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.

Educators teaching math typically start with the “mathy” stuff first. For example, for finding the sales price teachers may start with showing students the stepsÂ to calculate (photo below).

I start with the concept, either with a pictorial representation or actual objectsÂ to represent the underlying concept. In the photo above, I show an object (related to the student’s interest – this student is into weight training) on sale. The $50 circled in yellow represent the original price. I explain the concept of being on sale and discount and show that 20% is $10 to take awayÂ (marked out). This leaves $40 (in green) which is the sales price. This allows for conceptual understanding before showing him the “mathy” way of doing the problem.