 Open Middle  Johnson, Nanette; and Kaplinsky, Robert
"Open middle" problems, hints, and answers, all aligned to the Common Core State Standards (CCSS). Introduced by Dan Meyer, these kinds of math challenges have a "closed beginning," meaning that they all start with the same initial problem; a "closed
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 OpsResearch  DRA Systems
A collection of Java classes for developing operations research programs and other mathematical applications. The site includes documentation and tutorials, and software download is free. Also features a bookstore and related links.
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 ostermiller.org  Stephen Ostermiller
Converters, Calculators, and JavaScript include Multiplication Game, in which letters represent digits in a multiplication problem; Length, which converts between units of length and distance; Roman Numerals, which converts between Arabic and Roman numerals;
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 Pages Mathématiques  Lycée de Vienne SaintRomainEnGal (académie Grenoble)
Une série de cours de mathématiques: Géométrie du triangle; Transformations; Géométrie des cercles; Barycentres; Coniques et courbes; Solides; Statistiques; Fractales; Géométrie non euclidienne;
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 Papers on the History of Mathematics  Gregory Cherlin, Rutgers University
A random selection of term papers submitted in undergraduate, onesemester courses on the history of mathematics. Topics include zero, Fermat, Euler, Newton, Euclid's proof of the Pythagorean Theorem, Fibonacci, Vieta, conic sections, mathematics at Princeton
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 Pascal's Triangle  Math Forum, Ask Dr. Math FAQ
What is Pascal's Triangle? How do you construct it? What is it good for?
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 Passy's World of Mathematics
Lesson outlines by this Australianborn math teacher include Venn diagram word problems, combining like terms, translate word equations, and isometric drawing and 3d cubes; PowerPoint presentations include traversable networks, sharing using ratios, real
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 Pat Thompson's Home Page  Patrick W. Thompson
Research on students' development of algebra and calculus ideas in grades 316, on the nature of multiplicative reasoning and its role in learning sophisticated mathematical ideas, and on teaching and learning statistical and probabilistic reasoning.
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 Pearson Learning  Dale Seymour Publications
A leading publisher of educational materials, emphasizing math, science, and the arts. The site contains: an online catalog; math curricula include: CMP (the Connected Mathematics Project) and Investigations (Investigations in Number, Data, and Space,
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 A Penny Surprise  Ivars Peterson (MathTrek)
Flipping a coin in the air, catching it, then determining whether it has come up heads or tails is to many people a prototypical random process. In some sense, however, coin tossing isn't really random at all. A mechanical gadget can flip a properly positioned
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 Perplexus  flooble
A large archive of mathematically inclined puzzles and problems displayed by category. Includes logic, number theory, geometry, probability and other problems. All are rated by difficulty and quality and discussed in depth by visitors. Most with solutions.
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 Peter Ash's Thoughts on Math and Education  Peter Ash
Musings on doing and teaching mathematics, book reviews, and math problems both elementary and advanced from the creator of Cambridge Math Learning. Blog posts, which date back to August of 2007, include "Very Proper Fractions"; "Physical Models for NonEuclidean
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 Peter Doyle  Mathematics, Univ. of California at San Diego
Advanced tutorials, proofs and papers, mostly statistics, probability, geometry, and graph theory, but with examples from other mathematics areas as well. Don't miss Dr. Doyle's Flip Flops.
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 Phenomenological Probability (SMILE)  Robert Foote, Disney Magnet School
A lesson for grades 68 designed to find the difference between theoretical and experimental probability in three different experiments: rolling dice, using marbles and a spinner, and through a card trick. From the Probability and Statistics section of
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 Physicscatalyst
Study notes, videos, formula sheets, solved examples, solutions from India's National Council of Educational Research and Training (NCERT), and more for middle and high school maths.
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 Physics Forums
Discussions emphasize physics, but "PF" also includes an entire directory on mathematics: General Math; Calculus & Analysis; Differential Equations; Linear & Abstract Algebra; Topology & Geometry; Set Theory, Logic, Probability, and Statistics;
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 Picking Winners  Ivars Peterson (MathTrek)
One of the attractive features of spectator sports is the uncertainty of the outcome. Even when one team is overwhelmingly favored to win, the underdog may still come through with a surprising victory. Nonetheless, the ability to pick winners can be of
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 PlaneMath  InfoUse, in cooperation with NASA
Materials for elementary school students about math and aeronautics, designed to stimulate and motivate students with physical disabilities in grades 47 to pursue aeronauticsrelated careers via the development and delivery of accessible math education
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 Planetqhe (Probabilistic Learning Activities Network)  David Kay Harris
Outoftheordinary probability problems. The site focuses on using methods of probability to solve counterintuitive problems and deepen students' understanding and competence in the domain. Sections include: a brief history and rationale of the site;
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 Poisson Pit: Poisson Probability Calculator  Chuck Anesi
Variously called the Poisson Distribution, Poisson Law of Large Numbers, or Poisson Distribution for Rare Events, the probability function for this discrete distribution of one parameter is given on this site. The Poisson distribution is usually employed
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 Poker Probabilities  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about poker probabilities, such as "In a standard deck of cards, how many different ways are there to get a straight, a flush, a straight flush, one pair, or two pairs?"
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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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 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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 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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 Presidential Election and the Length of the Shortest Piece (Math Chat)  Frank Morgan, MAA Online
Presidential election with 48% of the US popular vote does not come close to the extreme possibility, even with just two candidates, of winning with less than about 22% of the popular vote. See Math Chat of November 8, 1996. Answer to the Challenge: 1.
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 Probabilistic Thinking  Richard Jeffrey, Princeton University
A 1995 book. Chapters include: Probability; Methodology; Expectation; Decision; Probabilism and Induction. Solutions to problems are included.
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 Probability Abstract Service  University of Washington, Seattle, WA
Latest abstracts, with some preprints and information about authors; all abstract titles (old and new titles and authors, a large file); old abstracts; submission and subscription information; and related WWW servers.
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 Probability and Quantile Applets  Balasubramanian Narasimhan
The Probability Applet calculates areas under the standard normal density curves. You are presented with two fields and three buttons on top of a normal density curve. The buttons allow you to calculate areas to the left or to the right or between. The
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 Probability and Statistics with Reliability, Queuing, and Computer Science Applications  Kishor Trivedi
Powerpoint slides of chapters of the John Wiley publication Probability and Statistics with Reliability, Queuing and Computer Science Applications.
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 Probability and Stochastic Processes  Elmer G. Wiens; Egwald Web Services Ltd.
Theory, diagrams, and examples of probability distributions used in hypotheses testing; graphs of random walks; normal, gamma, chisquare, studentt, and F distributions.
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 Probability by Surprise  Susan P. Holmes et al.
Experimenting Paradoxes  browsersensitive Java applets (try Internet Explorer first) to try out: The Birthday Problem; Say Red; The Collector; Banach's Matchbox Problem; The Matching Problem; The IID Sequence; Polya's Urn as a restaurant choice; Random
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 Probability Guide  Doru Barbu, INFAROM
Introduction to Probability Theory and its applications for nonmathematicians.
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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 in the Engineering and Informational Sciences  Sheldon M. Ross, Ed.; Cambridge University Press
A journal focusing on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, stochastic control theory and probabilistic networks and graphs. Online
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 Probability in the Real World  Math Forum, Ask Dr. Math FAQ
An introduction to the uses of probability in everyday life, including: weather forecasting, flipping coins, batting averages, lightning strikes, and the lottery.
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 Probability of Childhood Games (SMILE)  Robert Foote, Disney Magnet School
A lesson for grades 68 designed to explore the probability of several different events theoretically and experimentally using spinners and a Monopoly game board. From the Probability and Statistics section of a collection of almost 200 single concept
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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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 Probability (S.M.A.R.T.)  Math Share Shop
Counting principle; Probability reference sheet. By students at Theodore Roosevelt H.S., Bronx, & Edward R. Murrow High School, Brooklyn.
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 Probability (SMILE)  Ana Timbers, Stockton School
A lesson for grades 68 designed to teach students the relation between theoretical probability and experimental results as they draw marbles from a bag and record the results. From the Probability and Statistics section of a collection of almost 200
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 Probability (SMILE)  Emily Turner, Joplin Elementary School
A lesson designed to teach students to understand the concept of probability and the basic probability formula; and to predict the possible outcomes of an event. From the Probability and Statistics section of a collection of almost 200 single concept
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 Probability (SMILE)  Laura Willis Moss, South Shore Community Academy
A lesson designed to teach students to derive a general formula for the probability of a given event when each possible outcome is equally likely. From the Probability and Statistics section of a collection of almost 200 single concept lessons by the
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 Probability (SMILE)  Sandy Reed, Robert Fulton School
A lesson for grades 58 designed to help students learn, discover, explore and make a table of the number of times a specific event can occur, considering the results of two types of events: repeated sampling with replacement (events are independent)
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 Probability/Statistics and Calculus Problems of the Week (PCPOW)  Kentridge High School, Kent, WA
Probability, statistics, and calculus problems and solutions, some of which date back to 1999.
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 Probability/Statistics: First Semester Project  Lisa Stanfill; Math Forum Teacher Exchange
A culminating project developed as part of a probability and statistics class, designed to help students put the topics of data collection, organization, presentation and interpretation together to see how and why learning that content is important.
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 Probability Theory and Related Fields (PTRF)  Geoffrey Grimmett, Managing Editor
Editors' site. The electronic pages of PTRF are kept at the web site of the publisher, Springer. Subscribers or members of subscriber institutions may access recent issues electronically.
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 Probability Theory: The Logic of Science  E. T. Jaynes
An online textbook by E.T. Jaynes in PS format.
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 Probability Theory: the Logic of Science  E. T. Jaynes, Dept. of Physics, Washington Univ., St. Louis, MO
Chapters (entirely in PostScript files) include: Principles and Elementary Applications; Advanced Applications; Appendices; and References. The long table of contents is on the Web. The LaTeX source is available for download (gz).
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 Probability Tutorials  Noel Vaillant
An online course on measure theory, lebesgue integration and probability, with tutorials (in PDF format) designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved theorems, as well as clear definitions, are
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 Problem of the Week  Dr. Annalisa Crannell; Franklin & Marshall College
Puzzles to solve in number theory, geometry, probability, cryptography, and the like. See problems from 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998, and 1997.
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