### Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

### Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### 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:
This activity has been particularly created for the most able, and so pupils might be expected to work independently from an adult. So these notes are shorter than usual for our activities.

## Snake Coils

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?

#### Hint

This diagram for the five coils might help you to imagine what is happening.
Each set of circles should be the same size and on top of each other, but we could not show that in a diagram.

#### Final challenge

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

### Why do this problem?

This activity engages the pupils in both a spatial and numerical context. It gives them also the freedom to choose how they go about it - visualising in their head, using paper, string etc. that they have requested and/or making use of a spreadsheet. They can learn a lot from adopting one method and then realising that an alternative method would be better.

### Possible approach

Presented as on the problem page.