Make a cube out of straws and have a go at this practical
Reasoning about the number of matches needed to build squares that
share their sides.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
We received this solution from someone who
didn't give their name:
In a tetrahedron any two faces have a common edge so no two
faces can be the same colour. A tetrahedron needs 4 colours. If we
start by colouring one face, then the 3 faces adjoining it need 3
A cube needs at least 3 colours because 3 faces meet at a point.
Three colours are sufficient because each pair of opposite faces
can be painted in one of the 3 colours.
An octahedron needs 2 colours. At each vertex 4 faces meet and
they can be painted in alternate colours.
A dodecahedron needs at least 4 colours because if we start by
colouring one face then we have to use 3 more colours to paint the
faces around it. The net shows how the dodecahedron can be painted
with 3 faces of each colour so 4 colours are sufficient.