## Fractions as Functions First Group FFF Group

Introduce fractions as functions first. So 1/2 is defined as a function whose domain is even numbers.  This is before defining rational numbers.

When going to rational numbers, downplay the equivalence class part.  A rational representative or rational number representative is a pair p/q and we have rules.  That some of these are equivalent can be stated, but not in the same sentence.

Rational reps are a pair p/q, as long as q is not zero.  What rational number does a rep represent?  This is the next question and the student is led to ask it. This is a feature not a bug.

We don’t start with equivalence class. We start with reps. Then the student asks what they represent?  Then we go to the lowest denominator rep.  Each class is identified with its lowest denominator rep.  There is a 1 to 1 relation of equivalence class and lowest denominator rep.    So use the lowest denominator rep because it is concrete.  Math constructivists would tend to prefer this anyhow.  (Different from math ed constructivists.)