 101 Uses for the Quadratic Equation  Chris Budd, Chris Sangwin
Article on the value of the quadratic equation, in response to critics calling it a torture inflicted on schoolchildren.
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 2 Pi Productions  Jake Scott
Instructional math rap includes the original songs "Triangle Experts," "Special Right Triangles," "Graphing Trig Functions," "Quadratic Formula," and "The Best Pythagorean Rap Ever." Lyrics include "The cosine is sine with a phase shift of pi/If you think
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 Absolute Value  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about absolute value, such as reallife applications, its place in order of operations, and solving algebra inequalities that contain absolute values.
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 Addition and Subtraction of Signed Numbers (SMILE)  David Drymiller, Morgan Park High School
A lesson designed to help students master the addition and subtraction of signed numbers, and learn to recognize linear equations of the form x + a = b and their solutions. From the Arithmetic section of a collection of almost 200 single concept lessons
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 Age Word Problems  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
A problem with one variable: Al's father is 45. He is 15 years older than twice Al's age. How old is Al? But what if we can't express all the information in the problem using only one variable? Sometimes we must use two variables to express the given
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 Algebra Visualization Tools  Dennis Sullivan, Founder
Slide the controllers of these Java tools to change the parameters of these five types of equations  and see their effects on these graphs instantly: linear equations, absolute value, quadratic equations, vertex form, and rational equations. The applets
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 The Analemma 
Bob Urschel, Valparaiso, IN
The figure8 path that the sun makes in the sky is called the analemma. This site explores the paths of the sun and the earth, with investigations into the effects and the math of their elliptical orbits and earth's tilt, and a summation.
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 Babylonian and Egyptian Mathematics  MacTutor Math History Archives
Linked essay describing the character and accomplishments of these two early mathematical systems, with references and other related web sites.
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 Binomial Coefficients  Bill Hammel
A collection of identities and formulas involving binomial coefficients: defined by factorials, appearing in Pascal's Triangle, derived with choose notation and summation formulas, approximated by Stirling's Formula, and more.
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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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 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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 Casio Kingdom  Sean Tan
CFX9850 games and programs. A game and several programs, including: Sphere (solves where a point is in relation to a sphere, whether it lies outside, inside or on the sphere); Divide (finds the position vector that divides vector AB in the ratio a:b);
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 Cattle of the Sun  Ivars Peterson (MathTrek)
The story goes that Archimedes of Syracuse (287212 B.C.) was annoyed with Apollonius of Perga (262190 B.C.), who had criticized Archimedes' work on the multiplication of large numbers. For revenge, Archimedes devised a fiendish computational problem
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 Center for Technology and Teacher Education  Curry School of Education, University of Virginia
An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com
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 Coin Problems  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
Tony has 11 more nickels than quarters. How many coins does he have if the total value of his coins is $2.65?
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 Common Mistakes in College Mathematics  Eric Schechter
Pointers for students about mistakes in general mathematics and calculus. Errors include: everything is additive, loss of invisible parentheses, incorrect writing of fractions, derivative of x to the x, unbalanced differentials, and naive answers for
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 Commutative, Associative And Distributive Properties (SMILE)  James E. Breashears, Robeson High School
A lesson designed to teach students to compute expressions like (56 + a) + 4 and (50 * 7) * 2; to identify the commutative and associative properties; and to rewrite expressions by using the distributive property. From the Algebra and Trigonometry section
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 Conceptual Math Media, Inc.
Math educational products for both the classroom and family. Master multiplication facts and divisibility rules with PrimePak playing cards; create equations crosswordstyle with the Equate board game, also available via email. Order products online
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 The Constants and Equations Pages  Jonathan Stott
A growing reference resource providing alphabetically listed categories of some of the more important and useful aspects of maths and special sections on numbers, algebra, trigonometry, integration, differentiation, and SI units and symbols, with in addition
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 Continued Fractions, Infinite Continued Fractions, and Iteration  Don Cohen, The Mathman
Ten different ways to solve a quadratic equation  an area of mathematics with applications to population increase, finding the square root of a number, chaos theory, and fractals. Sample problems from Chapter 8 (Solving Equations and Iteration) of Don
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 Cubic and Quartic Equations  Math Forum, Ask Dr. Math FAQ
General solutions to cubic and quartic polynomial equations.
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 Digital Mathematical Performance  Gadanidis, George; Borba, Marcelo; Hughes, Janette; et al.
Watch video, liveacted dramatic storyboards, and animations of how people "perform" mathematics: Flatland, "Help Me, Fermi," Should Parallel Lines Never Meet," "The Pleasure of Making 10" (linear equations), "The Waiter" (the missing dollar problem),
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 Diophantine Equations  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about Diophantine equations, from "find all positive integer solutions to 43x + 7y + 17z = 400" to a general method for solving them.
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 Direct and Indirect Variation  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about direct and indirect variation, with explanations of the difference between them and how to graph variation.
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 Dividing The Plane  Jim Loy
A line divides the plane into two pieces (regions). Draw another line. The plane is now divided into three or four regions. It is three regions if the lines are parallel, four if they intersect. A third line divides the plane into seven regions. Find
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 DLK MathsWork Software
Selfdifferentiating, topicspecific math software for Windows 3.1 and above, on number, shape and space, and data handling. All of the practice modules have on screen monitoring at three levels. Six problem modules designed to improve users' application
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 Draining The Swimming Pool (SMILE)  William Byrne, Martin Luther King High School
A lesson that offers experiments that suggest a way to solve the general work problem: If A can do a job in X hours and B can do the same job in Y hours, how long will it take A and B working together to complete the job? From the Algebra and Trigonometry
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 Eighth Grade (AAA Math)  John Banfill
Interactive math exercises, lessons, and games covering basic arithmetic concepts and methods, for eighth grade.
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 The Essence Of Algebra  Jim Loy
Simple explanations of variables and equations for the beginning student of algebra.
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 Exercices on Mathematics  Luis Breda
Online math drills in English and Portuguese: lines, fractions, points and vectors, powers and radicals, firstdegree equations, seconddegree functions, trigonometry, circles, and derivatives.
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 Experiment and Explore Mathematics  A. Dendane
Java applets to explore topics in mathematics: graphing linear equations, graphing systems of linear equations, polar equations, rational functions, exploring translations and scaling of graphs, and matrix multiplication.
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 Exploratorium's Science of Hockey  The Exploratorium
This site takes you inside the game: you'll hear from National Hockey League players and coaches, as well as leading physicists and chemists. Divided into seven main sections: the ice (why is ice slippery?), skating (what are the mechanics involved in
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 ExploreMath.com  Third Millennium Press
Shockwave activities illustrating realtime correlations between equations and graphs to help students visualize and experiment with concepts from elementary algebra through precalculus: experiment with the graphs of functions, systems, and complex numbers.
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 Fahrenheit to Celsius  Jim Loy
Ways to convert: two equations, two unknowns.
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 Famous Equations and Inequalities  Peter Alfeld, University of Utah
An idiosyncratic and personal selection of particularly important or particularly intriguing mathematical equations, not all of them complicated. Mathematical Constants; The definition of Pi; The definition of e; A differential equation; The Pythagorean
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 Flying Between Two Trains  Math Forum, Ask Dr. Math FAQ
Two trains 150 miles apart travel toward each other along the same track, the first train at 60 mph, the second at 90 mph. A fly buzzes back and forth between the two trains until they collide. If the fly's speed is 120mph, how far will it travel?
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 Formula Determination (SMILE)  Clark Odom, Collins High School
A lesson designed to teach students to determine the number of degrees in any convex polygon. From the Patterns and Logic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Free Math Worksheets
Free math worksheets to download, print, and practice addition and subtraction; multiplying; divisibility and factors; greatest common factor (GCF); least common multiple (LCM); simplifying numerical fractions; converting percents, decimals, and fractions;
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 Fundamental Theorem of Algebra  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Some of the history of complex numbers, perfect numbers, irrational numbers, imaginary numbers, and the first proof of the Fundamental Theorem of Algebra (statement and significance), given by Carl Friedrich Gauss (17771855) in his Ph.D. Thesis (1799).
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 General Mathematics, AM (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on basic mathematics, including biographical information about mathematicians, from the abacus to Gaspard Monge.
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 General Mathematics, NZ (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on basic mathematics, including biographical information about mathematicians, from John Napier to Zeno of Elea.
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 HandsOn Equations  Henry Borenson
A visual and kinesthetic teaching system for introducing algebraic concepts to students in grades 38. Students physically represent and solve algebraic linear equations using game pieces consisting of pawns and numbered cubes. For families homeschooling,
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 Hexa Trex  Bogusia Gierus
Find a path through all the tiles to make a math equation. Read more rules about the Hexa Trex puzzle, and challenge yourself to solve the new challenges that Gierus blogs regularly.
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 Horazio's Educational Freeware  Horacio Vilches
Featuring a quiz program, and Equation Lab, for Windows. Equation Lab is a simple program that helps the user to work with single variable equations. You can add, multiply, and solve the equations.
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 How To Be A Little Gauss  Jim Loy
There is a story about Carl Friedrich Gauss. Supposedly, when he was a little boy, his teacher asked the class to add up the numbers one through a hundred (1+2+3 etc., all the way up to 100)... To the teacher's annoyance, little Gauss came up with the
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 An Introduction to Continued Fractions  Ron Knott
Continued fractions are just another way of writing fractions. They have some interesting links with a jigsawpuzzle problem of splitting a rectangle up into squares and also with one of the oldest algorithms known to mathematicians  Euclid's Algorithm
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 Introduction To Solving Equations (SMILE)  Mary Lynn Bochenek, Central Junior High School
A lesson designed to teach students to arrive at an equation of the form X = [ ] in which the variable is isolated and the solution is then obvious through use of equivalent equations. From the Algebra and Trigonometry section of a collection of almost
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 An Investigation using Parametric Equations  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
A paper examining the movement of triangles when one vertex is moved along the xaxis and another is moved along the yaxis. The movement of the third vertex is traced.
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 Irrational Numbers  Jim Loy
Pythagoras is said to have discovered irrational numbers, showing that the square root of 2 could not be expressed as any whole fraction m/n. Here's the proof...
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 Java Math Class  Snorre Narum
A Java applet that renders equations or expressions in graphical form, from TeXstyle entries.
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