Sketch a triangle on the IWB, then draw a quadrilateral and split it corner-to-corner with a diagonal so the class sees the two triangles appear. Take two or three hands-up predictions on "could you find the third angle without measuring?" — do not confirm or deny yet, that is the whole lesson.

Three triangles first, so the 180° rule lands before quadrilaterals appear.

Equilateral: three equal angles, 60°+60°+60°=180°.

Right-angled: right angle 90°, then 45° and 45°. Get a prediction before totalling: 90+45+45=180°.

Scalene: everything different-looking, still 50°+70°+60°=180°. Point: three different triangles, same total.

Square: four right angles, 90°×4=360°. Draw out that this is two lots of 180°.

Link back to the diagonal from Getting Started that splits a quadrilateral into two triangles, each 180°, so 360°. That is the reasoning, not just the fact.

Irregular quadrilateral: 70°+100°+80°+110°=360°. Point: total stays on 360° even when nothing is neat.

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Dragging a vertex is the only interaction here — there is no type-a-value box in explore mode, so don't ask pupils to hit an exact angle. This is the digital version of ripping the corners off a paper triangle.

Keep the whole class working through the 9 minutes: ask a fresh pupil to predict what the total will do before each drag, take a hands-up answer from the watching class, then let the pupil at the board drag and read the total. Every couple of drags, re-anchor by asking the room to read the total aloud with you. Let four or five pupils take a turn at the board so nobody watches for long. The point is that the total refuses to leave 180° no matter how extreme the triangle becomes.

Run the paper rip-and-line-up first (triangles_to_tear printable) so pupils have felt the 180° before the board work. Give a clear spoken cue when the class puts the paper down and turns to the board — the two halves of this step are separate and pupils need to know which they are doing.

Then the board work is the practice questions — 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 subtraction strategy is: 180° minus the two known angles.

• The paper wobble point: if a pupil's torn corners don't quite reach a straight line, that is measuring wobble — a real triangle can never truly disagree with the rule. Use it to talk about why the rule is certain, not just usual. This idea lives with the paper, not with the board problems, which are all clean and correct.
• Watch for the isosceles case — some pupils forget both base angles are 50°, giving 180 − 100 = 80°.

Quadrilateral worked example (board, after the five triangle challenges): sketch a rough four-sided shape, mark 85°, 100°, 70°, and ?. Steps out loud with the class: (1) known angles add to 85+100+70=255°; (2) missing = 360°−255°=105°. Link back to Getting Started: two triangles make 360°. Slip to watch: pupils subtracting from 180° by habit, or adding only two of the three known angles. The interactive challenges stay on triangles only; this quad example is teacher-led on the board.