 A Fibonacci Primer (SMILE)  Larry Freeman, Kenwood Academy
A lesson designed to challenge teachers and students to discover and prove some
interesting properties of the Fibonacci sequence and its unexpected relation to the geometry of the regular pentagon and the theory of limits. From the Recreational and
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 Fickled Fractions (SMILE)  Elizabeth Chambers, Keller Gifted Magnet Center
A lesson designed to review the ways in which fractions are made real in our world; to show the relation of cross multiplication and equivalent fractions; and to reinforce fraction skills. From the Arithmetic section of a collection of almost 200 single
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 A Fictional History of Place Value (SMILE)  Bette B. Jarrow, Goudy Elementary School
A lesson designed to teach students to rename a two or threedigit number in several different ways, including expanded form; and to perform addition and subtraction with the application of regrouping and the use of zero as a place holder. From the Arithmetic
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 Filling the Glass (Water, Air, and Fractions) (SMILE)  William R. Colson, Morgan Park High School
A lesson appropriate for elementary students who have a beginning knowledge of
fractions and measuring. Students associate the physical act of measuring a
fraction of a given amount of water with the arithmetic operations involved. Each
group uses
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 Finding Area and Perimeter in a Miniature House Using Standardized Units (SMILE)  June Muhammad, Park Manor
A lesson designed to teach students to find area and perimeter in a miniature house using standardized units of measure; to understand that the length of an object remains the same regardless of changes that occur in its position; and to experience handson
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 Finding the Sum of the Exterior and Interior Angles of a Polygon (SMILE)  David Drymiller, Morgan Park High School
A geometry lesson designed to teach students to find the sum of the interior angles and the sum of the exterior angles of any polygon; review linear measurement to the nearest sixteenth of an inch and angle measurement to the nearest degree; and construct
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 Flexagon  Magnus Enarsson
"A flexagon is a polygon folded from paper with a very remarkable quality: you can turn it inside out to make it reveal hidden surfaces." History, including the original discovery of the trihexaflexagon by Arthur H. Stone, as he folded strips of paper
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 Flexagon Re'flex'ions
Several possibly new trihexaflexagon phenomena are presented, with a wide spectrum of findings including explorations with magic squares, palindromes, and much more.
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 Flexagons  Conrad, Hartline
Introduction: The story of the Flexagon; Building and Operating the Flexagon; The Covering Space Representation of Flexagon Operation.
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 Flight Angles Of Inclination (SMILE)  Marie C. Smith, Anthony Overton Elementary School
A lesson designed to teach students to observe the flight of a glider; measure the distance flown from a given point; analyze the effect of a change of angle of inclination on the launch/flight of slinglaunched gliders; collect data on distance flown
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 FoldPlay
Upload your photographs, print them out in FoldPlay's templates, then fold them into hex kaleidocycles, oct kaleidocycles, invertible cubes, and foldbooks. Also, instructions for folding nerdcatchers, sphericon pies, polygon puzzles, and other origami.
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 Forming, Measuring and Labeling Angles (SMILE)  Essie Lee May, May Community Academy
A geometry lesson designed to teach students to form, measure, and label angles. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Formula Determination (SMILE)  Clark Odom, Collins High School
A lesson designed to teach students to determine the number of degrees in any convex polygon. From the Patterns and Logic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Fractiles7  Max Pelletier, Beverly Johnson
Magnetic tiles that use angles based on the number 7 and allow you to make designs with repeating and nonrepeating patterns. Create starbursts, spirals, butterflies, mandalas, flowers, spaceships, and more. Offers a good way to introduce tiling theory
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 Fraction Message (SMILE)  Charles Harper, Goldblatt Elementary School
A lesson designed to teach students to find pictorial representations of fractions and to decode messages. 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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 Fractions and Paper Folding (SMILE)  Bill Wagner, Hyde Park Career Academy
A lesson that develops the concept and properties of fractions using paper folding (origami). From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Fractions, Simplifying Parts of Shapes: 1/2, 1/3, 1/4 (SMILE)  Sarah Austin, Mary Bethune School
A lesson designed to teach students that parts are equal to their counterparts; that combined parts equal a whole; that any shape can be divided equally into parts; and to draw shapes, separate them into equal parts and write them in fractional form.
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 Fraperdec* (SMILE)  Connie Taylor, Holy Angels School
A lesson that uses playing cards to enrich and develop skills in conversion and sequencing of fractions, decimals and percentages, both in each individual set and in cross sets. From the Recreational and Creative Math section of a collection of almost
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 From Hypothesis To Conclusion...Reading Maps To Understand Proofs (SMILE)  Maryann Blaszak, South Shore Community Academy
A lesson designed to prepare students for writing twocolumn proofs by teaching them to write directions using a map; fill in missing data; understand the importance of diagrams in writing proofs; and develop a tentative understanding of writing proofs.
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 Fundamentals of Multiplication (SMILE)  Carl D. Mason, Suder School
A lesson for grade 3 designed to teach students the fundamentals of multiplication: that multiplication is a quicker and neater form of addition; how numbers in multiplication are placed into groups (or sets); and how students can simulate the concept
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 Fun with Fractals and the Platonic Solids  Gayla Chandler
A site rich with photographs and drawings of Sierpinski triangles and Platonic solids, made by hand, to inspire children of all ages to construct their own mathematical structures. See photographs, many set in marine environments, of dodecahedra, hexahedra
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 The Galileoscope™  International Year of Astronomy
Highquality, lowcost, easytoassemble telescope kits developed for the International Year of Astronomy (2009) in celebration of "... the celestial wonders that Galileo Galilei first glimpsed 400 years ago and that still delight stargazers today. These
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 Games Using Multiplication (SMILE)  Amaechi Onyeali, Carter Elementary School
A lesson for the elementary grades in which students play two games to reinforce their multiplication facts and their addition skills. From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science
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 The Generation Of Fractions (SMILE)  June Muhammad, Park Manor School
A lesson that uses a unique multiplication grid to help students realize that simple fractions (reduced fractions) may have many appearances but the same value; and which is designed to help students learn how to factor each denominator completely. From
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 GeoLeg  Peg Cannon
A quantitative geometry manipulative for grades 4  12. Associated lessons and tips for teachers offer ideas on visual and spatial learning for measurement and geometry.
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 Geometiles  Yana Mohanty
Interlocking tiles for exploring plane and threedimensional geometry, among other math topics. Purchase provides access to a variety of workbooks. Blog posts by creator Mohanty, an electrical engineer who earned a PhD in mathematics before teaching college
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 Geometric Bingo (SMILE)  Anne Lawrence, Wells Community Academy
A lesson for grades 710 designed to teach students to name and identify 20 geometric shapes. From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Geometric designs in the game of Life (SMILE)  Willaim Byrne, Martin Luther King High School
A lesson designed to predict and discover patterns generated in the game of "Life," using large checkerboards and checkers or flat counters. From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science
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 Geometric Factoring  Suzanne Alejandre
A Math Forum Web Unit. Understanding factoring through geometry: students work cooperatively to display a numeral as the area of a rectangle, and make as many rectangular arrangements as possible for each numeral given.
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 Geometric Models (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material describing physical objects corresponding to geometric constructions (and methods for creating such objects), particularly polytopes.
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 Geometric Shapes (SMILE)  Violet M. Nash, Spencer Math and Science Academy
A 2nd grade lesson on identifying geometric shapes using colors and math problems. Also see a followup lesson on geometric shapes and making a vest. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the
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 Geometry and the Geoboard (SMILE)  Jacqueline Darling, Simmye Anderson Community Academy
A 6th grade lesson designed to teach students to use geoboards: visualizing the concepts of squares, rectangles, triangles and polygons; exploring line segments, areas, and perimeters; demonstrating the phenomenological approach in learning geometry;
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 Geometry Distance of Triangles using a Protractor (SMILE)  Eileen Lally, A. Philip Randolph Magnet School
Students in the 7th grade learn how to use the protractor to measure angles, and use this ability to solve a problem involving distance. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science and
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 Geometry  Elmer G. Wiens; Egwald Web Services Ltd.
A collection of interactive geometric objects represented graphically including 3Dgraphics, space curves, trigonometric functions, hyperbolic functions, and
the trajectory of projectiles.
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 Geometry Web Page  Ephraim Fithian; Kutztown University
Sixteen geometry activities: Tangrams; Golden Ratio; Geoboard; Polygons; Symmetry; Constructions; Polyominoes and Polyiamonds; Star Polygons; Special Points in Polygons; Polygon Tessellations; Kaleidoscope Tessellations; Escher Tessellations; Space Cubes;
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 George W. Hart: Index  George W. Hart
An index to some of the areas covered by Hart's Web pages: Geometric sculpture; Encyclopedia of Polyhedra  over 1000 virtual polyhedra; Pavilion of Polyhedreality  images and geometry links; Hart's upcoming book about Zome Geometry; research and publications;
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 Getting the Goods on Graphing (SMILE)  Velma Elois Rouse, DeWitt Clinton School
A lesson designed to teach students to identify and graph ordered pairs in the coordinate plane; write the coordinates of points shown on a plane; and create designs or pictures using ordered pairs. From the Graphs and Visuals section of a collection
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 Getting To Know You (SMILE)  Kathy Koval, Randolph School
A lesson for any grade designed to teach students to use a ruler and measure accurately to the nearest inch; draw and label properly different graphs (line, pie, bar, pictograph); estimate/record measurement on a number line using intervals; and collect
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 God's Number is 20  Tomas Rokicki
An outline explaining how every Rubik's Cube™ permutation can be solved in twenty moves or fewer, established algorithmically by machine proof in July, 2010. Read "How did we solve all 43,252,003,274,489,856,000 positions of the cube?" and "What
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 The Golden Rectangle (SMILE)  Edwina R. Justice, Gunsaulus Academy
A lesson for grades 68 designed to teach students to measure using metric units;
to calculate averages; to compare and round decimals; to use calculators; to examine the relation between the Fibonacci Sequence and the Golden Ratio; and to relate mathematics
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 Grades 23: Lesson Plans (The Lesson Plans Page)  Kyle Yamnitz, Univ. of Missouri
A searchable archive of lesson plans for arithmetic, patterns, basic operations (addition, subtraction, multiplication, division), time, estimation, graphs, place value, fractions, measurement, number sense, and many more. Includes suggestions for games
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 Grades 45: Lesson Plans (The Lesson Plans Page)  Kyle Yamnitz, Univ. of Missouri
A searchable archive of lesson plans for arithmetic, patterns, basic operations (addition, subtraction, multiplication, division), time, estimation, graphs, place value, fractions, measurement, number sense, and many more. Includes suggestions for games
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 Grades 67: Lesson Plans (The Lesson Plans Page)  Kyle Yamnitz, Univ. of Missouri
A searchable archive of lesson plans for arithmetic, patterns, estimation, graphs, place value, fractions, measurement, number sense, geometry, and many more. Includes suggestions for games, manipulatives, calculators, and spreadsheets.
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 Grades PreK1: Lesson Plans (The Lesson Plans Page)  Kyle Yamnitz, Univ. of Missouri
A searchable archive of lesson plans for arithmetic, patterns, basic operations (addition, subtraction, multiplication, division), time, estimation, graphs, place value, fractions, measurement, number sense, and many more. Includes suggestions for games
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 Graphing Game (SMILE)  Thomas Lalagos, Hyde Park Career Academy
A lesson that introduces the graphing of ordered pairs on the cartesian plane. From the Recreational and Creative Math section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 Graphing Speed (SMILE)  Yolanda Smith, Douglass Math and Science Academy
A lesson for grades 35 designed to teach students to graph information (a running exercise); identify the horizontal axis and vertical axis; and compile information to make a graph. From the Graphs and Visuals section of a collection of almost 200 single
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 The Great Paper Airplane Challenge (TEAMS)  Jeannie Toshima; TEAMS Distance Learning, Los Angeles County Office of Education
Use origami to build the farthest flying airplane, and win the challenge. TEAMS looked for the farthest flying airplanes throughout the nation  the best
from each class. Students sent in the written directions (diagrams were acceptable) for folding
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 The Greenwood Institute  Greenwood School
A dyslexia, learning disabilities, and literacy resource site, with links to Web resources and publications. Comprehensive training of literacy instructors for mainstream and specialized schools; support for home schooling; research support; and consulting
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 Greg Tang Math  Greg Tang
Educational materials that combine problemsolving and arithmetic, and integrate math with language and art, from the author of The Grapes of Math, Math For All Seasons, The Best of Times, Math Appeal, Mathterpieces, Math Fables, and Math Potatoes. In
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 Hacktastic  Laura Taalman
Blog about "design, mathematics, and failure" by Taalman, a professor of mathematics at James Madison University, as she learns JavaScript, three.js, and WebGL. Posts, which date back to October, 2014, have included "Menger Menagerie," "Trigonometry Style,"
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