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Making Trains


Laura made a train with the Cuisenaire rods.
Her train was made from three rods which were all different colours.
It was the same length as three pink rods:

three pink rods

Laura's train looked like this:

black, red and green rods

Can you make a different train, the same length as Laura's, with three rods which are all different colours?

Can you make one the same length using no colours that Laura used?

Rob made a train that was the same length as Laura's using four differently coloured rods.
How did he do it?

Charlene made a train which was as short as it could be using four differently coloured rods. Can you find a rod that is the same length as Charlene's train?

Ben made a train using four differently coloured rods the same length as two black rods and a light green one:

2 black rods and a light green rod

He made it without using a white rod. How did he do it?

You may like to use this interactivity to try out your ideas. Click on 'Rods' to choose your rods:

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Why do this problem?

This problem will help pupils to apply and improve their knowledge of number bonds and to develop systematic ways of working.

The link between the Cuisenaire rods and the number they represent could be made more explicit by showing the rods on $1$ cm squared paper. Ideally, this could be done in front of the whole class using OHT rods and a grid.

Key questions

Which is the longest rod? Could you try with that one first?
How about the next longest?
How many white rods are there in Laura's train?
How many different ways can you find to make a train the same length as Laura's, with three rods which are all different colours?
How can you record what you have done?
Would it help to use squared paper?

Possible extension

Those who find this easy could find all the three-colour trains in all lengths from $6$ to $20$ or try Cuisenaire Counting.

Possible support

Suggest drawing round the Cuisenaire rods on $1$ cm squared paper and then colouring them.

Same Length Trains is a simpler problem that some pupils might like to attempt before trying this problem.