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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?

Spirals, Spirals

Age 7 to 11
Challenge Level

These are two kinds of spirals I made using squared paper.

The first (on the left) uses the little squares to make the spiral, the second (on the right) uses the sides of the little squares to build the spiral.

I gave myself some rules (often a good idea!):
1/ There is a space throughout making them a kind of "open" spiral.
2/ I finished each spiral in line with where it started in the middle.
3/ I made a number of spirals each one having one more "circuit" (going around) than the previous one.

So these would not do as they don't obey all the rules:


I then started exploring things like the number of little squares/lines in my group of spirals.

So now is the time for you for you to explore your growing spirals.

What do you notice?
You might like to look at the same idea when numbers are used instead of  blue squares.
Here is a starting idea;