Sketch the triangle on the board as you speak, marking one corner 50° and one 60° and leaving the third blank, so the class has the shape in front of them. Give five seconds of quiet think-time before any hands go up, then take three hands-up guesses. Do NOT confirm or deny yet, and do not name any rule. Write the three guesses on the board so the class can come back to them after the investigation.

This is a problem-first lesson — the aim is for pupils to make a real attempt with what they already know before the rule is discovered. Resist saying 180.

• First triangle — before revealing the sum readout, ask the class to add 30, 110, 40 aloud. Let them land on 180 themselves.
• Second triangle — a totally different shape; ask whether they expect a different total this time, then check. Note: this one happens to have two equal 80° angles, so it is technically isosceles, but do not flag that here — it is used only as a shape contrast. Save the isosceles idea for Class Challenge.
• Third triangle — the right angle makes 90 + the other two; ask what the other two must add to.

Name the pattern at the end of this step, drawn from what pupils saw — every one added to 180. Do not state it before the third triangle. To prove it isn't a coincidence, tear the three corners off a real paper triangle and lay them in a row: they make a straight line (180°).

Cross-curricular STE bridge: this is why triangular bracing makes structures rigid — the fixed angle sum keeps the shape.

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

Run the polygon-angles interactive in explore mode: drag the vertices and watch the three interior angles recompute live while the sum readout always confirms 180°. Ask pupils to predict the missing angle first, then drag to check. Listen for the method 180 minus the two known angles — revoice it when a pupil uses it: so you took the two we knew away from 180.

Watch for the pupil who adds the two known angles and stops there — head it off by asking and what do you still have to do with that total?

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 five triangles come up on screen one at a time, and every card gives two angles and asks for one missing angle. The order is: a triangle with all different angles; a right-angled one; an isosceles triangle where both base angles are given so you find the top; a straightforward find; and finally an isosceles triangle where the top and one base angle are given, so pupils find the remaining base angle by subtracting from 180. None of these five cards asks pupils to halve a remainder — that halving move is practised independently in the copybook task just done, where only the top angle was given. On the board, use the worked example above to remind the class how the halving works, then let the interactive rehearse the subtract-from-180 step. Revoice a strong answer: so you took the two angles you knew away from 180.