 Visualizing An Infinite Series  Cynthia Lanius
This lesson uses a trapezoid successively divided in 4ths as a visual representation of an infinite geometric series, a mathematical concept that is often only treated symbolically. Explorations are outlined for investigating a number of series, and links
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 Visualizing Math
Tumblr of mathematical images begun June, 2013, by two high school students from Minnesota. Images have included "A panorama on a Möbius strip," "Fractal Trees by Robert Fathauer," "elegantly constructed proofs through visual inspection," "animation
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 Visualizing Mathematics  Yerushalmy, Shternberg, Cohen, Talmon
A computeroriented inquiry curriculum for secondary mathematics. Visual Mathematics software programs include Calculus Unlimited; The Geometric Supposer; Modeling: MoveOn, The Function Sketcher & and Escalator. With descriptions, screen shots, ordering
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 Visualizing the Behavior of Functions  Cuoco
Cabri Geometry II figures and a macro accompanying the article "Visualizing the Behavior of Functions" by Albert A. Cuoco in the Technology Tips column of Mathematics Teacher magazine.
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 Visual Math for Java  Dr. Weiguang Huang
The Java applet Visual Math is an online symbolic math and computer algebra system powered by SymbMath. SymbMath (an abbreviation for Symbolic Mathematics) is a symbolic, numeric and graphic computing environment that performs exact numeric, symbolic
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 Visual Math: Functions  Centre for Educational Technology (CET)
Activities, tools, and tasks for learning about linear and quadratic functions.
Contents: Linear Functions  Functions Defined on Intervals  Equivalent Expressions of Functions  Addition and Subtraction of Linear Functions  Transformations of Graphs
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 VisualMath  G. Fonthal, VisualPhysics
Math shareware programs that feature visual and interactive techniques under Windows 95 may be downloaded from this site: for numbers (real, complex, binary); set theory (Venn diagrams); geometry (shapes and areas, 3D Geometry); algebra (equations, polynomials,
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 VisualMath  Software And Engineering Co.
A graphic language for solving all types of problems, providing over 80 components, all of which are capable of using matrix input. Many dialogs are used to define properties. A special 3D plotter and table viewer show the results of the solution. VisualMath
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 Visual Plane Geometry  Edu2000 America Inc.
A full curriculum on CDROM for Windows and Mac, combining hypertext and QuickTime animations to illustrate basic plane geometry concepts, triangles, polygons, circles, and the threedimensional world. Familiar real world examples help students visualize
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 Visual Solid Geometry  Edu2000 America Inc.
A full curriculum on CDROM for Windows and Mac, combining hypertext, graphics, and QuickTime animations to illustrate solid geometry concepts, polyhedra and solids of revolution, and surface areas and volumes of solid figures. Typical "experiments"
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 Visuals Patterns in Pascal's Triangle (SMILE)  Ulysses Harrison, Dunbar Vocational High School
A lesson for grades 5 and up that uses a phenomenological approach to show students the many visual and number patterns present in the sequence of numbers in Pascal's Triangle, and to encourage them to explore the patterns on their own. From the Patterns
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 Visual Structure of Postulates and Axioms in Algebraic Operations
(SMILE)  Sanford Olshan, Roosevelt High School
A lesson designed to reinforce and retain the use of axioms and postulates in various proofs and linear transformations of equations; and to have student build a physical model of the game of "PRUFF" either as a card game or as a board game. From the
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 Vizual Statistix  Seth Kadish
Blog of statistics graphed by a Geoscience PhD who describes data visualization as his passion. Posts, which date back to January, 2012, have included "A Summation of Square Usage over 432 Chess Games"; a tiled plot showing the number of unique configurations
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 Vlaamse Wiskunde Olympiade  Flanders Mathematics Olympiad  Paul Igodt
In Dutch: the site contains more than 20 years of challenging math problems.
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 Vocabulary PuzzleMaker  Glencoe Online
Make the following types of puzzles to go along with your Glencoe text in prealgebra through geometry: crossword, word search with words, word search with clues, or jumble. Available for free download in both Windows and Macintosh formats.
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 Voce Viva ScriviFacile  Danieli Alessandro, SLD Software (Scribit&Legit&Dicit)
Interactive software for the four basic operations and algebraic expressions, primarily in Italian. "Dimostrazione del software Voce Viva ScriviFacile, con sintesi vocale e con comunicazioni vocali interattive che guidano nello svolgimento delle divisioni
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 Volume and Surface Area (SMILE)  Charlotte Goldwater, Kenwood Academy
A lesson for grades K12 designed to teach students to understand the difference between surface area and volume. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative
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 Volume of a Tank  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about finding the volume of cylinders, cones, oblate spheroids, and other tanks, such as "How can I calculate volume of liquid in a cylinder that's not full and lying horizontally?"
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 Volume of a Torus  Paul Kunkel
An investigation into and explanation of the volume of a torus.
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 Volume of Water in an Aquarium  NASA Lewis Learning Technologies Project
How much water will fit in an aquarium that is shaped like a box and is 10 inches high, 6 inches wide, and 14 inches long? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Voronoi Art  Scott Sona Snibbe
Using a retroreflective floor to display the Voronoi diagram of people walking on it, exploring notions of personal space and individualgroup relations. See also Scott's other projects.
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 Vosenigmes.com  Kalimuse, LLC
In French: Vosenigmes.com permet de faire travailler ses cellules grises tout en s'amusant. Les petits comme les grands pourront se détendre tout en travaillant les mathématiques. Vosenigmes.com garde vos scores en mémoire, vous permettant de répérer
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 Voyager Learning Math Solutions  Cambium Learning, Inc.
Math curricula and programs from "your comprehensive intervention partner": Inside Algebra, Voyager Online Algebra, Vmath Summer Adventure, VmathLive, Showtime! Math, Vmath, TeachingBOT, and TransMath.
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 Voyager Sopris Learning  Voyager Sopris Learning, Inc.
Researchbased curricula, targeted interventions, assessments for Dynamic Indicators of Basic Early Literacy Skills (DIBELS), positive school climate resources, and professional services to educators working with preK12 students who have special needs
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 vrml.calculus.net (calculus@internet)  Curtis, Davis, Wayand
The visual study of threedimensional calculus using the power of VRML  Virtual Reality Modeling Language. The next generation of calculus course materials. Text in progress: Virtual Reality & 3D Calculus  addressing the question how virtual reality
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 VRML Gallery of Electromagnetism  Rob Salgado
A collection of VRML worlds that visualize the vector fields of electromagnetism. Subcategories: addition; wedge product; raising and lowering of indices; unit vectors; charged point (Coulomb); two charged points; charged dipole; charged sphere; charged
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 VulcanSoft
Win95/NT4 software. Includes a measurement converter with 15 categories and over 270 different measurement units, a financial calculator with 14 different financial calculations and table output, and a city distance calculator with over 1900 cities, which
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 Vygotsky's Distinction Between Lower and Higher Mental Functions and Recent Studies on Infant Cognitive Development  Eugene Subbotsky; Psychology Department, University of Lancaster, UK
One of the major theoretical advances of Vygotsky's approach to cognitive development was his thesis that human mental functions are social in origin. In making this claim, Vygotsky was confronted with the difficulty of reconciling it with the fact that
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 Waldomaths  Ron Barrow
Original applets on number, algebra and graphs; shape, space and measure; probability and data handling, including histograms; investigative tools (quadratic and cubic sequences); core (pure) mathematics; decision mathematics (network graphs and linear
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 Walking Randomly  Michael Croucher
Croucher's blog, which dates back to August of 2007, has included posts such as "Logo Programming on the pocket PC," "Christmas gifts for math geeks (like me!)," "Martial Mathematics," "R Compared to MATLAB (or 'learning a thing or two from your students'),"
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 WallaceBolyaiGerwien Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
According to the WallaceBolyaiGerwien theorem, all simple polygons of equal area are equidecomposable by dissection. The site offers a proof of the theorem and several dynamic illustrations of equidecomposition in special cases.
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 Wallpaper Groups (Plane Symmetry Groups)  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Mathematicians classify plane patterns such as wallpaper patterns by means of symmetry groups  groups of transformations of the plane that leave the pattern invariant. A transformation slides, rotates, and reflects the plane into another position. Such
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 Walpha Wiki  Derek Bruff and others
As collaborative site to record how secondary and undergraduate math educators use WolframAlpha, or Walpha as it's called here, in the classroom. In particular, the authors are interested in how students might use Walpha themselves, as well as how teachers
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 Wanted: A New Mix  Keith Devlin (Devlin's Angle)
An essay on the insularity of mathematicians. "...mathematics as a whole should be prepared to embrace as a useful and bona fide part of the enterprise, collaborative investigations involving mathematicians together with experts in other disciplines."
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 Waring Experiments  Ivars Peterson (MathLand)
You might suspect that, at some point, four squares would no longer be enough to express a given whole number. This reasonable supposition was overturned in seventeenth century, when Pierre de Fermat proved that every positive whole number can be expressed
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 Washington MESA
Washington MESA (Mathematics, Engineering and Science Achievement) is developing middle and high school curriculum units and middle school modules/books available through Cuisenaire Dale Seymour Publications that integrate concepts within mathematics
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 WASL Math Prompts  Port Angeles School District, Washington state
Sample questions for the WASL, Washington State Assessment of Student Learning. Most questions have answers printed above the questions. Sample questions are offered for kindergarten through high school levels, organized by mathematical content, and accompanied
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 Was Math Invented or Discovered?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about whether math was invented or discovered.
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 WatchKnowLearn  Community Foundation of Northwest Mississippi
Thousands of free online math educational videos, categorized into topics such as mathematics for young learners, number operations, math in the real world, precalculus, math study skills and test prep, and history of math.
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 Waterman Polyhedra and Maps  Steve Waterman
World maps based on close packing of spheres that resemble B.J.S. Cahill's octahedral butterfly world map, but with only five degree graticule. With links to the mathematics behind the cartography, polyhedra applications, and other original findings.
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 The Water Puzzle  Doug Ensley, Shippensburg University
Starting with a pail of water holding some unknown quantity greater than 8 quarts, and small (3 quarts) and large (5 quarts) vases as measuring devices, explore how to split 8 quarts of water from the pail equally between two people.
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 Water Puzzle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
There are three glasses  3, 5, and 8 oz. The first two are empty, the last contains 8 oz of water. By pouring water from one glass to another make at least one of them contain exactly 4 oz of water. Investigation into this puzzle by experimentation,
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 Water Tidbits: Questions and Answers  U.S. Geological Survey (USGS)
Topics covered include: Water use in the United States, USGS water data and measurements; Water use in your home; Chemistry and water. Links to other sites about water.
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 WatsonMath.com  Elaine Watson
A repository for ideas and links that support Watson's work as a K12 mathematics consultant, such as spreading the word about the Common Core State Standards in Mathematics and how they can be implemented by classroom teachers. Posts, which date back
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 WAVE: Web Access Virtual Education  University Laboratory High School; University of Illinois at UrbanaChampaign
The Illinois WAVE Project provides Mathematica Tutorial notebooks categorized as pertaining to Algebra, Applications, Calculus, Conics, Geometry, Precalculus, Statistics, or Trigonometry, for use in the high school mathematics curriculum. From the University
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 The Weather Calculator  National Weather Service, El Paso, TX
The El Paso National Weather Service Office's weather calculator provides temperature, moisture, pressure, and wind unit conversions for 16 different weatherrelated variables.
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 Weather Plots (MSTE)  John Meseke; University of Illinois at UrbanaChampaign (UIUC)
Students use current weather data to observe and answer questions about the relation between temperature and humidity.
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 Weather Underground  University of Michigan
One Sky, Many Voices: resources for collaborative study of current weather events for K12 classrooms, afterschool groups, and athome learning. Gather data on weather information on the Web, current conditions around the world, historical weather patterns,
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 WebCalc  Blaine Hilton
A collection of free, Webbased calculators that solve complete equations. Many of the calculators allow the user to solve for any of the variables. Subjects include algebra, geometry, trigonometry, fractions, complex numbers, and miscellaneous math;
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 WebCalC  The WebMath Group
An online calculus course with easy to read text, fully worked examples, problem solutions, quizzes, and online linking. To view WebCalC, you need the software Scientific Notebook (a free viewer version is available). The site includes links to publications
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