Annie, my coworker pointed me to a strategy she saw in a textbook for including financial context when teaching functions. I thought it was very well done and points out that for many concepts, it’s not too complicated to come up with a financial example to illustrate a particular math concept. This is an idea we’ve been tossing around at the Math Forum for a while, and it’s nice to see such a great example of it in a textbook.

Building Functions

Sasha  and Tony look at the deals on CDs at a music store Website

Sasha: Look, at the bottom of the page are all these CDs for 28% off.

Tony: Yes, but by the time you add in sales tax and shipping, you’d be better off going to the mall to get them.

Sasha: Are you sure? We’d better try pricing some. I’ll choose a bunch, but I won’t order them until we see how much they really cost.

They pick out six CDs and add them to the shopping cart. Then they click the checkout button.

Sasha and Tony’s checkout page looks like this:

1. Copy and complete this table

Sasha and Tony look at the checkout page, and the totals agree with their calculations.

Sasha: It’s pretty mechanical. Look, for the next one, I write this.

So the total cost is \$13.33 and that’s what’s in the table!

Tony: Look, the calculations are even more mechanical if you keep track of the steps. They go this way. Suppose the cost is some number C.

Now Tony writes on a piece of paper.

Sasha: Good job! The last line is like a machine that does it all.

(C – 0.28C) + (C – 0.28C) x 0.05 + 2

The rule calculates the total cost of any CD during the sale.

2. Use Sasha and Tony’s machine to calculate the total cost of each CD in their list. Check your results against the total costs that you found on the checkout page.

I like this example because it’s realistic context in terms of the kinds of decisions we regularly make as shoppers. Obviously, there are other factors that may come into play for such decisions — how far is the mall, how long does it take to get there, how much does it cost to get there (bus fare, gas cost, etc.), how much time do we have, but overall this problem represents a nice first step to thinking about this kind of decision and connects it to math we’d see in the classroom. More importantly, there’s nothing to prevent these other factors from entering a conversation in a math class about a problem like this.