Fraction notation and operations may be the most abstract math monsters our students meet until they get to algebra. Before we can explain those frustrating fractions, we teachers need to go back to the basics for ourselves. First, let’s get rid of two common misconceptions:
- A fraction is not two numbers.
Every fraction is a single number. A fraction can be added to other numbers (or subtracted, multiplied, etc.), and it has to obey the Distributive Law and all the other standard rules for numbers. It takes two digits (plus a bar) to write a fraction, just as it takes two digits to write the number 18 — but, like 18, the fraction is a single number that names a certain amount of whatever we are counting or measuring.
- A fraction is not something to do.
A fraction is a number, not a recipe for action. The fraction 3/4 does not mean, “Cut your pizza into 4 pieces, and then keep 3 of them.” The fraction 3/4 simply names a certain amount of stuff, more than a half but not as much as a whole thing. When our students are learning fractions, we do cut up models to help them understand, but the fractions themselves are simply numbers.
Denise Gaskins' Let's Play Math 