




Massachusetts Comprehensive Assessment System
2013, Grade 8 Mathematics
Question 20: OpenResponse 

Reporting Category: Functions Standard: 8.P.4  Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.
Standard: Mathematics.8.F.2.04  Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Some of the students from Eastwood School are taking a trip to a museum. In all, fewer than 60 students will go on the trip. The cost for food and admission to the museum is $18 per student. What is the total cost for food and admission to the museum for 15 students? Show or explain how you got your answer.
The students will travel on one bus to the museum. The cost of the bus is $800. In your Student Answer Booklet, copy and complete the table below to show the total cost for food, admission, and the bus for different numbers of students to go to the museum. Show or explain how you got your answers.
Student Trip to the Museum Number of Students  Total Cost for Food, Admission, and the Bus  0  $ 800  20  $1160  30   40   50    Write an expression that can be used to find the total cost for food, admission, and the bus for n students from Eastwood School to go to the museum.
 A total of 44 students go to the museum. What is the total cost, for food, admission, and the bus, per student to go to the museum? 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.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Functions concepts involved in constructing a function to model a linear relationship between two quantities. The student completes a table, uses the table to construct an expression, and then uses the expression to solve a problem. 
4 
3 
The student response demonstrates a good understanding of the Functions concepts involved in constructing a function to model a linear relationship between two quantities. 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 Functions concepts involved in constructing a function to model a linear relationship between two quantities. 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 Functions concepts involved in constructing a function to model a linear relationship between two quantities. 
0 
The student response contains insufficient evidence of an understanding of the Functions concepts involved in constructing a function to model a linear relationship between two quantities to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 8 Mathematics
 Question 11: Statistics and Probability
 Question 20: Functions
Return to the MCAS 2013 Student Work Directory
Last Updated: August 27, 2015


