 Eratosthenes Finds Diameter of Earth!  Mary Kay Hemenway, University of Texas at Austin
Students learn to estimate the diameter and circumference of the Earth by repeating Eratosthenes' experiment, exchange measured data and results, and use the Internet to research the mathematical and scientific contributions of Eratosthenes. Hemenway
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 Eric Buffington
YouTube lessons and other educational math videos by a Pennsylvania cyberschool teacher. See, in particular, Buffington's channels on "Math That Makes you Think," "Math in Real life," and episode 1 and episode 2 of "What Kids Say About Math."
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 Essay Ideas  Jim Wilson, Dept. of Mathematics Education, Univ. of Georgia
For a course on Using Computers in Mathematics Instruction. Friday the 13th (show there are at most three and at least one Friday the 13th in each year, consider when two consecutive months can be have Friday the 13th); Gingerbread Man (a Microsoft Excel
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 Estimating and Counting Money (SMILE)  Omega L. MinorClark, R. Nathaniel Dett Elementary School
A lesson designed to review estimating and rounding to the nearest dollar; teach skills and practice in counting money; and give students experience in estimating sums and products. From the Practical and Applied Math section of a collection of almost
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 Estimation Contest (SMILE)  Sandra A. KingBryson, Saucedo Magnet School
A lesson that uses breakfast cereal to give students a concrete understanding of the subtle difference between a guess and an estimate. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the Science and
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 Estimation of Pi (MSTE)  Nicholas Exner; University of Illinois at UrbanaChampaign (UIUC)
A Java applet that estimates the value of pi by firing random data points at a circle inscribed within a square. The probability of a data point landing within the circle is a ratio of the circle's area to the area of the square.
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 Estimation (SMILE)  Iona Greenfield, Carnegie Elementary School
A K1 lesson designed to teach students to solve problems by guessing and checking; to identify length by using informal units to estimate; and to guess and write an addition and subtraction sentence for the number of peas in a pod. From the Geometry
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 Estimation (SMILE)  Theresa W. Akpan, Wells Community Academy
A lesson for grades 58 designed to teach students to estimate numbers of objects by sampling; and to contrast and compare sampling with guessing. From the Practical and Applied Math section of a collection of almost 200 single concept lessons by the
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 e Teaching Assistance Program  eTAP, Inc.
Lesson plans, examples and exercises, review checks, and other instructional materials, including audio downloads, on the language of mathematics; basic operations; order of operations and combining terms; fractions; multiplying and dividing fractions;
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 Ethnomathematics and STEM Institute  University of Hawai'i at Mānoa
Exploring "culturally responsive science, technology, engineering, and mathematics (STEM) pedagogy" across the State of Hawai‘i through the Mathematics Common Core State Standards (CCSS) and Next Generation Science Standards (NGSS). Freely downloadable
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 e to the i pi  Kevin Bertman
Investigations for teachers to use in mathematics classes. Posts include Phantom Traffic Jams (velocities); Hypotrochoids (Spirographs); Cartograms; Rogue Waves; Fractal Trees; Stereoscopic Images; Six Degrees of Separation; Shoelaces (applying the Pythagorean
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 Euclid's Algorithm, Heron's Algorithm, Calculation of Pi (MSTE)  Kyte, Moore, Finch; University of Illinois at UrbanaChampaign (UIUC)
Problem (by HansGeorg Weigand): Euclid's Algorithm gives you the greatest common divisor of two natural numbers; explain the algorithm. Given two numbers (e.g. 121 and 33), calculate the gcd(121,33) (in EXCEL you need the "ifcommand"). Heron's Algorithm
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 The Euler Characteristic of an Orbifold (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
Suppose we have a symmetric pattern in the plane. We can make a symmetric map by subdividing the quotient orbifold into polygons, and then 'unrolling it' or 'unfolding it' to get a map in the plane...
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 The Euler Line of a Triangle  David Joyce; Dept. of Mathematics & Computer Science, Clark University
A draggable geometry applet illustrating the centroid, circumcircle and circumcenter, and altitudes and orthocenter of a triangle, and the straight line they all lie on, the Euler line.
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 The Euler Number (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
If we have a polyhedron, we can compute its Euler number, x=VE+F. In fact, we computed Euler numbers ad delectam. Why did we do this? One reason is that they are is easy to compute. But that is not obviously a compelling reason for doing anything in
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 The Event Inventor  Kye Ewing
Science, math, and technology explorations with no experience necessary. (Explorations can often be done by older children with no help.) Make your own quadrant and cross staff and explore the world around you  measuring heights of buildings or trees
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 Examples of Essays  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Extended Concurrencies of the Triangle, J. Wilson; Parabolas Inscribed in a Triangle, G. Giddings; Polygonal Spirals, L. Shook and M. Callinan; Roots 2 and 5, J. Wilson; Those Amazing Palindromes, Shareef Bacchus; Tangrams, Greg Huberty; Phi: That Golden
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 The Excellent Adventure  Shawsheen Valley Technical High School, Billerica, MA
A mathbased crosscurricular site where students take a trip from Philadelphia down the East coast to Disney World, with several required stops and activities along the way. A teacher's guide, worksheets, and activities are provided: students figure
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 Excel Traffic Problem (MSTE)  Kocinski, Clark; University of Illinois at UrbanaChampaign (UIUC)
Problem (by HansGeorg Weigand): there is a traffic jam on the highway when cars pass a building site. A model of this situation shows that cars drive with the same speed v and all have the same length l. For the distance d between two cars there are
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 Exemplars
Exemplars is meant to assist teachers, schools and districts implement authentic assessment and problem solving in their classrooms and to meet the challenging new standards developed in mathematics, science and humanities at the national, state and local
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 Exercises in Imagination (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
How do you imagine geometric figures in your head? Most people talk about their threedimensional imagination as 'visualization', but that isn't exactly right. A visual image is a kind of picture, and it is really twodimensional. The image you form in
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 Expected Value: Temperature of a Point on a 2D Plate (MSTE)  Ed Malczewski; University of Illinois at UrbanaChampaign (UIUC)
Find the temperature at a particular point of a rectangular plate using statistical methods. It is assumed that the temperature of the edges as well as the dimensions of the plate are known. The lesson includes a program that will run on Resampling Stats,
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 Experimentation, Graphing, and Algebraic Derivation  R. H. Logan
A scientific graphing lesson that details the derivation of the slope intercept formula; the slopeintercept formula in Chemistry; and linear relations in Chemistry and Physics.
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 Explorations of a Problem with Two Squares  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Given a square of side s and segments drawn from each vertex to the midpoint of the second side, counting counterclockwise, the segments intersect to form a new square. What is the ratio of the area of the shaded square to the area of the original square?
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 Explore Patterns in Pascal's Triangle  Jeremy Baer
In 1653, a French mathematician named Blaise Pascal described a triangular arrangement of numbers corresponding to the probabilities involved in flipping coins, or the number of ways to choose n objects from a group of m indistinguishable objects. It
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 Exploring Advanced Euclidean Geometry with Geometer's Sketchpad  Gerard A. Venema
A sequence of PDFs that show how to use dynamic visualization software to explore topics in collegiate Euclidean geometry. Each file is 0.2MB or smaller. The complete sequence runs 121 pages, and features a table of contents, bibliography, index, and
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 Exploring Data  Math Forum/USI
Pages for finding and displaying data sets, designed to support workshops on statistics given by the Math Forum for the Urban Systemic Initiative in Philadephia and San Diego. Included are: links by level to relevant statistics Standards (NCTM, California,
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 Exploring Fractals  Mary Ann Connors, Dept. of Mathematics & Statistics, Univ. of Massachusetts at Amherst
Exploring Fractal Dimensions of Strictly SelfSimilar Fractals: Cantor Dust to the Fractal Skewed Web: what are fractals? selfsimilar shapes; what is dimension; a mathematical interpretation; noninteger and integer fractal dimensions; generating fractals;
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 Exploring Geometric Solids and Their Properties (iMath Investigations)  Illuminations; National Council of Teachers of Mathematics (NCTM)
An online, interactive, multimedia math investigation. Investigating and then reasoning about the relationships within and between threedimensional shapes is important for students in grades 35 as they continue to develop understanding about geometry
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 Exploring Gravity  Becky Magan
A weeklong lesson plan for high school students and above, involving an experiment with dropped balls of different weights. Includes video, worksheets, grading rubric, experiment instructions, regression analysis, etc. Sample test data is supplied for
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 Exploring Parabolas (JavaSketchpad) (MSTE)  James P. Dildine; University of Illinois at UrbanaChampaign (UIUC)
Directions and descriptions for creating and simulating the creation of a parabola. The creation takes place within a Java Window in the browser and allows the user to interact with the sketch of a parabola he or she creates. The page includes tips and
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 The Exponential Curve  Dan Greene
A blog by a math teacher at Downtown College Prep charter high school (San Jose, California), where the students "... are primarily Latino, are far below grade level in their math and reading skills, and will be the first in their families to go to college.
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 Exponential Fit: Running to Conclusions (MSTE)  Ed Malczewski; University of Illinois at UrbanaChampaign (UIUC)
A lesson that explores the process of finding the best fitting exponential curve to sets of data like the world record times for running the mile. Requires Internet access, a bag of Skittles, and Microsoft Excel. Analyze exponential fit for population
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 Exponential Functions  Jim Rahn
Links to selected sites, projects, and graphing calculator explorations designed to foster understanding of the family of functions known as exponential functions, useful in such applications as population growth, compound interest, radioactive decay,
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 Extended Concurrencies of a Triangle  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
An exploration: take any triangle ABC. Construct equilateral triangles externally on each side and locate the center of each equilateral triangle. Label these centers A', B', and C' for the triangle centers opposite angles A, B, and C. Construct lines
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 Extending Our Knowledge of Place Value (SMILE)  Angie Morris, Burnham School
A lesson designed to reinforce the knowledge of place value for first and
second graders by using their auditory, visual, and/or kinesthetic learning styles and the numbers 1099 only. From the Arithmetic section of a collection of almost 200 single
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 The Factor Game (iMath Investigations)  Illuminations; National Council of Teachers of Mathematics (NCTM)
An online, interactive, multimedia math investigation. The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through
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 Factors (SMILE)  Edwina R. Justice, Gunsaulus Scholastic Academy
A lesson for grades 57 designed to teach students to find and record groups formed by using pennies; define factor, product, prime, and composite; write related number sentences; find the factors of whole numbers; classify numbers as prime or composite;
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 Famdays
A famday is a day on which the combined ages of family members add up to a whole number of years  in a sense, a family birthday, a reason for a celebration that contributes to strengthening family ties. Students can compute famdays for their families
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 Fantastic Fractals  ThinkQuest 1997
All about fractals: including: fully interactive fractal tutorials, a gallery, landscapes, music, a reference desk and types of fractals, downloads, a fractal workshop (build your own fractals), a fractal challenge (test yourself  how much have you learned
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 Fascinating Folds: Origami
A premier supplier for Origami and the Paper Arts with books, papers, and related products. Online ordering of supplies is available. Origami and Paper Products for sale include books, papers, videos, CDs, related products (cards, bookmarks, tshirts),
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 Fermi Questions  Sheila Talamo
Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. Students often believe that "word problems" have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage
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 The Fibonacci Numbers, Pineapples, Sunflowers, and the Golden Mean  Don Cohen (The Mathman)
Mathematics from a Pineapple: Infinite sequences, limit of a sequence, ratios, fractions, and decimals. Also Looking at a Regular Pentagon. Sample problems with some answers from Chapter 7 of Don Cohen's worksheet book.
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 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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 FifthGrade Empathy ... For Plants  William E. Ray; Kodak
Children were introduced to this project by taking them outside Pinoak Elementary School, Oil City, PA, in March and having each pair of them select a living
plant specimen. Buds were noticed as being a part of each plant and were the plant parts which
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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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 Financing Retirement Payments in the Future in Austria: Some Scenarios  Erich Neuwirth
An interactive spreadsheet to download for studying the effects of changing the retirement age. (Microsoft Excel 5.0 or higher must be installed on your computer.) The key number for judging the financiability of a retirement payment system is the ratio
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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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