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This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.


This activity investigates how you might make squares and pentominoes from Polydron.

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?


Age 7 to 11
Challenge Level


Some time ago I was walking past a garage. Down on the ground was the big sign that they have that tells motorists how much the petrol will cost. You've probably seen them yourselves and you may have been asked to look out for the cheapest petrol around. The signs usually tell you the price for the different kinds of petrol. Since we measure in litres it's the price for one litre.

Well, this sign was being prepared to be put up by the side of the garage. I went over and looked at the part that shows the price. I was interested in how the numbers were shown and how they altered when the price changed. This particular one, like so many, showed the numbers like they are on a calculator display.

The little lines on a calculator display can be called 'light bars'. This is how they generally look for the figures 0 through to 9:-


In this sign they were brightly coloured flaps which on one side showed the colour and on the other side were blank. As I walked away from the garage I got thinking. This is the challenge that came to my mind.

If we had 16 light bars we could only make certain numbers. For example:-


So, my challenge to you is to find all the numbers you can make, using 16 light bars all the time and forming the figures in the same way as I did them for 0 to 9.

When you've done a few you may be able to think of a method or system for helping you along the way. When you do, do write and let us know what it was, as well as sending us your solutions.

The last word, as usual, is to say when you are happy with what you have got, "I wonder what would happen if ...?''

Why do this problem?

This number exploration offers an opportunity for pupils to investigate different aspects of our number system.

Possible approach

Some younger pupils will like to have 16 little sticks or rods to see what they can do. Other pupils might work on squared paper drawing the numerals along the sides of the squares.

It is handy to have some calculators available for them to check how numbers are written (particularly the 4 and the 7 - 7 varies from calculator to calculator so look carefully).

Key questions

Tell me about the numbers you've found.
How did you find these?
It looks as if you have a kind of system for finding more, can you tell me about it?

Possible extension

If some of the pupils have been looking at taking a number like 565 and writing also 556 and 655; then taking different kinds of numbers and looking at all the possibilities just using those numerals, then this can be extended. They could look at the number of ways you can rearrange 3, 4, 5, etc different numerals and/or 3, 4, 5 numerals in which two are the same.
Searching for the largest and smallest numbers and maybe allowing a decimal point to be used where ever they wish is another possibility.

Possible support

Pupils who find it hard to make a start may need an adult to work alongside them in helping to construct the right shape for each digit.