 Between Arithmetic and Algebra  Cut the Knot!, Alexander Bogomolny
What is the difference between the arithmetic 3+5 = 5+3 and the algebraic a+b = b+c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives expression
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 Between Arithmetic and Algebra  Cut the Knot!, Alexander Bogomolny
What is the difference between the arithmetic 3 + 5 = 5 + 3 and the algebraic a + b = b + c? One is a specific fact, another is a pattern valid in a multitude of situations. While arithmetic may hint at some regularities, algebra, as a language, gives
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 Beyond Traditional Math
Blog by a teacher who "was appalled to be handed a math book in which all instruction was whole group," and who subsequently "went on a mission to change and move beyond that traditional model of math in the elementary classroom." Subtitled "Fostering
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 Biglearners  Biglearners LLC
Thousands of math worksheets, organized by grade. Subscribe for answer keys and unlimited access free of advertisement.
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 The Big List of Puzzle and Riddle Pages  MindBreakers Associates Inc.
An annotated list of links to sites with collections of math and word puzzles; also the best puzzles (the files), ranked for coolness and difficulty, with solutions and discussion: Gold for free; Just draw a line...; Turn on a lightbulb; the Wizard and
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 Bill Cutler Puzzles  Bill Cutler Puzzles, Inc.
Wooden puzzles for sale: six piece burr puzzles, rectilinear burr puzzles, nonrectilinear burr puzzles, boxfilling puzzles, and miscellaneous puzzles. The computer program BCPBOX solves boxpacking problems such as pentominoes; GENDA determines how
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 Binomial Coefficients  Jay's Corner
A binomial is an algebraic expression with two terms, like x + y. When we multiply out the powers of a binomial we can call the result a binomial expansion. Multiplying out an expression is just a matter of using the distributive laws of arithmetic, a(b+c)
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 The Binomial Expansion and Infinite Series  Don Cohen (The Mathman)
Pascal's triangle of numbers, although named after Pascal, was known much before his time. If there is one piece of mathematics that exhibits many patterns, this is it. There are triangular numbers and tetrahedral numbers, and even the Fibonacci numbers
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 The Birthday Problem  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
What if somebody offered to bet that at least two people in your math class had the same birthday? Would you take the bet? How large must a class be to make the probability of finding two people with the same birthday at least 50%?
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 The Boise Problem Book  Marion Scheepers; Dept. of Mathematics, Boise State University, Boise, ID
Combinatorial games and set theory. Chapters include: Covering games and Memory; Peculiar sets of real numbers and games; Gdelta properties and games; The precipitous ideal game; Cardinal numbers related to the real line; Embedding problems; Gaps; The
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 Bookfill Publications  C. J. Davis
Algebra and geometry workbooks formatted to facilitate writing all answers directly onto the book. These books, for Year 10 and Year 11 students who require GCSE maths revision, cover general Foundation and Higher level topics.
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 Bowland Maths  Bowland Charitable Trust
Case study problems and lessons designed to develop thinking, reasoning and problem solving skills in UK math pupils ages 1114. In particular, download series of standalone assessment items that challenge students to estimate the number of descendants
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 Boy or Girl?  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
In a twochild family, one child is a boy. What is the probability that the other child is a girl? What if the older child is a boy?
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 The Brachistochrone  Paul Kunkel
An investigation of the problem: We are given two fixed points in a vertical plane. A particle starts from rest at one of the points and travels to the other under its own weight. Find the path that the particle must follow in order to reach its destination
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 BrainBashers  Kevin N. Stone
A collection of logic, language and math puzzles, in a choice of easy/medium/hard. Rate the puzzles; show their answers. Logic puzzles include Einstein's Puzzle. Play games of strategy, such as "Four in a Row" (also known as "Connect Four") or games based
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 BrainBashers  Kevin Stone
Five math or logic challenges on a page, each with clickable hints and solutions. For games, visit http://www.brainbashersgames.com/.
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 Brain Boosters  Discovery Education
An archive of challenging puzzles, organized under: Categorization, Lateral Thinking, Logic, Number and Math Play, Reasoning, Spatial Awareness, Word and Letter Play.
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 Brain Food  Puzzles For the Brain To Gnaw On  Samuel Stoddard
Hundreds of online (CGI) puzzles, including logic puzzles, word problems, number puzzles, lateral thinking puzzles, scrambled equations, cryptograms, loginumber puzzles, discrete reasoning puzzles, mathematical reasoning puzzles, knight's dilemma, magic
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 Brainfreeze Puzzles  Riley, Philip; and Taalman, Laura
Free example puzzles and solving tips for colorful, handdesigned Sudoku variation puzzles with additional rules that challenge you to rethink your old Sudoku strategies and devise new ones. From the authors of the book, Color Sudoku.
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 Brainwave  Wognum Art
Ten visual puzzles, to test your visual and reasoning skills. Most have to do with symmetry recognition. There is a "top 5% brain" award to those who earn ten "smart bulbs."
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 Breaking Chocolate Bars  Cut the Knot!, Alexander Bogomolny
The chocolate bar puzzle has three parameters: two side lengths (m and n) and actual selection of lines along which to break the bar and its parts... An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem,
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 Bret Victor
From the creator of Kill Math, Victor's "umbrella project for techniques that enable people to model and solve meaningful problems of quantity using concrete representations and intuitionguided exploration" in pursuit of a "widelyusable, insightgenerating
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 The Bridges of Königsberg  Isaac Reed
This problem inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology.
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 Bridging Math  Jennifer Bell
Blog by a K5 math coach in the Pacific Northwest. Posts, which date back to July, 2015, have included "#TMC15 Recap," "K12 Fraction Fun," "Choral Counting in Kindergarten," "#OML16 Recap," and "Number Talks and #ObserveMe." Elaborating on the name of
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 Brightest Moon for Thousands of Millennia? (Math Chat)  Frank Morgan, MAA Online
Answer to the challenge: Was there any validity to the claim that the full moon of December 22, 1999 was the brightest that we shall see for millions of years? (Factors that coincided.) New challenge: Eric Brahinsky saw in an article on "New molecule
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 Brilliant
Weekly Olympiadstyle challenges that offer "rigorous, competitive, whimsical, and edifying" problem sets in math and physics. Register to explore the Brilliant Techniques Trainer's practice exercises; answer correctly to earn points redeemable for lanyards,
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 A Broken Calculator  Cut the Knot!, Alexander Bogomolny
Thoughts on the controversial question of using calculators in the classroom, and the author's belief that even a broken calculator may have its uses: the elementary mathematics curriculum may emphasize any or all of the paperandpencil, mental, or technologybased
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 Buffon's Needle  Paul Kunkel
An investigation of the problem: Consider a plane, ruled with equidistant parallel lines, where the distance between the lines is D. A needle of length L is tossed onto the plane. What is the probability that the needle intersects one or more lines?
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 Building Blocks  Doug Clements and Julie Sarama, University at Buffalo, State University of New York
Supplementary and enrichment math materials for young children. Project writings include "Mathematics in the Preschool"; "'Concrete' Manipulatives, Concrete Ideas"; "Mathematics for Young Children"; "Technology and School Change: New Lamps for Old?";
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 Burning 1Hour Fuses in 45 Minutes (Math Chat)  Frank Morgan, MAA Online
You have two onehour fuses: lighting one end of a fuse will cause it to burn down to the other end in exactly one hour's time. You know nothing else about the fuses; in particular you don't know how long any segment of a fuse will burn, only that an
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 The Burr Puzzles Site  IBM
A Burr Puzzle consists of at least three rods intersecting each other at right angles. The most wellknown type is the six piece burr where three sets of two rods intersect each other. This site lets you explore six piece burrs by selecting from a list
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 Byzantine Basketball  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A problem (with solution) sent by Prof. W. McWorter's: Byzantine Basketball is like regular basketball except that foul shots are worth a points instead of two points and field shots are worth b points instead of three points. Moreover, in Byzantine Basketball
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 C26: Geometry  Scott Thatcher; Dept. of Mathematics, Northwestern Univ., Evanston, IL
Syllabus for a Geometry course, with some solutions to problems in PDF format; Maple worksheets (version 4) for multivariable calculus.
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 Calculator City  1728 Software Systems
Online calculators for solving equations in 2, 3, or 4 unknowns, the Pythagorean theorem, sphere and cylinder area and volume, vector addition, resistors in parallel, chemistry gas laws, compound interest, and loan payments. Games and puzzles include
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 Calculatorium  Nenad Mitrovic
JavaScript calculators for determining area, perimeter, surface area, volume, trigonometry, algebra, statistics, finance, conversions, health, and more. See also Calculatorium's timed, autoscoring tests and typeset formulas.
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 Calcul à Plusieurs Variables  Pierre Joyal, Armel Mercier
Site in French. An abundant documentation on several variable calculus, including numerous Flash and Java animations.
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 CalculusABC.com  Chris Watson
A site for calculus teachers to share questions they've written and discuss
issues relating to the field. Sort multiple choice questions according to calculator use and representation type (verbal, numerical, analytical, or graphical). With web forums
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 Calculus: an Overview  Paul Pollack
Written by a 16yearold, this siteinprogress contains brief summaries of topics for the advanced high school student. Available pages include: Functions: a review; Limits: what they mean and how to find them; Integration practice problems; Taylor and
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 Calculus in Motion  Audrey Weeks
Geometer's Sketchpad animations of mathematical concepts from middle school through high school. Three products are offered: Calculus in Motion (161 animations Including animations of 20091997 AP Exam AB & BC Free Response Questions); Algebra in Motion
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 Calculus&Mathematica  University of Illinois at UrbanaChampaign, Ohio State University
A computerbased course about calculus, differential equations, and matrix theory, which the instructor can use as soon as the computers are unloaded at the classroom door. Includes a complete electronic text combined with a set of problems for the students
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 Calculus on the Web (COW)  Mendoza, Reich; Department of Mathematics, Temple University
A collection of autoscoring calculus modules organized into books, chapters, and sections, with help and hints for the problems. Modules with asterisks (including chain rule, Taylor polynomials, Riemann sums, and arc length) allow you to change values
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 The Calculus Page Problems List  D. A. Kouba, U.C. Davis Department of Mathematics
Problems, with detailed solutions, from beginning differential calculus (limit of a function, continuity of a function, "squeeze principle," chain rule, product rule, quotient rule, differentiation of trigonometric functions, and more); and beginning
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 A Calculus Review  Linda Valdes; San Jose State University, San Jose, CA
An interactive set of eight 12question quizzes on limits, differentiation, and
integration, with hints and reviews of technique. Requires Netscape 4.5 or later.
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 Calculus (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 calculus. Logarithms and Exponential; Sequences; Series; Techniques of Integration; Local Behavior of
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 Calculus VII  Leonid Kovalev
Blog by a Syracuse University professor whose research interests range from potential theory to geometric mapping theory, particularly biLipschitz maps. Kovalev's posts, which date back to January, 2012, often include Scilab code or plots: "Generalized
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 CalMaeth: Computer Aided Assessment and Learning of Mathematical Methods  Mathematics Dept., Univ. of Western Australia
A collegelevel interactive aided teaching and learning system that poses math questions on various topics and then evaluates the student's answer. It is designed for UWA students, but guest login is enabled. A set of demonstration questions will show
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 C.A.L.M. (Computer Assisted Learning Method)  Critical Thinking Inc.
An educational site to help high school students learn plane geometry, featuring algorithmic generation of questions providing individualized questions for each student, immediate feedback regarding the student's response, and tracking routines allowing
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 Camel and Bananas  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
What's the maximum number of bananas the camel can transport across the desert?
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 Card Colm  Colm Mulcahy
This blog "explores mathematical card principles and effects for fun." Inspired by Martin Gardner and his seminal Mathematics, Magic and Mystery, Mulcahy has posted since August, 2011: "A Call For A New Shuffle Principle (Need Rot Sextet?)," "Splitting
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 Carl Eberhart
Class information and/ or Maple worksheets for courses including multivariable calculus, linear algebra, linear programming, differential equations, numerical methods, and topics for mathematics teachers, as well as Maple and C++ programs for a course
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