Why "fair shares" comes before fractions

Before a kid can understand one-fourth, they have to understand that fourths have to be EQUAL, and a lot of them never quite get that memo. The deepest fraction misconceptions trace back to accepting any split as a fraction: shade "1 of 4 parts" and call it a fourth even when the parts are wildly different sizes. Fair-sharing problems, like "share 3 brownies among 4 kids," are how young kids invent fractions for themselves before they ever see notation. This tool trains both halves of that foundation: a flash judgment of fair versus not-fair parts, and sharing scenarios where the class watches equal cutting turn items-per-person into a fraction, including shares bigger than one whole, so a fraction never gets welded to "a piece of one thing."