Educational Goal: The Goal of this Lesson is to introduce the mathematical concept of the Golden Ratio to middle and high school age students. In this beginning lesson, the Golden Ratio will be introduced by showing it’s occurence throughout nature. 

Students will be able to connect the Golden Ratio to direct natural objects they might see in their everyday life. This book can compliment the student's math and science curriculum. Perceptual Options: 


Linguistic Options: 
Cognitive Learning Methods: The golden ratio concept is matched to student's prior knowledge of nature. This type of matching boosts each student’s working memory. Questions asked throughout the book demonstrate inquiry based instruction, using ‘self generated’ learning methods to increase students interest and attention. 

The repetition and repeating visuals of the golden ratio help store the lesson in the student’s long term memory and working memory. Identifying similarities and differences in of the golden ratio throughout nature allows students to consider and remember what was learned. Clarifying animations assist in keeping students’ sustained engagement. Assessment: Applications to Neuroscience Research: Source of Cognitive Research Information: http://bengal.missouri.edu/~vanmarlek/ Musings of the author: http://mcguiret560.edublogs.org 
Teacher's Curriculum Guide:
Introductory Information about the Golden Ratio
About the Golden Ratio: The Golden Ratio can be illustrated within special dimensions of Sprials, Triangles and Rectangles where the ratio of the length of the short side to the long side is .618, was noted by ancient Greek architects as the most visually pleasing rectangle and its dimensions were used to construct buildings such as the Parthenon.
The Golden Ratio has also been used extensively in classical paintings where it was believed to produce the most visually pleasing figures. The ratio also appears all over nature, such as the number of petals on some flowers, biological forms like the nautilus shell, mollusks, animal antlers, leaves, human proportions, galaxy spirals, and the relations between harmonious tones in music.
The Golden Ratio, Finding Spirals in Nature and Beyond.
Table of Contents
Page 1. A Basic Ratio Between A and B
Page 2. Using Squares and Rectangles to Build a Pattern
Page 3. The Golden Ratio in a Snail Shell
Page 4. The Golden Ratio in a Sea Shell
Page 5. The Golden Ratio in the Skin of the Pineapple
Page 6: The Golden Ratio in the Animal Kingdom
Page 7: The Golden Ratio in Astronomy
 The Golden Ratio between a and b 
The formation of the Golden Ratio spiral pattern can be shown using squares and rectangles. 

The Golden Ratio in the repeating spiral shape of the snail shell 
Next time you go to the Ocean, Can you find the repeating spiral pattern 
Look at the natural pattern in 
Page 7:
In addition to natural patterns
found here on earth,
the spiral pattern
of the golden ratio
can also be seen
in the pattern of
our galaxy.
\  
See if you can find more examples of the golden ratio
The End. 