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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?
Age 7 to 11 Challenge Level:
One block is needed to make an up-and-down staircase, with one step up and one step down.
$4$ blocks make an up-and-down staircase with $2$ steps up and $2$ steps down.
How many blocks would be needed to build an up-and-down staircase with $5$ steps up and $5$ steps down?
Explain how you would work out the number of blocks needed to build a staircase with any number of steps.
NRICH is part of the family of activities in the Millennium Mathematics Project.