fighting chaos the nature of geometry

Photography brought to you by AMSCO Math + Math Xhttp://www.perfectionlearning.com/math-overview

Fighting Chaos:

The Nature of Geometry

http://www.perfectionlearning.com/math-overview


Essential Questions• What are examples of geometry appearing in the

natural world?

• What is meant by the saying that “geometry helps make sense of the world”?

Enrichment: What is Chaos Theory? What is your opinion regarding the Butterfly Effect? Why do you think that we as human beings crave order? Or do we? Why are we “wired” to be so curious? Or are we?

http://www.kineticmath.com/trialTo learn more, go to

perfectionlearning.com

Math is a Global Competency

• What are ways that we can practice and apply these concepts?


http://www.kineticmath.com/trial

http://asiasociety.org/node/20785

What are examples of geometry appearing in the natural world?

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25 Examples of Perfect Geometry Found in Nature

Shapes, Patterns, Order, Structure… Jeff Hawkins, in his book On Intelligence, writes, "Your brain receives patterns from the outside world, stores them as memories, and makes predictions by combining what it has seen before and what is happening now... Prediction is not just one of the things your brain does. It is the primary function of the neo-cortex, and the foundation of intelligence."

“A Hunger for Certainty” by David Rock

http://list25.com/25-examples-of-perfect-geometry-found-in-nature/1/

Developing a Concrete Understanding of Mathematics

Nature Walk…. Collect examples of objects that you find at school, home, and your community that are representative of geometry in nature. Bring them to class for

further investigation.

• Pair-Share examples of the objects that you found. What makes these objects concrete examples of geometry? What shape(s) is (are) represented? Why?

• Choose your favorite example of geometry found in nature to share with the class. Why was this item chosen? What makes it the best concrete example of geometry found in nature?

• Choose the worst example of geometry found in nature to share with the class. Why were these chosen? Why was this item chosen? What makes it the worst concrete example of geometry found in nature?

Write a Compare and Contrast Essay

As a class, compile a list of characteristics that are similar and different based on the information that was discussed regarding the best and worst examples of geometry in nature.

• How are they alike?

• How are they different?

Use a Venn Diagram like the one found on the next slide to record your findings.

Extend: Writing Across the Curriculum



Object 1 Object 2SAME

Different Different



What can you deduce based on your findings?Please write this information down in your science journal. Remember to put this information in a format that will best inform your writing. It doesn’t necessarily have to be in sentence format.Next, using the notes you took in your science journal, write your compare and contrast essay.

Developing a Visual Understanding of Mathematics

Sketch your examples of geometry in nature that you found on your nature walk.

• Best example of geometry in nature that you found:


Identify Patterns and shapes that influenced your decision.


Sketch your examples of geometry in nature that you found on your nature walk.

• Worst example of geometry in nature that you found:


Identify Patterns and shapes that influenced your decision.

• Worst example of geometry in nature that you found:


Sketch these examples.

• Do you agree with these findings? Why or why not? Be prepared to explain.

In the photography that follows, questions regarding size, shape, and relative position of figures and with properties of space can be

answered.

Be prepared to answer how, when, where, and why to defend your observations.

Geometry Helps Make Sense of the World

Yes

No

Debate the Issue:• Divide into teams composed of groups of 3-5.

Make sure you have an equal number of teams.• Choose a Team Name based on whether you

believe or do not believe the statement above. • Two teams will face off against each other.• Team One: We believe that geometry does help

make sense of the world.• Team Two: We do not believe that geometry

does help make sense of the world.• Make sure to provide proof of your stand.

No

Yes

Developing an Abstract Understanding of Mathematics

Applications for utilizing math in the “real world” is critical for you to develop a deep understanding and appreciation of math and how it impacts your daily life. Distance Learning is a great way to explore this concept, and it gives you the opportunity to be introduced to people whose careers depend on their understanding of math. Through live, interactive lessons, you will be able to explore mathematical concepts as they relate to the following locations:

More virtual field trips available at www.fieldtripzoom.com


Mathimals

How much hay do you need to feed seven elephants? Can you draw an animal exhibit design to scale? This interactive program will include videos, live animals, and hands-on activities that demonstrate the importance of math in the Zoo world. Please specify grade level and concepts being studied when requesting the program.

Over 400 programs from highly recognizable providers around the world!

Join Kimberly Hoormann, Outreach Coordinator, at the zoo in St. Louis, MO,

for a live, interactive lesson!

www.fieldtripzoom.com



Geometry in Nature

Did you know that math is fundamental to the shape and

structure of seashells, honeycombs, and leaves? Investigate the natural

patterns found all around us. Located in historic Liberty State Park,

neighboring the Statue of Liberty and across the river from Lower

Manhattan, Liberty Science Center first opened its doors in 1993.


Join Fanny Cruz for a live, interactive lesson at the Liberty Science Center

Jersey City, NJ!




In this one hour, interactive program, students utilize the sport of baseball and playing field to identify and investigate the many shapes that make up the game. AT&T Park provides the perfect backdrop to illustrate the importance and application of geometric concepts in both its construction and design. Dependent upon grade level, students will calculate either perimeter or area of home plate and discover how the Pythagorean Theorem can be applied to the baseball diamond.


Join Linda Vessa, Educational Tours Coordinator, at the AT&T Park: Home of the San Francisco Giants Baseball Team!

𝑎2+𝑏2=𝑐2




Math Connections in Art

Students are introduced to the work of American painter and printmaker Chuck Close and learn to apply math concepts and skills used by the artist to transfer photographic images to another working surface. Using photos of themselves, students will measure, grid, and reproduce their portrait as a painting or pencil rendering that may be finished later at home or in the classroom. Concepts such as ratio, percent, and area are reinforced.


Join Dale Hilton at the Cleveland Museum of Art for a live, interactive

lesson!




Circling the Bases

Examine how geometric concepts, such as circumference, area, perimeter and diameter apply to baseball. Students play an interactive baseball game to test their skills!


Join Bruce Markusen, Manager of Digital and Outreach Learning, at the National

Baseball Hall of Fame live from Cooperstown, NY, for an interactive

lesson!



Enrichment:What is Chaos Theory? What is your opinion regarding the Butterfly Effect? Why do you think that we as human beings crave order?

Or do we? Why are we “wired” to be so curious? Or are we?


Describe how this picture makes you feel?


Develop an innovative project based on your research into Chaos Theory and the Butterfly

Affect

Peters Projects.....

The Creators Project....A True STEAM Initiative

Chaos and Fractals

Getting Started:

The New England Complex System Institute...Solving Problems of Science and Society

Frogly Speaking: When Pop Culture Meets the Butterfly Affect

http://petersprojects.com/artists/ryan-wolfe.html/art/wolfe-1.html

http://thecreatorsproject.vice.com/en_us

http://www.stsci.edu/~lbradley/seminar/index.html

http://necsi.edu/guide/concepts/conceptmap.html

http://froglyspeaking.blogspot.com/2010/08/butterfly-effect-when-science-meets-pop.html

Article by Timothy J. Seppala Robotic Vines Illustrate Chaos Theory and the Butterfly Effect

THE CREATIVITY, ART, AND TECHNOLOGY OF RYAN WOLFE

http://www.engadget.com/about/editors/timothy-j-seppala/

http://www.engadget.com/2015/06/28/robot-vines-butterfly-effect/








Complimentary Resources Brought to You By:

• Asiasociety.org• List 25 (post by Elaine Dimdam)• FieldTripZoom.com• Flavorwire (article by Alison Nastasi)• Peters Projects (Ryan Wolfe—artist)• The Creation Project• The New England Complex System Institute• Perfection Learning• Frogly Speaking• Moore4Education (photographs and Power Point by Kim Moore)

Thank you for your contribution to the knowledge of children everywhere!

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