A pseudo- concrete representation of a sales price problem is shown below. This is what I use as an entry point for teaching these problems.

The entire shape represents the total price of $80. This is 100%, which in student language is “the whole thing.”

The discount rate is 25%. Cut with scissors to lop off the 25% which also lops off $20, which is the actual discount. Explain to the student that this 25% is part of the “whole thing.”

What remains is 75% or $60. This is the “new price” which is called the sales price.

This is a photo of matching cards for the topic of percent discount and percent tax.

Students are given a card with an item to buy, a percent discount and our state tax rate of 6% (not listed). We’ve identified 4 steps for to find the total amount to pay the cashier: compute discount, compute new price, compute tax, compute the total cost. There are two cards for each step, one that shows the step completed correctly and one with an incorrect step. Students are to identify the correct steps and arrange them in order.

This activity is useful for a variety of reasons.

By having the steps listed there are no calculations. The students can focus on the steps and the concept.

To figure out the correct order students engage in higher level thinking. They analyze and justify their choices.

Because the problems are worked out and students simply focus on choosing cards they can do much more on their own. This is engaging.

While they are engaged the teacher can circulate and ask leading questions.

It can be very surprising how poorly understood discount and tax can be for students yet most have bought something and paid tax, even items on sale. As such this is an important topic.