Why do this problem?
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.
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: Word
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?
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
Pupils will find this task easier if they have access to concrete apparatus.