An idea for the classroom - perimeter
In Issue 31, I talked about an article in ‘Mathematics Teaching’ 211 – November 2008 written by John Mason. Included in the article are some activities which are ‘designed to promote work on the awareness which underpin perimeter and area’.
Following on from John’s ideas, I was inspired to do some more work on perimeter.
The resource shows a rectangle.
If you know the length and width of the rectangle it is possible to work out the perimeter. If the length and width are a and b, the perimeter is 2a + 2b. Similarly, if indents are made to the rectangle, the perimeter can still be expressed in terms of a and b.
The resource goes on to show progressively more complicated shapes, each derived from the previous one, whose perimeters can be expressed in terms of the original length and width.
Having used the shapes on the resource, students can be asked to draw their own rectangle and progressively modify the shape, at each stage determining the new perimeter in terms of the original. Using your own starting point and making your own modifications 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 does your new shape relate to your original shape?
- Is the width of the indent important?
- Is the length of the indent important?
- Can you draw a shape whose perimeter is 4a + 2b, etc.
- Can you draw a shape whose perimeter is 3a + 2b, etc.
Although pupils calculate the perimeter of the shape, the main focus is to use mathematical reasoning to justify the decisions the pupils make in order to perform the calculations.
Have you got a nice activity to reinforce pupils’ understanding of perimeter? Why not tell us about it?