Ask your students to write down which one they’d use. Some students will assume you should always use $20 off. Others will assume you should always use 20% off. Still others will (rightly) understand that it depends on the cost of the item you’re buying.
Our goal here is to get all of those responses on paper, emptied out of the students’ head. If one student in the class blurts out “It depends!” we’ll lose a lot of the interesting and productive preconceptions lurking about.
Take a show of hands. Ideally you’ll find some disagreement. At this point, students should try to convince each other of their position.
Offer the material from act two here: a bunch of items that will test out their hypotheses.
Once we reach the understanding that it’s better to take a percentage off the
large expensive items and better to use the fixed value with the small cheap items, it might seem natural to ask:
Where’s the break-even point? Where do cheap items become expensive items? For what dollar cost should you use one coupon versus the other?
Then generalize some more:
If the coupons read “x% off” and “$x off”, where is the break-even point? Does your answer work for every x?
“If you are allowed to apply one coupon, and then the other on a purchase, does it matter in which order you apply them?” is also a really nice question.
You need to be careful in your use of “small” and “large.” An iPod is small (yet expensive) compared to a large bouncy ball (inexpensive).
2014 Dec 9. Shaun Errichiello has created a series of printable cards for students to sort:
We asked students to physically sort the cards into groups. One group contains all the cards where the 20% coupon is the better choice, the other group contains all the cards where the $20 coupon is the better choice. We changed one of the prices (the desk) to be exactly $100.