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Fibonacci Number Sequence

 

Introduction:  
  Sequences are an exciting area of mathematics, with lots of every day applications. We are going to discover the amazing use of Fibonacci number sequences in nature. These patterns are all around us in our every day life. Patterns are in geometric designs, leaves on plants, music, planets movements, shells, bones, animals, weather, and astronomical patterns. You will learn to recognize and extend this sequence and see it in the world around you.
Task:  
  You will explore resources online to answer specific questions on Fibonacci, whom he was and why he was so important to math. What kinds of sequences are there? Where do they exist in nature? Do people use this information to help them solve problems? You will become engaged in finding information and learn from what you have found.
Process:  
  1. Browse these web sites and learn about Fibonacci and the Fibonacci number sequences.
http://www.mathsisgoodforyou.com/people/fibonacci.htm
http://math.about.com/od/mathematicians/a/fibonacci.htm
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#petals

2. Create a spreadsheet of Fibonaccis numbers. http://spreadsheets.about.com/od/spreadsheetlessons/qt/Fibonacci_Numbe.htm

3. Print, read, and fill out the worksheet about Fibonaccis rabbits.
http://www.mathsisgoodforyou.com/worksheets/fibonaccirabbits.pdf

4. Construct the Golden Ratio and use it to draw the Golden Rectangle and the logarithmic spiral.
http://www.mathsisgoodforyou.com/worksheets/fibonaccirabbits.pdf

5. Watch this movie on illustrating Fibonaccis sequence. Write a short one page paper about mathematical sequences in nature.
http://boingboing.net/2010/03/22/dreamlike-animation.html
Resources:  
  http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html
http://mathforum.org/
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html
http://faculty.evansville.edu/ck6/bstud/fibo.html
http://www.math.temple.edu/~reich/Fib/fibo.html
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#petals
http://math.about.com/od/mathematicians/a/fibonacci.htm
http://www.mathsisgoodforyou.com/people/fibonacci.htm
Evaluation:  
  3 The student provided useful ideas when participating in the classroom discussion.
Perfectly constructed the Golden Rectangle and logarithmic spiral. Correctly answered the answers on the worksheet. Routinely used time well throughout the project and ensured that all things were turned in on time.

2 The student usually provided useful ideas when participating in classroom discussion
Provided high quality work in constructing the Golden Rectangle and logarithmic spiral. Answered most of the questions on the worksheet correctly. Usually used time well throughout the project and turned in most things on time.

1 The student sometimes provided useful ideas when participating in the classroom discussion.
Provides low quality work in constructing the Golden Rectangle and logarithmic spiral. Answered some of the questions on the worksheet correctly. Did not turn in project on time.
Conclusion:  
  Do you know more about Fibonacci now? What other mathematical theories did Fibonacci discover? What other sequences could still be explored?

This Web Quest is available at www.teach-nology.com