Percents is a very challenging concept for students often because it is presented in symbolic terms, e.g. 40% of a 25 is what? Students typically understand what 100% and 50% mean. The concept of percent can build on this intuitive understanding. Here is my approach using a Concrete-Representation-Abstract approach (from a lesson taught today).
First, I ask the students to match common terms used for various percents on a percent number line. The students typically understand the first four terms.
I build on their knowledge of 50% first by having them cut (see below) a pizza into 50% then 25%. Then they cut $200 into 50% then 25% and then count the money.
Many struggle with 1/4 and 3/4 (25% and 75%). The little less than half is the building block because it is the first step away from 0%, 50% and 100%. Here’s how I use this step (below). The students compute 50% or half of the $200 then estimate 40% which is “a little less than 50%.” If a student struggles with this step, we go back to the cutout money and they cut a little off of the 50% and guess how much money is left.
