Why count unit fractions?

Every fraction is built from a unit fraction the same way every whole number is built from 1: five-sixths is just five copies of one-sixth, and eight-sixths is eight of them — you simply don't stop at the whole. That last idea is the crux. Students with whole-number bias believe a fraction can't be bigger than one, because "you can't have more than a whole pizza." Iterating unit fractions end to end on a number line — and watching the count sail right past one whole to keep going — directly contradicts that belief (this is core to the learning-trajectories work of Clements & Sarama and to the Common Core's treatment of fractions as built from unit fractions). Counting "one-sixth, two-sixths, three-sixths…" also builds the crucial link between a fraction's name and its size. Flash a target, have the class predict where it lands, then build it one unit fraction at a time and count together — especially when you cross into the second whole.