Same Length Trains

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
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Problem

Same Length Trains printable sheet

 

Matt and Katie were using Cuisenaire rods. They placed rods end to end to make 'trains'.

Here are their two trains:

Image
Same Length Trains
 

What is the same about the two trains?

What is different?

You might have noticed:

  • the trains are the same length as each other
  • the top train uses rods that are all different (light green, black, pink and dark green)
  • the bottom train uses rods that are all the same (white)
  • there are four rods in the top train
  • there are 20 rods in the bottom train
  • the white rods are the shortest
  • the white rods are all the same length
  • each colour rod is a different length

Can you make some more trains the same length as Matt's and Katie's trains, each using rods of just one colour?

How many different trains can you make?

How do you know you have found all the possible trains?

If you haven't got any Cuisenaire rods, you may like to use the interactivity below to try out your ideas.

 

You may be interested in the other problems in our Cuisenaire Feature.