1. Solving geometrical problems
GM5.2 Core Starter
Jot down as much information as you can about the symmetry of these figures and anything else you notice about them.
Preamble
Initially allow pupils to work in pairs, jotting down anything of note, then collect and discuss these ideas as a whole group. Wherever appropriate, challenge pupils’ statements so that they have to explain how they know their findings to be true.
If there is sufficient time available, the session can end with some quickfire questions based on the regular polygons in the second figure, such as name, angle sizes etc.
Possible content
Transformations and symmetry, simple properties of polygons.
Resources
None.
Solution/Notes There are numerous correct responses, here are some possibilities.
Left-hand figure:
No reflection symmetry but the whole shape has rotation symmetry of order 4.
Formed by 90 clockwise turns of an ‘N’, moving to the right or down.
Right-hand figure:
No rotation symmetry
Just one (vertical) line of reflection symmetry
Made up of all the regular polygons up to 10-sided (decagon).