Discovering Fractions

Half an apple and half a sheet of paper look nothing alike, and yet both are called one half. That is exactly where it is decided whether fractions are understood or merely handled by rule. Eight stations lead from the idea of a share to the notation with numerator and denominator and on to the number line, showing why expanding and reducing only rename the same share. Every station follows the same course: a short story, something to try out, a round of noticing, the concept, exercises, a diagnostic task and a look back. Teachers can reorder the stations and follow in a cockpit of their own where the class is getting stuck.