### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### I'm Eight

Find a great variety of ways of asking questions which make 8.

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

# Round and Round the Circle

##### Stage: 2 Challenge Level:

I started with a clock without hands or the minute divisions (except for those where there is a number). The $12$ was replaced by a $0$ and the numbers placed outside the face.

I ruled lines joining up the numbers.

I started by counting in ones and I got a $12$-gon (that is a $12$-sided polygon - if you like long words you can call it a dodecagon).

Then I ruled lines counting round in $2$s. And I got .....?

Perhaps you do not need to put the numbers round the circles.

I tried $5$s (wow!) and $6$s (well!).

Each time I go on drawing lines until I get to the point where I first started.

Then I tried $7$s, $8$s, $9$s, $10$s, and $11$s.

Something interesting was happening.

Why don't you try it? What patterns do you notice emerging?

And what about counting round in $12$s?

Which shapes are the same? Can you think of a reason why?

Can you see a connection between the number in which you are counting around the circle and the number of sides in the shape you are making?