# Mastery: Reasoning and Problem-Solving

• Create a net for a tetrahedron. Fold it up to ensure that it works. Is this the only way to draw a net for a tetrahedron?
• Imagine a 3 by 3 by 3 cube hanging in front of you with just the front face facing you.
The cube is made up of three 3 by 3 layers, that is 27, small cubes.
You drill a hole through the four corner cubes that are facing you, all the way through to the back.
A friend looks down on the cube, from above, and they also drill four holes through their four corner cubes all the way through to the bottom.
You and your friend then examine all the 27 small cubes.
How many small cubes will then have holes drilled in them?
• Find out what a dodecahedron is. Build one using a construction kit, then write a description of it, using all your best mathematical shape language for someone who has never seen one.

In-depth Investigation: Soma Cube
Children create specified 3-D shapes using 2-D representations and then combine these to create other 3-D shapes including a cube.