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Class of Gold

Activity Overview

Students investigate Fibonacci numbers and the ratios of successive Fibonacci numbers.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 47 - 53 from the attached PDF file for your class

    • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Enter the first 20 numbers of the Fibonacci series in a column
  • In a second column enter the 2nd to 21st number of the Fibonacci series
  • Divide numbers in the second column by numbers in the first column to get a ratio of successive Fibonacci numbers as decimals rounded to the nearest thousandth
  • Enter values of the ratio in a third column
  • Notice that the ratio tends to point toward the value of the Golden Ratio of 1.618
  • Measure and record the height and navel height of each student as lists
  • Calculate the ratio of height to navel height
  • Find the mean average of the ratios
  • Create a scatter plot of navel height versus height, and use the manual-fit option to draw a line that passes through most points plotted
  • Use the mean average to find the approximated equation of the line
  • Convert the measurements from centimeters to inches and observe the ratio of height to navel height

    • After the Activity

    Students will complete the Worksheet and analyze the results.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

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