Introduction | Tasks | Process | Group Member Roles | Bio Links | Task 2 | Topics |Due Dates | Evaluation

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Numbers in Nature.

What does 1, 1, 2, 3, 5, 8, 13......have to do with rabbits, flowers and shells?

Fibonacci (around 1175 - 1250 AD)

(a webquest for Algebra 2B)

In this webquest you're going to find out who he was and why his name is so important in mathematics.

California Math Standards:

22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.

Big Idea: Understanding series and sequences

Essential Question:

After this assignment Students will be able to:

Introduction

"Real mathematics is not crunching numbers but contemplating them - and the mystery of their connections."

--Charles Krauthammer, Pulitzer Prize winning essayist

The natural world is loaded with patterns. From leaves on plants to the shape of a nautilus shell, numbers can help us to describe and understand these patterns.
In 1202 A.D., Leonardo Fibonacci discovered a unique mathematical sequence that has importance today. It is one way in which many of nature's most beautiful, strange, and seemingly unrelated objects show similarities.

So, are you ready to learn something new?!!! Well take out a pen or pencil and a piece of paper and lets get started!!!!

The Tasks:

Roles of Group Members:

Each member of the group will take on a different responsibility. Choose in your group who will take on each role.

Navigator - This person will be responsible for reading the instructions for the data sheets in Task 2. It is your job to make sure the instructions are being followed accurately.

Recorder: This person will be in charge of recording the data found in Task 2. This person will also be in charge of writing the answers that the group comes up with to the questions in this task Make sure the Recorder has neat handwriting.

Geometer: This person will be responsible for drawing out the geometric figures in Task 2.

Task 1. Find out facts about Fibonacci and his sequence
Your report should answer most of these questions and include anything else you discover that you find interesting.

1. Where and when was Fibonacci born? Did he live there all his life? How old was he when he died?
2. What besides mathematics was Fibonacci interested in?
3. Where did he get his schooling?
4. Aside from the Fibonacci numbers what other contributions did he make to mathematics

MAKE SURE YOU INCLUDE A PARAGRAPH ON WHAT MAKES THE FIBONACCI SEQUENCE SO SPECIAL.

You can use the following links or any others you find to get your information. Make sure you write where got your information.

Each individual is responsible for turning in their own paper (minimum 1 page, typewritten, double-spaced)

Who was Fibonacci?
Wikipedia Bio
Fibonacci Biography

Task 2: Demonstrate an understanding of Fibonacci numbers.
Each group will use the following materials

As a group, look at the following sequence of numbers.
1,1,2,3,5,8,13,21,34,……
These are the Fibonacci numbers

Take the data sheet Mr. Berlin handed out and as a group answer the first three questions. Have the recorder note the answers. Answer the 4th question for extra credit.
After you've completed this task take the chart paper and follow the directions given on the data sheet (Part 2).Have the navigator read the directions and the geometer draw the squares on the chart paper.Make sure to label the sides of the squares with their lengths. The recorder marks down the findings on the chart provided. .(It might be helpful to sketch the squares out on regular graph paper first).
After this is done answer the next set of questions (7 of them) as a group. Have the recorder write the answers neatly.
After these questions are answered get out the protractor and the chart paper with the rectangles you've constructed and follow the instructions found on Part 3 of the Data Sheet. When you are finished. Observe your drawing. Does it look like anything you have seen in nature? When you think you know what it is present your findings to Mr. Berlin.

When you turn in your group data sheets each individual needs to turn in a paragraph explaining how the construction you created in the activity relates to the sequence.

Task 3: Choose a topic from the Fibonacci website.
Click on the following links which will take you to a website about Fibonacci numbers. You will find a wide variety of informative sections on this site. Several of these include activities. Your group is to select one of the topics, explore it. Each individual will submit a summary of their topic which demonstrates their understanding and the group will make a presentation of their topic to the class.

Fibonacci Topics
The Mathematical Magic of Fibonacci Numbers
Using Fibonacci Numbers to Represent Whole Numbers
A Formula for the Fibonacci Numbers
The Golden Section Ratio: Phi

You may also try one of the Fibonacci puzzles found on these pages:
Easier Fibonacci puzzles
Harder Fibonacci puzzles


Task 4: Presentation
Each member of the group needs to participate in putting together some aspect of the presentation. Be as creative as possible. Write a skit or a song, create a video or a PowerPoint. Use whatever resources you have to make the presentation as interesting as possible.
You will have class time to go on the computer and research the project.

 

Summary of What is Expected:

Task 1: INDIVIDUAL turns in a written 1 page paper on Fibonacci and his sequence. Focus on the essential question "Where can we see sequences in nature?" (DUE: MONDAY APRIL 30)
GROUP: Collects facts from individual reports and incorporates it into their 5 minute presentation.
(PRESENTATIONS WILL BEGIN THE WEEK OF APRIL 30)

Task 2: INDIVIDUAL turns in a paragraph explaining how the construction you created in the activity relates to the sequence.
GROUP: Group is reponsible for turning in Data Sheet packet with all questions answered and their geometric representation of the sequence on chart paper.
(PACKETS, CHART PAPER AND INDIVIDUAL PARAGRAPHS DUE FRIDAY APRIL 27)

Task 3 and 4: INDIVIDUAL will submit a summary of their topic which demonstrates their understanding. Summary should be a minimum of 1 page.
GROUP will prepare and make a presentation to the class explaining their topic. Presentation should last approximately 5 minutes, use graphics and include everyone.
(PRESENTATIONS WILL BEGIN THE WEEK OF APRIL 30 - Individual summaries will be due the day after presentation)

The Evaluation:
Your grade for this assignment is based on your ability to meet the above tasks. Below the tasks have been broken down into five overall objectives. Read below to see what you think your score would be. I hope you are all in the green.

Individual Achievement

 

Beginning

1

Developing

2

Accomplished

3

Exemplary

4

 Score
Identify interesting facts about Fibonacci and his sequence and incorporate them in your paper. Unable to identify any facts Able to identify at least one fact Able to identify at least three facts Able to identify at least 5 fact  
Presentation of Paper Paper is handwritten and has no real content. Paper is handwritten and contains limited content. Paper is typewritten and clearly states facts about Fibonacci. Paper is type written and shows insight and details about the life of Fibonacci  
State the Fibonacci numbers and be able to describe how they are obtained and how they relate to nature Unable to state the sequence, or identify any places where it can be seen Able to state the sequence but not able to tell how the numbers are derived, or how they relate to nature Able to state the sequence, explain how the numbers are derived and give several examples of how they relate to nature Paper is typewritten and shows insight and details about the Fibonacci and his numbers
Able to state the sequence and give a formula for generating the numbers. Also give examples of where these numbers are found in nature.
  

Group Work

 

Beginning

1

Developing

2

Accomplished

3

Exemplary

4

 Score
Presentation of biography and topic Unable to adequately present biography or topic. Presents facts about Fibonacci but fails to adequately explain topic. Presents facts and adequately explains topic Presents very interesting facts and shows complete understanding of topic selected.  
Answers to data sheet questions Less than 3 of the ten questions are adequately answered Less than 6 but more than 3 of the ten questions are adequately answered. Less than 9 but more than 6 of the ten questions are adequately answered All of the ten questions are adequately answered and show significant insights
  

Conclusion:
So how did you do? I hope you found Fibonacci to be an interesting character and gained some insight into the fact that math is not just calculations.
This is not Fibonacci!!!