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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?

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It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Bracelets

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

Counting Cogs

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2
Which pairs of cogs have you found that work?
Which pairs didn't work?
Do you get a sense of why?
What do you notice about the numbers of teeth in each case?