### Counting Counters

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?

### 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?

# Rope Mat

##### Age 7 to 11 Challenge Level:

I have a square table-mat made from rope that spirals from the centre. It is rather like this one:

The mat is a $14$ centimetre square. The rope is $2$ cm wide.

How many centimetres of rope will I need to make another mat just like it?

How much rope would I need to make a $12$ cm square, or a $16$ cm square?

Is there a quick way to work this out?