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 five copies of one-sixth, and eight-sixths is eight of them, you just don't stop at the whole. That's the crux. A lot of kids 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, knocks that belief down. Counting "one-sixth, two-sixths, three-sixths..." also builds the 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, counting together, especially when you cross into the second whole.