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.
