Mike Ollerton’s Problems

RF, DSE and AG went to a session on a Saturday morninng by Mike Ollerton, to get stuck into some problems. Here is one, that DSE and AG presented back to the team.

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Answers handed out promptly – ensures that you could discreetly check your own, and importantly, that everyone now has the same labels for each triangle
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Linking to collecting like terms
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Order through intuitive reasoning – no need to get bogged down in surds. Good application of telescoping sums in the extension.
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A level extensions

To solve the question on the left…

  • Alberto dived into trigonometry, using double angle formula for tangent.IMG_6082.JPG
  • I dived into analytic geometry (after first “cheating” and finding the answer on geogebra), working out the equation of each line, the intersection of the lines, and then using the shoelace formula to work out the area

There surely must be a simpler way to work out the area, but nobody could find it yet.

 

An excellently stretchy task – plenty of further questions:

  • How many triangles in a 4 by 4 grid?
  • What about an m by n grid?
  • Explore areas? Angles?

Sphinx: other example of stretchy problem

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