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Same Length Trains


Matt made a train with the Cuisenaire rods. It looked like this:

light green rod, pink rod, black rod, dark green rod

Katie made one too, exactly the same length, with just white rods. Hers looked like this:

20 white rods

Can you make some trains the same length as Matt's train, with rods of just one colour?
How many different ones can you make?

You may like to use the interactivity below to help you. Click on 'Rods' to choose your rods.

Full Screen Version
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Why do this problem?

This problem is a good way for children to gain familiarity with factors and multiples in a non-threatening environment.

You could also make this an opportunity to encourage the children to have a system for making sure that they find all the possible solutions.

Possible approach

Using the interactivity on an interactive whiteboard or via a projector would be a good way to introduce the problem.

Ideally, it would be good for the pupils to then work in pairs with "real" Cuisenaire rods and talk about how they are solving the problem.

Returning again to the whiteboard and interactivity will allow the whole group to share their solutions.

You could model starting with the red rod and working up to the green, then pink, then yellow etc if the children themselves do not find some good ways.

Key questions

How many white rods did Katie use?
How many red rods did you need to make the same length?
Which colour rods fit in exactly?
Which colour rods cannot be fitted in exactly?
How will you know that you have found them all?
How can you record what you have done?

Possible extension

Learners could try using different numbers of white rods to make "same length trains" with rods of just one colour. Using $21$, $22$, $23$ and $24$ could prove interesting.

Pupils who enjoy this problem might like to try Making Trains.

Possible support

Try to use real Cuisenaire rods if at all possible, otherwise use the interactivity and work through the different lengths. You could suggest recording on squared paper.