Friday, August 5, 2016

Continued Fractions Planning

I saw this from a reference on twitter and I'm thinking about basing the second session on it. What's cool is that there are plenty of bridges to the golden ratio, pi and irrational numbers we can jump off on.  Currently I think I'll take some of these ideas and break it out into a lecture format so I can stop and have the kids make conjectures and work on questions in small groups.

Starters

Practice simplifying complex but not infinite fractions to get a hang for the process.
Talk about Egyptian fractions?
Convert repeating decimal back to a fraction.

Problems:

  • The first "bad" proof would make a good breakout to explain what was wrong.
  • Looking for patterns in the golden ratio expansion. Can they find the Fibonacci sequence?
  • Therorize about infinite vs. finite continued fractions.
  • https://nrich.maths.org/555 (a bit advanced)

Resources

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