In this module students will discover the interconnectedness of math (the Fibonacci Sequence and the Golden Mean) with art and nature, using resources on the World Wide Web.
 

Rationale
  
Students are always asking the question:  " When are we going to use this?" They need to experience the relationships that exist  between math and the real world.  These relationships are embedded in real world phenomena but are seldom observed by students.  Our module is intended to motivate students to experience common phenomena from a different point of view while aligning this experience with the following state goals:  Math (6,7 and 9), Science (11) and Art (27).   The students will work with virtual images and real images to make these discoveries. The Web will take the student to locations where they will look for patterns that show the relationship among math, art and nature. Sites on the web will provide multimedia  images that would be difficult or impossible to demonstrate in the classroom.
 

Objective

• Use the language of math to describe the dimensions in architecture.

• Students will use the language of math to describe plant part relationships.

• Students will explore electronic plant encyclopedia to determine if plants in the same family  have one of the Fibonacci Sequence values.

• Students will be able to identify and generate the Fibonacci Sequence.

• Students will be able to determine Golden Mean geometrically and  algebraically.

• Students will be able to measure buildings and determine if their proportions fall within the Golden Mean.

• Students will identify the connection between Fibonacci Sequence and the Golden Mean.

• Students will be able to understand the role of proportion plays in   architecture and painting.

• A series of different size rectangles will be presented to the students and they will survey which is the most "pleasing" to the most students.

• Find the ratios of the width to length of all the presented rectangles.

• Use the WWW as a resource tool for researching examples of the golden mean.

• Learn how to determine n terms of the Fibonacci Sequence and how it relates to the Golden Mean .STATE GOAL 27: Understand the role of the

 arts in civilizations, past and present.

• Describe and solve the hare and bee problem.

• Analyze plants for the existence of the Fibonacci Sequence.

• Students will publish a Web site with examples and findings.

DEMONSTRATE AND APPLY A KNOWLEDGE AND SENSE OF NUMBERS, INCLUDING BASIC ARITHMETIC OPERATIONS, NUMBER PATTERNS, RATIOS, AND PROPORTIONS.
 
     STATE GOAL 7:

ESTIMATE, MAKE, AND USE MEASUREMENTS OF OBJECTS, QUANTITIES, AND
RELATIONSHIPS, AND DETERMINE ACCEPTABLE LEVELS OF ACCURACY.
 

    STATE GOAL 9:

USE GEOMETRIC METHODS TO ANALYZE, CATEGORIZE, AND DRAW CONCLUSIONS ABOUT POINTS, LINES, PLANES, AND SPACE. 

  STATE GOAL 11:
               HAVE A WORKING KNOWLEDGE OF THE PROCESSES OF
               SCIENTIFIC INQUIRY AND TECHNOLOGICAL DESIGN TO
               INVESTIGATE QUESTIONS, CONDUCT EXPERIMENTS, AND
               SOLVE PROBLEMS.
 

  STATE GOAL 27: Understand the role of the
 arts in civilizations, past and present.