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# A Puzzling Cube

## A Puzzling Cube

**Why do this problem?**

Possible approach

### Key questions

Possible extension

Possible support

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Here are the six faces of a cube - in no particular order:

Here are three views of the cube:

Can you deduce where the faces are in relation to each other and record them on the net of this cube?

You might like to use this interactivity to keep track of your thinking. You can drag the picture of each face onto the net.

This problem is a little more difficult than it looks. It requires children to visualise the adjoining faces of the cube and transfer them to a net of the cube.

Possible approach

You could start by showing the group the problem on an interactive whiteboard. Once you have discussed what needs to be done, children could work in pairs so that they are able to talk through their ideas with a partner. If tablets or computers are available, they could use the interactivity to keep track of their thinking. In addition, they could use a print-out of this sheet or draw the faces of the cube for themselves. Some children might request cube-shaped objects, such as large dice, to help them work on the task. Scissors, sticky tape and blutak would also be useful!

As you walk around the room, look out for different ways of approaching the task. Some children may want to construct the cube from individual squares, then 'undo' the construction to create the net. Others may prefer to visualise the arrangement of faces and transfer them straight on to the net. (Learners could use a different arrangement which can be folded into a cube, not necessarily just the conventional cross-shaped net given on the sheet.)

At the end of the lesson, it would be worth inviting some pairs to talk through their approach. Do all the resulting nets look the same? Why or why not? The class' nets and cubes would make a great display, along with a copy of the challenge itself.

This sheet gives larger coloured faces of the cube which can be made from card or stuck onto six square 'Polydron' pieces so the puzzle can be done again and again.

Why do you think these two faces are next to each other on the cube?

Look at these two faces. Which other one goes near them?

Possible extension

Some learners can be challenged to make the net of the octahedron from this sheet.

Possible support

Suggest making a net from this sheet and leaving it so it can be folded and unfolded. Then draw or paste on the faces one by one. If 'Polydron' squares are available the cube can be built up using the pieces from this sheet.

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.