Snake Coils

Age 7 to 11

Challenge Level Yellow star

Colin the snake is 600cm long and is coiled into a circle, with his nose touching the tip of his tail.

He is going to coil himself around to make a double circle, then a triple circle, and so on. When he coils himself around, his head slides along the top of his body so that he ends up looking a bit like this rope coil.

Challenge

Imagine that Colin is in a circle, looking like he does in the picture at the top of this page. His head is going to slide around until his nose is above the tip of his tail again, making a double circle. (As he does this, his whole body will gradually move inwards, and will end up being a tighter circle.) How far along his body will Colin's nose travel?

Next, Colin's head slides over his body again so that his nose is above the tip of his tail, making a triple circle. How much further has Colin's nose travelled along his body?

Now Colin wants to get from this point to a quadruple circle, making a coil of thickness four. How much further will his nose travel to make four circles?

How much further will his nose travel to make five circles?

Can you write each of these four distances as a fraction of his total length?

Final Challenge

When Colin's nose has slithered a total of 550cm along his body length, making smaller and smaller circles of his body, how many circles will there be?

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Snake Coils

Final Challenge

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