Why do this problem?
provides opportunities for children to develop their drawing skills and to learn to follow detailed instructions. It also offer opportunities to explore a number of different ways of creating spirals.
For a whole class activity you could ask different groups to work on creating the different spirals and compare their results. Group collaboration and discussion will help them to make sense of the instructions and to follow them accurately. During the holidays investigating and spotting spirals might be a family project as you travel around or explore the internet for images and
Where should you start?
What do you need to do next?
Have you counted/measured accurately?
Children could take photographs of spirals they notice in their surroundings and compare these with the ones they have created. They could investigate rules for making spirals. The analysis of spirals and their equations takes you into some pretty tricky mathematics that is likely to be beyond most children at this level but even looking at the equations can be interesting.
It would be possible to create some supporting resources such as sheets with the squares started on them. Children could then engage with creating images and spotting similar spirals around them or in pictures.