An idea for the classroom - area and perimeter
I have been reading an article in ‘Mathematics Teaching’ 211 – November 2008, written by John Mason concerning his address to the Easter 2008 conference. Included in the article are some activities which are ‘designed to promote work on the awareness which underpin perimeter and area’. It is one of these activities that I have adapted and want to offer here as our idea for the classroom. It caught my eye because I have often been surprised that students have problems with perimeter and area, and thought for a long time that they merely got the labels wrong – confused the two things. More recently, I have changed my mind and am now aware that pupils do not actually get the concept of perimeter or the concept of area so I am keen to engage them with some activities which develop their understanding of the concept rather than just rehearse how to calculate ‘it’.
The resource (which can be downloaded here) gives a shape drawn on squared paper. Students are invited to draw two other shapes on the grid as follows:
- a shape which has the same area and a longer perimeter
- a shape which has the same perimeter and a greater area.
It would then be good to ask pupils to draw the shape:
- a shape which has the same area and the longest perimeter
- a shape which has the same perimeter and the greatest area.
Good questions to ask would be:
- have you got a technique for increasing the perimeter and keeping the area the same?
- have you got a technique for increasing the area and keeping the perimeter the same?
- can you explain how your new shape relates to the original shape?
- how do you know you have the longest perimeter?
- how do you know you have the longest area?
Having done some work on the two shapes provided, pupils could suggest their own shapes to work with – this is an integral part of the activity rather than a ‘bolt on’ for those that finish quickly.
Good questions to ask pupils would be:
- how did you choose the starting shape?
- why was this a good shape to choose?
At no time is the intention of the activity to calculate the area or perimeter, but to use mathematical reasoning to justify the decisions the pupils make.
Have you got a nice activity to reinforce pupils’ understanding of these concepts? Why not tell us about it?