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!

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