 On Roman Numerals
Learn the basics of Roman numerals and how to write them, from I (1) to M (1,000) and above. Also, submit an Arabic numeral and click to convert it into its Roman numeral equivalent; or vice versa.
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 OpenEnded Math Problems  Gwenn Holtz and Mary Lee Malen, Levering School and the Franklin Institute
An eightmonth slate of openended problems for middle school students to solve in preparation for standardized testing. The authors have composed and selected problems that lend themselves to multiple solution paths, and then organized them into three
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 ostermiller.org  Stephen Ostermiller
Converters, Calculators, and JavaScript include Multiplication Game, in which letters represent digits in a multiplication problem; Length, which converts between units of length and distance; Roman Numerals, which converts between Arabic and Roman numerals;
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 Palindromic Numbers and Other Recreational Topics  Patrick De Geest
Many odd facts about big (and little) numbers, including circular primes and palindromic triangulars, tetrahedrals, squares, cubes, and primes. Also assorted odd puzzles, etc.
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 Panamath  Panamath.org
Have you ever tried to guess how many jelly beans are in a jar without counting? The Panamath test measures your number sense  your intuitive recognition of numbers and their relationships  and approximate number system (ANS) aptitude. Practice estimating
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 Papers by Dr. Bert K. Waits  Dr. Bert K. Waits
In PDF format, essays include "The Role of HandHeld Computer Symbolic Algebra in Mathematics Education in the TwentyFirst Century: A Call for Action!"; "The Role of Graphing Calculators in Mathematics Reform"; "The Evolution of Instructional Use of
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 Papers on the History of Mathematics  Gregory Cherlin, Rutgers University
A random selection of term papers submitted in undergraduate, onesemester courses on the history of mathematics. Topics include zero, Fermat, Euler, Newton, Euclid's proof of the Pythagorean Theorem, Fibonacci, Vieta, conic sections, mathematics at Princeton
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 Pascal's Fractals  Ivars Peterson (MathLand)
It's possible to convert Pascal's triangle into eyecatching geometric forms. For example, one can replace the odd coefficients with 1 and even coefficients with 0. Continuing the pattern for many rows reveals an everenlarging host of triangles, of varying
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 Pascal's Triangle and its Patterns
All kinds of information about Pascal's triangle: sums of the rows; prime numbers; hockey stick pattern; magic 11's; Fibonacci sequence; triangular numbers; square numbers; polygonal numbers; points on a circle; connection to Sierpinski's triangle.
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 Pascal's Triangle from Top to Bottom  Matthew Hubbard and Tom Roby
A comprehensive resource for the study of Pascal's Triangle. The section "Applications" addresses questions such as "What types of questions are answered by the binomial coefficients?" and "What number greater than 1 shows up most often in Pascal's Triangle?"
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 Pascal's Triangle Interface  Andrew Granville
A form that lets you visualize the entries of Pascal's triangle with respect to a modulus between 2 and 16. Select values for the number of rows, modulus, and the size of the image, and submit.
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 Pascal's Triangle  Ken Williams
Pascal's triangle, written out through row 19, by Ken Williams of the Math Forum.
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 Pascal's Triangle  Math Forum/USI
A Web unit designed to support workshops given by the Math Forum for the Urban Systemic Initiative (Philadelphia and San Diego). Read about the history of Pascal's triangle and learn to construct it; view illustrations of number patterns to be discovered;
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 Pascal's Triangle: Number Patterns  Math Forum
Some history and an interactive exploration of number patterns and an exploratory Internet Web unit for elementary, middle school, and high school, with lessons, number pattern studies, and links to relevant sites on the Web.
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 Pascal Triangle Applet  Sergey Butkevich
An applet that graphically presents Pascal's triangle modulo an integer number p; i.e. it computes the binomial coefficients. It can draw triangles with up to 650 rows with a p value between 2 and 30,000 (though it's not very clear above 15,000). The
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 Pat's Math & Problem Solving Links  Pat McQuatty
Site recommendations from the math consultant for the Western Quebec School Board. See, in particular, Special Days (Hundredth Day of school, Math with the number 2000  twenty suggested math activities for the year 2000). Also mathrelated links for
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 Patterns and Magic Squares  Recmath
This page looks at a particular subset of Magic Squares, those of order four which are 'continuous' (also known as pandiagonal, Nasik and Jaina). It explores the patterns possible when the numbers in these kinds of squares are
represented by a set of
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 Paul Trow's Math Page  Paul Trow
Trow's interactive web pages and perl software let you graph the LotkaVoltera equations and see interconnected predator and prey populations plotted over time; model the trajectory of a cannonball for different muzzle velocities and angles of elevation,
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 Pédagogie  Olivier Batteux
MathsRix et Labymath sont des logiciels présenté sous forme de labyrinthe où il faut choisir des portes qui correspondent à des choix opératoires en vue des résoudre des problèmes concrets. Découvre
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 Perfect, Amicable and Sociable Numbers  David Moews
Definitions, descriptions, and discussions of perfect, amicable, and sociable numbers; aliquot sequences, related problems, and other definitions of divisibility, with a short bibliography.
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 A Perfect Collaboration  Ivars Peterson (MathLand)
Euclid and Euler seem an unlikely pairing. One was the most prominent mathematician of antiquity, best known for his treatise on geometry, the Elements. The other was the most prolific mathematician in history, the man whom his 18century contemporaries
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 Perfect Numbers  Math Forum, Ask Dr. Math FAQ
What is a perfect number? How many are there? How can you calculate a perfect number from a Mersenne prime?
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 PhotoMath  Martha Jean Barrett; Kodak
A project where students created their own mathematical board games for use with younger or less advanced students, for grades 48. Working in teams, advanced students covered seven math categories: whole numbers, decimals, fractions, measurement, geometry,
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 Pi Approximation Day Greeting Cards  123Greetings
123Greetings  Send Free Electronic Greeting Cards to Friends and Families all over the World. There are no images available for Pi Approximation Day, but backgrounds and a variety of slogans are available, and you can write your own.
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 Pick a number from 1 to 10 ... for SCIENCE!  Alec Perkins
"When asked 'pick a number from 1 to 10,' people tend to pick certain numbers more than others, in particular 7 and 4 over the extremes...." Participate by choosing your own number; see bar graphs and line plots of data submitted thus far according to
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 Place Value  Cut the Knot!, Alexander Bogomolny
Dictionary definitions of place value and what they lack; the emphasis on place value in the NCTM Standards; its importance in understanding our numeration system; how it arises from one of several possible representations of grouping in the counting
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 PlaceValue: ProblemSolving and Written Assessment Using DigitCorrespondence Tasks  Ross, Sunflower
This study examined the effects of researcherdeveloped lessons on students' understanding of two and threedigit numeration. Digitcorrespondence tasks, often used for individual interview assessment of place value understanding, were adapted to be
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 Place Value (SMILE)  Dwayne Belle, Fuller School
A lesson designed to teach students to identify the value of numerals through 10 digits. From the Arithmetic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 PlaneMath  InfoUse, in cooperation with NASA
Materials for elementary school students about math and aeronautics, designed to stimulate and motivate students with physical disabilities in grades 47 to pursue aeronauticsrelated careers via the development and delivery of accessible math education
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 The Playground of Mathematics  Cilenia
JavaScript practice in addition, subtraction, multiplication, division, time, and comparison ("greater than, equal to, or less than"). Select difficulty, complexity, position of unknown, duration, and other settings. Also available in Russian, Italian,
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 A Playground of Thoughts  Takasugi Shinji
Takasugi's "Number Systems of the World" lists dozens of languages; how to count from zero to one hundred in each; and the mathematical meaning of the expressions for each numeral. For example, the French say "93" with quatrevingttreize, which means
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 Plouffe's Inverter  Simon Plouffe
A database of more than 84,800,000 mathematical constants like Pi, Sqrt(2), Catalan and Euler's gamma. Enter a number, search or browse, and the programs will find what the number is made of. From the author of the Encyclopedia of Integer Sequences (with
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 Portion Distortion  National Institutes of Health (NIH)
How do the portions served in today's fast food restaurants compare to those available 20 years ago? Take the "Portion Distortion" quizzes to learn exactly how much portions have "super sized," as well as the amount of physical activity required to burn
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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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 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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 Prime Curios!  G. L. Honaker, Jr., Chris K. Caldwell
A collection of curiosities, wonders and trivia related to prime numbers. Look up a number (up to 10^21+) and find what connections it has to the primes. The database has over 3400 curios corresponding to more than 1960 different numbers. The number of
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 Primes and Composites (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: Consider the sequence of integers 10n + 1: 11, 101, 1001, ... Are there infinitely many primes? Infinitely many composite numbers? Whenever n is odd, 10n + 1 is divisible by 11. Modulo 11, 10n + 1 = (1)n + 1 = 0 if n is odd,
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 Prime Talent  Ivars Peterson (MathTrek)
Whole numbers have all sorts of curious properties. Consider, for example, the integer 1998. It turns out that 1998 is equal to the sum of its digits plus the cubes of those digits (1 + 9 + 9 + 8 + 13 + 93 + 93 + 83). What's the largest number for which
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 Printables: Student Handouts  The Learning Network
PDF format printable handouts. Browse by grade or subject; check out the featured handouts; or search for a topic of your choice. Other resources also available through the Lesson Planning Center links on the site.
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 ProblemoftheWeek  David Poole; Department of Mathematics, Trent University, Canada
Most of these problems can be done using only high school mathematics and logical reasoning. Eight problems with solutions and one without, from the fall of 1997, at Trent University, Canada. An email contact is listed, for those outside the university
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 Problem Pictures  Richard Phillips
A CDROM of 184 attractive, unusual, or puzzling color photographs accompanied by activities for mathematics teaching. Images may defy explanation, motivate investigation, or inspire the viewer to answer a question. Other pictures may be the starting
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 Problem Solving in Mathematics  Jim Wilson; Univ. of Georgia
Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links
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 Project IMPULS  Tokyo Gakugei University
Project IMPULS (Project for International Mathteacher Professionalization Using Lesson Study) offers opportunities and ideas for mathematics teachers using lesson study. The library includes lesson study about positive and negative numbers; division;
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 Properties Glossary  Math Forum, Ask Dr. Math FAQ
What is an operation? What is an identity? What are the associative, commutative, and distributive properties? What is the property of closure? What is the inverse of something?
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 Properties of Numbers (SMILE)  Leon Steinfelds, King High School
A lesson that contrasts the "mean" behavior of 0, 1, 2, and regular numbers, likening numbers to students. From the "Miscellaneous" section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 PseudoNumerals  phonetic symbols for numbers  Allan Krill
A method for remembering IDnumbers, etc., as words. The techniques used here have been used for 200 years, but now are formally defined as numerals. Presented in August at Mathfest 2002.
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 The Published Data of Robert Munafo  Robert Munafo
Mathematical data includes MuEncy, The Encyclopedia of the Mandelbrot Set (History, Exploring, Area, Algorithms, Naming, etc), properties of specific numbers, such as 2.68542 . . . and 143, and very large numbers and ways to write them. Programs include
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 Puzzle University  Amy Galitzer
A nonaccredited "university," created solely for fun. Everything is free to play and take part in. Register, pass a simple test, and advance from freshman to sophomore to junior to senior to grad student this way. The puzzles get harder as you progress.
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 Pythagoras: Music and Space  J. BoydBrent
A brief introduction to Pythagoras' observations on the relation between music and number. Graphics show music intervals expressed as mathematical ratios. Pythagoras observed that when the blacksmith struck his anvil, different notes were produced according
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 The Pythagorean Theorem and the Maya Long Count  Charles Wm. Johnson; Science in Ancient Artwork 
Various essays dealing with the possible extension of the Pythagorean Theorem to the third power in relation to the mathematical and geometrical appearance of the Maya long count fractals within progressive series of right triangles. It would appear that
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