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
Related Links-Sites:
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
5) Patterns, Patterns Everywhere http://cte.jhu.edu/techacademy/web/2000/heal/index.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
http://newton.dep.anl.gov/askasci/math99/math99004.htm
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
  
After visiting several of the websites, complete one or more of the following activities.
 
Create Kaleidoscope Designs Online. Follow the instructions found at Kaleidoscope Painter (Javascript Capability Required) by F. Permadi.
 
Identify Some Patterns. Print out (1) Dinosaur Patterns from Enchanted Learning. Then circle the animal that comes next in the pattern. Also you may want to try (2) Which One Comes Next? from Suessville University, (3) What Comes Next? from mathSURF, and (4) Pattern Mania from Primary Games.
 
Create Music Patterns. Go to Pattern Builder from Harcourt School Publishers and explore creating and listening to your own music patterns.
 
Explore Some Wallpaper Designs. Create wallpaper patterns at Java Kali by M. Phillips from Geometry Center (Requires Java Capabilities).
 
See If You Can Construct A Fault-Free Wall. See how you do with the Brick Activity from the Math Forum. Use dominoes for hands-on exploration. What is the smallest fault-free wall that you can construct, remember the wall has to be a square or rectangle and you cannot cut these "bricks."
 
Complete A Patterns WebQuest. Follow or adapt the procedures found at the following webQuest sites:
1) BeadQuest (Grade 3) by S. Kimmel http://www.guilford.k12.nc.us/webquests/beadquest/beadquest.htm
2) Patterns in Nature WebQuest (Grades 4-8) by J. Wilson
http://www.web-and-flow.com/members/jwilson3/pattern/webquest.htm
3) Patterns of Poetry by E. Gorman (Grade 6)
http://www.sinc.sunysb.edu/Stu/egorman/poetrywebquest-1.html
4) Webquest on Patterns http://www2.corvallis.k12.or.us/lincoln/Webquests/patterns/Webquest.htm
 
Make A Ukrainian Egg. (Advanced Level) Note that this activity involves heating and melting wax over a flame an should not be completed by young learners without direct supervision. But if you are interested in learning or just in viewing these neatly patterned eggs, visit How to Make Ukrainain Easter Eggs (Pysanky) by A. Morash and Georgia's Ukranian Easter Eggs. Click on any design and you'll be taken to the instructions for it.
 
Create A Hex Sign. The "Pennsylvania Dutch" or "Pennsylvania Germans", best known as the "fancy" Dutch, created beautiful folk art type designs commonly referred to as "hex signs." These signs were painted on barns and houses. This is a very old art form and the precise significance of the shapes and colors is not known for certain. You can find the instructions for creating your own at Design and Paint Your Own Hex Sign!!
 
Draw Your Own Navajo Rug Design. Navajo rugs are collected the world over for their beauty and exquisite craft work. Select a color scheme of two, three, or four different colors and use them to draw your own Navajo rug design on 10 x 10 grid paper. Find more information at Navajo Rugs from Prentice-Hall, Inc.
 
Photograph Patterns In Nature, Architecture, and Our Lives. Find some examples at (1) Pattern from Gary Luhm Photography, (2) Patterns in Nature from Kaufman Photography, (3) Patterns in Nature (Slide show-Be patient, Slow loading site), and (4) Patterns in Nature, a Corbis E-Card site. You also may find some subject ideas at (5) The Patterns in Nature by W. Lynch and A. Lang. Then photograph your own images and display your own collection.
 
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.