We don’t teach fractions.
We let the material teach.
A short lesson on equivalent fractions, taught the Montessori way.
live · try it0/4 placed
1
HALF-SPACE ↓
TAP A PIECE ↑
12
Tap a quarter to place it on the half-space.
eight principles · borrowed from maria montessori
We didn’t invent these. A child does the work; the material teaches; the adult observes.
Each principle below is interactive — toggle, drag, or scroll to see how it lands in our lesson.
01
Concrete before abstract.
The child taps the chocolate first — splits it, finds a half, finds a quarter, covers a half with two quarters. The names sit alongside the action, never replace it.
lesson order
1.manipulatePlace quarter-pieces on the half-space.
2.manipulateFold the paper to prove it again.
3.abstractThen — and only then — ½ = ²⁄₄.
02
Control of error lives in the material.
Two quarter-pieces visibly cover the same area as one half. Wrong attempts don’t fit. The material teaches; the adult doesn’t.
self-correcting material
place 2 quarters
↳ fits
The material itself shows when it’s right. No adult has to say so.
03
The three-period lesson.
Introduce → recognize → recall. A canonical Montessori sequence that maps cleanly onto our six beats. Recall is the material itself — cover the half with two quarters, then fold a paper to prove it again.
three-period lesson
"This is one half."
Period 3 is the material itself: cover the half with two quarters, then fold the paper to prove it.
04
Description, not praise.
“Great job!” stops thought. We say: “You put two quarter-pieces together — they covered the same space as one half.” Observational language keeps the child noticing.
how Ari responds
↳ observational
You put two quarter-pieces together. They covered the same space as one half.
Mirrors what the child did. Invites them to keep noticing.
05
The prepared environment.
Introduce on a bar. Recognize on a mixed mat. Recall on a sheet of paper. The tray reshapes per period — only what the child needs sits in front of them.
the tray, per period
½
Each Montessori period reshapes the same chocolate. Nothing else is in the way.
06
Self-paced reveal.
The notebook never advances on a timer. The guide is observing — it opens the next cell when the child is ready, never before.
the lesson waits
01chocolate — name one halfactive
02chocolate — name one quarterlocked
03paper — fold it twicelocked
…and so onlocked
Cell 01 is open. 02 stays closed.
07
Aesthetic minimalism.
No badges, no streaks, no confetti. Calm type, generous whitespace, a soft palette. Everything competing for attention is removed.
what we strip out
08
Redirect, never reprimand.
When the child picks wrong, every hint points back to the material. Never “you’re wrong” — always “that’s a quarter — find the half”.
when a child picks wrong
↳ redirect
Let's look at the chocolate. What if you stack two quarters on the half-space?
Every hint points back to the material — never away from it.
now you
½=²⁄₄
Six minutes. Two materials.
One idea you’ll see, not be told.
Best opened on an iPad. Works with a mouse and keyboard too.
Open the lesson