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Combining Cuisenaire

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Combining Cuisenaire

Here are two different Cuisenaire rods:

two different rods

How many different ways can you find to line them up end to end?
How many different ways are there to line them up if both rods are the same?

Now there are three different rods:

three rods

In how many different ways can you line up the three rods?
Imagine two of the rods are the same. How many different ways are there to line them up now?
How many different ways are there if all the rods are the same?

What would happen if there were four different rods? How many ways can you line them up now?
If two rods are the same, how many ways could you line them up?
And how many ways are there to line them up if three are the same?
How about if they are all the same?

You might like to use the interactivity below to try out your ideas.
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This problem is a very basic introduction to combinations and permutations. The hints would make good questions to ask children once they have had a first go and encouraging them to talk about what they are doing is invaluable. Using "real" Cuisenaire rods (and OHT rods for demonstration purposes) will give children a chance to try out ideas if they are not able to use the interactivity. One of the main aims of this problem is to give pupils the opportunity to work in a systematic way, which might need discussion and modelling.