 Geometric Arts  Ghee Beom "Quincy" Kim
A site dedicated to geometry and visual perception: patterns, fractals, structures, rotations, spirographs, optical arts, knots, and more. Some constructions include the artist's reflections, instructions, and links to related sites and interactive applets.
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 Geometric Bingo (SMILE)  Anne Lawrence, Wells Community Academy
A lesson for grades 710 designed to teach students to name and identify 20 geometric shapes. From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Geometric Factoring  Suzanne Alejandre
A Math Forum Web Unit. Understanding factoring through geometry: students work cooperatively to display a numeral as the area of a rectangle, and make as many rectangular arrangements as possible for each numeral given.
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 Geometry and the Geoboard (SMILE)  Jacqueline Darling, Simmye Anderson Community Academy
A 6th grade lesson designed to teach students to use geoboards: visualizing the concepts of squares, rectangles, triangles and polygons; exploring line segments, areas, and perimeters; demonstrating the phenomenological approach in learning geometry;
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 Geometry Daily  Tilman Zitzmann
A new "geometric minimal composition" every day since January, 2010. Zitzmann, an interaction and graphic designer, "draws simple shapes, combines them and experiments until they start to 'sing,'” then Photoshops them to have the look of "analog paper."
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 Geometry Distance of Triangles using a Protractor (SMILE)  Eileen Lally, A. Philip Randolph Magnet School
Students in the 7th grade learn how to use the protractor to measure angles, and use this ability to solve a problem involving distance. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and
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 Geometry Gallery of Imaginary Animals (TEAMS)  Jeannie Toshima; TEAMS Distance Learning, Los Angeles County Office of Education
Students choose geometry terms and create drawings of imaginary animals from those geometric shapes. In writing, they describe their appearances, behaviors, and habitats. They send their completed drawings and stories to Jeannie to include in her Geometry
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 Geometry Homepage  ThinkQuest 1997
Illustrated tutorials on many aspects of geometry, including: triangular geometry, the Pythagorean Theorem, polygonal geometry, polyhedra, and nonEuclidean geometry. Also includes a list of important geometric formulas.
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 Geometry in Motion  Daniel Scher
Direct interaction with geometric diagrams, courtesy of JavaSketchpad. The contents include a variety of curvedrawing devices (Intersecting Circles, Falling Ladder, Van Schooten's Parabola, and more); also other activities such as Constant Perimeter
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 Geometry Online  Cynthia Lanius
Geometry activities from a geometry class at Milby High School in Houston, Texas. Topics include: History of Geometry (contributions of Egyptians, Babylonians, and Greeks, with links to biographies of major contributors to geometry); Hidden Polygons (locate
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 The Goal Angle Problem  Ken Koedinger
Two solutions to the following problem: as you are running down a soccer field with the ball, when is the angle subtended by the goal at its maximum? There is also a sketch illustrating a construction used in one of the solutions (quadrature of the rectangle).
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 GoKidding  Sarveshwar Rao
Flash activities on counting, adding, subtracting, and naming shapes (polygons). Worksheets include circle mazes, fun with circles, and fun with triangles.
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 Grand Illusions  Hendrik Ball
A "site for the enquiring mind, with optical illusions, scientific toys, visual effects, and even a little magic." Includes a number of feature articles on vision, photography, mirrors, optical toys, movies, etc. See, in particular, the geometrical optical
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 Hamilton's Math to Build On  Johnny & Margaret Hamilton
Simple, straightforward explanations, drawings, questions and answers from the book Math to Build On by Johnny & Margaret Hamilton (copyright 1993). Excerpts offer pages on: Angles, Degrees, Variables & Constants; Squaring Numbers; Square Roots;
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 Hand Made Manipulative Instructions  Margo Lynn Mankus
Pattern block cutouts: triangles, squares, smaller and larger rhombuses, trapezoids, and hexagons. Baseten blocks in sets of ones, tens, and hundreds; and basefive blocks in sets of ones, fives, and twentyfives. XYblock sets of X, X2, XY, Y, and Y2
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 Heron's Calculation of Triangle Area (MSTE)  James P. Dildine; University of Illinois at UrbanaChampaign (UIUC)
The area of a triangle can be calculated using a formula attributed to Heron of Alexandria. This calculation requires that the lengths of all three sides be known. This activity includes an Excel file to calculate the area of a triangle, and Java and
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 Heron's Formula  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about Heron's formula, including proofs, derivations, and applications of it.
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 Hero's Formula  Jim Loy
An elementary introduction to Hero's (or Heron's) Formula, which is used to calculate the area of a triangle, given the lengths of the three sides.
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 The Honeycomb Conjecture  Ivars Peterson  Science News Online
Mathematician Thomas C. Hales of the University of Michigan at Ann Arbor has formulated a proof of the socalled honeycomb conjecture, which holds that a hexagonal grid represents the best way to divide a surface into regions of equal area with the least
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 HOT Math  Pauline Vos
Handson tasks in the mathematics classroom, a resource site for teachers of students around 14 years of age. Among the topics are angles, symmetry, scale drawing, balance algebra, tables, combinations, statistics, probability, reasoning, finding rules
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 How Many Regular Polyhedrons Are There In This or Any Universe? (SMILE)  Lawrence E. Freeman, Kenwood Academy
A lesson designed to teach the idea of "regularity" in geometry, exploring regular polygons and polyhedra. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning
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 Hypergami (Geometry Forum Summer Institute)  Michael Eisenberg, Ann Nishioka
A program for the creation of paper sculptures of various types  particularly polyhedral models and the larger, multipart sculptures that can be created from polyhedra. Description of a Geometry Forum Institute program (summer 1995).
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 Imaging the Imagined  Paul Flavin
Modeling with Math and a Keyboard: the art and science of modeling; the math, theory and practice of rendering, imaging, and animation. An introduction to raytracing and the Quadric surfaces; Platonic Solids and Polyhedra; 'Tensegrity' (tension) structures;
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 Information on Pentomino Puzzles  Frank Ruskey; Dept. of Computer Science, Univ. of Victoria, B.C., Canada
A pentomino is an arrangement of 5 unit squares (or sometimes cubes) that are joined along their edges. Up to isomorphism (rotating and flipping), there are 12 possible shapes, which are illustrated. Each piece is labelled by the letter that most accurately
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 Interactive and animated Geometric Algebra with Cinderella  Eckhard Hitzer
More than 90 JAVA applets that range from the elementary concepts of vector, bivector, outer product, and rotations, to triangle relationships, oscillations, and polarized waves. A special group of 21 applets illustrates three geometrically different
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 Interactive Mathematics Miscellany and Puzzles  Alexander Bogomolny
"The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based  the more beautiful is the result." This awardwinning site offers
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 Introducing Powers and ModelsI (SMILE)  Sarah Barrett, Mars Hill School
A lesson for grades 410 designed to teach students to discover how to square numbers; that squares are areas; the meaning of terms (exponent, to the power of, etc.); to visualize powers; to construct models and describe shapes; and to manipulate puzzle
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 Introduction to Geometry for Primary Students  Varnelle Moore
A Web unit designed to introduce young children (K2) to beginning concepts in geometry: describing shapes, making patterns, building shapes, rotational symmetry, and line symmetry. Each lesson includes an interactive, manipulativebased project, technology,
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 Investigating Patterns: Symmetry and Tessellations  Jill Britton
Thirty activities from a variety of Web sites, coordinated with a forthcoming book by Jill Britton for Cuisenaire/Dale Seymour, Exploring Pattern: Symmetry and Tessellations (March 1999). Topics include an introduction to symmetry; symmetry in the alphabet,
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 Investigating Polygons  Margo Lynn Mankus
The lesson plan for What is the Sum of My Angles? has the objectives of investigating the sum of the measure of the interior angles of a triangle using several methods, and making a mathematical conjecture from observations. The lesson plan for Regular
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 Investigating Tessellations Using Activity Pattern Blocks  Suzanne Alejandre
A lesson plan with activities for investigating tessellations with pattern blocks, keyed to the NCTM Standards, and student tessellation samples. Links to a Patterns Program in which you can drag an unlimited number of standard pattern block shapes into
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 Investigations in Mathematics  Eric S. Rowland
Openended problems for high school and college students to "approach creatively and in their own way": Pascal's simplices ("What is the generalization of Pascal's triangle?"), Pythagorean triples, regular polygons ("What is the area of a regular polygon
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 Isosceles Triangles  Jim Loy
Two proofs showing that not just the two sides but also the two angles of an isosceles triangle are congruent.
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 Isotiles  John Everett
Isotiles are specially designed tiles, in just two triangular shapes, by
which a wide range of topics in geometry can be studied. Topics include: different types of angles; lines and angles; angles of a triangle; isosceles triangles; similar triangles;
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 James P. Dildine  James P. Dildine
Interactive math lessons for exploring parabolas, triangle areas, Pythagorean triples, triangle angle sums (powered by a Cabri Java applet), cancer and mathematics (image analysis, and determining the area and perimeter of nonregular figures), systems
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 Jim's GSP Library  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Geometer's Sketchpad (GSP) sketches to download, from a course on Algorithms and Computers in Mathematics Education: Centroid of a triangle; Orthocenter of a triangle; Circumcenter of a triangle; Circumcircle of a triangle; Incenter of a triangle, Incircle
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 John Olive's Home Page  John Olive, Department of Mathematics Education, The University of Georgia
Course descriptions and requirements for Computers in Mathematics Education and Investigations into the Teaching of Mathematics Grades 712. Recent articles, available online, include Computer Tools for Interactive Mathematical Activity in the Elementary
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 Journey to the Center of a Triangle  Cathleen V. Sanders
What is the center of a triangle? A reflective exploration by high school geometry students in Honolulu using interactive geometry software to pursue the question in three different scenarios: as a city planner selecting a site to build a recreation center
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 JuniorHighMath.com
Free printable worksheets from a middle school teacher: algebra, one variable; algebra with coefficient; twostep algebra with addition; twostep algebra with subtraction; exponents; Pythagorean Theorem; and circles.
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 The Kaleidoscope Collector: How Kaleidoscopes Work  Hand of the Craftsman
Graphics from The Kaleidoscope Collector show the basis of and the dramatically different images produced by the three mirror, two mirror, twin mirror, and four mirror scope. Includes a brief kaleidoscope history.
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 Kids Math Games Online  Rene Smith
Free interactive games on addition, counting, division, geometry, money, multiplication, number (including mean median mode), problem solving (bridge crossing, hourglass time, wolf and sheep), and subtraction. Logic games include a 3D puzzle cube, Mastermind,
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 KidsPsych  Magination Press
Flash games to help young children develop cognitive thinking and deductive reasoning: Oochina on the Farm, Rotating Faces, Oochina in Space, I Spy, Oochina the Archeologist, Oochina's Doughnut Dilemma, Oochina the Treasure Hunter, Oochy's Cube Adventure,
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 Kirigami  Kevin S. Whitley
Kirigami is the Japanese art of making figures out of paper by cutting. This applet lets you create similar figures on your computer by cutting a polygonal wedge from a virtual piece of folded paper. You can change the regular polygon, your wedge, and
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 KRN Software
Free online games for Javaenabled browsers. Java Edutainment games require matching shapes and colors in Space Cargo and Cargo Bay, simple addition in Numeric Defenders, and odd and even number identification in Even Steven, Jr.
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 Learning Game Finder  Media Match, LLC
Subscribe to search peerreviewed lists of learning games along with the rules for play and the technical requirements to run the game.
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 Learning Jolt  Robert Croisant
"Quick and repeatable" mathematics problems for students, who gain points at specific milestones which they may then use to choose their own rewards in the Learning Jolt store. With statistical reports and other tools for parents and teachers to track
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 Learn Math 3D on Orbital One  Peter Richards
A software math course set within a real time 3D environment. Topics covered include counting, the number system, addition, subtraction, multiplication, division, 2D and 3D shapes, simple fractions, and telling the time.
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 Length and Width  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about length and width, such as whether the length of a rectangle is always the longest side, and if there is a difference between "width" and "base."
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 Lesson for Multiplying and Dividing Fractions with Post It Notes (SMILE)  Robert Foote, Disney Magnet School
A 7th grade lesson designed to teach students to measure various dimensions of rectangles to the nearest fraction of an inch, dividing fractions to predict the number of Postits needed to meet the length and width of the rectangles. From the Arithmetic
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 Lesson Plan For PartWhole Meaning For Rational Numbers  Michele Gahala
Students use the Geometer's Sketchpad and work as a class to represent parts of a whole using fractional parts of a triangle, and to determine the relation among parts of a whole that are unequalsized pieces.
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