Mathematics

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50 mins

Teacher/Student led

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Learning Outcomes

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+80 XP

Teacher-led from the board. Pupils do not need a device, but can follow on one.

What you need:
IWB/Projector/Large Screen

Angle Sums in Triangles and Quadrilaterals

Discover why the three angles of any triangle always add to 180°, and why quadrilaterals add to 360°. Use these rules to find missing angles.

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Sketch the Angles in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

Your turn

Your teacher is running this lesson on the board. Here is the part you can try yourself.

Your written work is on page 78

Polygon angles

1 - Getting Started ~4 mins

A large triangle viewed straight on, each of its three corners marked with a small coloured angle arc, and beside it a four-sided shape with a dashed straight line running from one corner to the opposite corner so it is divided into two triangles, the two shapes arranged side by side on a plain background with generous white space Here is a triangle. Before we work anything out: if I told you two of its angles, do you think you could work out the third one without measuring it? Have a think.

Key point

Now look at the four-sided shape beside it, and the dashed line running corner to corner. It splits the shape into two triangles. Keep that in the back of your mind, because it is going to tell us something surprising about the angles of a four-sided shape.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

The interactive shows five shapes, one at a time: three triangles, then two four-sided shapes. Keep your eye on the total of the angles each time. What do you notice?

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~9 mins

Today we drag the corners of a triangle and watch its angles change on the board. We'll pull one vertex to make it tall and pointy, then squash it flat and wide, then twist it into a shape none of us have seen before. Each time, before the numbers settle, predict what the total of the three angles will do.

Key point

The three angles will keep changing as we drag, but keep your eye on the running total. However sharp or squashed the triangle gets, we're checking whether that total ever leaves 180°.

Drag the corners: does the total ever leave 180°?

+15 XP

4 - Sketch the Angles in Your Copy ~3 mins

COPYBOOK MOMENT

In your maths copy, sketch one triangle and one quadrilateral. For each shape, write its angles in a column, one under the other. Add them up and underline the total at the bottom — 180° for your triangle, 360° for your quadrilateral.

+10 XP

Pupil practice

Module 6 · 2D and 3D Shape, Angles, Symmetry Shape & Space

Lesson 83 · Angle Sums in Triangles and Quadrilaterals

Download Activity Book page (PDF)

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