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For younger learners

  • Early Years Foundation Stage

Colouring Curves Game

Age 7 to 14
Challenge Level Yellow star
  • Game
  • Teachers' Resources

This game is for two players, and you will need paper and a pencil.

Start by drawing a curve on the paper. The curve can cross over itself as many times as you like, but must join back to where you started (this is called a closed curve).
Here is an example of the sort of curve you might draw:

closed curve
Now take it in turns to choose a region and colour it in. The only rule is that shaded regions can't share an edge, although it's ok for them to meet at a corner or vertex.
This is what the curve above might look like after each player has had two turns:
shaded regions
Eventually, you will run out of regions to shade without shading regions which share an edge. The last person who can shade a region is the winner!

Here are some ideas to think about as you play:

  • Is it better to go first or second? Does it depend on the curve?
  • Can you design some simple curves where you can guarantee that you will win?
  • What do you notice about the number of regions that meet at each vertex?
  • Can you come up with any strategies to help you to win?

Another way to play the game is to take it in turns to shade regions each using a different colour, without shading adjacent regions in your own colour, so the game might look a bit like this:

coloured curve



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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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