 Pick's Theorem  Cut the Knot!, Alexander Bogomolny
A description with proof of Pick's theorem, including links to further pages including exercises with an applet for the geoboard, Farey Series, and SternBrocot Tree. An interactive column for MAA Online that uses a Java applet to simulate a puzzle or
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 'Picture This': Tangram Puzzles  Sarah A. Keith
Each week a new tangram puzzle is featured in "Picture This" in the Sunday cartoon section of newspapers worldwide. Children are invited to mail their tangrams for possible inclusion, and to be featured in the Kid's Gallery on the Web. Read the legend
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 The PiFactory  David Whitfield
Revision notes, boardshots, and Excel worksheets to download, from when the author used to teach in North London. The PiFactory includes an opensource assessment suite, classroom resources, and concept maps. The PiFactory conveniently pulls together
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 The Pi Pages  Centre for Experimental and Constructive Mathematics (CECM)
"Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. It has been a part of human culture and the educated imagination for more than twenty five
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 The Pi Trivia Game  Eve A. Andersson
Test your knowledge of history, mathematics, and even a little physics. Here are 25 (given to you 5 at a time) pirelated questions, picked randomly from a pi question database. Also at http://cid.com/~eveander/trivia/.
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 Plane Geometry Web Pages  David Jaffe
Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity;
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 The Playground of Mathematics  Cilenia
JavaScript practice in addition, subtraction, multiplication, division, time, and comparison ("greater than, equal to, or less than"). Select difficulty, complexity, position of unknown, duration, and other settings. Also available in Russian, Italian,
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 A Playground of Thoughts  Takasugi Shinji
Takasugi's "Number Systems of the World" lists dozens of languages; how to count from zero to one hundred in each; and the mathematical meaning of the expressions for each numeral. For example, the French say "93" with quatrevingttreize, which means
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 POLYA: Cooperative Solutions of Difficult Problems in Elementary Mathematics  Paul Yiu and Xiaodong Zhang, Moderators; Department of Mathematical Sciences, Florida Atlantic University
An archived discussion group for the cooperative solution of difficult problems in elementary mathematics through calculus, "preferably nontechnical in nature."
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 Polyhedron: An application in solid geometry  Stelian Dumitrascu
Software based on "deductionfree geometry," which allows the user to perform various actions upon solids as if holding these solids in your hands. It simulates a number of tools, such as the ruler, protractor, setsquare, compass, bisector, saw, and eraser.
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 Polymath Love  Gary Smith
Free and lowcost Macintosh software for middle school mathematics: over
200 programs written by a classroom teacher. Program descriptions and some free programs are available to download from the Web, or order the CDROM for $100 U.S., which includes
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 Polyominoes  Cynthia Lanius
What do dominoes and Tetris have in common? Both games use pieces that are formed of squares placed side by side. Dominoes use 2 squares; Tetris pieces (or tetrominoes) use 4 squares. Mathematician Solomon Golomb, in a 1953 talk at the Harvard Mathematics
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 Polyominoes  Kevin Gong
Information and Polyominoes software to download. A polyomino is a piece made up entirely of squares connected edgetoedge. For example, a domino is a polyomino with 2 squares. In this program, you can use pentominoes, tetrominoes, trominoes, hexominoes,
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 Polyominoes  Slavik Jablan
A plane topological disk (i.e. a plane region without "holes") consisting of n edgetoedge adjacent squares is called a polyomino. This site offers a shape description: in every border square cell of a polyomino we could introduce twosided mirrors perpendicular
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 Ponder This  IBM Research
Match wits with the minds in IBM Research, who post a new puzzle every month (some suggested by users at large), and welcome your solutions. Archives of previous challenges.
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 Population Education  Population Connection
Browse the Population Connection's catalog for population education teaching materials and posters. The library contains newsletters, quick facts, reference materials such as free activities and frequently asked questions, quizzes, and more. Population
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 Portion Distortion  National Institutes of Health (NIH)
How do the portions served in today's fast food restaurants compare to those available 20 years ago? Take the "Portion Distortion" quizzes to learn exactly how much portions have "super sized," as well as the amount of physical activity required to burn
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 The postIMO97 web page  Olimpíada Matemática Argentina
Problems and results from the math olympics held in Argentina in July, 1997. Available in English and Spanish, with problems also in French, Russian, German, and a host of other languages.
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 Power Cards: A Mathematical Puzzle  Cynthia Lanius
Choose a number from 131. Tell me which cards below contain the number, and I can tell you the number. How do I do it? (A hint and directions for making more cards are given.)
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 Powers of 5 and Traveling to the North Pole (Math Chat)  Frank Morgan; Christian Science Monitor
What is the remainder when you divide 5^999,000 by 7?
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 PQRST Puzzle Competition  Cihan Altay
PQRST is a quarterly online puzzle competition open to all, with competitions in January, April, July and October. Download the test as PDF, then solve and rate the puzzles within seven days. The PQRST site highlights top competitiors and puzzles receiving
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 Practice "Maths" Perfect: Online Maths Quiz For Young Children / Students  PMP Online Tech
This is a simple but interactive maths quiz for young children or students aged 4 to 8 (requires a small membership fee). Based on the Singapore Mathematics methods.
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 The Practice of Statistics  Yates, Moore & Starnes; W. H. Freeman & Co.
A free resource for students and instructors using the statistics textbook The Practice of Statistics. Take online quizzes for each chapter; read EESEE (Encyclopedia of Statistical Examples and Exercises) case studies ranging from "Is Old Faithful Faithful?"
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 Praktick  Praktick Learning private Ltd.
Autoscoring practice problems aligned to the UK's Central Board of Secondary Education (CBSE) Standards, from prekindergarten to grade seven. Questions adjust dynamically based on performance, while a timer counts up response time; incorrect answers
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 PreAlgebra Problem of the Week  Math Forum
Math problems for students learning algebraic reasoning, identifying and applying patterns, ratio and proportion, and geometric ideas such as similarity. The goal is to challenge students with nonroutine problems and encourage them to put their solutions
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 PreCalc/Calculus (Math for Morons Like Us)  ThinkQuest 1998
Lists of important concepts, a quick reference sheet with key calculus formulas, and a calculus message board.
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 PreCalculus: A Teacher Quality Grant Project  State of Texas, Texas Higher Education Coordinating Board
A precalculus "courseinabox" for all teachers, particularly those new to teaching precalculus under the guidelines of the Texas Essential Knowledge & Skills (TEKS). It includes content information, activity sheets, videos of best teaching practices,
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 The Precalculus Page
Lesson plans and staff development activities with a problemsolving approach to precalculus, with materials on logarithms, the binomial theorem, and the law of sines, and problems (without answers) on algebra, exponential and logarithmic functions, other
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 PreCalculus Problem of the Week  Math Forum
Math problems for students who had finished studying topics commonly covered in firstyear algebra and high school geometry. From 2002 to 2003, problems involved probability, statistics, discrete math, and trigonometry. The goal was to challenge students
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 The Precalculus Weblet  Dynamic Educational Materials
A partially online precalculus course with the following centers: Instruction (extending the instructional opportunities beyond the textbook; see Explore the Concepts and Starred Exercises), Reference (technology, glossary, history, sites that complement
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 PrimaryMath  David Dee
Paperless arithmetic learning for school and home. Create lessons composed of interactive problems in addition, subtraction, multiplication and division (including long division) with optional decimals and signed numbers.
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 PrimeNumbers.net  John Barth
Answers to commonly asked questions about primality: What are prime numbers? What are composite numbers? How do I find prime numbers? What are some types of prime numbers? What is the biggest prime number? Other resources include original worksheets available
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 The Prime Puzzles & Problems Connection  Carlos B. Rivera
An anthology of the most interesting problems and puzzles explicitly related to prime numbers. Organized into: Records (to convert you into a "prime hunter"  you'll discover that all you need to top a record is a PC, a good code, and a certain amount
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 The Prime Puzzles & Problems Connection  Carlos Rivera
Problems and puzzles having to do with prime numbers. A new puzzle is posted each Saturday morning. Also links to related Web pages, and a short bibliography.
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 Principles of Calculus Modeling, an Interactive Approach  Donald Kreider and Dwight Lahr, Department of Mathematics, Dartmouth College
Web pages that correspond to each section of the book Principles of Calculus Modeling: Modeling Discrete Data; Modeling Rates of Change; Modeling with Differential Equations; Modeling Accumulations; and Culminating Experience. With quizzes, applets, worked
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 Printable Math Worksheets  Homework for Kids
Practice worksheets, most with randomly generated problems, on the following topics: learning numbers, addition and subtraction, multiplication and division, fractions, decimals, time, measurements, perimeter, area and volume, integers, set theory, equations,
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 Printable Math Worksheets  TestDesigner.com
Free printable math worksheets, with answer keys, on number concepts, measurement, geometry, algebra, and statistics. Customize your own tests by selecting from the growing database of questions  or create your own.
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 The Prisoner Problem  Anne Arundel Community College
A classic logic problem about three prisoners, each of whom tries to determine what color his own hat is in order to be set free.
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 The Prisoners' Dilemma  F. Heylighen, Principia Cybernetica Web
Cooperation in game theory: the principle of suboptimization. A game that has been and continues to be studied by people in a variety of disciplines, ranging from biology through sociology and public policy. It is a "nonzerosum" game: the best strategy
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 Prisoners' Dilemma  Wayne Davis
An interactive game simulation inspired by Prisoners' Dilemma game theory as described in the book The Selfish Gene by Richard Dawkins. The payoff is a reduction in prison sentencing of very good, fairly good, fairly bad or very bad, which is translated
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 Probability  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A short essay on probability theory, with links to some wellknown problems: Monty Hall Dilemma; Three pancakes problem; Lewis Carroll's problem; Bertrand's Paradox; Bear cubs problem; Misuse and Misconception of Statistics; Pauling's joke; Probability
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 Probability of Getting Doughnuts  NASA Lewis Learning Technologies Project
A box of doughnuts contains 4 glazed, 3 creamfilled, and 2 jelly doughnuts. What is the probability of getting a creamfilled doughnut, eating it, and then getting a glazed doughnut? A detailed answer is provided. From NASA's 9th Grade Math Proficiency
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 Probability: Rolling Dice  NASA Lewis Learning Technologies Project
Probability: If a die is rolled 18 times, how many times is the number 2 expected to come up? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Problem at the Art Gallery  Ivars Peterson (MathLand)
The Crystal Art Gallery was being readied for its grand opening, and I had to figure out how many guards were needed to make sure that every wall of paintings was under scrutiny. I was also ordered to keep costs as low as possible. The trouble was that
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 ProblemAttic  EducAide Software
Thousands of questions from New York State Regents exams, the National Assessment of Educational Progress (NAEP), the Trends in International Mathematics and Science Study (TIMSS), academic competitions, and other test banks. Sign up for a free account
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 Problem Corner  Les Reid; Southwest Missouri State University (SMSU)
High School, Advanced, and Challenge problems, updated monthly (approximately). High School: solutions are not solicited, although feedback (generalizations, suggestions for future problems, etc.) is appreciated. Each month, the solution to the previous
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 The Problem of Points  Isaac Reed
An ageold gambling problem led to the development of probability by French mathematicians Pascal and Fermat in the 17th century.
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 Problem of the Month  Grovedale Secondary College, Grovedale, Victoria, Australia
Elementary level problems posted monthly for local elementary school students. Examples include: Sums of square numbers; Trial and error spacial arrangement problem; Sums of whole numbers; Jokes/Riddles in code; Order of operations using number cards;
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 Problem of the Week  Alberto L. Delgado, Bradley University, Peoria, IL
Collegelevel problems, posted weekly for the current semester, with archives of problems and solutions starting in spring 1997, for number theory, combinatorics, probability, calculus, etc.
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 ProblemoftheWeek  David Poole; Department of Mathematics, Trent University, Canada
Most of these problems can be done using only high school mathematics and logical reasoning. Eight problems with solutions and one without, from the fall of 1997, at Trent University, Canada. An email contact is listed, for those outside the university
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