Fractions are currently being introduced to my son who is in third grade. The initial skills covered in this introduction include recognizing equivalent fractions as well as comparing two fractions and deciding which one is bigger. To help the student acquire these skills, the following models, for example, are used:
Models are effective when these help children see what various mathematical operations do. In fact, individuals who understand fractions can easily appreciate the usefulness of these drawings. One needs to be careful, however, and be aware that sometimes models may be acquiring more from a child.
Forty years ago, I was taught that one way to compare fractions is to use multiplication. Using the specific example of 2/5 versus 3/8, the following is done: