 Online Math Help & Learning Resources
Learn basic concepts behind arithmetic, algebra, geometry, statistics and set theory. Includes some SAT test preparation help, math games, math worksheets, math riddles, math quotes, math mnemonics and math trivia.
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 The Online Test Page  Elias Saab
Math and vocabulary drills, including MathCOUNTS, SAT, ACT, and Missouri MMPT questions, as well as links to relevant sites.
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 On Motivation and Understanding  Cut the Knot!, Alexander Bogomolny
Fourth in a series of columns that draw on Frank Morley's fundamental paper On the Metric Geometry of the Plane nLine  dealing with what amounts to his proof of the Trisector Theorem. Bogomolny outlines Morley's reasoning first and then supplies necessary
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 OOG: the Object Orientation Game  MCM Productions
MCM Productions' first publicly released software application. This 4in1 tiling puzzle game for the MSWindows environment allows players to test their problem solving ability with over 300 puzzles, including Tangrams, Pentominoes, Hexagons and Polyominoes.
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 OpenEnded Assessment in Math  Cooney, Thomas J.; Sanchez, Wendy B.; Leatham, Keith; and Mewborn, Denise S.
Over 450 openended, fieldtested assessment items, distributed more or less equally among elementary, middle school, and high school grade levels. The questions relate to five major content areas, based on the NCTM Standards: number and operation; probability
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 OpenEnded Math Problems  Gwenn Holtz and Mary Lee Malen, Levering School and the Franklin Institute
An eightmonth slate of openended problems for middle school students to solve in preparation for standardized testing. The authors have composed and selected problems that lend themselves to multiple solution paths, and then organized them into three
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 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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 OPenn  University of Pennsylvania Libraries
Highresolution archival images of manuscripts from the University of Pennsylvania Libraries and other institutions, along with machinereadable descriptions and technical metadata. Digitized cultural heritage materials on mathematics include "Treatise
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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  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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 Optical Data School Media
A publisher of math and science programs, including Windows on Math, an activitybased laserdisc and videotape curriculum built around the NCTM standards. Most products are for levels K8. Find Correlations for Optical Data products to a wide range of
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 Optimalcut Web Software
Fee JavaScript optimization solver for cutting stock and bin packing problems. Specify pieces and rolls to linearly cut rectangles out of bars, pipes, tubes, metal profiles, extrusions, linear wood boards, and more (1D cutting); or sheets made of glass,
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 Origami Mathematics  Tom Hull
Information on origami and the mathematics of paper folding. With an origami math bibliography and pictures and tutorials in origami geometric construction, as well as links to other origami sites and events.
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 OrigamiUSA
Resources for origami enthusiasts and for those just learning the art of paper folding: Events (calendar, convention, and exhibit information); Resources (model index, links, email discussion list, folding groups directory, and lending library); Shopping
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 Original Lesson Plans  Mathematics  Thirteen/WNET New York
Original Webbased activities developed by Thirteen Ed Online Master Teachers. Each lesson consists of an overview with learning objectives, procedures for teachers, and "organizers" for students  handouts, bibliographies, and other materials. Math
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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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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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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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 Palmer's Ponderings  Christina Palmer
Blog by a high school math teacher in Massachusetts. Posts, which date back to June, 2013, have included "I wonder...... (Cheerios in a chimney box)," "Four = Eight (almost)," "Today I Shut Up," "State Test Questions That Make Me Angry," "TMC14," "Compounding
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 Panagiotis Stefanides
Geometry presented at national conferences in Greece. Contents include: Quantization of Circle Duality; Logos Pyr Chronos; 'Buena Fortuna' (artwork); Geometric Mean Ratio (T) by Ruler and Compass; Quadrature Master Theorem; Corollary (Circle Circumference
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 Paper Cup Mathematics  Jerry Neidenbach, Sue Harvey, and Marilyn McArthur; Park City Mathematics Institute
In this classroom activity, a PCMI Resource for Teachers, students investigate whether paper cups roll out the pattern of an annulus and how you can tell, how the dimensions of the cup relate to the dimensions of the annulus, and whether you can predict
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 paperfolding.com  Eric Andersen
Learn to fold origami from diagrams; read about the history of paperfolding, including the origin of the term "origami." The origami & math essay contains sections such as Origami, Geometry, and the Kawasaki Theorem; and Origami and Topology.
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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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 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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 Pasta by Design  George L. Legendre
Photos of architect Legendre's 2011 book by the same title. Pasta by Design provides an illustrated taxonomy of over 90 forms of pasta, along with the mathematical formulae, descriptions of special attributes, and advice on specific cooking uses for each
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 Pattern  Drew, Wallace; Mathematics Across the Curriculum, Dartmouth College
An interdisciplinary course in textile design and elementary group theory. Syllabus, course pages (notes, figures, questions, group work and homework), final project and class artworks from a 1996 math and art crosscurricular class at Dartmouth College.
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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 Mathline: Math at the Movies
Math concepts, challenges, and more, from the movies. For kids: solve puzzles from the movies; explore movie math concepts; and learn about a movie career involving math. Teachers, there are teaching and assessment tips here as well, not directly connected
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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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 PentoMania  Douglas Twitchell, Virtu Software
This pentominobased puzzle game for Windows allows students to solve geometric puzzles or create puzzles and designs of their own.
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 Pentomino Relationships  Adrian Smith
The site describes how pentominoes (twelve pieces of wood, each a different shape and each made of five cubes) fit together into rectangles or cuboids, as well as the subsequent challenge of finding as many other solutions as possible from the one just
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 Perimeter Efficiency  William Blackwell
Perimeter Efficiency, also known as Isoperimetric Inequalities, compares the actual perimeter of a shape with the circumference of the circle that would be required to enclose the same area. Since a circle will enclose any given area with the least amount
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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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 Personalized Programming Service Inc.
Educational software for teachers and students. Topical software in Math, English, Social Studies, and Science, as well as Quizmaker and Testmaker programs. Download demos and upgrades, browse the products, or order on site.
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 Personal Tutor  Memory Banks Pty. Ltd., Australia
Maths and science software designed to complement the secondary school math syllabus. A comprehensive learning system usually used by students and schools as a supplement and aid to coursework, but thorough enough that it can be used by individuals without
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 Perspective Images  H. B. Meyer
The computation of image points of perspective images by the use of similar triangles ("numerical perspective") is shown. By inversion of the corresponding mapping equations the determination of proportions of various distances in the real scene becomes
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 Perspective Study  Hop David
David suggests a mapping from half of 3D space onto a plane, feeling that traditional perspective drawings are similar to the image projected by a pinhole camera. Perspective illustrations of arches, looking up or down at a skyscraper, peripheral vision,
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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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 Peter J. Lu  Department of Physics, Harvard University
Lu's mathematical and historical research has revealed new insights in medieval Islamic quasicrystalline tilings and the earliest machines, such as the one he suggests precisely interconverted the linear and rotational motion responsible for the distinctive
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 peterlu.org  Peter Lu
Publications and research into medieval Islamic geometry (e.g., decagonal and quasicrystalline tilings in its architecture), softmatter and colloid physics, highperformance imaging, ancient Chinese technology (e.g., first use of diamond, early precision
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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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 Philosophy of Science  David Banach
A syllabus and collected resources for a course in the philosophy of science, including excerpts from various books. Topics include ancient Greek science and mathematics: the Golden Section, Pythagoras, infinity and continuity, and Plato and Aristotle,
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 PhotoMath  Martha Jean Barrett; Kodak
A project where students created their own mathematical board games for use with younger or less advanced students, for grades 48. Working in teams, advanced students covered seven math categories: whole numbers, decimals, fractions, measurement, geometry,
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 Pieces 'n Creases: A Fun Guide to Origami  Herring, Long, Haeggquist, Jeremy; ThinkQuest Junior
Contents include the history of origami; uses and benefits; terms, symbols, and tips; origami and peace; poems about origami; activities, and resources for folding paper. An awardwinning entry from Vidor Middle School.
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 Plane Geometry by Shalosh B. Ekhad, XIV  Doron Zeilberger
A textbook entirely written in Maple, "by" Shalosh B. Ekhad, XIV (ca. 2050), "downloaded from the future" by Doron Zeilberger. Code provided, with illustrations and instructions.
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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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 Plane Graphic Calculator  J. E. Lillge
A Java calculator that can plot graphs of mathematical functions. Intended primarily as an educational aid to understanding the geometric interpretation of mathematical functions, it also supports complex numbers, vectors, and parametrically defined functions.
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 Plane Isometries  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of basic facts and partial explanations on plane isometries. With accompanying Java applets for translation, reflection, rotation and glide reflection.
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