Nix the Tricks: Areas of quadrilaterals, triangles
A great deal has been mentioned in recent years about ‘cognitive load’ and reducing this for students studying mathematics. Tina Cardone’s book ‘Nix the Tricks’ has some interesting ideas around this in relation to area formulae.
When teaching area the order in which I have previously approached topics has been; rectangles, right-angled triangles, and then non-right-angled triangles.
Tina suggests switching this order and teaching parallelograms after rectangles. Since any triangle is half of a parallelogram (and a rectangle is a special case of a parallelogram), this eliminates the need to treat right-angled and non-right-angled triangles separately.
Making parallelograms more of a focus has an additional pay-off when considering trapeziums. By making a copy of a trapezium, rotating it 180 degrees, and placing the result adjacent to the original, a parallelogram is formed. Finding the area of the trapezium is reduced to halving the area of the resulting parallelogram.
Taking this thinking to its logical conclusion there may even be an argument for teaching parallelograms first, and deriving the area of the rectangle as being a special case. If you do give this a go then please let the community know how your students get on by leaving a comment to this post.
A final consideration is around language. The usual description of calculating the area of a rectangle is unique amongst shapes in using the words ‘length’ and ‘width’. Switching to ‘base multiplied by height’ the area for each of the shapes is then a variation using the same words.
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