# Activities

• ##### Download

• • ##### Subject Area

• Math: Algebra I: Sequences and Series

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 6 from the EXPLORATIONS Book:
Discovering Mathematics with the TI-73: Activities for Grades 7 And 8

The following materials are required for this activity:
• Meter stick
• Transparency

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