 10th Grade Math Assignments  Richard Briston
A math teacher designs Web pages to serve as monthly math assignments, and as an introduction to the Internet and email for his students at St.Mildred'sLightbourn School in Oakville, Ontario, Canada. Student solutions are included for some assignments.
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 The 14 Different Types of Convex Pentagons that Tile the Plane  Ed Pegg, Jr.
Diagrams of the 14 types, sources, and links to related pages on the Web.
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 42eXplore  Annette Lamb and Larry Johnson
Web projects that offer definitions, activities, four good starting points, and many more links and resources for thematic topics such as charts and graphs; codes, ciphers and secret messages; fractals, tessellations, geometric shapes, and figures; number
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 7puzzle  Paul Godding
School visits by the UK's "Puzzle Man" feature numberrelated board games, card games, tricky puzzles, and other math activities that involve logic, strategy, and spatial/visual awareness to improve children's mental arithmetic skills and feed their enthusiasm
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 ABCya.com  ABCya.com, L.L.C.
Free educational math games that introduce basic computer skills: Geometry Practice, Addition with Manipulatives, Subtraction Match Game, Math Facts Basketball, Interactive 100 Number Chart, Math Bingo, Place Value ShootOut, Fraction Tiles, Tower of
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 Alex Bateman's Origami Page
Models by Alex Bateman, Dino Andreozzi, Nick Robinson, and a duck by Edwin Corrie. Includes directions for folding some origami tessellations: square dance, honeycomb, linked circles. Spirals based on Voderberg's tilings, tessellations based on 6.3.6.3
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 Algebra (Seeing is Believing)  De Silva, D'Andreti; ThinkQuest 1997
An algebra tutorial, comprising: mathematical numbers; real number system; numerical representations in algebra (algebraic expressions); algebraic techniques (factoring); quadratic equations and inequalities; graphing (coordinate systems, conic sections,
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 Alphabet Geometry  Jamie Tubbs, MisterTeacher.com
Learn about geometry by looking at letters. Included are interactive Flash movies on transformations, angles, and similar letters. Movies on parallel and perpendicular lines are planned.
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 Amsterdam Tessellation Projects  M. HosMcGrane
Student tessellations created using the software program Tesselmania, inspired by a class trip to the Escher Exhibition in Rotterdam, The Netherlands.
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 Analysis & Knowledge  Sanford Aranoff
Download data analysis software, such as Patterns, which analyzes and charts trends in stock market using Andrews concepts. See also this former Rutgers University physics professor and current high school educator's thoughts on teaching and help file
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 Anisohedral Tilings Page  John Berglund
Tilings and tessellatings with 2anisohedral and other isohedral tilings. With explanations and a bibliography. Berglund's JavaSketchpad applets include circles in a lattice shape; affine polygons, which extends Napoleon's theorem from a triangle to a
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 Arabesco
 Hasan Isawi
Freehand designs elaborated with Autocad and Photoshop to create arabesque images. Site is in Italian.
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 Archimedes' Laboratory  Gianni A. Sarcone and Marie J. Waeber
Archimedes' Laboratory invents, creates, and develops handson thinking games which help teach mathematical applications. They also create and manufacture original educational manipulatives and puzzles to support promotional activities. The resources
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 Artlandia Kaleidoscope  Artlandia, Inc.
A fully interactive program based on and available free with the purchase of the software program Artlandia (requires Mathematica 3.0 or higher; available for all platforms that run Mathematica). It
is as easy to use as an ordinary kaleidoscope  create
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 Artlandia  Software for Programmable Creative Graphic Design  Artlandia, Inc.
A Mathematicabased application for artistic interpretation of data and creating mathematical and algorithmic art. The software provides a selection of tools for constructing geometrical objects from numerical arrays, distributing geometric shapes over
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 Artlandia SymmetryWorks  Artlandia, Inc.
A plugin for Adobe Illustrator that automates creation of surface designs and ornaments based on seventeen wallpaper groups.
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 Association of Teachers of Mathematics (ATM)
A U.K.based association that aims to support the teaching and learning of mathematics by encouraging increased understanding and enjoyment of mathematics. It addresses all those concerned with mathematics education in primary schools, secondary schools,
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 Bee Alert  University of Montana
Bees and portable computers can now be used to assess environmental hazards through the development of electronic hives, toxicological models, extensive databases, and patternrecognizing software that help assess risks posed by metals, radiation, carcinogenic
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 Beyond the Block: Tessellating Patterns  Linda Hampton Schiffer
An article about using tessellations in quilt design.
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 A Bibliography of Mathematics Education  Paul Ernest, University of Exeter, U.K.
A 1994 electronic bibliography prepared for students at the University of Exeter, U.K. Contents: Society, Diversity And Mathematics Education; The Learning Of Mathematical Topics; The Psychology Of Learning Mathematics; Teaching Approaches And Resources
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 Biography of M. C. Escher  Thames and Hudson's Escher Interactive
A biography of the wellknown, early 20th century artist. Escher's work is famous today for the imaginary worlds he created. He combined bizarre creatures and spatial illusions with craftsmanship and love of detail. Born in Holland in 1898, the son of
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 Bits and Bytes  Brian Metcalfe, Editor; Winnipeg School Division No. 1
A K12 education newsletter distributed throughout Winnipeg School Division No. 1 since October 1984. Its focus is to provide educators with tips and techniques to help them integrate technology to enhance learning in their classrooms. The site includes
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 Border Pattern Gallery  John Wolfe; Geometric Structures Class, Oklahoma State University
A gallery developed as a class project: creating and classifying border patterns (also called frieze or band patterns) provides an engaging introduction to symmetry for students of all ages. Examples and explanations for seven different border types.
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 Brainwave  Wognum Art
Ten visual puzzles, to test your visual and reasoning skills. Most have to do with symmetry recognition. There is a "top 5% brain" award to those who earn ten "smart bulbs."
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 Build Your Own Blocks  Mönig, Jens; Harvey, Brian
Turn, move, animate, and iterate figures with this visual programming language, which also lets you draw simple and complex fractals through recursion. Download Build Your Own Blocks (BYOB); watch tutorials; report bugs; and more. Originally designed
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 The Butterfly Website Picture Galleries  Mikula Web Solutions, Inc.
Symmetry in nature: butterfly and moth images from a variety of sources. In most cases, a small picture is included for speed of transmission, and a larger picture is available by clicking on the small picture.
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 Center for Geometry Analysis Numerics and Graphics (GANG)  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
An interdisciplinary Differential Geometry research team. The GANG Geometry Archive is an online library of papers, preprints, images, animations and software connected with their research. The Library includes: Knot (energyminimizing knots and links);
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 Center for Technology and Teacher Education  Curry School of Education, University of Virginia
An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com
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 Charlotte and the World Wide Web  Santrach, Carpenter, Young, Young; The Geometry Center
An introduction to the World Wide Web, its potentials, and links to some geometry software (The Geometer's Sketchpad, Tesselmania, Geometric Golfer, Kali, Kaleidotile), for secondary school educators. A final project created for Math 5337, Technology
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 Classification of Patterns  BrownHerbst, Donnelly, Stratton, AndersonNielsen; The Geometry Center
Materials about symmetry and classification of repeating patterns for students in grades 710 using wallpaper patterns, to be used as either an introduction or a review: a classroomready source of information. A final project created for Math 5337, Technology
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 Clusters and Decagons  Ivars Peterson  Science News Online
A novel pattern made up of overlapping, 10sided tiles may serve as a model of how atoms arrange themselves into a quasicrystalline structure.
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 Collaborative Maths Resources  Collaborative Learning Project
Freely downlaod PDFs of "talkforlearning" lesson plans such as "12 and 24 hour Card Sorting" (clock times), "Buy a Ted" (collect all the parts of a teddy bear, which introduces the concepts such as exact amounts and making change), "Factors Four in
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 Coloring Penrose Tiles  Ivars Peterson (MathTrek)
One set of Penrose tilings consists of a pair of diamondshaped figuresone fat and one skinny. Attempts to color such Penrose diamond tilings led some people to conjecture that three colors suffice. Now, mathematicians Tom Sibley of Saint John's University
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 Computer Art and Tessellations  Hans Kuiper
A site about tessellations (tiles, tessels or regular patterns), infinity pictures, optical art, Islamic art, optical illusions, auto stereograms, company logos, quilt patterns and palindromes. Figures, patterns, textures and wallpaper drawings inspired
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 Computer Generated Islamic Star Patterns  Craig S. Kaplan
Islamic star patterns are a beautiful and highly geometric art form whose original design techniques are lost in history. This site describe one procedure for constructing them based on placing radiallysymmetric motifs in a formation dictated by a tiling
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 Connect with Music  Finn, Rudolph, O'Malley, Frankel, Ordway, and Langol
Thirty free interdisciplinary lesson plans that use multimedia, music, and technology to aid in the instruction of Language Arts, Mathematics, and Science at the middle school level. Lesson plans include comprehensive scoring rubrics, links to standards
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 Constructing SemiRegular Tilings  Kevin Mitchell
A document based on a talk given at the Spring 1995 Meeting of the Seaway Section of the Mathematical Association of America. Contents include: Introduction and Historical Background; Notation and Definitions; General Theorems; Hyperbolic Results; and
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 coolmath.com: Cool Math  Karen
A searchable "amusement park of mathematics" for exploring math: functions, tessellations, polyhedra, limits, logs, fractals (with galleries), puzzles and problems, fun with numbers, how to succeed in math, careers in math. Also Cool Links for Math for
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 Cool Math Sites  Nina Heal
A links list in the following categories: puzzles, algebra, geometry, calculus, discrete math, statistics and probability, trigonometry and precalculus, books and reference, calculators and other technology, data, history, other links sites and internetbased
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 Coordinates and similar figures  Mark Motyka, Math League Multimedia
Definitions and illustrations: What is a coordinate?; Similar figures; Congruent figures; Rotation; Reflection; Folding; Symmetric figure.
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 Course Project Suggestions (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
An list of suggestions for projects in geometry, topology, symmetry, making geometric solids, calendars, spherical and hyperbolic trigonometry, puzzles, models, etc. Projects were to be exhibited at the Geometry Fair at the end of the course.
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 Dave's Geometric Pix Gallery  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Mandelbrot and Julia sets, with a generation form and an Explorer on which you can point and click to get more refined images;
Newton Basins and a form to generate them; a page describing tiling the hyperbolic plane; some wallpaper groups; a gallery
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 David Bailey's World of Tessellations  David Bailey
Some high quality tessellations of a "representational" nature, as exemplified by M.C. Escher. Includes notes on the designs themselves, the design process, the history of tessellations, and references.
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 Delta Blocks  Hop David
A way to model different 3D tessellations and a tool for studying geometry, crystallography, and polyhedra. Delta blocks were inspired by M. C. Escher's print "Flatworms," which he said demonstrates that one can build a house not only with the usual
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 Demiregular Tessellations  Totally Tessellated
Color renditions and a real example of a demiregular tessellation. Templates allow you to print renditions of each tessellation suitable for coloring activities.
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 Design Ideas  Julie Coghill
A series of articles that discuss quilt design using proportion, asymmetry, and Pythagorean triples.
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 Designs with Circles  Suzanne Alejandre
A Math Forum Web Unit. Includes some background on circles in Islamic cultures, and an activity exploring the geometry involved in some circle designs.
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 Dice and Valentine's Day Symmetries (Math Chat)  Frank Morgan; Christian Science Monitor
A dice challenge from S. H. Logue: The six faces of four dice have these numbers on them: A 1 1 5 5 5 5 B 4 4 4 4 4 4 C 3 3 3 3 7 7 D 2 2 2 6 6 6. You and your opponent each choose one die to use throughout the game. Each round you both roll, and the
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 Discovering Polygons and Polyhedra  Paul Scott; applets by Bob Allanson
To encourage exploration of polygons and polyhedra in an interactive way, and to appreciate their
beauty. The site contains many diagrams and applets, and invites readers to explore and find
answers for themselves.
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 Dissections: Plane & Fancy  Greg Frederickson, Cambridge University Press
A book that explores an area of mathematical recreations, called geometric dissections, or the cutting of one or more figures into pieces that can be rearranged to form other figures. With an emphasis on using as few pieces as possible, these geometrical
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