 Three Door Puzzle  Sky Coyote
In interactive page with an explanation of this classic, controversial problem, sometimes referred to as "Monty's Dilemma" or the "Game Show Problem." Links to a game simulation, the answer to problem, and an Ndoor generalization are provided.
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 Three for the Money: The Degree/Diameter Problem (MegaMath)  Nancy Casey; Los Alamos National Laboratory
Students can understand and work on an unsolved problem in mathematics. There is a good chance that this problem can be solved by someone who spends enough time experimenting with it. The only skills required to work on it are the ability to draw dots
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 Three Houses, Three Utilities  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
You are to draw a line from each house to each utility, without the lines ever crossing. Can you connect the houses to the utilities?
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 The Three Jugs Problem  Cut the Knot!, Alexander Bogomolny
Two friends who have an eightquart jug of water wish to share it evenly. They also have two empty jars, one holding five quarts, the other three. How can they each measure exactly 4 quarts of water? ... The description of the 3 Jugs problem as a triple
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 Through Mazes to Mathematics  Tony Phillips; Dept. of Mathematics, SUNYStony Brook
Material about a class of mazes that have a complete mathematical description. Includes building your own labyrinth, an activity suitable for 4thgraders and up. Explores the relationship between mazes and mathematics. Examples and calculations with Simple,
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 Tickling the Mind  Ivars Peterson (MathTrek)
... Different math teachers may use different styles and methods, and they may favor different topics. However, they all share the goal of building an appreciation of both the usefulness and the intellectual wonder of mathematics. Much of the current
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 TierneyLab Puzzles  John Tierney
Challenging word problems that "put ideas in science to the test," from The New York Times' science columnist. Solve and comment on the puzzles and their extra credit extensions. See also Tierney's blog entries on mathematics.
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 Tiling and Packing results  Torsten Sillke
Packing problems, mostly, in English, with some in German. Packing Polycubes and Polyspheres; Tilings with Matching Conditions; links.
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 Tilton's Algebra  Ken Tilton
Guided, selfpaced algebra discovery in the Socratic style. Tilton's tutorials provide several sequences of whiteboard videos, demonstrations, hints, and feedback at each step of a student's work on a problem. Formerly known as Theory Y Algebra and Algebra
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 Time4Learning  John Edelson, Founder
An online homebased learning system with multimedia lessons, interactive exercises, printable worksheets, assessments and quizzes for use in homeschool, tutoring, or summer programs. See, in particular, their Homeschool Math Curriculum. Sample lesson
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 Time Math  Education 4 Kids, Inc.
Time, at different levels of complexity (clock and calendar). You are presented with two times (in one of the formats selected) and asked to determine the difference between the two.
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 Time: Minutes and Hours  NASA Lewis Learning Technologies Project
Roberta left for her dancing class at 3:45 p.m. Her dancing school is a 15 minute walk from her house, and her class lasted one and one half hours. What time did she get home if she went straight home? A detailed answer is provided. From NASA's 9th Grade
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 TimeMonsters.com
Learn and practice telling analog time on a clock face with Doctor Tempo, an animated talking head who reads aloud, provides oral explanations, and otherwise lends a voice as you work through lessons and quizzes on interpreting hour hands and minute hands.
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 Time Table Rhyme  Jane Hague
Help teach children the multiplication times tables using visual and auditory memory techniques. Equations include colorful illustrations and simple rhymes to create a picture in the child's imagination, enabling quick learning and random recall. Includes
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 Tim's Interactive Puzzle Solution Center  Alex Sakharov
A growing collection of interactive online logic puzzles including Cannibals and Missionaries, Eight Queens, Gunport, and math puzzles of various difficulty levels.
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 Tim's Triangular Page  Alex Sakharov
Information, definitions, and illustrations of triangles, their parts, and congruency. Includes a few min/max problems relating to triangles at the end.
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 Title III MSS Final Performance Report  Dana Lee Ling
Dana Lee Ling is a mathematics and science software specialist at the College of MicronesiaFSM. Articles document the College's attempts to increase the success of prealgebra and algebra students through "conceptual" and technologybased approaches.
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 To Accumulate a Rate — Integrate!  Kaleb Allinson
Allinson teaches trigonometry and AP Calculus AB at Lake Stevens High School (WA), where he also serves as the math department head. He describes his blog as a venue to "help me reflect on my teaching.... and record the unique [ideas] I came up with for
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 Toads And Frogs Puzzle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An interactive exploration of the Toads and Frogs puzzle, also known as Hares and Tortoise; Sheep and Goats; Hop, Skip, Jump; and Traffic Jam.
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 Tomás Oliveira e Silva
From an assistant professor in the Electronics and Telecommunications Department of the University of Aveiro, Portugal. On the Collatz problem: maximum number tested (N): 91·2^50 = 102456891522678784.
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 Toothpick Puzzle: a Math Line Puzzle  Math Forum
Starting with the configuration shown, move exactly two toothpicks to form four 1x1 squares. You must use all the toothpicks, without any overlap. The final product will consist of exactly four squares, all the same size as the five in the original configuration.
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 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 Calculus  E. Lee Lady; University of Hawaii
Files in PDF, DVI, and Postscript formats, to help students learn to use calculus in applications and to have confidence in setting up formulas using derivatives and integrals. Contents include: a conceptual approach to applications of integration, maxmin
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 Topics in High School Mathematics  Martin Cohen
Lesson ideas on geometric series, mathematical induction, Pythagorean triples, combinatorics, continuity, modular arithmetic, rotations and revolutions, and more.
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 Topics in Integral and Differential Calculus  Teresinha Kawasaki
Interactive, illustrated introductions to polynomial functions, trigonometric functions, exponential and logarithmic functions, the derivative, differentiation formulas and the chain rule, differentiating trigonometric functions, maxmin problems, integration,
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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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 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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 A Tour of Measurement  Math Forum
A central resource for people teaching and learning about measurement. For teachers there are links to lessons and materials, questions and answers from Ask Dr. Math, and recommended software, grouped by level (elementary, middle school, high school).
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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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 Toying with Reality: Java Applets and VRML  Paul Flavin
Virtual Reality: Modeling with Math, and a little Java. Applets to manipulate: The Pythagorean Theorem; Equation Grapher: "You type, I Graph"; Graphing Vector Calculator; Java 3d Visualizer; Virtual Rubik's Cube; Raytracing applet; Java Calculator; Play
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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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 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 Traveling Salesman Problem (TSP)  Vasek Chvátal
The problem: given a finite number of cities and the cost of travel between each pair of them, find the cheapest way of visiting them all and returning to your starting point. This site includes a link to TSPLIB, Gerhard Reinelt's library of some hundred
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 Travelling Salesman's Problem  Gunno Törnberg
Algorithms to solve the travelling salesman's problem (a travelling salesman is to visit a number of cities; how to plan the trip so every city is visited once and just once and the whole trip is as short as possible?) Links to Java applets; the shell
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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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 Triangle in Square Puzzles  Erich's Puzzle Palace; Erich Friedman
Eight puzzles involving cutting squares into triangles under certain constraints. Answers provided.
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 Triangle Puzzle  Evelyn Sander, Geometry Forum Archives, The Geometry Center
Pick an arbitrary point in the interior of an equilateral triangle. Now go halfway towards one of the three vertices (you get to pick which vertex). Now you are at a new point in the triangle. Again go halfway towards any vertex. Continue this process.
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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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 triangular prism  Manjit Singh Atwal
Download lessons and worksheets about triangular prisms, including finding surface areas and volumes.
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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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 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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 Trigonometry and Calculus Problem of the Week  Math Forum
Trigonometry and calculus problems from a variety of sources, including textbooks, math contests, NCTM books, puzzle books, and reallife situations, designed to reflect different levels of difficulty. From 1998 until 2002, the goal was to challenge students
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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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