Colouring Flags

This activity is designed to get children thinking permutations, how many different ways things can be arranged.

You need a paper and pencil and some colouring pens.

Imagine you have been asked to design a new flag for a country. 

They want you to use just two colours, red and green.

The flag is made up of 6 rectangles like this:


Draw a series of flags and colour them in.

IMPORTANT: You must colour 2 rectangles red and 4 rectangles green.

Here are three different examples:

How many different flags can you make?

Is there a way to organise your colouring so you can check that you have found all of them?

  • Have A go

  • answer

Draw several flag shapes, two rows of three rectangles. See how you can colour them using 2 red rectangles and 4 green rectangles.

Draw some different flags. How many different ones can be made ikf you vary the number of colours?

What about:

  • 3 red and 3 green rectangles
  • 1 red rectangle and 5 green ones
  • 2 red, 2 white and 2 green rectangles

Which of these gives you the smallest number of different flags?

Try working with flags with more rectangles, what about a flag that is 3x4 rectangles?

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