 The "TwoDimensional Factorial" and a New Solution for the Probability of Completing Sets in Random Sampling  Jeffrey D. Lindsay
In finding a new solution to a classic probability problem, The Collector's Problem, concerning the collection of items in a set, a new and useful recursive function has been found, the "twodimensional factorial." A Web adaptation of J.D. Lindsay, "A
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 Tying Down a Random Walk  Ivars Peterson (MathTrek)
For many men, the ordeal of fashioning a neat tie knot is fading into the distant past. It seems ironic that two physicists have now put necktie knots back on center stage. Thomas M. A. Fink and Yong Mao of the Cavendish Laboratory in Cambridge, England,
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 The UK National Lottery  MerseyWorld
Using real data allows due emphasis to be given to the context and so may encourage crosscurricular links. The UK lottery site has links to many pages with varied statistical information about winning ticket numbers and prizes (see Lottery Links).
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 Uncovering Mathematics with Manipulatives and Calculators  Texas Instruments, Inc.
A text that provides K6 activities emphasizing problem solving, reasoning, communications, and connections, clustered into four content strands: number sense; patterns, relations, and functions; measurement and geometry; and probability and statistics.
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 Unfair Dice  Ivars Peterson (MathTrek)
Dice represent an intriguing example of the interplay between randomness, chance, and physical law. The simplest mathematical model of a standard die is based on the assumption that the die is a perfect cube. A cube has six faces, and each face has an
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 University of South Carolina High School Math Contests  David Sumner
Problems from the University of South Carolina (USC) High School Math Contests, since 1994. Walk step by step through illustrated solutions to each problem using the "next step" button. The delivery of questions is designed for competitive timing. Also,
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 Unizor  Zor Shekhtman
Whiteboard lectures for teenagers on algebra, trigonometry, vectors, matrices, combinatorics, probability, and statistics. Sign in for structured study, assignment functions, and more.
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 Unlucky in Cards (Math Chat)  Frank Morgan, MAA Online
In his Contract Bridge syndicated column Phillip Alder says that the odds against getting a "Yarborough  a hand with no card higher than a nine" are 1827 to 1, and that the odds against two players getting a Yarborough on the same deal are about 182
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 Usenet FAQ Archive : Recreation : Puzzles  Netmeg Internet
Problems and puzzles, with solutions, from the rec.puzzles archives, in the categories: analysis, arithmetic, combinatorics, competition, decision, geometry, group, induction, instructions, language, logic, physics, pickover, probability, real life, references,
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 Utah Elementary Mathematics  David A. Smith
Blog of conceptual frameworks and other classroom resources for Utah educators implementing the Utah Core State Standards. Smith, the Elementary Mathematics Specialist at the Utah State Office of Education (USOE), has posted since October, 2013; and also
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 Vancouver Math Tutor  Vlad
Tutoring services for the Vancouver, B.C. (Canada) area; articles on tutoring; and algebra and probability materials used in tutoring.
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 Video Lectures in Mathematics  Jerry Farlow
An online pinboard gathering thousands of visual links to a broad range of math videos. Categories include applications of math; famous mathematicians; math education; math humor; math on TV, movies; STEM math initiatives; and "instructional: K12." Farlow
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 Villainy, Inc.: Thwarting World Supremacy through Mathematics  Maryland Public Television
To thwart the evil Dr. Wick, ID, middle grade students take on the role of an advisor to his company, Villainy, Inc.  while secretly using their math skills to make sure Wick never succeeds. As undercover double agents for the AntiVillainy Unit (the
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 The Virtual High School
The Virtual High School project is a collaborative of high schools from around the country. In exchange for contributing a small amount of teaching time, a school in the collaborative can offer its students webbased courses ranging from advanced academic
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 Virtual University (VU)  Stephan Nicolas
Math lessons: Introduction to Topology; Arithmetic; Introduction to Probability; Mathematical Approach to Probability; Random Variables, Expected Value, Variance.
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 VisualMath  G. Fonthal, VisualPhysics
Math shareware programs that feature visual and interactive techniques under Windows 95 may be downloaded from this site: for numbers (real, complex, binary); set theory (Venn diagrams); geometry (shapes and areas, 3D Geometry); algebra (equations, polynomials,
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 Waldomaths  Ron Barrow
Original applets on number, algebra and graphs; shape, space and measure; probability and data handling, including histograms; investigative tools (quadratic and cubic sequences); core (pure) mathematics; decision mathematics (network graphs and linear
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 WASL Math Prompts  Port Angeles School District, Washington state
Sample questions for the WASL, Washington State Assessment of Student Learning. Most questions have answers printed above the questions. Sample questions are offered for kindergarten through high school levels, organized by mathematical content, and accompanied
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 WebCab XL  WebCab Components
Range of math and finance techniques implemented within a free Excel addin for Windows. Techniques include: interpolation, probability and statistics, optimization, portfolio theory, options and futures pricing theory. Menu driven application development,
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 The Web Wizard's Math Challenge  J. Mooser
An ongoing Internet contest; register (free) to submit answers and score points. Problems are designed to be readily understood but not readily solved. Speed counts, because points are awarded based on the order in which contestants submit correct answers.
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 Weighing the Evidence  Keith Devlin (Devlin's Angle)
Hundreds of thousands of years of evolution have equipped us with many useful mental abilities  our instinct to avoid many dangerous situations and our use of language are two obvious examples. However, evolution has not equipped us to handle statistical
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 Weird Dice (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
In the dice game Piggy, you and your opponent take turns rolling a pair of ordinary dice. Your score is the sum of the face values of the dice, so if you roll a three and a four, you get seven points. The first player to reach 100 points wins. Suppose
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 Welcome to WebDice! (MSTE)  Nicholas Exner; University of Illinois at UrbanaChampaign (UIUC)
A Java applet that simulates the rolling of a set of dice. Use the pulldown menus to set the parameters for the trial.
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 West Contra Costa Unified School District Mathematics Center  Kennedy High School
Common Core mathematics resources, presentations, instructional videos, lessons, mathematics applets, parent guides, and other materials developed by the Richmond (California) school district.
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 What2Learn  John Rutherford
For free, a range of fun, interactive games and puzzles. Math topics covered include algebra, times tables, fractions, decimals, percentages, ratios and probability. Feebased service includes more activities, the option for teachers to add their own
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 Whistler Alley Mathematics  Paul Kunkel
Kunkel's Geometer's Sketchpad lessons convey a conceptual understanding, usually without rigorous proof, with questions and suggestions for extensions: Buffon's Needle (an old probability exercise); Chinese Handcuffs (questions with applications for geometry,
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 Who's Counting  John Allen Paulos
Columns by Prof. John Allen Paulos, the author of Innumeracy, Mathematician Reads a Newspaper, and other popular books. Humorous and enjoyable articles by a keen observer of the world around him whose mind has been sharpened by mathematical practice.
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 Who Wants to be a Millionaire? (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: On ABC TV's "Who Wants to be a Millionaire," to maximize your expected winnings how sure should you be of your answer to the $500,000 question to answer? Somewhere from about 22.5% to about 46.5%, probably closer to the latter.
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 WisWeb  Freudenthal Institute
The Freudenthal Institute, a Dutch organization for secondary education, provides applets to support/extend the math instruction of students 12 years and older. For this site, WisWeb recommends versions 5 or higher of Internet Explorer, Netscape or Opera.
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 The Wizard of Odds  Michael Shackleford
As a rule of thumb, the harder a game is to understand the better your odds of winning if you do understand it. By understanding the more complicated games such as blackjack, baccarat, and craps you can have an expected return of at about 99 cents per
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 Word Problems for Kids  St. Francis Xavier University; Canada's SchoolNet
Word problems by level for students in grades 512, which can help improve problemsolving skills. A hints link is available for difficult problems. Complete solutions are available upon request to teachers with email addresses. From students, principals,
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 Worksheet Works  WorksheetWorks.com
This site generates high quality PDFs of worksheets with the flick of a few checkboxes. Just specify level of difficulty, range of numbers, font size, or other parameters.
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 XP Math  Tak L. Hui
Features include free materials designed to excite learners in mathematics and technology, a free eBooks
library, a collection of math sites, a database of mathematical careers, an interactive math games league and an active forum.
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 Yahoo! Science: Mathematics  Yahoo! Inc.
All the best on the Web in math including Indices, alphabetically listed by category: Academic Papers; Algebra; Applied Mathematics; Books; Calculus; Chaos; Combinatorics; Complex Systems; Conferences; Education; Employment; Entropy; Equations; Ethnomathematics;
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 ZeroKnowledge Proofs  John Scammell
"Random thoughts about teaching math" from a high school math consultant who taught math for 18 years prior. Scammell's blog posts, which date back to May, 2010, have included "Lecture Method vs. Peer Instruction," "Mozart’s Dice Game," "Let the Kids
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