 The ABACUS International Math Challenge  Tivadar Divéki, Grace Church School
The ABACUS International Math Challenge is open to students in three categories (grades 34/ages 910; 56/ages 1112; 78/ages 1314), with 8 problems posed each month. The challenge begins in September and ends in April. It originated with the ABACUS Math Challenge started 5 years ago in Hungary by Sándor Róka, for students in grades 48.
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 AIMS Education Foundation
"Activities Integrating Mathematics and Science." A nonprofit, independent organization established to develop integrated math/science materials for grades K9. See, in particular, the AIMS Puzzle corner (a new puzzle each month), the AIMS@Kids Interactive Area (facts and trivia, contests, sights and sounds, interactive puzzles, kid links, stories), the Sample Activities Archive, and the Sample Math History Activities.
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 A+ Math
A site developed to help elementary school students improve their math skills interactively, offering: educational math games (learn basic operations and geometry by playing MATHO  bingo and math combined; Hidden Picture; and Concentration), Web flash cards for practicing rounding, area, square roots, inequalities, fractions, counting money, geometric shapes; and Homework Helper, which lets you enter your addition, subtraction, multiplication or division problem and your answer, then checks to see if it's correct. Also Advanced Problems which allows you to select the kind of problem you want to practice and checks your answers.
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 AMOF: The Amazing Mathematical Object Factory  Frank Ruskey
Combinatorial objects are everywhere. How many ways are there to make change for $1 using unlimited numbers of coins of all denominations? Each way is a combinatorial object. AMOF is part encyclopedia and part calculator, a teaching tool that generates mathematical permutations for such combinatorial objects as subsets and combinations, partitions, magic squares, and Fibonacci sequences by allowing the user to define the parameters of discrete objects. The Object Factory returns a list of all objects that satisfy those parameters. The site can be used to learn more about many types of discrete mathematical structures; descriptions of objects progress in complexity for students at different levels. For more advanced materials, see the Combinatorial Object Server (COS).
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 Aritm  Mikael Bonnier
A Java applet for simple mental calculation, drilling on basic arithmetic (addition, subtraction, multiplication, or division, with 1 or 2digit terms), in digits, words, or Roman numerals. It will tell you when your answer is wrong, and how many problems per minute you've done. In English, Swedish, and Finnish.
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 BEATCALC Archive  Math Forum
An archive of B. Clay's BEATCALC weekly mailing list. Amaze your friends by memorizing a few simple rules and doing mental math tricks faster than they can do them on a calculator. Squaring, multiplying, dividing, adding, and subtracting numbers; finding percents; calculation practice exercises.
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 Bricks Activity  Suzanne Alejandre
A classroom activity (also called the Masonry Problem; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored through manipulatives (dominoes). Students explore different possibilities of making brick walls with and without fault lines, using diagram, process, and solution in their problem solving. A teacher lesson plan is provided.
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 Cryptarithms  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Cryptarithms are brain teasers obtained when digits in numerical calculations have been replaced by letters. Customarily, distinct letters stand for different digits. Another term, Alphametics, denotes cryptarithms in which letters form meaningful words, often in meaningful phrases [i.e., son to father: SEND + MORE = MONEY, and father to son: SPEND + LESS = SONNY]. This site offers Java implementations of various cryptarithms and alphametrics, as well as the opportunity to send in your favorites.
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 Fibonacci Numbers and the Golden Section  Ron Knott
Information about the Fibonacci series, including a brief biography of Fibonacci, the numerical properties of the series, and the ways it is manifested in nature. Fibonacci numbers are closely related to the golden ratio (also known as the golden mean, golden number, golden section) and golden string. Includes: geometric applications of the golden ratio; Fibonacci puzzles; the Fibonacci rabbit binary sequence; the golden section in art, architecture, and music; using Fibonacci bases to represent integers; Fibonacci Forgeries (or "Fibonacci Fibs"); Lucas Numbers; a list of Fibonacci and Phi Formulae; references; and ways to use Fibonacci numbers to calculate the golden ratio.
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 Interactive Mathematics Miscellany and Puzzles  Alexander Bogomolny
"The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based  the more beautiful is the result." This awardwinning site offers games and puzzles, quotes, and much more on a variety of topics from arithmetic and algebra to geometry and probability, and includes solutions and the mathematical theory behind each puzzle. There are also the CTK Exchange (a small discussion group for questions and answers about math problems); the Eye Opener Series (Java applets that illustrate and help solve or prove math problems); a math bookstore; a glossary; a monthly interactive column using Java applets for MAA Online; and the CTK Insights blog. The whole site is available on CDROM.
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 John and Betty's Journey into Complex Numbers  Matt Bower
A children's bookontheWeb from Australia, designed to introduce complex numbers in story form in a way that is intuitive and enjoyable for students. John, Betty, and their dog Trevor solve a series of problems designed to introduce integers, fractions, surds, imaginary numbers, complex numbers, Argand diagram; vectors, multiplication in polar form, relating polar and Cartesian form, De Moivre's theorem; and the Mandelbrot set.
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 K12 Math Problems, Puzzles, Tips & Tricks  Math Forum
Links to calculation tips (Beat the Calculator, Divisibility Rules, Multiplication Tips), Math Problem sets, and math number and line puzzles.
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 K12 Teaching Materials (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
An extensive list of Internet sites with significant collections of materials that can be used in the teaching of mathematics at the K12 level. Organized into categories: lesson plans, schools, software and other K12 Internet math sites.
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 Ken's Puzzle Sites  Ken Duisenberg
Links to more than 50 interesting puzzle sites Ken has found.
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 Kids' Place Brain Teasers  Houghton Mifflin Company
Math puzzles for grades 34, 56, and 7+. You don't need to be a math whiz to solve them, just to be patient and find different ways of looking at things. New puzzles and the answer to the previous week's puzzles are posted each Thursday. Helpful hints and an archive are included.
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 Locker Problem  Suzanne Alejandre
A classroom activity (also called 1000 Lockers) aligned to the NCTM and California Standards, to be explored through the use of manipulatives and a ClarisWorks spreadsheet. Students then look for patterns and write the answer algebraically. The problem: imagine you are at a school that still has student lockers. There are 1000 lockers, all shut and unlocked, and 1000 students. Suppose the first student goes along the row and opens every other locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.) The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the thousand students have followed the pattern with the thousand lockers. At the end, which lockers will be open and which will be closed? Why? A teacher lesson plan is provided.
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 Magic Squares: Math, History, Geography  Suzanne Alejandre
Designed primarily for middle school and older elementary school students, this Math Forum Web unit includes classroom activities for four different squares: Lo Shu, Sator, Dürer, and Franklin, three of them demonstrating increasing complexity using numbers, and one made up of letters, with number and symmetry questions and links and suggestions for history / geography / writing activities for teachers interested in interdisciplinary work. Includes directions for building magic squares, definitions, discussion of some special properties of magic squares, a Java applet, and links to other magic square Web sites.
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 Mathematical Games and Recreations  MacTutor Math History Archives
Number games, geometrical puzzles, network problems and combinatorial problems by famous mathematicians, starting around 1850 B.C. and continuing on to the present, with links to biographies of mathematicians who invented the games, pictures, and graphs. Rhind papyrus, Fibonacci, Archimedes, Dodgson, Durer, Recorde, Cardan, Lucas, Tartaglia, Bachet, Euler, and many more. 13 references.
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 Monthly Themes  NRICH Maths, Univ. of Cambridge
Past problems from the NRICH Online Maths Club, archived by month. Each problem has a symbol indicating the stage, which tells you how little or how much mathematics you need to know to solve the problem but is no indication of its difficulty. The five stages correspond to ages 57, 711, 1114, 1416 and 1618, and indicate that students in the UK normally meet the maths required during that key stage.
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 Problem Solving in Mathematics  Jim Wilson; Univ. of Georgia
Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links to papers, including "Mathematical Problem Solving" (Wilson, Fernandez, & Hathaway), a synthesis of research on problem solving [published as ch. 4 in Wilson, P. S. (Ed.) (1993), Research Ideas for the Classroom: High School Mathematics, New York: MacMillan].
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 The rec.puzzles Archive
The index of the rec.puzzles archive. Puzzles are categorized by subject area and include solutions compiled from various sources and supposed to be definitive. Subjects include: analysis, arithmetic, combinatorics, competition, decision, geometry, group, induction, language, logic, physics, pickover, probability, reallife, references, series, trivia.
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 Tangrams  Tom Scavo
Tangrams, a puzzle that helps develop spatialvisualization skills, may also be used to introduce or reinforce geometric concepts such as congruence, similarity, symmetry, etc. This unit for grades 4 through 6 uses tangrams to compute the area of polygons without formulas, introducing the terms congruent and similar. Contents: Constructing Your Own Set of Tangrams; The Area of Tangram Pieces; More Tangram Activities. Links to other tangram resources on the Web are also provided.
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 Traffic Jam Activity  Suzanne Alejandre
A classroom activity (also called Hop, Skip, Jump) aligned to the NCTM and California Standards, to be explored through large movement experience, manipulatives, and an interactive Java applet. Students then revisit the activity, look for patterns, and write the answer algebraically. The activity: there are seven stepping stones and six people. On the three lefthand stones, facing the center, stand three of the people. The other three people stand on the three righthand stones, also facing the center. The center stone is not occupied. Everyone must move so that the people originally standing on the righthand stepping stones are on the lefthand stones, and those originally standing on the lefthand stepping stones are on the righthand stones, with the center stone again unoccupied. A teacher lesson plan is provided.
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 Trigonometry (S.O.S. Mathematics)  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and precollege trigonometry. Trigonometry: Angle Measures, Trigonometric Functions (magic identity, Addition Formulas, DoubleAngle and HalfAngle Formulas, Product and Sum Formulas), Trigonometric Equations, Table of Trigonometric Identities. Hyperbolic Trigonometry: Hyperbolic Functions, Inverse Hyperbolic Functions.
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 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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 The World of Trotter Math  Terry Trotter, Escuela Americana, San Salvador, El Salvador
A page of problems, problem sheets, and investigations, with links to image files of an inclass math newsletter, Trotter Math News. Of particular interest to the author are numbers: happy and dizzy numbers; palindromes; super squares; perfect, amicable, and admirable numbers; and math poetry and limericks. Also calculator poker; prime numbers; decimal time; Pythagorean triples; Paul Erdos; Russian multiplication; Egyptian math; Trigg numbers; trinomials; ladder math; and many more.
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