generalisations can emerge

and created patterns can be justified by relating them to the diagram(s)

a ppt is here

for these tasks:

- it is simple enough to experiment with and record (dotty paper being better than squared)
- you can appreciate that longer diagonal lines don't seem to help achieve a maximum
- it is helpful to have a regular pattern, with symmetries sometimes
- different 'routine' growing patterns can be compared
- number patterns are created from a diagram so justifications can relate to the pictures
- odd and even 'n' numbers need to be considered - as is often the case
- there are depth (proof) and breadth (e.g. angle sums) extensions

the 36 sided maxagon for a 6 by 6 grid:

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