Discovering Phi: The Golden Ratio

Fe, phi, fo, fum. This activity leads pairs to find the ratio of consecutive terms of the Fibonacci sequence. The pairs find that the Fibonacci sequence can be found in many places. A discussion with the class shows that the ratios found were very similar and close to the rational approximation of the number Phi.

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CCSS: Designed
Instructional Ideas

  • Use at the high school level and focus on the Fibonacci sequence
  • Facilitate a discussion on how precision will affect outcomes
Classroom Considerations

  • Fibonacci squares puzzle needs to be made on poster board
  • Laminate copies of Natural Pictures handout
  • LEGO NXT robot needs to be built and programmed
Pros

  • The activity is based on a classic activity of finding Phi
  • Using the robot catches the attention of pupils
Cons

  • Phi is not directly referenced in CCSS
  • LEGO NXT robot not available to all classes
  • PDF version of MATH Adventurers Worksheet Answers does not have the answers