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