 Positive and negative Euler characteristic (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A symmetry pattern on the sphere always gives rise to a quotient orbifold with positive Euler characteristic. In fact, if the order of symmetry is k, then the Euler characteristic of the quotient orbifold is 2/k, since the Euler characteristic of the
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 Positive and Negative Numbers (SMILE)  Lincoln R. Siegel, Cregier High School
A lesson designed to teach students using concrete examples that zero is not the lowest number used in mathematics or real life, and that there are negative numbers and how to use them. From the Algebra and Trigonometry section of a collection of almost
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 PositiveNegative Charge Model For Integers (SMILE)  Barbara Williams, J. N. Thorp School
A lesson designed to teach students to represent operations on integers with positive and negative charges. From the Algebra and Trigonometry section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning
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 Positive/Negative Integer Rules  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about positive and negative integer rules, such as "When do two negative numbers equal a positive?"
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 The PostCALC Project  Duke University
The PostCALC Project is a branch of the Connected Curriculum Library that presents interactive, mathematicallybased modules designed for high school students who have finished a yearlong course in calculus. These modules, each appropriate for several
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 The postIMO97 web page  Olimpíada Matemática Argentina
Problems and results from the math olympics held in Argentina in July, 1997. Available in English and Spanish, with problems also in French, Russian, German, and a host of other languages.
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 Potent Problems  Institute for Studies in Educational Mathematics
A database of problems that deepen understanding of mathematics through multiple answers, approaches to an answer, interpretations, extensions, perspectives on a mathematical idea, layers of complexity, or algorithms. Potent problem content topics include
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 POVRay  Persistence of Vision Raytracer Pty. Ltd
The Persistence of Vision RayTracer creates threedimensional, photorealistic images using a rendering technique called raytracing, which calculates an image of a scene by simulating the way rays of light travel in the real world. Download the latest
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 Powell's Books
Located in Portland, Oregon, USA; the largest independent bookseller in the United States, specializing in technical books and new, used, hardtofind, and antiquarian titles. An extensive subject and keyword list is available  search database of titles,
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 Power and Pedagogy: Transforming Education through Information Technology  Robbie McClintock
A book from the Institute for Learning Technologies (ILTweb), Teachers College, Columbia University. Chapters include: The Computer as a System; The Educator's Mission; The Span of Pedagogical Possibility; Making a New Educational System; and Education
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 Power Cards: A Mathematical Puzzle  Cynthia Lanius
Choose a number from 131. Tell me which cards below contain the number, and I can tell you the number. How do I do it? (A hint and directions for making more cards are given.)
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 Power Conversion  MedCalc.com
Convert to and from watts, btus, cals, ergs, ftlbs, horsepower, kilowatt.
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 Power Maths  A precalculus project  Sidney Schuman
A precalculus investigation designed to enable students to discover each calculus power rule independently (albeit in simplified form), and hence their inverse relationship. Students are required only to do simple arithmetic and some elementary algebra,
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 PowerMath: the Virtual Reality Mathematics Teacher  Alexandre Menezes, PowerClassroom Software, LLC
Modular, studentcentered instruction software for Windows, based on visualization of mathematical ideas. Available in licenses from one to unlimited users. Demo CD available. Pricing and topics listed on web site.
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 The Power of Innovative Scheduling  Robert Lynn Canady; Educational Leadership Journal
A November 1995 article. "Alternative schedules may not add hours to the school day, but they can vastly improve the quality of the time students spend at school." Issues facing all schools; scheduling tips for elementary, middle and high schools; references.
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 The Power of One  Robert Matthews, The New Scientist
Benford's law demands that around 30 per cent of the numbers in a given data set will start with a 1, 18 per cent with a 2, right down to just 4.6 per cent starting with a 9. This essay provides a mathematical history behind the counterintuitive law,
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 The Power of Partitions  Ivars Peterson  Science News Online
A year before his death in 1920 at the age of 32, mathematician Srinivasa Ramanujan came upon a remarkable pattern in a special list of whole numbers that gave, for each of the first 200 integers, the number of their partitions, which range from 1 to
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 Powersim
A simulation software development company, offering consultant and support services for simulator design, construction, and use as well as the complementary software needed to build models and simulators. The site offers discussion groups, products, newsletters,
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 Powers of 10  Michael W. Davidson, The Florida State University
This telescoping Java applet illustrates powers of ten. View the Milky Way at 10 million light years from the Earth, move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree  then begin to move from the
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 Powers of 5 and Traveling to the North Pole (Math Chat)  Frank Morgan; Christian Science Monitor
What is the remainder when you divide 5^999,000 by 7?
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 Powers of Ten  Bruce Bryson
A series of images based on the book Powers of Ten, by Philip and Phyllis Morrison and the Office of Charles and Ray Eames. Each picture's subject is ten times wider or narrower than the next. Images range from quarks at 1016 meters to groups of galaxies
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 Powers of Ten  Eames Office
An "adventure in magnitudes" that depicts the relative scale of the universe in factors of ten, originally written and directed by Ray Charles Eames in 1968. Starting at a picnic by a Chicago lake, every ten seconds this nine minutelong documentary short
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 Power Spreadsheets  Jorge A. Gomez
Illustrated tutorials for Microsoft Excel, with accompanying practical examples and sample workbooks: formulas and functions, data analysis, PivotTables, Visual Basic for
Application (VBA), and more.
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 PQRST Puzzle Competition  Cihan Altay
PQRST is a quarterly online puzzle competition open to all, with competitions in January, April, July and October. Download the test as PDF, then solve and rate the puzzles within seven days. The PQRST site highlights top competitiors and puzzles receiving
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 Practical Assessment, Research & Evaluation  PAREonline.net
Practical Assessment, Research and Evaluation (PARE) is an online journal providing education professionals access to refereed articles that can have a positive impact on assessment, research, evaluation, and teaching practice, especially at the local
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 Practical Money Skills for Life  VISA
For educators, parents and students to practice better money management for life. Available online or in a binder format, the free classroom curriculum consists of a teacher's guide, student worksheets and quizzes. Teacher's Guide lessons cover topics
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 The Practice of Statistics  Yates, Moore & Starnes; W. H. Freeman & Co.
A free resource for students and instructors using the statistics textbook The Practice of Statistics. Take online quizzes for each chapter; read EESEE (Encyclopedia of Statistical Examples and Exercises) case studies ranging from "Is Old Faithful Faithful?"
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 Pre 20th Century Computing Devices  Rokeby High School, Rokeby, Tasmania
Contents include: Stone Computers; Abacus; Napier's Bones; The First Calculating Machine; Blaise Pascal's Adding Machine; Gottfried Leibnitz; The First Pocket Calculator; Jacquard's Loom; Luddites; Charles Babbage; The First Programmer; Herman Hollerith.
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 PreAlgebra (Middle School Math)  Homeworkhelp.com, Inc.
Free prealgebra lessons on: types of numbers (numbers and their properties, negative numbers); fractions (reducing, multiplying, dividing, adding and subtracting, mixed numbers, comparing fractions, ratios & proportions, percentages, decimals, scientific
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 PreCalc/Calculus (Math for Morons Like Us)  ThinkQuest 1998
Lists of important concepts, a quick reference sheet with key calculus formulas, and a calculus message board.
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 PreCalculus: A Teacher Quality Grant Project  State of Texas, Texas Higher Education Coordinating Board
A precalculus "courseinabox" for all teachers, particularly those new to teaching precalculus under the guidelines of the Texas Essential Knowledge & Skills (TEKS). It includes content information, activity sheets, videos of best teaching practices,
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 PreCalculus  Math Forum
Links to some of the best Internet resources for precalculus: classroom materials, software, Internet projects, and public forums for discussion.
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 The Precalculus Page
Lesson plans and staff development activities with a problemsolving approach to precalculus, with materials on logarithms, the binomial theorem, and the law of sines, and problems (without answers) on algebra, exponential and logarithmic functions, other
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 Precalculus  Preparing Students for Calculus  Warren Esty, Montana State University
A text designed to prepare students for calculus, with chapters on functions, powers, polynomials, logs, exponentials, and trigonometry. Models a new approach to learning through nontraditional homework (explanatory rather than computational); an emphasis
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 PreCalculus Problem of the Week  Math Forum
Math problems for students who had finished studying topics commonly covered in firstyear algebra and high school geometry. From 2002 to 2003, problems involved probability, statistics, discrete math, and trigonometry. The goal was to challenge students
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 PreCalculus  Trevor Roseborough
An introduction to calculus for the student who is about to learn the subject. It makes clear the connection between the integral and the derivative and suggests a more consistent notation before the student becomes hopelessly confused.
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 Precalculus Tutorial  John W. Bales
A tutorial for students enrolled in a precalculus, college algebra, or trigonometry course. Bates explains, "It does not, and cannot, replace the textbook or other class resources or assignments. At the instructor's discretion, all or part of this tutorial
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 The Precalculus Weblet  Dynamic Educational Materials
A partially online precalculus course with the following centers: Instruction (extending the instructional opportunities beyond the textbook; see Explore the Concepts and Starred Exercises), Reference (technology, glossary, history, sites that complement
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 Precision Mathematics, "Home of the Merbs"  Joseph Balcuk, Precision Mathematics
Site for "The Spoils of Civilization", a game students can play through the entire school year. Students are required to compete in class and work together to build a civilization for the main characters, Merbs. Students can also use the online game forum
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 Precollege science and math 'lack focus'  Janet Raloff  Science News Online
A National Science Foundation report finds no one at the helm of U.S. science and math education, with the result that students are exposed to smatterings of topics that vary regionally and encourage little indepth learning. The analysis, released in
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 A Preliminary Analysis of SATI Mathematics Data for IMP Schools in California  R. James Milgram
An analysis of the performance of Interactive Mathematics Program (IMP) students on the SATI mathematics examination, and a brief look at the supporting literature for IMP.
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 Preparing for Assessment  Math Forum, Teacher2Teacher FAQ
Answers to a frequently asked question: How can I prepare my students for assessments?
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 Preparing for the Workplace: Charting A Course for Federal Postsecondary Training Policy
Job training has taken a central place among strategies to boost U.S. competitiveness in the world and ensure a high standard of living. Decision making in this area has a major impact on American workers who do not earn 4year college degreesfully
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 Preparing for University Calculus  Mathematics and Statistics Committee of the Atlantic Provinces Council on the Sciences (APICS)
Answers frequently asked questions about university level calculus courses, such as "What math will I need in university?" and "What is calculus?" Also download the booklet, which offers sample questions and hints of the sort often found on calculus placement
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 Preparing Teachers of Mathematics: Asking the Right Questions  Lynn Arthur Steen; St. Olaf College
Lynn Steen writes that the problems of teacher preparation arise from multiple sources and require correspondingly different solutions. About mathematics teachers, prospective mathematics teachers, and curriculum issues.
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 Prependix A: Math Notation On KCT
 Karl Hahn
Math notation over the Web: symbol conventions used by Karl Hahn for his Calculus Tutor Notes.
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 Preservice Teachers' Conceptions of Mathematics and How to Teach It  Annie and John Selden; Mathematical Association of America
"The way teachers explain mathematics depends, to a large extent, on the conceptual grasp they acquire in their college classes. In addition, they often teach as they were taught, modeling themselves after their college mathematics teachers as much as
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 The Presidential Awards for Excellence in Mathematics and Science Teaching  National Science Foundation
The Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) is the nation's highest commendation for K12 math and science teachers. Read program information and facts, application packets, and press releases; look up awardees dating
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 Presidential Election and the Length of the Shortest Piece (Math Chat)  Frank Morgan, MAA Online
Presidential election with 48% of the US popular vote does not come close to the extreme possibility, even with just two candidates, of winning with less than about 22% of the popular vote. See Math Chat of November 8, 1996. Answer to the Challenge: 1.
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 President's Column (MAA)  Ken Ross
MAA President Ken Ross wrote this column for Focus on the need to connect K12 and collegelevel reforms.
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