Formative Assessment 41

Assessment Problem: 

Refund Problem (direct variation/proportionality)
In some states, a deposit is charged on aluminum pop cans and is refunded when the cans are returned. In New York, the deposit is 5 cents a can.
a) What would be the refund for returning 6 (10 or 12) cans?
b) Describe how the storeowner would figure the amount of refund for any number of returned cans.
c) Let R represent the amount of refund and let C represent the number of cans returned; write an equation for the amount of refund.
d) Can you use your equation to find out how many cans would have to be returned to get a refund of $3.00? How much refund would you get for 100 cans?

Common Responses: 

This problem was used in an interview with 10 six-grade students:
All 10 students were able to compute specific cases correctly.
9 students were able to describe the functional relation.
7 students were able to represent the problem symbolically (writing an equation)
However, only 2 students were able to use the equation to solve the problem.

Mathematical Issues: 

Students can translate a word problem into an equation, but cannot use the equation to solve the problem.

Algebraic Relations
Common Core Standards: 
A-SSE: Seeing Structure in Expressions
Research References: 
(Swafford &Langrall, 2000)