The Number Sieve

About this tool

The Number Sieve is a projectable field of every number in range, all of them lit, and a small deck of sealed clue cards. Turn a card and it says nothing at all: it acts on the field, and the numbers it excludes go dark and drop out. What is left standing is the answer, and the tool never announces it.

That is the whole idea. Because no card ever names its rule, the class has to read the rule off the pattern of what died — "why has the whole bottom half gone?" — which turns a listening task into a reasoning task, and does it without a single word on the apparatus. A child who cannot read yet can run the whole routine.

Before the first card turns, children park a marker on the number they think it is. From that moment the marker cannot be moved, so when its number goes dark it is the material that takes it off the field, and nobody has to say anything at all. There is no score, no timer, no chime, and nothing on screen ever congratulates anybody.

Shuffle the deck and run the same board in a different order, and the survivors are identical every time — which is a thing a class can test rather than be told. The free tool carries the whole apparatus, all six kinds of card, all three fields and a builder that makes a fresh board around any number you tap. The Teacher plan adds the curated library and printing.

How to use it in class

• Pick a field: one to twenty for the youngest children, one to a hundred, or one to a hundred and twenty.
• Ask the class to park a marker on the number they think the cards are hiding. With a whole class, each child parks on their own number strip or slate and only the two or three children whose turn it is park on the board. Once the first card turns, every marker is fixed.
• Tap the next card. Watch the field, then wait — the question is what went dark, and why.
• When three or four numbers are still alight, ask the move that matters: what would a card have to take away to leave just one?
• Tap a number yourself and choose "New cards" to build a fresh board around it in a second.
• Shuffle and run it again in a different order, and let the class notice that the answer did not move.

Classroom ideas

• Warm-up: one board a day on the one-to-twenty field, four cards, five minutes.
• Prediction round: before each card turns, ask which numbers the class thinks are about to go.
• Silent sieve: turn every card without saying a word, then ask what the cards must have been.
• Two orders: run a board, shuffle, run it again — and ask why the same numbers survived.
• Build it backwards: pick a number together, let the tool make the cards, and see who can spot the clue that did the most work.