This problem offers opportunities for children to visualise a 3D shape. It also encourages conjectures and justifications.

To begin with, encourage children to make conjectures about the number of different tetrahedra, asking pairs of children to come up with justifications for their ideas.

Having polydron available for children to make tetrahedra would be helpful. Alternatively, stickers could be stuck on ready-made tetrahedra. Children might also want to draw nets so isometric dotty paper would be useful.

Where could the other colours go?

Can you find another way?

How do you know the tetrahedra are different?

How will you record your tetrahedra?