 The Twelve Days of Christmas and Pascal's Triangle  Judy Brown, DIMACS and The Math Forum
A lesson in which, using Pascal's triangle, students find the number of items given each day in the song, "The 12 Days of Christmas."
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 The Twelve Days of Christmas  Judy Brown, DIMACS and The Math Forum
A lesson in which students find the number of items given each day in the song, "The 12 Days of Christmas." This project is designed to be used as a warmup activity during the 12 days preceding Christmas.
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 Two Points of View  Tom O'Brien
"Children are not stones or recording devices. They are, first of all, sensemakers." In summarizing his work with practicing teachers on the four basic operations, the author responds to H. H. Wu's article, "What's Sophisticated about Elementary Mathematics?"
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 Twos Complement  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about two's complement, a way to encode negative numbers into ordinary binary so that addition still works.
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 UMass Lowell WebMathematica Scripts  Kenneth M. Levasseur, Department of Mathematical Sciences, University of Massachusetts Lowell
Download Mathematica scripts. Abstract Algebra: generate Cayley tables of EAAM groups, Zn, and the ring Zn; connect the dots to visualize finite cyclic groups; polynomial extensions; and a game on finding a morphism between two groups. Modeling: exponential
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 UMIGO  UMIGO, Inc.
Games, music videos, and "appisodes" for early math literacy and skills: "Let's All Umiball," "Scootie Doo," "Dr. Screwloose Strikes Again," "Double Trouble," "The Pizza Party," "Nobody Rides the Soakster," and "Who Woke the Mummy?" and "Who Stinks Greater?"
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 Uncle Bob's Puzzles  Robert & Claire Mead, Haverhill, NH, USA
Math and logic problems (no solutions); if you have questions, want a hint, or want to submit a solution you're invited to email the author. Asterisks indicate greater difficulty: Blind Cowboy; A Game of Catch; The Next Three; Grandpa's Birthday; Square
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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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 Using Virtual Manipulatives on the Web to Develop Number Sense  Margo Lynn Mankus
Java applets, activities, handmade manipulatives, and links related to the topic.
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 VedicMaths.Org  Clive Middleton, Kenneth Williams, and Mark Gaskell
Learn about the ancient system of mathematics of the Vedas through interactive tutorials, research and teaching articles, recommended books and websites, a list of sutras translated from the original Sanskrit, a calendar of events, newsletter, and references
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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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 Visuals Patterns in Pascal's Triangle (SMILE)  Ulysses Harrison, Dunbar Vocational High School
A lesson for grades 5 and up that uses a phenomenological approach to show students the many visual and number patterns present in the sequence of numbers in Pascal's Triangle, and to encourage them to explore the patterns on their own. From the Patterns
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 The Web Classroom  Eagle Eye Web Masters
An educational site from Australia that provides lessons and tests to help students understand concepts in Mathematics and build language skills in English. Elementary and Middle School math pages offer Fun with Fractions, "What Number," Times Tables,
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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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 What, How, and the Web  Cut the Knot!, Alexander Bogomolny
More on place value. "There is an obvious confusion there between two questions, what to teach and how to teach it. Does the failure of the New Math to present a specific topic necessarily imply that teaching this topic has no merit? The New Math has
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 What If...  Clare Williams, Deputy Head; Four Dwellings Infant School, Birmingham, U.K.
Some Mathematical Challenges for Key Stage One: part of the Year of Numeracy sponsored by the Birmingham City Council's Education Department. Questions posed such as: 1. What if you started writing numbers at 1… What is the biggest number you could get
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 What's Special About This Number?  Erich's Puzzle Palace; Erich Friedman
A list of the integers from zero to 9,999, each annotated with one significant mathematical property and colorcoordinated by that property's category.
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 what's your favourite number?  Alex Bellos
Enter your favorite number and the reasons for your choice. Part of a research project concerning how humans relate to numbers, this international survey is being conducted by Alex Bellos, author of Alex's Adventures in Numberland and Here's Looking At
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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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 Wild About Math!  Sol Lederman
Math posts, which date back to October, 2007, have included "10 ways to get wild about Math," "How to square large numbers quickly (part 1)," "26 tips for using learning styles to help your kids with Math," "The algebra of crossmultiplication," "Flexagon
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 Wired Math  Dean Murray, Soo Go, Jamie Pearson; University of Waterloo (Canada)
A free website created for students and teachers by a teacher for the University of Waterloo. The online games, drills, "follow up exercises," and answers
address topics common to middle grades on every continent. Also availalble from http://www.wiredmath.ca/
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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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 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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 XNumber World  James Redin
With the Extended Numerical Keyboards with Structured DataEntry Capability method, enter a number in the same way as you think on the number; for example, input one million and fiftyseven with the four keystrokes 1, million, 5, and 7, in that order.
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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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 Zahlen  Peter Hartmann
A list of many different types of numbers, with references. In German.
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 Zero in Four Dimensions: Cultural, Historical, Mathematical, and Psychological Perspectives  Prof. Hossein Arsham; University of Baltimore
A critical panoramic view of basic mathematical fallacies surrounding zero, such as dividing by zero, taking the limit, IEEE special floating point, the notion of zero throughout history, when zero is "not there," the origin of infinity and its symbol,
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