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You might like to look at the same idea when numbers are used instead of blue squares.
Here is a starting idea:
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
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?