3-D shapes GM3.3 Extension Plenary What is the least number of colours needed to paint these solids, so that no two faces next to each other are the same colour? A cube A tetrahedron A square based pyramid Preamble Allow pupils to wrestle with this problem, before suggesting/hinting that sketching the appropriate nets might be a useful strategy, coupled with a systematic approach. It may be necessary to explain that ‘next to’ means ‘sharing a common edge’, so faces of the same colour may meet at a point, but not along an edge. Possible content Visualising 3-D shapes and possibly their nets. Resources None – the whole exercise should only involve visualisation or, at most, sketches. Solution/Notes Three colours Four colours Three colours