math patterns power point
TRANSCRIPT
MATHEMATICS IN
NATUREPresented by:
Jay Gallagher & Laura Lieberman
Definition of Mathematics
“Mathematics is the science of patterns and order” (Van De Walle, 2004)
Study of PatternsThe National Council of Teachers of Mathematics suggests
that,
“The study of patterns should start at a very early age with rich and interesting experiences to facilitate a better understanding of the concepts related to functions and algebra that students will encounter later in upper middle school and throughout secondary school”
Recognizing
PATTERNS INNATURE
is a rich and interesting way for
elementary and middle school
students to study mathematics
Patterns in Nature
“The natural world contains an infinite variety of patterns. Patterns are found in plants and animals. All living things create patterns. Patterns are constantly being created by simple physical laws”
Flower Patterns
Flower Patterns
Patterns can be – Described in numbers
and words– Repeated– Compared
Can you describe and compare these patterns?
Are any patterns repeated?
Fibonacci Numbers
• Leonardo Fibonacci is famous for a pattern or series of numbers
• The series starts with 0 and 1• Every subsequent number in the series
is the sum of the previous two numbers
0,1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,...
Fibonacci Numbers in Nature• “Flowers often have a Fibonacci number of petals, daisies
can have 34, 55 or even as many as 89 petals!”
• “The patterns of seeds in a sunflower appear to be spiraling outwards. There are a Fibonacci number of spirals. This pattern keeps the seeds uniformly packed no matter how large the seed head.”
• Pinecone Spirals: These two numbers, 8 and 13, are consecutive numbers in the Fibonacci series
Nature WalkLet’s take a nature walk to
examine more patterns in nature
Patterns in Objects
Patterns in Actions
• Ducks in a Row• Migration Routes of
Monarch Butterflies• Weather Patterns• Conservation and
the water cycle• Time
Patterns in Characteristics
Patterns in Sounds
• Cricket sounds
• Bird Sounds
• Waves
Studying patterns will lead to …
• Variables and Equations
• Variables as pattern generalizations
And other problems to solve…
Problems Using Patterns
The surface area of one cube is 6 units:
By understanding the relationship in patterns, problems that involve patterns, like the one below can be solved!
This is how one student solved the problem:
M.C. Escher• Escher uses patterns in his artwork
that connects mathematics and nature
.
Visit http://www.mcescher.com/
Recommended BooksLots & Lots of Zebra Stripes:
Patterns in Nature, by Stephen R. Swinburne
Nature’s Paintbrush: The Patterns and Colors Around You, by Susan Stockdale
Nature’s Patterns, by Joyce R. Becker
Right in Your Own Backyard: Nature Math (I Love Math), by Time Life Book Series
Plant Math, by Patricia Whitehouse
Images and References• http://www.indoorooss.qld.edu.au/04studgl/fibonacci/webs/nature.html• http://www.pvplc.org/photocontest/photo99/photos/twofriends.jpg• http://raysweb.net/patterns/index.html• http://www.tomtezak.com/• http://atschool.eduweb.co.uk/sirrobhitch.suffolk/patterns_nature/animals.htm• http://www.greeneclipse.net/thewavfiles/animal_e.html• http://www.blazingpaddles.on.ca/photography/tips/mud.htm• http://illuminations.nctm.org/imath/across/connections/pattern/index.html• http://www.intermath-uga.gatech.edu/topics/algebra/patterns/links.htm• http://www.nctm.org• http://www.mcescher.com• http://www.accessexcellence.org/AE/AEC/AEF/1995/welch_patterns.html• http://www.42explore.com/patterns.htm• http://www.uen.org/themepark/html/patterns/naturepatterns.html