I have started working on finding the area of 2D shapes with year 9 and I wanted them to see the connections with the area of a rectangle. Firstly because they are most confident with that shape but mostly because when given a formula they don’t remember the considerations that need to be made. For example; if they learn area of a triangle is 1/2 x b x h they don’t remember that you can’t just take 2 of the lengths as ‘b’ and ‘h’ unless they are the two lengths connected by a right angle.
Show a class an equilateral triangle with sides 6cm and if they calculate 1/2 x 6 x 6 then its time to reinforce the idea of a triangle being half a rectangle.
I plan to show my class the following images and ask them to find which shapes are half the rectangle, which are more and which are less.
Then i plan to get students to try and derive the areas of triangles, parallelograms, kites and ultimately trapeziums from the rectangle. I have used a rectangle that i cut and reform to show this too.
I have found with compound area involving rectangles that i give the same problem but split it differently each time. I ask the class to find the area of each and if they notice they are all the same shape each time then see if they can prove it 3 different ways.
I was pleased that students imagined pieces moving or cut the shapes up in order to see if the shaded part was more, less or equal to a half.
We then derived the areas of other 2D shapes from the area of a rectangle.
I made another similar task
Students have to group the shapes so that the shapes in each group have the same area as one another.
I’ve been rethinking some questions for 2D shapes. I want Ss to consider whether they should split or form a rectangle to find the area of compound shapes