# Fibonacci’s Cows

Purpose

This is an activity based on the short illustrated novel Fibonacci’s Cows

Achievement Objectives
NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
Specific Learning Outcomes
1. Students will be able to identify examples of natural and human made structures that represent the Fibonacci sequence.
2. Students will be able to explain the relationship between members of the sequence and how the next number is generated.
3. Students will explore the Golden Ratio and the Golden Angle through natural and human made structures.
Description of Mathematics
1. The numbers of the Fibonacci sequence and The Golden Number, Angle and Ratio can be found occurring in both the natural and human made world.
2. The proportional relationships between numbers within the Fibonacci sequence create the “golden” numbers.
Required Resource Materials
Fibonacci’s Cows by Ray Galvin

Digital cameras

Internet access

Activity

Picture this!
This activity is based on the book: Fibonacci’s Cows

Author: Ray Galvin
Illustrator: Susanna Burton
Publisher: Shortland (2001)
ISBN: 0-7901-2550-1

Summary:
Ryan is challenged by his teacher to make a mathematical connection, and through his dreams (short chapters) he explores the Fibonacci sequence and the other discoveries of the famous mathematician. He also discovers the relations between the sequence and geometry and measurement. At the back of the book there are biographical notes for students about Fibonacci and notes about the “Golden” number and a glossary of terms. This book may take several sessions to cover.

Lesson Sequence:

1. Prior to reading, explore the cover of the book with students asking about whether they can see or know of any connections between the illustrations and whether they have any prior knowledge of the mathematician, Fibonacci.
2. Discuss any examples the students have of mathematics in nature. Record some of these ideas to re-visit once you complete the book.
3. Share the book with your students as a read-aloud or as assigned reading if you have multiple copies. As you read chapters, explore the mathematical ideas together and keep records of the key words and understandings.
4. During the reading, ask students to collect photographic examples of the Fibonacci numbers in nature. One place that is a rich source of these is the plant world with the number of petals on different flowers and the branching of stems or leaf organisation. There are many examples on the internet through Google Images that can inspire students and guide what they will be looking for in their environment.
5. Following the reading, explore and discuss the Golden Number, Golden Ratio and the Golden Angle (pp. 42-45). Ask students to explore the ratio within the school structures (the hall, the classroom, etc) and the angle within natural examples (sunflowers, pinecones, shells, etc). Record examples with photos.
6. Revisit the notes made prior to reading and ask students to reflect on the images on the cover now and make connections between the images and the content of the book. Record the new understandings and connections.
7. As a class put together a slideshow of Fibonacci evidence at your school or within the community with slides explaining the mathematics of the plants and buildings.