## 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?

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?