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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?

Cut it Out

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An equilateral triangle can be dissected into four (equal) smaller equilateral triangles.

Can you dissect an equilateral triangle into six smaller ones, not necessarily all the same size?

Is it possible to dissect a larger equilateral triangle into any number of smaller equilateral triangles?

Are there any numbers that are impossible?