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Colour Building

Age 11 to 14 Challenge Level:
In this activity, you will need to use Cuisenaire rods, or the interactive Cuisenaire environment which you can find below. If you have not used the Cuisenaire Environment before, you might find it helpful to look at the instructions and video.

I wonder how many different ways there are of combining white rods (1) and red rods (2) to make the same length as the orange rod (10) ...
There are going to be quite a few, so let's start with a simpler challenge...

In how many ways can you combine white rods (1) and red rods (2) to make the same length as the pink rod (4)?



Once you think you've found them all, click below to check.

There are five different ways to make the same length as the pink rod:
 

Note that I count "white, white, red" and "white, red, white" as different, even though they both use two white rods and one red rod.

Using just red and white rods, there's only one way of making the same length as the white rod, and only two ways of making the same length as the red rod.

Can you find all the ways of making the following lengths using just reds and whites:
  • the light green rod (3)?
  • the yellow rod (5)?
  • the dark green rod (6)?
Can you spot a pattern that will help you to predict how many different ways there are to make up the black rod (7)? Use the interactivity to check your prediction.

Without using the interactivity, can you work out how many different ways there are to make up the orange rod (10)?

Can you explain the pattern?

Extension
Try making different lengths using combinations of white, red and light green rods.
Can you use the patterns you observe to make predictions about how many ways there will be?