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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 expression ...more>> 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 ...more>> 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 ...more>> Biglearners - Biglearners LLC Thousands of math worksheets, organized by grade. Subscribe for answer keys and unlimited access free of advertisement. ...more>> 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 ...more>> Bill Cutler Puzzles - Bill Cutler Puzzles, Inc. Wooden puzzles for sale: six piece burr puzzles, rectilinear burr puzzles, non-rectilinear burr puzzles, box-filling puzzles, and miscellaneous puzzles. The computer program BCPBOX solves box-packing problems such as pentominoes; GENDA determines how ...more>> 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) ...more>> 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 ...more>> 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%? ...more>> 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 ...more>> 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. ...more>> Bowland Maths - Bowland Charitable Trust Case study problems and lessons designed to develop thinking, reasoning and problem solving skills in UK math pupils ages 11-14. In particular, download series of stand-alone assessment items that challenge students to estimate the number of descendants ...more>> Boy or Girl? - Math Forum, a Classic Problem from the Ask Dr. Math FAQ In a two-child 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? ...more>> 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 ...more>> 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 ...more>> BrainBashers - Kevin Stone Five math or logic challenges on a page, each with clickable hints and solutions. For games, visit http://www.brainbashersgames.com/. ...more>> 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. ...more>> 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, logi-number puzzles, discrete reasoning puzzles, mathematical reasoning puzzles, knight's dilemma, magic ...more>> Brainfreeze Puzzles - Riley, Philip; and Taalman, Laura Free example puzzles and solving tips for colorful, hand-designed 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. ...more>> 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." ...more>> 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, ...more>> 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 intuition-guided exploration" in pursuit of a "widely-usable, insight-generating ...more>> 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. ...more>> Bridging Math - Jennifer Bell Blog by a K-5 math coach in the Pacific Northwest. Posts, which date back to July, 2015, have included "#TMC15 Recap," "K-12 Fraction Fun," "Choral Counting in Kindergarten," "#OML16 Recap," and "Number Talks and #ObserveMe." Elaborating on the name of ...more>> 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 ...more>> Brilliant Weekly Olympiad-style 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, ...more>> 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 paper-and-pencil, mental, or technology-based ...more>> 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? ...more>> 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?"; ...more>> Burning 1-Hour Fuses in 45 Minutes (Math Chat) - Frank Morgan, MAA Online You have two one-hour 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 ...more>> The Burr Puzzles Site - IBM A Burr Puzzle consists of at least three rods intersecting each other at right angles. The most well-known 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 ...more>> 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 ...more>> 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 multi-variable calculus. ...more>> 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 ...more>> 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, auto-scoring tests and typeset formulas. ...more>> Calcul à Plusieurs Variables - Pierre Joyal, Armel Mercier Site in French. An abundant documentation on several variable calculus, including numerous Flash and Java animations. ...more>> 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 ...more>> Calculus: an Overview - Paul Pollack Written by a 16-year-old, this site-in-progress 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 ...more>> 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 2009-1997 AP Exam AB & BC Free Response Questions); Algebra in Motion ...more>> Calculus&Mathematica - University of Illinois at Urbana-Champaign, Ohio State University A computer-based 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 ...more>> Calculus on the Web (COW) - Mendoza, Reich; Department of Mathematics, Temple University A collection of auto-scoring 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 ...more>> 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 ...more>> A Calculus Review - Linda Valdes; San Jose State University, San Jose, CA An interactive set of eight 12-question quizzes on limits, differentiation, and integration, with hints and reviews of technique. Requires Netscape 4.5 or later. ...more>> 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 pre-college calculus. Logarithms and Exponential; Sequences; Series; Techniques of Integration; Local Behavior of ...more>> Calculus VII - Leonid Kovalev Blog by a Syracuse University professor whose research interests range from potential theory to geometric mapping theory, particularly bi-Lipschitz maps. Kovalev's posts, which date back to January, 2012, often include Scilab code or plots: "Generalized ...more>> CalMaeth: Computer Aided Assessment and Learning of Mathematical Methods - Mathematics Dept., Univ. of Western Australia A college-level 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 ...more>> 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 ...more>> 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? ...more>> 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 ...more>> Carl Eberhart Class information and/ or Maple worksheets for courses including multi-variable calculus, linear algebra, linear programming, differential equations, numerical methods, and topics for mathematics teachers, as well as Maple and C++ programs for a course ...more>>
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