Angles and their rules

A sequence of resources designed to help teach angle rules to KS3. Approximately 4 lessons.

Lesson 1   Start with the "Angle Estimation Game". This can be done as a class by picking pupils at random after giving them thinking time, or in teams and keeping a tally over 5 rounds. If each pupil has a computer they could attempt this 5 times and highest score wins.

After this, use the "Shape Games for Students aged 11-13"  (angle estimation) resource to set up a paired game.

As they work, you take a chance to pick out certain pupil's angles and use these at the end as part of a discussion, introducing acute, obtuse and reflex angles, as well as any methods pupils have devised for measuring or drawing these.

After pupils have played one version of the game, they could set themselves a target score for the next games, swap partners, and demonstrate progress by getting a lower score the second time around. Encourage more able to explore methods for drawing certain obtuse or reflex angles.

Lesson 2   Starter; Pupils define the words Alternate, Interior and Corresponding, makng links with English and other subjects, as well as exterior influences.

Main: Using the mymaths resource, introduce the three different angles within parallel lines, and allow pupils to attempt the questions that follow.

Plenary: Pupils are to arrange themselves into groups and play the jeopardy game. The resource can be used for estimation as well as classifying angles. Pupils compete for points, but to make sure other groups are involved they are to write their answers down on whiteboards and keep it in case the other team gets it wrong, thus stealing points and keeping the entire class involved even when it is not their turn.

Lesson 3 (Resources and instructions for 'Lesson 4' from the "Will it or Wont it" resource.)

Starter:   Ask pupils to imagine walking around a big regular hexagon where each side is 5m long. They can only understand the instructions ‘walk forward for x metres’, ‘turn left through x degrees’ and turn right through x degrees’. Ask pupils to work in pairs to give instructions to walk round the hexagon.

Main:  Give pupils the regular polygons sheet (Resource sheet 4.1). Use the starter activity to explain the meaning of exterior angle. Ask them to find the exterior angle of each shape, working in pairs with one sheet between two. They should find the angles by calculation – not measurement.

Have a discussion after activity focusing on if they could find the exterior angle just by knowing the number of sides of a regular polygon. Check with a decagon.
Ask what is happening as the number of sides increases. What about 7 sides, 15 sides, 20 sides, 100 sides, 1000 sides (allow calculators)? Pupils should consider this in pairs. They should use whiteboards to draft a reply.
Possible extension: To reinforce pupils’ graph work they could plot the graph (number of sides, exterior angle).

Plenary: Pose the question: how can you find the interior angle from the exterior angle?

Lesson 4    Starter: Draw regular polygons from triangle to hexagon on board and have pupils recap what knowledge they currently know.

Main: Pupils are to draw these shapes and measure internal angles in an appropriate table, including a 'total of all angles' column.

Stop for a discussion focusing on how much bigger the total gets with each step. Build to th rule (N-2)x180, where N is the number of sides/corners.

Plenary: Have pupils draw any shape with sides greater than those already done, find the total number of the angles, and estimate each angle based on this, this will be an easy calculation if the shapes are regular, and a more taxing task if they have not drawn a regular shape.