This is a problem-first lesson — do not state the 360° rule yet. Take three hands-up predictions and write them on the board without confirming any of them; the class tests them across the next two steps.

Give five seconds of quiet think-time before hands go up. Listen for a pupil who reasons two triangles, so two lots of 180 — hold that thought rather than confirming it.

These three snapshots sit side by side — point at each one in turn rather than explaining it in advance.

• First two — the right-angled shapes; the class can total four 90s in their heads and check it against the printed total.
• Third — the irregular one is the point. Nobody can guess it, yet its printed total still reads 360°.

Only after the third do you name the rule, and pull it from the two-triangles reasoning a pupil offered in the hook: one diagonal, two triangles, 180 each, so 360 altogether.

Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.

Bring individual pupils up to drag a corner. The move that lands the idea: make one angle huge and watch another shrink to compensate, while the sum readout holds at 360°. Revoice: so the angles trade off, but the pot is always 360.

Rest of the class watches the readout and predicts which angle will shrink before the drag.

This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Roughly two minutes per problem keeps four board turns inside the slot; keep the board work brisk rather than over-explaining.

• First — the easy start: three 90s leave 90° (it is a rectangle).
• Second — a friendlier subtraction, 360 − 280 = 80°.
• Third — 360 − 280 = 80° again, but the numbers look less obvious, so pupils must trust the method.
• Fourth — the closing stretch: 85 + 95 + 130 = 310, so 50°. Watch for pupils who add the three known angles wrongly rather than the method itself.

Method cue: add the three you know, then take that from 360.