 Topics in Arithmetic and Elementary Mathematics  E. Lee Lady; University of Hawaii
Materials used in a university course for prospective elementary school teachers, to teach them how to be interested in mathematics. Materials are in PDF and DVI, and include: representing numbers in other bases, divisibility tests, periodic decimal expansions,
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 Topics in Mathematical Recreations
Arithmetic and geometric puzzles; polyhedra; fractals and chaos; board and positional puzzles; pi and its calculations, and tiling patterns, which can be thought of as making an infinite polyhedron. Includes a bibliography ranging from Abbott's Flatland
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 Topology and Geometry Software: Fun and Games  Jeff Weeks
Fun math toys for all ages, from the author of Exploring the Shape of Space (grades 610) and The Shape of Space (grades 1216). Applets and software for various platforms. Play with tictactoe, mazes, and the like, on a torus or Klein bottle. Draw
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 Topology (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
Topology is the theory of shapes that are allowed to stretch, compress, flex and bend, but without tearing or gluing. For example, a square is topologically equivalent to a circle, since a square can be continously deformed into a circle. As another example,
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 TopSecretMath.org  Donald Endriss
Stepbystep JavaScript tutorials for learning how to factor several different kinds of trinomials using the CAB method.
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 Tostaky.Biz  Jerome Verstrynge
JavaScript utilities formatted for the smaller screens of tablets and smartphones: timer, stopwatch, world clocks, and other timekeeping tools; and unit converters for area, force, length, torque, weight, and more.
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 Totally Tessellated  Bhushan, Kay, & Williams
A comprehensive introduction to tessellations and tilings  the basic underlying mathematics and examples of tessellations in real life. The highly illustrated, printerfriendly site includes history (tessellations in mathematics and science, decorative
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Tour: M.C. Escher  Life and Work  National Gallery of Art, Washington, DC
A tour of four virtual rooms devoted to the art of M. C. Escher. For each graphic a larger picture with accompanying commentary is available by clicking on a small picture. The gallery has more than 400 works by Escher with many images available online.
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 Tournament of Towns  Math Net, University of Toronto
A worldwide problem solving competition in mathematics. The contest attracts students of all mathematical interests and abilities with its inclusive rules and creative problems  some as challenging as those of the International Mathematical Olympiad.
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 A Tour of Fractions  Math Forum
The Web often seems more like a maze than an organized set of resources. To help you find what you need, the Math Forum presents a 'tour' of fractions, offering links to lessons, activities, and materials, questions and answers from Ask Dr. Math, and
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 Tous pour les mathématiques au collège  David Monbru
Courses mathématiques de niveaux sixième, cinquième, quatrième, et troisième. Exercises avec autovalidation incluent calculs avec ou sans parenthèses; calculs de fractions; opérations sur les nombres relatifs;
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 The Tower of Hanoi  Andrew Cumming
Interactive version of the famous logic puzzle, in html and VRML versions, with a separate page about solving it.
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 Tower of Hanoi  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
There are three posts. Disks of different sizes are placed on the lefthand post, arranged by size with the smallest on top. You are to transfer all the disks to the righthand post in the fewest possible moves, without ever placing a larger disk on a smaller
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 Tower of Hanoi on the Web  Miroslav Kolar
The legend: A group of Eastern monks are the keepers of three towers on which sit 64 golden rings. Originally all 64 rings were stacked on one tower with each ring smaller than the one beneath. The monks are to move the rings from this first tower to
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 Tower of Hanoi (SMILE)  Paul Eubanks, Washington High School
A lesson for grades 612 designed to teach students to discover a pattern and to evaluate an exponential expression. From the Patterns and Logic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for
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 Toys from Trash  Arvind Gupta
Stepbystep photographic instructions for building elegantly simple, colorful "Math Magic" doityourself manipulatives: Abacus, Flexagon, Triangle Grid, Flat Flexagon, Slipper Insets, Folding Pentagon, Tangram, Paper Octagon, Cylinder and Cone, Area
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 Trachtenberg Basic Multiplication Tutorial  Moshe Berlin
TracMath is a freely downloadable tutorial (MS Windows) for the basic system of Trachtenberg Multiplication. This system teaches a set of algorithms that perform the same function as the times tables. When students ask "How does it work?" you can use
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 Trachtenberg Speed Math  Alpha Centauri Software
Software that teaches Jakow Trachtenberg's speed system of basic mathematics that he invented while imprisoned by Hitler during WWII. For Windows only. Demo version available.
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 Trachtenberg Speed System  Math Forum, Ask Dr. Math FAQ
An introduction to Trachtenberg's system of performing highspeed multiplication, division, addition, subtraction, and square root, all in one's head, with references.
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 Tracking  Education Week on the Web
Should schools  as the engine of democracy  provide relatively similar curricula for all students? Or should they instead sort students by skill levels and prepare them for their different roles as adults? A discussion of the pros and cons of tracking,
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 Tractrix Java Applet Class  PHD Computer Consultants Ltd
Download Tractrix.zip, a Java applet that makes the kind of pretty swirling patterns which Dutch mathematician Huygens originally named in 1692. Specify applet width and height, background and foreground color, coordinate pairs that will identify corners,
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 Traditional Schooling: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on traditional schooling issues: Academic Acceleration; Advocacy; Bullies; Curriculum Adjustments; Early (or late) Kindergarten; Educational Theories; Grouping; Individualized Education Profiles (IEPs); Mentors; Success Stories; Testing
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 Traffic Jam  Math Forum
Equal numbers of people face each other with one open slot between them. Everybody faces the open slot. If there are 6 people there will be 7 slots, 6 of
which must always have people in them. People must attempt to exchange places without turning around.
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 Traffic Signs  Richard C. Moeur
Graphics of the most commonly used traffic signs in the United States, useful for challenging students to find symmetrical signs (in addition to polygons).
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 Transformations  David A. Reid
A transformation is a onetoone mapping on a set of points. The most common transformations map the points of the plane onto themselves, in a way which keeps all lengths the same. These transformations are called isometries. Another common sort of transformation
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 Transversal of a Latin Square  Jay's Corner
A transversal in a Latin Square is a collection of positions, one from each row and one from each column, so that the colors that are in these positions are all different. This page shows an example of a transversal in a 4x4 Latin square
See also Transversals
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 The Travelling Salesman's Problem  Manu Konchady
A trucking or delivery company is focused on optimum delivery cost. This can be achieved by using a system which determines the best highway route for each load. An optimum highway route can be displayed on a map. A route with 16 nodes is used to test
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 Travel Triangles (SMILE)  Sarah Barrett, Mars Hill School
A middle and high school geometry lesson designed to teach students to review and demonstrate an understanding of the three kinds of angles (by degrees). From the Geometry and Measurement section of a collection of almost 200 single concept lessons by
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 The Treb Challenge  GlobalSpec, Inc.
Custom build a trebuchet for three challenges: distance, accuracy, and power. Between launches, continue modifying the catapultlike seige engine's projectile weight, launch angle, gravity, wind, counterweight mass and height. After each challenge, the
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 Triangle Formulas (Ask Dr. Math FAQ)  Math Forum
Formulas for finding the area, perimeter, etc. of an equilateral, isosceles, right, or scalene triangle.
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 Triangles and Pyramids: Playing Math!  Hollis Easter
A "teachable" on the construction of freestanding pyramids made "by folding a single piece of paper, with only a single piece of tape to hold them together...." This blog post goes on to include photos of a net, diagrams, and "things to investigate":
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 Triangle with one 90degree Angle  NASA Lewis Learning Technologies Project
A triangle with one 90 degree angle is always: an equilateral triangle; an acute triangle; an obtuse triangle; or, a right triangle? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Tribute to Invariance  Cut the Knot!, Alexander Bogomolny
As a competitive activity, the Squares and Circles game is not very challenging in itself. That is to say, the outcome of the game does not depend on how the game proceeds. The challenge is to come up with this realization and establish its veracity.
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 Tricks for Learning Math  Math Forum, Teacher2Teacher FAQ
Answers to a frequently asked question: What are some math tricks and mnemonic devices I can use with my students?
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 Tricky Crossings  Ivars Peterson (MathLand)
Have you heard the one about an itinerant entertainer traveling with a wolf, a goat, and a basket of cabbages? The showman comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can't leave the wolf
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 Tricky Dice  Ivars Peterson (MathTrek)
The game involves four specially numbered dice. You let your opponent pick any one of the four dice. You choose one of the remaining three dice. Each player tosses his or her die, and the higher number wins the throw. Amazingly, in a game involving 10
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 Tricky Tables (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The shape of a billiard table has a lot to do with the types of shots you can make in a game of billiards. Which of the odd tables pictured do you think would be your best bet for hitting another ball? Suppose you have a circular table, or a rectangular
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 Trigonometric Identities  David Manura
Table of Common Angles, Law of Sines, Law of Cosines, and more.
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 Trigonometry (Manipula Math)  International Educational Software (IES Inc.)
More than 20 Java applets designed to demonstrate principles of trigonometry, including sine, cosine, and tangent function boxes; graph of y=sin x, y=cos x,
y=sin ax, y=A sin (Bx+C), and y=sin x + cos x; Fourier series; sin t = a;
cos t=a; sin(A+B);
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 Trigonometry Reference Sheets (S.M.A.R.T.)  Math Share Shop
Basic curves. By students at Theodore Roosevelt H.S., Bronx, & Edward R. Murrow High School, Brooklyn.
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 Trigonometry (S.O.S. Mathematics)  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and precollege trigonometry. Trigonometry: Angle Measures, Trigonometric Functions (magic identity, Addition Formulas,
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 Trigonometry Table  Industrial Press
Tables that give corresponding sine, cosine, tangent, secant, cosecant, and cotangent values for angles 0 to 90 degrees.
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 Trimathlon
Site centered around a book featuring activities from number theory and geometry beyond the realm of the typical school curriculum. The site features a discussion forum, a sample online game (with others promised), and a periodic puzzler with hint.
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 TriMathlon: A Workout Beyond the School Curriculum  A. K. Peters, Ltd.
Companion site to the book TriMathlon: A Workout Beyond the School
Curriculum, by Judith and Paul Sally. Discuss math, the book, or the site with members of the Trimathlon community; explore the current "Periodic Puzzler"; or play one of the Shockwave
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 Trisecting an Angle  MacTutor Math History Archives
Linked essay tracing the history of the classical Greek problem of trisecting an
arbitrary angle using for the construction only ruler and compass (which is
impossible)  but, failing that, finding some other method.
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 Triumph of the Nerds: A History of the Computer  Robert X. Cringely; PBS Online
A companion Web site for the Public Broadcasting System television special hosted by Robert Cringely, "Triumph of the Nerds: The Rise of Accidental Empires." Learn how youthful amateurs, hippies, and selfproclaimed "nerds" accidentally changed the world.
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 Trouble with WildCard Poker  Ivars Peterson (MathLand)
Poker originated in the Louisiana territory around the year 1800. Ever since, this addictive card game has occupied the time and teased the minds of generations of gamblers. It has also attracted the attention of mathematicians and statisticians. The
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 Truel in the Sun  Ivars Peterson (MathTrek)
Brilliant sunshine bakes a huddled row of ramshackle, weatherbeaten buildings lining a dusty thoroughfare. Two gunfighters slam out of a decrepit saloon and stalk toward their posts at either end of the street. Facing each other, they prepare to draw
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 The Truth Tree's Math and Logic Board  Bob Scott, Ron Savori
A collection of math and logic problems, from Pascal's Pizza Parlor and Leaning Ladders to The Old Lady and the Eggs and The Rickety Table Disaster. Register to solve these and other problems and compete with other visitors to The Truth Tree.
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 Tumblehome Learning
Makers of educational products such as Lost in Tangrams and  through a partnership with TERC, with funding from the National Science Foundation (NSF)  Mixing in Math (MiM) cards, gameboards, and books.
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