 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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 Open Problem Garden  Matt DeVos and Robert Šámal
A collection of unsolved problems  mainly, graph theory, combinatorics, and number theory. A wiki for each open problem includes relevant bibliographical citations, importance rating, and recommendation for undergraduates. Navigate by math subject,
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 Open Problems for Undergraduates (DIMACS)  Robert Hochberg, Center for Discrete Mathematics and Theoretical Computer Science, Rutgers Univ.
A collection of open problems in Discrete Mathematics in the areas of Graph Theory; Combinatorial Geometry; Geometry/Number theory; and Venn Diagrams, currently being researched by members of the DIMACS community. These problems are easily stated, require
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 Open Problems in Dynamical Systems  Dept. of Mathematics, State Univ. of New York at Stony Brook
A collection of papers outlining unsolved problems in dynamical systems.
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 Open Problems in Dynamical Systems & Ergodic Theory  Sergiy Kolyada
This collection of problems originated in the Katsiveli2000 Open Problems Session (Chairman  Benjamin Weiss). New problems are being added. Copies of the page are also at http://iml.univmrs.fr:80/~kolyada/opds/ and http://www.math.iupui.edu/~mmisiure/open/.
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 Open Problems  Jeff Erickson
Open problems, mostly in geometry, including folding, combinatorial, and algorithmic problems. Contents include: Existence Problems: Does Object X exist?
Combinatorial Problems: How complex is Object X? Algorithmic Problems: How fast can Problem X be
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 Open Problems (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on open problems in geometry: antipodes; bounded degree triangulation; centers of maximum matchings; chromatic number of the plane; combinatorial complexity of spheres; covering points by rectangles; cube
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 Operations Research  J. E. Beasley
ORNotes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). Beasley includes practice questions ("tutorials"), links to other web resources, and past exams.
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 Optical Illusions (SandlotScience.com)  SandlotScience
Interactive explorations of optical effects, illusions, distortions, animations, artwork, stories, PDF projects, games, and more. Impossible objects include columns, an endless staircase and animated stairs, Java triangle models, an interlaced tribar,
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 Optimization Links  Tom Cavalier; Industrial and Manufacturing Engineering, Penn State Univ.
Links to online information on various aspects of optimization; interactive guides/case studies; optimization software/test problems; and other sites. Also general operations research sites; OR/Optimization people. Location/Routing/ Conference Information;
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 The Orbifold Shop (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A symmetry project: the Orbifold Shop offers a free coupon for $2.00 worth of parts, installation included, to anyone acquiring a new orbifold. There are only a few kinds of features for twodimensional orbifolds, but they can be used in combinations:
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 The OU Calculus I Problem Archive  Dept. of Mathematics, Oklahoma University (OU)
Sample problems, with hints, answers, and "the grisly details": 1. Functions, calculus style; Graphs; Machine graphics; What is a function?; A field guide to elementary functions. 2. Amount functions and rate functions; The geometry of derivatives; The
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 Overview of "Mathematician's Secret Room"  Hisanori Mishima
Challenges to unsolved problems in Number Theory, some translated into English from the Japanese.
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 Packing Pentominoes  Mark Michell
For rectangles with a given ratio of height to width, what is the smallest rectangle that will allow the construction of a complete set of pentominoes?
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 Packing Videotapes  NASA Lewis Learning Technologies Project
Roger had to pack videotapes 10 to a box. If he had 178 tapes of one kind and 121 of another kind, how many boxes would he need in order to pack them all and not mix the different types? A detailed answer is provided. From NASA's 9th Grade Math Proficiency
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 Paginedimatematica  Bruno Tomaino
In Italian: Analisi, trigonometria, equazioni differenziali, test a risposta multipla.
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 The Pai Intersect  Jimmy Pai
Blog by an Ottawa (Canada) secondary mathematics teacher and graduate student in education. Posts, which date back to August, 2012, have included "Understanding Fraction Division #2  Part 1," "$100 Tablet Project," "Spiraling through the curriculum,"
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 Palindromic Numbers and Other Recreational Topics  Patrick De Geest
Many odd facts about big (and little) numbers, including circular primes and palindromic triangulars, tetrahedrals, squares, cubes, and primes. Also assorted odd puzzles, etc.
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 Panthera's Puzzle Contest  Dr. Amy Galitzer; Puzzle University
A weekly contest of math, logic, and word puzzles sponsored by the American Mathematical Society and the University of Maryland Mathematics Department. You can submit your own puzzle for the next contest by signing up to participate, or simply read the
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 The Paper Challeran  Ryosuke Ito & TOSS
Starting with a score of 1, trace a route through the Paper Challeran. Add to, multiply, or subtract from this score, as indicated at every edge along the way. Compete by registering scores online. Numbers around each block change every month. Find rules,
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 Parent's Page  Chicago System Initiative (CSI)
A list of informative sites for parents who have questions about parenting and how to get involved in their children's education. Topics include Family Math (a page on math education); Helping your child learn math; Math and Your Child (information on
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 Pascal's Triangle using Clock Arithmetic  Jay's Corner
Exploring Pascal's triangle when the modulus is a prime; when the modulus is a power of a prime; and when the modulus has at least two different prime divisors. From mod 2 to mod 12, illustrated. (See also Part II.)
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 Passalgebra.com
Pass algebra with this online study guide. Practice with hundreds of problems, with answers worked out step by step. Examples of study guide and exercises provided. $27 for 1 year; stepbystep instruction for $2.50/problem.
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 Path Puzzles  Erich's Puzzle Palace; Erich Friedman
Sixteen paththroughagrid puzzles; can you fill in the correct path? Answers provided.
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 Pat's Math & Problem Solving Links  Pat McQuatty
Site recommendations from the math consultant for the Western Quebec School Board. See, in particular, Special Days (Hundredth Day of school, Math with the number 2000  twenty suggested math activities for the year 2000). Also mathrelated links for
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 Patternbee Multiplayer Spatial Reasoning  Jordan Pollack
In this version of tangrams, pairs of learners create the puzzles for each other to solve, which can be at different levels of difficulty. Requires free registration to play, as this is an educational psychology research project.
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 Patterns and Magic Squares  Recmath
This page looks at a particular subset of Magic Squares, those of order four which are 'continuous' (also known as pandiagonal, Nasik and Jaina). It explores the patterns possible when the numbers in these kinds of squares are
represented by a set of
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 Patterns in Mathematics (Teachers' Lab)  Annenberg Media
This lab, based on the professional development series and workshops broadcast on the Annenberg/CPB Math and Science Project Channel, explores patterns as they occur in logic, numbers, and words, focusing on how to develop "function sense" without simply
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 Paul's Page of Pi  Paul A. Gusmorino 3rd
Most of the content of this site is focused on methods of calculating pi: Archimedes' method; Wallis' formula; Gregory, Leibniz, and Machin; Newton's fluxions; and Paul's 8192 digits. Also Pi Poems, Music of Pi, and Pi Links.
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 paulus gerdes's Storefront  Paulus Gerdes
Purchase print editions or download Gerdes' titles, some also available in Portuguese, Dutch, and French: Drawings from Angola: Living Mathematics, Enjoy Puzzling with biLLies, Puzzle Fun with BiLLies, The Bisos Game: Puzzles and Diversions, Introducing
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 PBS Teachers: Math  PBS Teachers
The Public Broadcasting System's Math Service, combining computing and telecommunications technologies to offer interactive data services and interactive video and voice services for education based on the NCTM Standards. The site features: resources,
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 PCTM Online Puzzle of the Week  Judy Brown; Pennsylvania Council of Teachers of Mathematics
Weekly illustrated math puzzle online competition from 199697, with an archive of past puzzles. Since 1997 this project has moved to the Math Forum to become its Middle School Problem of the Week.
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 Pédagogie  Olivier Batteux
MathsRix et Labymath sont des logiciels présenté sous forme de labyrinthe où il faut choisir des portes qui correspondent à des choix opératoires en vue des résoudre des problèmes concrets. Découvre
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 The Penrose Puzzle Room  World of Escher
Mathematically based Pentaplex Puzzles designed by Sir Roger Penrose, the wellknown English mathematician. The original 45 piece Gamebirds, 190 piece Perplexing Poultry  2 designs, 500 piece Jigsaw Puzzles  4 designs.
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 Pentangle  U.K.
To buy: wooden, mechanical, interlocking, mathematical and logical thinking puzzles; brainteasers, games, toys, gifts, threedimensional puzzles, promotional items, and collectors' puzzles,
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 Pentominoes  Robert Simms; Dept. of Mathematical Sciences, Clemson University
A Java applet spatial relations game. Try to place the pieces in the box with no overlapping. With detailed instructions, source code, development stages of the applet, and related links.
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 Pentomino  K.S.O. Glorieux Ronse, Belgium
An introduction to polyominoes, with a sitewide focus on pentominoes. The site features puzzles and contests, as well as galleries of pentomino constructions and problems, such as how to form letters of the alphabet and silhouettes of zoo animals. Available
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 Perfect Problems  Vasek Chvátal
Unsolved problems on perfect graphs, a collection for people with at least a basic knowledge of the subject. Contents include: Perfection of special classes of Berge graphs; Recognition of special classes of Berge graphs; Decompositions of perfect graphs;
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 Periodic Points of Quadratic Polynomials  Cut the Knot!, Alexander Bogomolny
The main purpose of the Mandelbrot set is to index Julia sets corresponding to various values of the parameter c... iterations inside M evolve differently depending on the value of c. (You may explore some iterations via the applet supplied.) An interactive
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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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 A PersonalMathOnlineHelp.com  Marko Ignjatijevic
Practice the basic operations of adding, subtracting, multiplying, and dividing singledigit and multidigit positive whole numbers. Submit your answers online to check them, or click the "show solutions" buttons to see the correct answers; the "try again"
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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 Winton's Radical Home Page
Math topics include puzzles, a gallery of fractals, and Visual Basic programs to download (count the grains of rice on a chessboard, or graph different curves).
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 Petran Mathematics  Petro Greffrath
From South Africa: grade 11 and 12 math problems, tests, and answers. Teachers may register their students (R360/year for 110 students; the Petran academic year starts 1st February and ends 31st January the following year). Includes access to an EnglishAfrikaans
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 Phenomenological Pizza (SMILE)  Robert Foote, Disney Magnet School
A lesson for the middle grades designed to teach students to calculate the area of a circle, find how many twotopping pizzas can be made using 14 toppings, and determine cost per square inch. From the Geometry and Measurement section of a collection
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 The Physics Classroom  Tom Henderson, hosted by StudyWorks! Online
A physics tutorial for high school students, including explanations, animations, quizzes, and practice problems.
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 Physics Problems for the Next Millennium  David Gross, Institute for Theoretical Physics, University of California, Santa Barbara
The ten most important unsolved problems in fundamental physics, as formulated by participants of the University of Michigan's Strings 2000 Conference: Are all the (measurable) dimensionless parameters that characterize the physical universe calculable
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 Pi Across America  University of Phoenix
Join the "Pi Pilot" for a "journey to one of humankind's most intriguing and celebrated numbers." Activities include "The Great Chain of Pi," "Taking Pi to Court," "Your Place in Pi," "Freehand Circle Drawing Competition," "Pi Party," and "Pi Bee." Scenario
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 Pi and Square Roots  Don Cohen (The Mathman)
Kohler (a 5thgrader) follows Archimedes. A graph and a program for iterating the square root of 10. Sample problems with some answers from Chapter 10 of Don Cohen's worksheet book.
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 Pi and the Fibonacci Numbers  Ron Knott
Contents: How Pi is calculated (Measuring the steepness of a hill; The tangent of an angle; The arctan function; Gregory's Formula for arctan(t); Radian measure; Gregory's series and pi; Using Gregory's Series to calculate pi; Machin's Formula; Another
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