How many right-angles?

After a week of exploring angle sums in polygons, both through interior and exterior angles, we attacked an excellent problem by Don:

I have a shape with 100 sides. What is the maximum number of right-angles the shape can have?

Fascinating to see different reactions to the problem:

Go straight for the jugular: try and draw a 100-sided shape
A similar (but digital) attempt
Overly keen pattern spotting. (The odds/evens pattern breaks for n = 11,12)

One group came up with a hierarchy for solving the problem, that I would struggle to improve on:

  1. Guess
  2. Draw it out
  3. Understand the pattern and apply it

Students worked in trios:

  • Geogebra master (in charge of using technology to quickly sketch ideas)
  • Pattern spotter (in charge of generalising any results)
  • Organiser (ensuring good communication within the group)



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