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Reasoning about the number of matches needed to build squares that share their sides.

Little Boxes

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Tetrahedron Faces

Age 7 to 11
Challenge Level

Why do this problem?

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

Possible approach

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.

Key questions

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?