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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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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?
Bracelets
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Age 7 to 14
Challenge Level
Here's a game to play with an adult!
How do you play?
You'll need an adult to play with. You'll also need a grid of numbers from 1 to 100 (you can print one from here), or you can use the interactive version.
The grown-up chooses a positive even number that is less than 50, and crosses it out on the grid. You then choose another number to cross out. The number must be a factor or multiple of the first number. Take it in turns to cross out numbers, at each stage choosing a number that is a factor or multiple of the number just crossed out by the other player.
The first person who is unable to cross out a number loses. Try playing again with you going first.
Do you have any winning strategies?
Are there any numbers you shouldn't go to?
This game can replace standard practice exercises on finding factors and multiples. In order to play strategically, pupils must start to think of numbers in terms of their factors, utilising primes and squares to develop winning moves.
Easier version: use a smaller grid, eg 1 to 50
Harder version: see what happens when the first person is allowed to choose a number greater than 50. Switch the challenge from winning the game to covering as many numbers as possible.
There's a classroom version of this game here.
NRICH is part of the family of activities in the Millennium Mathematics Project.