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Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Magic Constants

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This investigation gives a lot of opportunities for a wide range of abilities to exercise both their spatial/number awareness.

Possible approach

It might be neccesary for the pupils to be introduced to simpler more common magic squares.

If there is a problem in identifying the 2 x 2 little squares within the 4 x 4 square the first one in the bottom left hand corner could be selected.
87,2

Key questions

Can you tell me about the way you are doing this?
What have you decided to do to the first set of numbers?

Possible extension

Questions 7, 8 & 9 act as a good set of extension activities, further ones could be suggested by the pupils. Then magic squares of a different size could be explored.

Possible support

Some pupils will find it useful to have small square cards with the numbers on a a prepared grid to place them on.