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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?


Age 7 to 11
Challenge Level

Remember that you must have two or more sticks to make a set.
Try starting with a set of $2$. How many sticks would be in the set placed across these $2$? How many crossings would that make?
If you can't have a set of $1$ stick, what number could you try next?
Do you notice anything about the number of sticks in each set and the number of crossings? How do these numbers relate to the total number of sticks?