### 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?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

### 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?

# Up and Down Staircases

##### Age 7 to 11Challenge Level

How many blocks are needed for a $3$ step up-and-down staircase?

Try making a table of the number of blocks needed for each numbers of steps.

Can you rearrange the blocks for each staircase to make a square pattern? How might this help?