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## An interesting discussion

Yesterday I was teaching perimeter of compound shapes with my year 9s. After they had been solving problems based on shapes made up solely from squares and rectangles one if the pupils asked “Sir, will the perimeter always be even?” I thought this was a great point for discussion so I opened it up for the class.

They decided that for the type of shape we were looking at the perimeter would indeed always be even, as you had to cover every distance twice, meaning 2 was always a factor of the perimeter. I was impressed with their reasoning, but a little disappointed that one had to prompt non-integer side lengths. When I did they quickly dismissed this with “of course we knew that sir, but be were only considering whole numbers!”

I then asked them to consider is this applied to all shapes. They quickly concluded that triangles could have odd perimeters with integer side lengths, and circles, then they extrapolated to any shape with an odd number if sides. They concluded quickly that regular polygons with an even number of sides couldn’t have an odd perimeter if it had integer side lengths. Irregular polygons provided a more difficult challenge, and I left them to ponder it over the weekend!

Categories: Commentary, Maths, Teaching
1. March 21, 2015 at 2:28 pm

Nice. What about compound shapes made from a rectangle minus a smaller rectangle? Why is it always the same as the perimeter of the original rectangle? Does this work for more complicated compound shapes? Why?/Why not?

• March 21, 2015 at 2:31 pm

Nice, although its not always the same, only if you take the smaller one from a corner. If you take it from the middle of a,side (ie to make a u shape) the perimeter is altered.

1. April 28, 2015 at 1:07 pm