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?

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.

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