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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?

Cuisenaire Squares

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


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?

Simple Train Journeys

Age 5 to 11
Challenge Level
How will you record the different journeys?
Have you got a way of making sure you have got them all?
Perhaps there is a way you could use the three-station journeys to help you find all the four-station journeys?
When you're looking for a pattern in the numbers, it might help to go even simpler as well - how many journeys would there be for just two stations?
Can you see any way that the numbers of different journeys are connected to each other? It might help to write them in a list or table.