a modeling context to merit any points.

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

Question 17:
Question 20:
Question 21:
Question 36:
Question 41:
Question 42: