don steward
mathematics teaching 10 ~ 16

Thursday, 5 April 2012


finding the maximum number of sides that a (closed) polygon can have on a square dotty grid

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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