FractionsExplorer

Build improper fractions to understand them — not just compute them.

Click each pizza slice to place your pieces. Watch wholes form — then see the fraction revealed as a number. This is how your brain builds lasting understanding.

Your challenge

You ordered 7 pizza slices. Each pizza has 4 slices. How many whole pizzas do you have?

Click each slice to place your pieces into pizzas.

Slices placed0 / 7

Pizza 1

Pizza 2

Try another fraction:

Halves
Thirds
Quarters
Fifths
Sixths
Why this works

Area model beats number lines

Area model training produced significant gains on improper fractions for P4 and P5 students. Number line training produced no improvement at all in the same age group.

Tian, J., Lewis, M. R., & Siegler, R. S. (2021). Development of fraction concepts in students aged 7–12. Journal of Cognition and Development.

Story first, symbol second

Analogy-based instruction produces gains that last at one-week follow-up. Partition-drag alone fades. The pizza scenario here is not decoration — it is the instructional mechanism.

Viegut, A. A., & Matthews, P. G. (2023). Building fraction magnitude knowledge with number lines. Developmental Psychology, 59(10). ↗

Concrete to abstract (CPA)

Students who learn with manipulatives often never connect the concrete model to symbols without explicit bridging. This tool follows Singapore's own CPA framework — you build it first, then see the number.

Willingham, D. T. (2017). Ask the cognitive scientist: Do manipulatives help students learn? American Educator.