 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Cryptarithms are brain teasers obtained when digits in numerical calculations have been replaced by letters.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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 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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 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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 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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 Math for Morons Like Us  ThinkQuest 1998
Students talk to students about math: a site designed to help you understand math concepts better. Tutorials, sample problems, and quizzes for PreAlgebra, Algebra, Geometry, Algebra II, and PreCalc/Calculus, designed assuming you know some of the basic concepts but need reinforcement, or want to review things you learned in the past. Interactive resources include a message board, calculus board, formula database, quizzes, math links, and a place to send feedback.
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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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 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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 WIMS (WWW Interactive Mathematics Server)  Université de Nice  Sophia Antipolis
Interactive mathematical applications, also available in French, with documentation. The server's exercises and programs are designed to find a polynomial with given values; find the Taylor expansion of a function; find a polynomial from its curve; given function and epsilon, find delta (on the definition of continuity); and find the root of a function by successive tests. Mathematical tools will: expand a real number into a continued fraction; factor integers, rational numbers, polynomials, and rational fractions; calculate onevariable functions (Integrals, limits, roots...); calculate determinant, inverse, eigenvectors... matrices; and solve linear systems, including systems with parameters. Also a visual exercise on the definition of maps (Javascript), exercises on minima/maxima, and a mathematical puzzle based on finite fields. These materials could be useful in a U.S. precalculus course.
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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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