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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?

Which Is Quicker?

Age 7 to 11 Challenge Level:

1, 2, 3, ... 10, 20, 30, ... Which is quicker, counting up to $30$ in ones or counting up to $300$ in tens? Why?
Which is quicker, counting up to $40$ in ones or counting up to $4,000$ in hundreds?

Which is quicker, counting up to $10$ in ones or counting up to $1,000,000$ in hundred-thousands?

Which is quicker, counting up to $20$ in ones or counting up to $140$ in sevens?

Which is quicker, counting up to $25$ in French or in English?

Maybe you could work on this with a partner!
When you have timed yourselves and decided about the reasons for your results, you could invent some other examples for yourselves.
You could predict which was going to be quicker and then try them out to test your prediction.