Friday, August 22, 2008

3D trigonometry

3D Trigonometry in year 10 is one of those subjects that lots of kids have issues with. Students traditionally learn just one topic at a time, are tested and then move to the next topic. With 3D trigonometry are all of a sudden faced with using lots of maths all at once.

Topics that all come together:
  • Parallel lines (in 3D)
  • Alternate/Complementary/Supplementary etc angles
  • Polygon properties
  • Trigonometric ratios
  • Pythagoras' theorem
  • Sine Rule
  • Cosine Rule
  • Oblique and isometric drawing
  • 3d visualisation
  • Volume, Surface area
  • Algebra (in all its guises)

My students have seen some success in this topic through the use of "wireframes" (made of skewers and connected with a hot glue gun) and templates placed in the wireframes to indicate various right angled and non right angled triangles. It also helps them see parallel lines and equivalent lengths/angles. This seems to be the concrete element they need to put all the other stuff in place.

I also try to introduce the topic multiple times throughout the year as new concepts are introduced (eg. parallel lines - > volume -> pythagoras -> trig ratios -> sine rule -> cosine rule)

Also useful is the discussion on solving triangles here.

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