Cuisenaire Squares

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Rod Fractions

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Cuisenaire Spirals

Cuisenaire Spirals

Here are two open spirals made from cuisenaire rods.

I used only the even numbered rods.
You can experiment making spirals using the rods on our Cuisenaire interactive environment.
There may be some sets of real Cuisenaire rods in your school.

When you've done a lot of exploring you might like to try the something similar with numbers.
If you do, have a look at Number Spirals here.

Why do this problem?

This exploration provides a good environment for discovery and surprise. There are lots of different ways of exploring the ideas once the main ideas have been grasped. It can develop into a visual pattern spotting exercise as well as a numerical pattern spotting one.

Possible approach

If possible it would be good for all the pupils to see the interactivity and observe closely the gradual formation of the example shown. The activity can then take several different routes according to the questions that are asked.
If there is no access for pupils to use or see the interactivity then using Cuisenaire rods would be best. It would also be possible to create a set of laminated rods in different colours by using this sheet: Wordpdf

Key questions

What do you notice?
Is there some reason why that happens?
What other groups of rods could you use?
Can you predict the pattern that using different rods produce?

The two shown have a clear pathway in between the rods. It's a spiral too! Could we form a spiral with a sequence of rods that would leave no spaces?

Possible extension

Challenge the pupils to form a spiral in which the lengths of the rods increase in a pattern and they create longer rods to continue it further. Further extension work can be found by moving competent pupils to Number Spirals found here.