Janet Brack

TEEL 362

Mathematics and Science Methods

Germaine Taggart, Ed.D.

November 23, 1998

Lesson Information

Grade: Middle School

Key idea: Fibonacci patterns in nature

Goals: Math process - connections

Math product - patterns

Science process - collecting and interpreting data

Science product - fibronacci sequence and ratio

Prerequisite concepts: Patterns Ratio Rate Proportion Percent

Skills: Convert fractions to decimals and using a compass to draw an arc

Lesson Activities

1. Exploration Phase:

Objective - The students will explore the concept of patterns in nature by

examining natural objects and sharing observations with the class.

Materials - pine cones, sea shells, celery, other natural objects

Introduction to lesson - Story about Fibonacci's life.

Procedure - Students will examine natural objects as groups and look for patterns

Evaluation - Groups will share their findings

2. Invention Phase:

Objective - The students will demonstrate knowledge of fibonnaci ratio by applying it to

rectangles in a pencil and paper activity.

Materials - graph paper, markers, compass,

Procedure - Fibonacci's sequence and ratios will be presented to students. Following along with an overhead demonstration, students will construct Fibonacci Rectangle. Students will compare their picture with a picture of a cut away of a sea shell.

Evaluation - Use questioning strategies to prompt students to make connections between their observations of natural objects and the Fibonacci sequence and ratio.

3. Expansion Phase:

Objective - The students will relate the Fibonacci sequence and ratio to their everyday life by determining the ratio of the sides of ordinary objects.

Materials - 2x3 photo, 3x5 card, greeting cards, sheet of paper

Procedure - Students will discuss what is "most appealing": shape of face and placement of features, merchandisers, art, architecture (Parthenon in Athens Greece 440 BC)

Evaluation - Complete worksheet

Patterns - arrangements of shape or color

Ratio - relationship of one number to another

1 to 2 1:2 1/2

Percent - a ratio that compares a number to 100

Proportion - an equation that shows two ratios are

Equal 3/5 = 24/40

Rate - quantity, amount, or degree of something

measured per unit of something else

0+1 1+1 1+2 2+3 3+5 5+8 8+13 13+21 21+34

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

1:1 = 1.000000

1:2 = .5000000

2:3 = .6666666

3:5 = .600000

5:8 = .625000

8:3 = .615384

13:21 = .619047

21:34 = .617647

34:55 = .618181

55:89 = .617977

89:144 = .618055

144:233 = .618025

1:1 = 1.000000

2:1 = 2.000000

3:2 = 1.500000

5:3 = 1.666666

8:5 = 1.600000

13:8 = 1.625000

21:13 = 1.615384

34:21 = 1.619047

55:34 = 1.617647

89:55 = 1.618181

144:89 = 1.617977

233:144 = 1.618055

2.0 _______________________________________

1.5 _______________________________________

1.0 _______________________________________

0.5 _______________________________________

0 _______________________________________

1 1 2 3 5 8 13 21 34 55 89 144 233

Garland, T. H. (1987). Fascinating Fibonaccis. Palo Alto, California: Dale Seymour

Publications.

Gies, J. & Gies F. (1969). Leonard of Pisa and the New Mathematics of the Middle Ages.

New York: Thomas Y Crowell Company.

Reimer, L. & Reimer W. (1995). Mathematicians Are People, Too. Palo Alto, California:

Dale Seymour Publications.

Taylor K. (1992). Pattern. New York: John Wiley & Sons.

Department of Computing, School of Electronic Engineering, IT and Mathematics,

University of Surrey, Guildford, Surrey, UK

http://www.ee.surrey.ac.uk./Personal/R.Knott/Fibonacci/fib.html