 The Evolution of the Real Numbers  Lawrence Spector
An introduction to real numbers, including such topics as: the ratio of natural numbers; continuous versus discrete; fractions; unit fractions; rational numbers; measurement: geometry and arithmetic; common measure; squares and their sides; incommensurable
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 EWorld  Glenn Elert
A homepage including links for his Midwood High School classes, Teachers College (Columbia) materials, especially papers on mathematics (Chaos, Fractals, Dimension; Ptolemy's Table of Chords; Mathematics Packages) and education reform (School Choice;
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 Exactly How Is Math Used In Technology?  Mathematics Dept., British Columbia Institute of Technology
A table of examples of how various areas of mathematics are applied to various areas of technology. Areas of technology include biomedical engineering, food technology, building technology, chemical sciences, civil and structural engineering, graphics
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 Exambot  Exambot Educational Services
A free database (requires registration) of math and physics questions with fully worked solutions; also an exam set generator that will produce customized practice exams to match the profile of any course.
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 EXAMgen
Computerized test itembanks for secondary school teachers. Math assessment databases cover curricula from 78th grade: Basic Math, Integrated Math, High School Exit Level, Algebra modules and Geometry modules. The databases have multiple choice, short
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 Examinations Home Page  Department of Education and Science, Government of Ireland
Leaving Certificate Examination Papers, Junior Certificate Examination Papers, marking schemes, annual results and statistics, brochure, timetables, Chief Examiner's Reports, and other material documenting Ireland's "leaving certs." Mathematics (Matamaitic)
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 Examining How Mathematics is Used in the Workplace  Annie and John Selden; Mathematical Association of America
Abstracts of studies on how much mathematics is used in various occupations: Mathematics in Automobile Production; Proportional Reasoning by Nurses; Modeling the Mathematics of Banking; Mathematical Models as Seen by Biologists; How do Scientists Interpret
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 Examples of Essays  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Extended Concurrencies of the Triangle, J. Wilson; Parabolas Inscribed in a Triangle, G. Giddings; Polygonal Spirals, L. Shook and M. Callinan; Roots 2 and 5, J. Wilson; Those Amazing Palindromes, Shareef Bacchus; Tangrams, Greg Huberty; Phi: That Golden
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 ExamsClub
Free exams from Australia for use by math teachers and students (mostly 12th Grade).
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 ExamSolutions
ExamSolutions.co.uk is designed to help revision for maths A level. It contains questions, answers and worked solutions to past exam papers from Edexcel, OCR and AQA exam boards, all in PDF format. Some are free.
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 ExamView Pro  FSCreations, Inc.
A tool that simplifies the process of constructing math equations for tests, with downloads of demos available for Windows and Mac. Includes Internet testing/study guides, a fullfeatured equation editor, and a spellchecker. Tests can be taken on the
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 Excel Everywhere.com  Framtidsforum I&M AB
Automatically converts a spreadsheet into a goodlooking and calculating web page. It can be used to present mathematics on the web, and for creating selfcorrecting tests. Teachers can get free licenses for student projects, so that these can be presented
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 ExcelGrade eLearning
Online tutoring in math, science, and English, using a proprietary headset and whiteboard. Details, including testimonials and pricing, on the web.
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 The Excellent Adventure  Shawsheen Valley Technical High School, Billerica, MA
A mathbased crosscurricular site where students take a trip from Philadelphia down the East coast to Disney World, with several required stops and activities along the way. A teacher's guide, worksheets, and activities are provided: students figure
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 Excel Models Blog  Jess
Blog about the use of Excel to analyze realworld problems mathematically. Posts, which date back to October, 2011, have included "Simple Excel Sales Dashboard," "Tutorial Using Concatenate Function In Excel," "Teacher Grade Book," "Buying House To Rent,"
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 Excel Traffic Problem (MSTE)  Kocinski, Clark; University of Illinois at UrbanaChampaign (UIUC)
Problem (by HansGeorg Weigand): there is a traffic jam on the highway when cars pass a building site. A model of this situation shows that cars drive with the same speed v and all have the same length l. For the distance d between two cars there are
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 Excel Tutorial and Training  Tomasz Decker
Free illustrated primers on a variety of Microsoft Excel features, including entering and editing data, data types, data validation, selecting cells, merging text with numbers, aligning data, simple fractions and decimal fractions, currency and accounting
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 Excel Tutorial  www.exceleasy.com
Free, stepbystep tutorials on functions, data analysis, VBA, and more features of Microsoft's spreadsheet software. All primers include illustrative screenshots and sample download .xls files.
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 Exemplars
Exemplars is meant to assist teachers, schools and districts implement authentic assessment and problem solving in their classrooms and to meet the challenging new standards developed in mathematics, science and humanities at the national, state and local
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 Exercices de Géometrie en Troisième  T. Touré
Révisions de vacances: de nombreux exercices de géométrie. Thalès/Droite des milieux; Pythagore; Sinus, cosinus, et tangente; Cercle et triangle rectangle; Droites remarquables; Distance et aire; Volume; Symétrie, rotation
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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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 Exercises in Imagination (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
How do you imagine geometric figures in your head? Most people talk about their threedimensional imagination as 'visualization', but that isn't exactly right. A visual image is a kind of picture, and it is really twodimensional. The image you form in
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 Exercises in Math Readiness for University (EMR)  Dept. of Mathematics and Statistics, University of Saskatchewan
A collection of exercises with solutions/tutorials for high school mathematics topics important for university study in mathematics, sciences, engineering and commerce. Exercises at three degrees of difficulty, covering graphing, solving inequalities,
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 Expanding Universe: a classified search tool for amateur astronomy  Daniels, Enright, Gliddon, & SenRoy
A collection of sites organized using a modified Dewey Decimal Classification, to make searching the web more like browsing a library shelf. Includes an alphabetical terms list for searching and a request for more sites.
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 Expectations of Mathematics Education  EXTEND  Perspectives on Mathematics Education
Links to articles about society's conflicting expectations for the goals (ends) and pedagogy (means) of school mathematics. Concerns about the relation of skills to understanding, about connections with other disciplines, and about preparation for employment.
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 Expected Value: Temperature of a Point on a 2D Plate (MSTE)  Ed Malczewski; University of Illinois at UrbanaChampaign (UIUC)
Find the temperature at a particular point of a rectangular plate using statistical methods. It is assumed that the temperature of the edges as well as the dimensions of the plate are known. The lesson includes a program that will run on Resampling Stats,
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 Experiencing Geometry in Euclidean, Spherical, and Hyperbolic Spaces  David W. Henderson; Cornell University
A book that presents a series of problems. Most of the chapters start intuitively and are accessible to a general reader with no particular mathematics background; however, the discussions were written for mathematics majors and mathematics teachers and
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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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 Experimentation, Graphing, and Algebraic Derivation  R. H. Logan
A scientific graphing lesson that details the derivation of the slope intercept formula; the slopeintercept formula in Chemistry; and linear relations in Chemistry and Physics.
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 Experiments with the 3n+1 Sequence  Alfred Wasserman
An online program tests numbers for convergence under the 3n + 1 sequence. Also available in German.
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 Expert Math Tutoring in New York  Expert Tutor NY
Ivy League chemistry graduate and certified test prep course teacher offers private instruction for math at high school and college levels in metropolitan New York area  Regents, SAT, SAT II, algebra, geometry, trigonometry, calculus, precalculus.
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 Explained Visually  Powell, Victor; and Lhe, Lewis
Interactive JavaScript to "make hard ideas intuitive." Drag sliders and select values to simulate sine and cosine, exponentiation, Markov chains, conditional probability, and more.
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 Explaining Logarithms  Dan Umbarger
"Explaining Logarithms" is a free 109 page PDF which tries to explain the origin and use of logarithms in a different logical progression than exists in the traditional textbooks. Site includes philosophy behind the work, how to order multiple copies
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 Explorations of a Problem with Two Squares  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Given a square of side s and segments drawn from each vertex to the midpoint of the second side, counting counterclockwise, the segments intersect to form a new square. What is the ratio of the area of the shaded square to the area of the original square?
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 The Exploratorium
Home page of San Francisco's museum of science, art and human perception. Online exhibits, cool sites, archives, sport and science, and the digital library (the Exploratorium AtoZ).
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 Exploratorium's Complexity  The Exploratorium
A collection of information related to the Turbulent Landscapes exhibit at the Exploratorium museum in San Francisco. Includes a timeline of important developments in the study of chaos, complexity, and dynamics, and CompLexicon, a guide to key concepts,
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 Exploratorium's Science of Baseball  The Exploratorium
Interactive (Shockwave) exhibits from San Francisco's science museum include Fastball Reaction Time (can you hit a 90mph fastball?) and Scientific Slugger (see what makes a home run: vary the angle of the ball, bat speed, and pitch speed, then watch
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 Exploratorium's Science of Cycling  The Exploratorium
Organized into seven sections. Introduction: What is the Science of Cycling? The wheel: Why do road bikes have thin tires, while mountain bikes have fat tires? Drives and gears: What is a gear ratio? And how do gears help make the bicycle so efficient?
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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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 Exploratorium's Skateboard Science  The Exploratorium
Watch a webcast (RealPlayer) of professional skateboarders performing as an Exploratorium staff physicist explains the physics behind this extreme sport; also, an interview with a skateboard designer, and a Flatland Freestyle demo. "Trickscience" looks
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 ExploreLearning.com  ExploreLearning
A library of virtual manipulatives called "Gizmos", primarily for grades 312, in math and science. Math topics include the major strands of instruction according to national standards, as well as developmental math, college algebra and collegelevel
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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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 Explore Patterns in Pascal's Triangle  Jeremy Baer
In 1653, a French mathematician named Blaise Pascal described a triangular arrangement of numbers corresponding to the probabilities involved in flipping coins, or the number of ways to choose n objects from a group of m indistinguishable objects. It
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 Exploring Algebra With Creative Designs  Iftikhar Husain
A workbook intended to teach algebraic concepts through creating designs on a graphing calculator using equations of mathematical functions. Examples of designs and instructions are available on the site, as well as ordering information, and a description
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 Exploring Chaos and Fractals  RMIT Publishing
An electronic textbook on CDROM which covers the subject of chaos theory and fractal geometry and includes text, worksheets, sound, video, and animation. Course material is presented with multiple entry points and themes, and can be used within a single
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 Exploring Data  Math Forum/USI
Pages for finding and displaying data sets, designed to support workshops on statistics given by the Math Forum for the Urban Systemic Initiative in Philadephia and San Diego. Included are: links by level to relevant statistics Standards (NCTM, California,
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 Exploring Emergence  Resnick, Silverman; Epistemology and Learning Group, Massachusetts Institute of Technology (MIT)
An active essay that uses Java applets to explore the idea of emergence, examining how objects and patterns can arise from simple interactions in ways that are surprising and counterintuitive. Examples with simple squares that turn on and off and give
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 Exploring Fractals  Mary Ann Connors, Dept. of Mathematics & Statistics, Univ. of Massachusetts at Amherst
Exploring Fractal Dimensions of Strictly SelfSimilar Fractals: Cantor Dust to the Fractal Skewed Web: what are fractals? selfsimilar shapes; what is dimension; a mathematical interpretation; noninteger and integer fractal dimensions; generating fractals;
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 Exploring Gravity  Becky Magan
A weeklong lesson plan for high school students and above, involving an experiment with dropped balls of different weights. Includes video, worksheets, grading rubric, experiment instructions, regression analysis, etc. Sample test data is supplied for
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 Exploring Parabolas (JavaSketchpad) (MSTE)  James P. Dildine; University of Illinois at UrbanaChampaign (UIUC)
Directions and descriptions for creating and simulating the creation of a parabola. The creation takes place within a Java Window in the browser and allows the user to interact with the sketch of a parabola he or she creates. The page includes tips and
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