Understanding Area: Teacher Led Discussion

    *	Discuss the idea of area as a measure of how much surface an object has. e.g. a 	handprint. We can measure this by counting the number of thumb prints can fit 	inside. Better if we have a standard measurement.
      	Already have length base unit: metre 

Other units (cm2, mm2) for area can be found in a similar way. Also discuss hectares (100 ares, 1 are is 10m2)

*	So we need to find out how many of these squares fit into our problem.

We count 30 squares. A quicker way is
A=base x height (6cmx5cm = 30cm2)

*Link back to the problem at the beginning of the lesson. Pair students to solve the problem.

Regular shapes - Paper cutting

*using rectangles of paper (eg A4) and scissors the formula for most regular shapes can be developed.

*Triangle Start with 1st sheet of paper marked with base and height. Blue-tack to the board formula A = b x h alongside.

*Triangle. Cut the next sheet diagonally. We have cut the rectangle in half therefore, the area of the triangle with base length b and height length h will be half of the rectangle with the same measurements. Write this explanation on the board.
Formula: 

Also demonstrate that a non-right angled triangle will have also have area half of the original rectangle by fitting the white smaller triangles in to the shaped part.

*The formula for the area of a parallelogram can be demonstrated by cutting a triangle off as shown in the diagram and moving it to the other side of the shape. Since the area of the rectangle was b x h and we have lost no paper when making the parallelogram the area of the parallelogram is also b x h. Emphasise that the height is perpendicular to the base and that we didn't need to find the length of the sloping side.

*The area of a trapezium can be developed by starting with a trapezium and thinking of the base measurement in the b x h formula as the average of the lengths of the 2 parallel sides. i.e. 

Take care with the symbols, since a and b are commonly used as the lengths of the parallel sides and we have been using b to represent the length of the base.

*Area of a Circle. Start with a circle and divide into many sectors. Cut out and organise into an approximate parallelogram as shown in the diagram.

The base of this parallelogram is half the circumference of the original circle. The height is the radius. Therefore the area of the circle can then be shown to be:

 which simplifies to  

Discuss what happens as we take more and more sectors.