median
don steward
mathematics teaching 10 ~ 16

## Saturday, 24 November 2007

### rectangles

in dealing with perimeter and area it's useful to work on the two measures together, at least then you see who's getting them muddled up...

asking students to draw three or four rectangles and record their perimeter and area enables any misconceptions to (hopefully) be identified

then someone can be asked to give their P and A value, other students have to identify the rectangle from this information (rather than having drawn it themselves)

why are all the perimeters even?
can they ever be odd?

perimeter =14, area = 12

find more rectangles where P is greater than the  A value
also find some where P is less than A

for a given rectangle (3 by 4), how can you create a shape with a larger perimeter but the same area?

for a given perimeter (e.g. a given rope length of 20m), what rectangle has the largest area?

looking at areas and perimeters of rectangles, some people are surprised that when the area gets bigger the perimeter doesn't have to (and vice versus)

it's also of interest to find the two rectangles (which includes squares of course) for which the perimeter has the same numerical value as the area, P = A