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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?

Twenty Divided Into Six

Age 7 to 11 Challenge Level:

Katie had a pack of twenty cards numbered from $1$ to $20$.

20 cards numbered from 1 to 20.

She arranged the cards into six piles. 

The numbers on the cards in each pile added to the same total.

What was the total and how could this be done? Are you curious enough to find out?