The Topic: Patterns

Easier - Patterns are things that repeat over and over. Patterns can be sets of objects, actions, or characteristics. They are things that are arranged or occur naturally. Examples of patterns are a set or combination of repeated lines, colors, letters, numbers, shapes, forms, figures, and actions or behaviors. You can find many patterns in nature such as honey combs and snow flakes.

Harder - A pattern can be a sample, a guide, or model that someone copies such as a pattern for a foundry casting, a machine part, or a piece of clothing. Patterns are also the typical activities of a thing, a person, or a group. Events or qualities can happen in the same way or in the same order. Things sometimes behave according to a pattern. A pattern occurs or can be used over and over again.

Patterns by S. Alejandre from MathForum
http://www.rialto.k12.ca.us/frisbie/patterns.html
This links-site contains information on a wide array of patterns.
Note: Above site has broken links but is still a useful collection.
Another Website from the MathForum:
2) Symmetry and Pattern: The Art of Oriental Carpets http://mathforum.org/geometry/rugs/index.html
3) Investigating Patterns: Symmetry and Tessellations http://ccins.camosun.bc.ca/~jbritton/jbsymteslk.htm
4) Number Patterns: Fun with Curves & Topology http://ccins.camosun.bc.ca/~jbritton/jbfunpatt.htm

Patterns from Utah Education Network's Themepark
http://www.uen.org/themepark/html/patterns/
A pattern whether part of nature, representing mathematical concepts, or imbedded in art relies upon three characteristics: a motif or unit, repetition, and a system of organization.

Patterns in Mathematics from D. Cohen, the Mathman
http://www.shout.net/~mathman/html/patterns.html
Some people say that mathematics is the science of patterns. That's not a bad description. Not only do patterns take many forms over the range of school mathematics, they are also a unifying theme.
Related Sites:
2) Chaos Theory and Patterns from Ask A Scientist: Mathematics Archive
3) Patterns in Mathematics from Ask Jeeves
http://www.learner.org/teacherslab/math/patterns/index.html

What is a 'Natural' Pattern? by I. Alexander
http://easyweb.easynet.co.uk/~iany/patterns/natural.htm
The whole of human scientific and artistic endeavor can be seen as the attempt to discover pattern in nature.
Related Website:
2) Fibonacci Numbers and Nature (Advanced Level) by R. Knott
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
3) Finding Out How the Patterns of Nature Develop from ScienceNet
http://www.sciencenet.org.uk/slup/CuttingEdge/Sep01/patterns.html
4) Patterns in Nature from Sir Robert Hitcham's Primary School
http://atschool.eduweb.co.uk/sirrobhitch.suffolk/patterns_nature/index.htm
5) Patterns in Nature: Rhythms of Life (Advanced Level) by R. Pellegrino
http://www.microweb.com/ronpell/PatternsInNature.html

Websites By Kids For Kids
Pattern Palace (ThinkQuest Project)
http://library.thinkquest.org/CR0213184/
Read poems about patterns, find out about symmetry, tessellations, fractals, and palindromes, and have fun with the royalty of Pattern Kingdom.

More Websites
Cinquain Poetry
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/5-6/activities/poetry/cinquain.html
Learn the pattern used in a cinquain, a five line poem.
Related Website:
2) A MAZE : The Cinquain Journal by L.J. Cohen
http://www.amaze-cinquain.com/front.html
Another Poetry Pattern:
3) Diamante Poetry
http://teams.lacoe.edu/documentation/classrooms/amy/algebra/5-6/activities/poetry/diamante.html

M.C. Escher - Life and Work from National Gallery of Art
http://www.nga.gov/collection/gallery/ggescher/ggescher-main1.html
Wander the four virtual rooms devoted to the art of M.C. Escher.

Musical Patterns (Advanced Level) by B. Hammel
http://graham.main.nc.us/~bhammel/MUSIC/compose.html
This is an essay on patterns in musical composition transformations, mathematical groups, and the nature of musical substance.

Repetition
http://www.english.upenn.edu/~afilreis/88/repetition.html
Here is a detailed look at how repetition of a sound, syllable, word, phrase, line, stanza, or metrical pattern is a basic unifying device in all poetry.

Those Amazing Palindromes by S. Bacchus from University of Georgia
http://jwilson.coe.uga.edu/emt669/Student.Folders/Bacchus.Mohamed/pal/pal.html
Here you find some history of the palindrome, a few examples, and the mathematical proof.

Websites For Teachers
Calculator Pattern Puzzles by A. Holsten
http://www.col-ed.org/cur/math/math06.txt
This lesson was designed to allow young children to explore number patterns and relationships while introducing them to the calculator at the same time.

Emergent Literacy: Building Patterns, Solving Problems (Grades K-1)
http://www.lite.iwarp.com/cra2000.html#patterns
This thematic unit plan directs students to locate, explore and create patterns with shapes and text.

Math Patterns in Children's Literature (Pre-K to Grade 2) from Carol Hurst's Children's Literature Site
http://www.carolhurst.com/subjects/math/patterns.html
In problem solving, facility with patterns enables children to see the important information in a real-world math problem, how the various pieces of information relate to each other, and the possibilities for predicting the outcome.

Patterns
http://www.tlp.on.ca/DICE/DICE6_Group_4/index.htm
This patterns project involved teachers from three different schools across several grade levels and a variety of subject areas: music, science, social science, mathematics, and social studies.
Related Website:
2) Patterns Exist in All Aspects of Life (Scroll down for entire content) http://www.op97.k12.il.us/instruct/Iarts/Patterns/index.html

Patterns in Music and Math from Family Education Network, Inc.'s TeacherVison
http://www.teachervision.com/lesson-plans/lesson-10343.html
Students learn how to solve music and math problems by finding patterns.
Related Lesson Plan:
2) Math/Patterns (K - Grade 1) by A. Lund from Lesson Plans Page
http://www.lessonplanspage.com/MusicMathPatterns.htm

Patterns in Nature by P. Welsh from Access Excellence
http://www.accessexcellence.org/AE/AEC/AEF/1995/welch_patterns.html
In this interdisciplinary learning project, students research patterns in nature which illustrate biological and mathematical concepts. They design group projects that model these concepts in a cooperative setting with fourth graders.

Patterns in Nature from Boston University, Center for Polymer Studies
http://polymer.bu.edu/pins/index.html
These activities encourage students to explore how fundamentally random microscopic events can give rise to fractal macroscopic patterns.

Patterns in Nature Booklet (Grades K-3) from CanTeach
http://www.canteach.ca/elementary/pattern4.html
Students will examine patterns on objects in nature, then use rubbings of these patterns to create pattern booklets.

Patterns Here, There and Everywhere by A. Hanlin & B. Amundrud
http://mathcentral.uregina.ca/RR/database/RR.09.96/hanlin1.html
The goal for this lesson is an understanding of numbers, patterns, counting, and operations.

 pattern shape linear pattern nonlinear pattern concentric repetition procedure poetry routine symmetry branch number system M. C. Escher palindrome predict microscopy spiral maze stripe ambigram polygon tessellation circle kaleidoscope set of actions inversion ray recognition cryptography characteristics fractal sample observation guide model motif

Created by Annette Lamb and Larry Johnson, 10/02.