 Rectangle Perimeter and Side Length  NASA Lewis Learning Technologies Project
A rectangle with a perimeter of 24 inches might have adjacent sides measuring: 6 inches and 4 inches; 11 inches and 13 inches; 9 inches and 3 inches; or, 2 inches and 12 inches? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Rectilinear Geometry (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric problems defined on squares and rectangles, higher dimensional boxes, cubes, and hypercubes, right triangles and other rightangled figures, and "taxicab geometry" in which distances are measured
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 Religious Beliefs Made Visual: Geometry and Islam  Jane Norman, Consultant, Metropolitan Museum of Art
Although the shapes and structures are based on the geometry of Euclid and other Greek mathematicians, Islamic artists used them to create visual statements about religious ideas. A discussion of the use of geometric motifs in Islamic art, with instructions
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 Research Ideas  George Gadanidis
Disseminating math education research through performance, and studying the process and impact of research performance. Funded by the Fields Institute, Random Acts of Math brings math ideas to young children and their parents. Music videos of the Math
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 The RightAngle Triangle Solver  Steve Ayers
Input two sides of a right triangle, or one of its sides and one of its angles, and this site calculates the remaining sidelengths and angles. Also, convert decimals and fractions, and imperial and metric units of measure. Requires JavaScript.
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 Rigol'Math: énigmes, problèmes et curiosités mathématiques  JeanMarc Deleuze
Le calcul de Pi; le Jeu de Nim; Convertisseur base 10 > base 2; Multiplier sur les doigts; Multiplication égyptienne; Le carré magique; TicTacToe; Coloriage; et beaucoup plus.
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 Rite Item  Jim Preston
Software to download: ANYANGLE (Windows, DOS; a geometry solver that provides a method of finding answers to problems involving triangles, and offers scale views and supplementary data to back up the numerical results); and PARTYDOT (a program for creating
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 River Crossing (Math Exploration Quilt)  Rik Littlefield; Hanford School
You want to cross a river to reach a point exactly opposite where you are currently standing. Explore this problem stepbystep, encountering the following basic ideas: 1) Pythagorean theorem; 2) time = distance / speed; 3) distance = time * speed; 4)
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 Rockin' the Standards
Musical recordings by a rock band led by a veteran elementary school teacher who takes the lyrics from common tunes and changes them to help kids remember what they've been taught in school. Each of the fourteen songs on the album "Rockin' the Standards
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 Ron Blond  Ron Blond
Circle geometry applets to explore inscribed and central angles, tangents and radii, and tangents and inscribed angles. Also, applets illustrating the quadratic function (completed square and the discriminant), transformations of the sine and cosine functions,
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 Science Museum Math Exhibit  The Geometry Center
A museum exhibit on triangle tilings that contains sophisticated concepts such as tilings of the sphere and the relation between tilings and the Platonic and Archimedean solids: the sum of the angles of a planar triangle is always 180 degrees. Repeated
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 Science Museum of Minnesota
Natural history and technology. See the world's largest Camptosaurus dinosaur skeleton, touch a tornado, play the congas, do some serious Internet surfing, or test the waters of the Mississippi River. The museum is Minnesota's most popular indoor cultural
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 Search New York Journal of Mathematics (NYJM)  Department of Mathematics and Statistics, State University of New York (SUNY) at Albany
Search the contents of all years of the journal, or search individual years, 1994present.
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 Secondary Math Units  Margaret Sinclair
Units for grades 912. For grades 910: Data Collecting in the Classroom, Algebraic Problemsolving using Spreadsheets (a unit that emphasizes moving from numerical to symbolic representation), and a newspaper review unit on the Skydome. For grades 1112:
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 Secrets of the Beehive  Keith Devlin; Guardian Unlimited Archive
The 4th century geometer Pappus was one of several ancient Greek mathematicians who suspected that the elegant shape of the honeycomb was a result not of an innate beesense of geometric beauty but of nature's efficiency. The repeating pattern of sixsided
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 Semiregular Tessellations  Totally Tessellated
Color renditions and real examples of the semiregular tessellations. Templates allow you to print renditions of each tessellation suitable for coloring activities.
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 ShapeGame  Architectronics, Inc.
Drag shapes on, drag shapes off: triangles, squares, hexagons, rhombuses, and trapezoids. Also, change their color, orientations, and more.
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 Shelley Walsh
Syllabi and notes for math courses from arithmetic review to beginning calculus. Download MathHelp a tutorial program with problem sets for Mac or PC, or learn how to use MathHelp to create your own tutorials. Brief Mathematics Articles present concepts
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 The Shikaku Room  Paul Hutchinson
Given a few numbered squares in a larger grid, block out rectangular and square sections so that each component piece contains the one number that represents its area. Randomly generate or create your own grids — from 4 × 4 up to 20 ×
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 Similarity  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Scaling multiplies lengths by the same factor and produces a similar figure. It
preserves angles and
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 Similarity (SMILE)  Natalia Kee, Harlan Community Academy High School
A lesson designed to teach students to discover the factor of proportionality in similar polygons and relate this factor to the perimeters and areas of similar polygons. From the Geometry and Measurement section of a collection of almost 200 single concept
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 simpsonsmath.com  Sarah J. Greenwald and Andrew Nestler
The animated sitcom The Simpsons "contains over a hundred instances of mathematics, many designed to expose and poke fun at innumeracy," which make it "an ideal source of fun ways to introduce important concepts to students, and to reduce math anxiety
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 Sketches for Cabri Geomètre (v. 1)  L. J. Dickey, University of Waterloo
Cabri Geomètre (the original version of of the program) figures to download (binhexed): Conic Given by Five Points; Ten Sketches of Desargues Theorem; Harmonic Conjugates; The Inverse of a Circle; The Inverse of a Line; The Inverse of a Point;
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 The Sliding Triangle  Paul Kunkel
Investigate ellipses by tracing triangle transformations.
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 Software  Bill White
These Flash apps provide online practice deriving some unknown property of a figure given its other measures. Find the area of a trapezoid given its two base lengths and height; find one of its bases given its area and height; find its height given its
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 Some Variations on the Theme of Polyominos  Recmath
Patterns that illustrate how the squares of polyominos are connected to each other. Examples of polyominos with a grid superimposed to illustrate the individual squares; with a line that joins the midpoint of two adjacent square if the squares are connected.
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 Spidron System  Daniel Erdely
Erdely calls a planar, planefilling object a Spidron. Upon threedimensional deformation subject to specific constraints, the planar system generates a regular, dynamic, geometrical construction. Erdely's experiments have led to the idea of creating
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 Square Machine (Early Childhood Art Lessons, Arts Wire)  The Incredible Art Department
A "lesson plan" for ages 35. "What's a square? Squares are all over the place. Look at these square things..."
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 Square of the Hypotenuse  Ivars Peterson (MathTrek)
Some history of the legend of the discovery of the Pythagorean theorem: in his textbook The History of Mathematics, Roger Cooke of the University of Vermont describes how the Babylonians might have discovered the Pythagorean theorem more than 1,000 years
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 Square Wheel (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
A square wheel may be the ultimate flat tire. There's no way it can roll over a flat, smooth road without jolting the rider again and again. Stan Wagon, a mathematician at Macalester College in St. Paul, Minnesota, has a bicycle with square wheels. It's
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 The STEM Collaborative  Maryland Public Television, Arkansas Educational Television Network, Alabama Public Television, and Kentucky Educational Television
The four online adventures Scale City, ProportionLand, Math by Design (architecture), and Rock 'n Roll Road Trip (music) engage students to use geometry, algebra, and proportional reasoning for skateboard ramps, cooking, amusement park roller coasters
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 Stickets  Wanderlands
A puzzle game for iPhone "that forgot Tetris existed": drag tricolored Lshaped blocks onto a grid and tap contiguous, similarly colored areas comprised of three or more squares in an ongoing quest to preserve space on the grid. The app also challenges
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 The Story of Pi  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Although pi is the ratio of circumference to diameter of a circle, it appears in many formulas that
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 Tangram Page  S. T. Han
All about tangrams, an ancient Oriental toy that has 7 pieces: 5 triangles in different sizes, 1 square, and 1 parallelogram. The object of the game is to form a given shape using all 7 pieces. Introduction, Puzzle of the Month, PC/Mac Software, Articles
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 Tangrams: History, Puzzles, Make It, and Links  Randy Crawford
Follow the "history" link to learn about tangrams through the ages; click on "puzzles" for over 100 silhouettes to reconstruct, with solutions. "Make it" provides instructions for building your own tangram set. With references to more sites, software,
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 Tangrams  J. L. Read; Enchanted Mind
A tangram applet that allows you to rearrange the seven forms to exactly reproduce the given image. To move the pieces, drag them with the mouse. To rotate pieces, click with the right mouse button or (on the Mac with a onebutton mouse) click while holding
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 Tangrams  Tom Scavo
Tangrams, a puzzle that helps develop spatialvisualization skills, may also be used to introduce or reinforce geometric concepts such as congruence, similarity, symmetry, etc. This unit for grades 4 through 6 uses tangrams to compute the area of polygons
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 Tanzzle™  Franco Cocchini
Software for exploring tangrams. View published patterns and/or submit one of your own. Request a free license for schools and educational programs. Free 30day trial; free viewer download. Choose from four different sets of pieces: Tangram (traditional
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 Teaching Ideas for Primary Teachers: Maths
Math activities for ages 511 include a puzzle display, shapes worksheets, ideas for making a maths dictionary, a questioning technique, and many more games, worksheets, and activities for the classroom.
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 TeachingTools.com  TeachingTools
Create math practice worksheets: multiplication tables with exercises, whole numbers, decimal and fraction operations, matching exercises for math terms, geometry terms, and 'story problems' clue words, an identifying geometry shapes exercise, and an
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 Team Umizoomi  Viacom International Inc.
Milli, Geo, and Bot solve everyday math problems with their "Umifriend" preschoolers. Get Mighty Math crafts, games, printables, and recipes. Download episodes of this animated liveaction series broadcast on Nickelodeon's Nick Jr. television show.
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 Technologies: Past and Future  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
A discussion of the similarities in browsing through books and surfing the Internet, the serendipitous discoveries that can be made, fallacious geometric and other puzzles, and an interesting integer matrix, with recommendations of books to read and sites
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 A Template for Napoleon's Theorem Explorations  Steve Weimar, with Sarah Seastone
Some suggestions for things to investigate related to Napoleon's Theorem. Includes a sample sketch.
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 Tessellated Polyhedra  Jill Britton
Fullpage printable nets of each of the regular polyhedra, decorated with individual surface tessellations in full color. A higherresolution blackandwhite version of each tessellated net appears in Polyhedra Pastimes, by Jill Britton, published by
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 The Theorem of Pythagoras  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Several animated proofs of the Pythagorean theorem are presented, with applications to reallife problems
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 There are trisectable angles that are not constructible  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Why certain angles that are trisectable cannot be constructed by traditional methods.
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 TheXorb  Jagan Deb
Online calculators for the slope and yintercept of linear equations; standard deviations; mean, mode, and range; the Pythagorean Theorem; and properties of geometric figures such as triangles, squares, circles (circumference given area; area given diameter;
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 A Thing In Common  Cut the Knot!, Alexander Bogomolny
Two applets, both of which use the Pythagorean theorem: a puzzle (Draw an {N/D} star polygon  a polygon whose N vertices are uniformly distributed on a circle, but each vertex is connected to its Dth neighbor. Regular polygons correspond to D = 1, and
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 Things Impossible  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Essays on impossible things, including trisecting an angle, doubling a cube, squaring a circle, moving pegs five places in one direction (via checkerjumps), finding the center of a given circle with the straightedge alone, representing the square root
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 Thinking Fountain  Science Museum of Minnesota
Thinking Fountain offers surprising and personal connections to science. It's a living card file full of ideas and activities. Includes the opportunity to add your own projects. See Shapes Cluster: Shapes & Math: Shape Walk, I C Shapes, Bubble Geometry,
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