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## 'Chairs and Tables' printed from http://nrich.maths.org/

## Chairs and Tables

I made a chair from interlocking cubes. It looked a bit like this:

Can you make a chair too? It need not be the same as mine.

Now can you make a table to go with your chair?

When you have done that you could try making chairs for the Three Bears: a big chair, a middle-sized one and small one.

Please send us photos of your chairs and tables if you can.

### Why do this problem?

Although

this problem sounds straightforward, children will find the matter of scaling the table to match the chair quite a challenge. Tackling this will help to develop children's spatial awareness. It is also a great opportunity to encourage discussion among the class or group.

Possible approach

A hands-on approach is absolutely necessary for this problem. You could start by making a chair from interlocking cubes yourself and showing the group, and then challenging them to make one of their own. (Do not make a chair that looks too good -some children find this discouraging!) You might like to put your chair somewhere it can be seen easily so children can refer to it as they build
their own. Alternatively, you may decide to hide it at first to see how learners get on.

Children could then work in pairs or small groups to make a chair and a table under which the chair will fit. This should promote much discussion about space and shape. At the end the whole group could come together to see each other's handiwork.

Key questions

How many cubes have you used for that leg of the chair?

How many cubes will you use for the seat of the chair?

Does your chair fit under the table with enough space for someone to sit down?

Possible extension

Making three chairs and three tables should prove extension enough! If more is needed, you could challenge the children to draw what they have done.

Possible support

You could encourage those who are struggling by asking them to make the legs first and then a seat for them fit into. Finally, they could put a back onto this "stool".