Task# Fractions and Rectangles

Illustrative MathematicsVaries

Students usually first see fraction equivalence by subdividing the pieces into smaller, equal sized pieces and realizing that you haven't changed the amount that represents the fraction. This explains why if you multiply the numerator and denominator by the same whole number, you get an equivalent fraction: This task helps set students on the path to understanding that if you divide the numerator and denominator by the same whole number, you get an equivalent fraction. It is as if we are 'putting smaller pieces together to form bigger pieces,' as opposed to subdividing the pieces.