## Saturday, November 14, 2009

### Teaching Surface Area

I've been examining the issues with teaching surface area.

Here's an approximate sequence:

Prior knowledge required
(easily takes 3 weeks+ yr 10 with a weak group filling gaps)
• Notation for parallel and perpendicular sides
• Perimeter of Rectangles, Squares, Triangles (with all sides given)
• Area of Rectangles & Squares, Triangles (with all sides given)
• Circumference and Area of circles
• Area of Trapezium, Sectors
• Area of Composite Shapes (with all lengths given)
• Area of Composite shapes (finding missing sides using subtraction)
• Area of Composite shapes (using ratios of the area of known shapes to find area eg. 1/2 circle)
• Arc length
• Pythagoras, Trigonometric ratios
• Area of Composite shapes (using Pythagoras & Trigonometric ratios to find missing sides)
Surface Area Topic
• Identifying 3D shapes (cylinders, spheres, pyramids & prisms)
• Constructing 3D shapes using Nets (cylinders, pyramids and prisms)
• Identifying cross sections of 3D shapes
• Finding the area of cross sections of 3D shapes
• Finding the surface area of simple 3D shapes using defined formula (cylinders, spheres, pyramids and prisms)
• Using surface area of simple 3D to solve composite surface area problems (and using subtraction to subtract shared hidden sides)
• Deconstructing 3D shapes into constituent 2D shapes
• Finding the surface area of composite 3D shapes using deconstruction and 2D shapes
• Finding surface area of simple 3D shapes that have had sections removed using ratios
• Finding the surface area of composite shapes using simple 3D shapes, deconstruction and ratios.
• Using Pythagoras and Trigonometry with planes in 3D shapes to find surface area

It's a big topic!