Working out the formula that has been used to produce a series of numbers can be tricky. How easy is it then to work out a formula using polyhedra properties that always equals 2?
By studying the number of faces, vertices and edges various polyhedra have to find a common relationship will challenge pupils to manipulate numbers.
Once they have a table of figures and some possible answers introduce them to Euler’s formula.
F + V – E = 2
Consider a cube – F (faces) = 6, V (wertices – corners) = 8 and E (edges) = 12.
F + V – E = 6 + 8 – 12 = 2
Now challenge them to find the exception to the rule (polyhedra with holes through them).
These ideas are taken from How to be Brilliant at Shape and Space, which contains 40 photocopiable worksheets designed to improve Key Stage 2 (KS2) pupils’ understanding of shape, their understanding of position and movement and their understanding of measure.