Counting unit fractions, one at a time, right past one whole

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, said one at a time — "one-sixth, two-sixths, three-sixths…" — the same choral counting routine as sequence counting, just with a different unit. Franke, Kazemi & Turrou's Choral Counting & Counting Collections shows that the accumulating, never-erased record is what lets a class notice pattern instead of just reciting, and here that pattern includes something whole-number counting never shows: the count sailing straight past one whole and continuing — "six-sixths, seven-sixths, eight-sixths." Students with whole-number bias — the well-documented tendency to treat a fraction's top and bottom as two separate whole numbers, roots traced by Ni & Zhou (2005) — believe a fraction can't be bigger than a whole, because "you can't have more than one whole pizza." Watching the tally cross the line while still counting the exact same-sized unit fraction directly contradicts that belief, which is central to the learning-trajectories work of Clements & Sarama and to the Common Core's treatment of fractions as built from unit fractions. Counting forward and backward from any start value follows Kathy Richardson's counting routines in Developing Number Concepts: backward counting through a whole — watching it break back apart into unit fractions — is just as informative as building one up.