Place fractions on lines that run past one whole. Improper fractions and mixed numbers by default — number-line magnitude is the most evidence-backed fraction intervention there is.
Open toolJudge fair vs. unfair parts in a flash, then turn equal-sharing stories into fractions. The K–2 foundation: fractions require equal parts.
Open toolBuild a target fraction by counting copies of a unit fraction end to end — and watch the count sail right past one whole. The antidote to "fractions can't be bigger than one."
Open toolCompare two fractions by magnitude on a shared number line or aligned strips — never by cross-multiplying. Presets target the exact patterns where bias shows up.
Open toolSee one fraction as area, length, and set at the same time, and prove all three are the same number — breaking overreliance on the "pizza" model.
Open toolCount unit fractions one at a time on a shared number line — halves through eighths, forward or backward — and watch the count sail right past one whole.
Open toolWhole-number bias — treating a fraction's top and bottom as two separate whole numbers — is one of the most persistent errors in elementary mathematics (Ni & Zhou; Braithwaite & Siegler). Every routine here is designed against it: fraction magnitude on the number line with feedback (Siegler and colleagues), equal partitioning and equal sharing as the K–2 roots (Common Core; Empson), unit-fraction iteration through learning trajectories (Clements & Sarama), and deliberately varied representations so no single picture — especially the circle — carries all the meaning (Mao, Sutherland & Fainstein, 2026).