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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?

Snake Coils

Stage: 2 Challenge Level: Challenge Level:1
Imagine a $600$ cm snake that coils into a circle, but he's not going to eat himself.
He is going to coil himself around to make a double circle, then a treble circle and so on until he is coiled round like this rope.

Challenge 

Once in a circle how much further will he have to slither to make a double circle of his body?  What's this length as a fraction of his total length?

How much further will he have to slither to make three circles of his body?
What's this length as a fraction of his total length?

 

How much further will he have to slither to make four circles of his body?
What's this length as a fraction of his total length?

How much further will he have to slither to make five circles of his body?
What's this further length as a fraction of his total length?


Final challenge


When the snake has slithered a total of $550$cm along his body length, making smaller and smaller circles of his body, how many circles will there be?