Showing posts with label sequences. Show all posts
Showing posts with label sequences. Show all posts

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!