 Phi's Fascinating Figures  Ron Knott
More properties of the number Phi, its multiples and powers, continued fractions, formulae, and numerical relations between Phi and its powers.
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 'Picture This': Tangram Puzzles  Sarah A. Keith
Each week a new tangram puzzle is featured in "Picture This" in the Sunday cartoon section of newspapers worldwide. Children are invited to mail their tangrams for possible inclusion, and to be featured in the Kid's Gallery on the Web. Read the legend
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 Pieces 'n Creases: A Fun Guide to Origami  Herring, Long, Haeggquist, Jeremy; ThinkQuest Junior
Contents include the history of origami; uses and benefits; terms, symbols, and tips; origami and peace; poems about origami; activities, and resources for folding paper. An awardwinning entry from Vidor Middle School.
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 Place Value Chart  Ulrich Kortenkamp
Tap below this interactive place value chart app's headers labeled "ones," "tens," and "hundreds" to create tokens and begin experiencing bundling and debundling in our decimal number system. Compatible with the Apple iPhone, iPod, and iPad; also available
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 Place Value: K3  Andra McLeod
A "box full" of place value manipulatives for the classroom, with descripion, lesson ideas, and objectives listed for each of five types of manipulative.
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 Place Value (SMILE)  Ceopal Porter, Dr. Ralph J. Bunche School
A lesson for grade 2 designed to teach students to know the place value of the ones and the tens; to know how many ones are in one ten; and to be able to write numbers using more than one place value. From the Arithmetic section of a collection of almost
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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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 Platonische Körper  Klaus Bernt
Nets of the Platonic solids to fold. Download in postscript format for printing. In German.
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 Play Ball (SMILE)  Roslyn N. Matthews, South Shore High School
A baseball lesson designed to teach students to compute batting and earned run averages; given general dimensions of the playing field and some equipment, change the units to the metric system; find the diagonal distance from 3rd base to 1st base; and
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 Plexagon  Pleated Hexagon  Paul Bourke, Ron Evans
Plexagon is a new modular geometry based on the radial pleating of polygonal plates, and their joining or cobracing into 3D modules. This engineering approach can form a very practical basis for modular greenhouses (using recycled plastic sheeting) and
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 Polydron
British vendors of two and three dimensional, handson, geometric modelling systems and other geometric toys. Polydron Corporation history, online catalogue, and order form. To purchase Polydron products in the United States, contact Polydron International
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 Polygons Made To Order (SMILE)  Loretta Malone, Washington High School
A lesson designed to teach students to construct a regular polygon inscribed in a circle by using isosceles triangles with vertex angles at the center of the circle and legs as radii; determine the values of the angles; and discover that as the number
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 Polyhedra Collection  V. Bulatov
Galleries of polyhedra shown using JPEG pictures and 3D objects in VRML2.0 format. Uniform polyhedra; Duals; Compounds; Johnson's solids; 59 stellations of icosahedron; 270 stellations of deformed dodecahedron; symmetric stellations of rhombic triacontahedron:
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 Polyhedra in the Classroom  Suzanne Alejandre
Middle School student activities to pursue with a computer in the classroom. Introduction to Polyhedra; paper nets to print out and fold; Kaleidotile; Buckyballs; Crystals (paper nets, systems); Cube coloring problems; links to polyhedra on the Web.
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 Polyhedral Solids  Tom Gettys
The study of polyhedra is one of those special areas of Mathematics which allow the amateur and expert to work with an equal delight. The Platonic Solids; The Archimedean Solids; The KeplerPoinsot Polyhedra; Compound Solids; Stellated Polyhedra. See
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 Polyhedra plaited with paper strips  H. B. Meyer
A guide to generating certain polyhedra (Platonian, Archimedian and other solids) by plaiting paper strips (glueless method). In several cases pattern download of the paper strips is possible. In German and English.
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 Polyhedron Templates  Dan Grunberg
Design your own polyhedron paper models to print out, cut, fold, and assemble with glue. Build a net by choosing from among the five Platonic solids (tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron), or use the advanced button to specify
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 Polymorf  Rick Engel
A math manipulative, construction set toy, model building kit, and 3D puzzle all in one, used for modeling polyhedra and the structure of molecules and crystals. Build lifelike geometric models of creatures, vehicles, and structures. For all ages.
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 Polyominoes  Cynthia Lanius
What do dominoes and Tetris have in common? Both games use pieces that are formed of squares placed side by side. Dominoes use 2 squares; Tetris pieces (or tetrominoes) use 4 squares. Mathematician Solomon Golomb, in a 1953 talk at the Harvard Mathematics
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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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 Preschool and Kindergarten Math  Elaine Engerdahl
Early childhood math lesson plans and accompanying manipulatives. Full themes include Bugs, Dinosaurs, Space and Robots, Apples and Numbers, and Three Little Pigs and Fairy Tales; minithemes include Nursery Rhymes, Safety, and topical holidays. Watch
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 Primary Geometry (SMILE)  Barbara Pitra, Marconi Community Academy
A lesson designed to teach students to name, identify and categorize geometric shapes (triangle, square and rectangle) by the number and length of the
sides; identify triangles, squares and rectangles in their environment; through observation, comparison
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 Primary Understanding and Use of Place Value (SMILE)  Eleanor Brzozowski, Hanson Park School
A lesson designed to teach students about some of the peoples that have
contributed to the development of modern arithmetic (number systems); to provide a better understanding of our base 10 number system and its application to real life problems; and
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 Prime and Composite Numbers (SMILE)  Charlotte Goldwater, Kenwood Academy
A lesson for grades 59 that presents a systematic method of deciding whether a number is prime. 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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 The Private Eye  Kerry Ruef
A handson, investigative teaching approach that attempts to stimulate the wonder of looking closely at the world, thinking by analogy, changing scale, and theorizing. It uses everyday objects, a jeweler's loupe, and a series of simple questions, which
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 Proactive Play  Punitha Jayaraman
Articles on cognitive development research into, and activities to improve, spatial skills. Posts, which date back to October, 2012, have included "Hari Builds with Construction Set," "Piaget and van Hiele: Compare, Contrast and My Thoughts ...," "Hari's
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 Probability of Childhood Games (SMILE)  Robert Foote, Disney Magnet School
A lesson for grades 68 designed to explore the probability of several different events theoretically and experimentally using spinners and a Monopoly game board. From the Probability and Statistics section of a collection of almost 200 single concept
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 Probability (SMILE)  Ana Timbers, Stockton School
A lesson for grades 68 designed to teach students the relation between theoretical probability and experimental results as they draw marbles from a bag and record the results. From the Probability and Statistics section of a collection of almost 200
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 Probability (SMILE)  Emily Turner, Joplin Elementary School
A lesson designed to teach students to understand the concept of probability and the basic probability formula; and to predict the possible outcomes of an event. From the Probability and Statistics section of a collection of almost 200 single concept
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 Probability (SMILE)  Laura Willis Moss, South Shore Community Academy
A lesson designed to teach students to derive a general formula for the probability of a given event when each possible outcome is equally likely. From the Probability and Statistics section of a collection of almost 200 single concept lessons by the
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 Probability (SMILE)  Sandy Reed, Robert Fulton School
A lesson for grades 58 designed to help students learn, discover, explore and make a table of the number of times a specific event can occur, considering the results of two types of events: repeated sampling with replacement (events are independent)
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 Problem Solving (SMILE)  Marilyn McCree, District 12
A lesson that uses a grocery store in the classroom to teach students to solve word problems using addition, subtraction, multiplication or division. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the
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 Problem Solving
(SMILE)  Patricia Rogers, Edward Hartigan School
A lesson designed to demonstrate some common ways problems can be solved; to list some basic steps in problem solving; and to suggest some useful strategies for solving word problems. From the Practical and Applied Math section of a collection of almost
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 ProblemSolving: Steps and Strategies (SMILE)  Sarah G. Barrett, Mars Hill School
A lesson designed to teach and reinforce strategies for problemsolving. Sample problems are included. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning
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 Problem Solving Using Percentages (SMILE)  Thelma A. Rex, Rosa L. Parks Middle School
A lesson designed to teach students to recognize three basic percentage problems: using M&Ms to find what percent one number is of another; find a percentage of a number; and find a number when the percent is known. From the Practical and Applied Math
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 Properties of Dice  Klaus Mogensen
An essay on Proper Dice (illustrated) and Dice Roll Probabilities.
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 Properties Of Quadrilaterals (SMILE)  Margaret A. Olson, Morgan Park High School
A lesson designed to teach the names, definitions, and properties of quadrilaterals, and how to apply the correct property to each different quadrilateral. From the Geometry and Measurement section of a collection of almost 200 single concept lessons
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 Proving Pi (SMILE)  Gwendolyn D. Williams, Paul Robeson High School
A lesson designed to show the ratio of pi by revolving a circle one complete time, and to teach students why the ratio is true. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and Mathematics
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 Putting the Pieces Together (Making a Fractional Quilt) (SMILE)  Demetria E. McKnight, Bateman Elementary School
An lesson designed to motivate students to develop a sense of equivalent fractions; explore addition of fractions with unlike denominators; and learn to divide a whole number into specified equal parts. From the Arithmetic section of a collection of almost
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 Puzzles  Martin Watson
Blogs, comments, musings, design sketches, and photographs of mechanical puzzles by an avid collector and craftsman. Puzzle news, the author's own burrs (Watson's wormhole, digigrams, Dutch cubist), indepth explorations of manipulative puzzles (Puzzles
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Puzzles/Oneplayer Games  Jürg Nievergelt
Rubik's Cube and its variants. The 3*3*3* cube; Rubik's Revenge (4*4*4 cube); Pyramix (tetrahedron); Rubik's Clock; Rubik's Magic. Also Cryptequations, polyominoes, and links to a list of similar puzzles.
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 Puzzle Up  Binary Arts Corporation
A collection of others' Java puzzles, baffler and logic questions, "for serious puzzlers," best of the week, and mazes and mysteries, each organized into the three different skill levels of young, brisk, and expert. Also, information on the company's
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 Pythagorean Puzzle (SMILE)  Earl Zwicker, Illinois Institute of Technology
A lesson that models the phenomenological approach to enable students to prove the Pythagorean Theorem on their own using puzzle pieces and working together.
From the Geometry and Measurement and Algebra and Trigonometry sections of a collection of almost
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 Quilt Block Patterns  Hester ButlerEhle
Links to a variety of quilt block patterns (fourpatch, fivepatch, ninepatch, and more). Several are suitable for replication using pattern blocks.
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 Quilt Design Program MiniReviews  Robert G. Holland, The Virtual Quilt Company
A brief review of several quilt design programs. Links permit you to download a demo version of some programs. QuiltPro is the Windowsbased program of choice.
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 Random (Blog)  Neil Bickford
Bickford writes "about mathematics, cellular automata, programming, Rube Goldberg Machines, and overall randomness." Posts of the selfdescribed "mathematician/programmer/scientist," dating back to May, 2009  when Bickford was 11 years old  have included
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 Ratio and Proportion (SMILE)  Valesta Cobbs, John Fiske Elementary School
A lesson designed to teach students to calculate ratios and proportions and compare and contrast group data with class data. From the Arithmetic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for
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 Ratio and Proportions (SMILE)  Barbara Trotter, Ole A. Thorp School
A lesson designed to teach students to read and write proportions; identify the means and extremes of a proportion; solve proportions and problems using proportions; and to make a scale drawing. From the Practical and Applied Math section of a collection
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 Ratio, Percent & Proportions (SMILE)  Rosalyn Winston, Walt Disney Magnet School
A lesson on fractions as percents, designed to teach 7th graders to find the percent of a number; find percents using proportions; calculate the weight of objects (beads) in grams given specific percents; and verify the weight of objects (beads) on a
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