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Cuisenaire Spirals

Stage: 2 Challenge Level: Challenge Level:1

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 this computer activity below.
There may be some sets of real Cuisenaire rods in your school. 

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Click on 'Rods', to choose rods and and drag them onto the squared background. 
A rod can be rotated by $90^\circ$ by clicking any key whilst dragging.
You can change the  background squares (smaller or larger) using the 'View' menu.

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.

Possible support

Pupils will find this task easier if they have access to concrete apparatus.