Three pencils cost 90c in the school shop.
What would one pencil cost? And how would you work out the price of seven?
Give five seconds of quiet think-time before any hands go up. Take two or three answers — some pupils will jump straight to seven, others will find one first. Don't confirm yet; the two-step route (divide to one, then multiply up) is what the lesson builds.
Watch the four function machines. They show the two moves in turn: first divide to find what one costs, then multiply up to the amount we want. Watch for the divide step every time — that is where the price of one comes from.
Four machines in order, drawing out the divide-then-multiply pattern each time.
Pencils, find one: 90 ÷ 3, ask what one costs before the reveal (30c) — the divide is the make-or-break move.
Seven pencils: × 30 → 210. Now the value of one lets us jump anywhere; pause before the reveal.
Apples (€1.20), find one: 120 ÷ 4, ask what one apple costs (30c) before revealing, so they see where the unit price comes from.
Six apples: × 30 → 180. Same multiply move; watch for pupils multiplying 4 by 6 directly instead of pricing from one.
Name it: divide to find one, then multiply up — the unitary method.
Flour prediction, no machine: if 2 kg cost €1.50, what does 1 kg cost? Take two spoken answers (75 c) to check the divide move has landed.
We'll do these together on the machine, one problem at a time. An individual pupil comes to the board for each problem while the rest of the class follows and agrees. Each time, we key in a divide rule first to find the value of one, agree the answer as a class, then switch the same machine to a multiply rule to scale up.
Each time it's the same two moves: divide to find one, then multiply up.
Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud. Do one problem at a time so the watching class can track which numbers are on the machine. Each problem is re-keyed into the same machine: set the divide rule first (÷ 6 for oranges, ÷ 5 for buns, ÷ 3 for the car), read the value of one, then switch the machine to the matching multiply rule.
Insist on the divide first every time. The common slip is jumping straight to the answer without pausing on the value of one. Revoice a good move: so once we know one, the rest is just multiplying. For the car example, name that km-per-hour is exactly the same idea as price-per-item — dividing 30 by 3 gives 10 km in one hour, and we say the unit aloud.
In your maths copy, take the three problems we just did: six oranges for €1.80, five buns for €2.00, and the car going 30 km in 3 hours. For each one write "÷ to find one: ___" then "× up to find the answer: ___". Box your final answer.
Keep the three problems visible on the board while pupils write. Walk the room glancing for the two labelled steps on every problem — no marking, this is whole-class copybook practice. Catch any pupil who has written only the final answer with no divide line.
We'll work through these together at the board. Divide to find one, then multiply up:
That last one asks for fewer tickets, not more — but the same first move still works. Find the value of one ticket by dividing, then multiply up to five.
Use the unitary method — divide to find the value of one, then multiply up to find the value of many.
Ways to start:
Stretch:
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
The bottle problem gives a non-whole value of one (0.75 l). Hold out for the divide step aloud before anyone multiplies. The ticket problem is a stretch for pupils who finish the three core problems: name that scaling down to five still starts with the value of one — divide to get €7.50, then multiply up by five. If a pupil finishes early, they wait and predict the value of one for the next problem rather than working ahead on paper.
The function machine from the Try It Together step is still the model here: if the class needs it, key the divide rule then the multiply rule back in and work a problem on the machine before returning to the board.
You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.