 Adventures in Statistics  Scavo, Petraroja
A Web unit preprint of a paper by teachers Tom Scavo and Byron Petraroja that describes a mathematics project involving fifth grade students and the area of classrooms, including measurement, graphing, computation, data analysis, and presentation of results; to appear in "Teaching Children Mathematics".
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 Algebra  Fun with Calendars  Cynthia Lanius
Take any calendar. Tell a friend to choose 4 days that form a square. If your friend tells you only the sum of the four days, you can tell her what the four days are. How does the puzzle work? Includes a extension page for designing your own puzzle, teachers notes, and links to calendar pages on the Web. Mathematics topics: assigning variables, solving simple linear equations, factoring.
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 Bricks Activity  Suzanne Alejandre
A classroom activity (also called the Masonry Problem; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored through manipulatives (dominoes). Students explore different possibilities of making brick walls with and without fault lines, using diagram, process, and solution in their problem solving. A teacher lesson plan is provided.
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 Classification of Patterns  BrownHerbst, Donnelly, Stratton, AndersonNielsen; The Geometry Center
Materials about symmetry and classification of repeating patterns for students in grades 710 using wallpaper patterns, to be used as either an introduction or a review: a classroomready source of information. A final project created for Math 5337, Technology in the Geometry Classroom, at the Geometry Center, University of Minnesota.
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 Does the Number e have Special Meaning?  Spencer, Chan; Univ. of Toronto Mathematics Network
Answers, explanations, and expositions of the question, Does the number e have any real physical meaning, or is it just a mathematical convenience? Addresses the topics: Simple and Compound Interest; A Physical Meaning for the Number e; The General Situation; The Number e as a Limit; and The Number e in Calculus.
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 Dominoes Activity  Suzanne Alejandre
A classroom activity (similar to Pentomino + 1 = Hexomino; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored through manipulatives (paper dominoes). Students explore whether it is possible to cover a 6x5 grid with 15 dominoes, then build a variety of "brick walls" and create a brick wall catalogue. A simple freeware program (Macintosh only) by Kurt Kaufman can be used very easily to model this problem. Links to related pentomino and Fibonacci sites on the Web and a teacher lesson plan are provided.
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 EggMath  Bradlow, Sullivan, Levy, UIUC
A collection of modules (including many interactive applets) for K12 classrooms, based on the theme of eggs. Topics include: the shape of an egg (addressing symmetry and crosssection, surfaces of revolution, pin and string construction of ellipses, Cartesian and Cassini Ovals), the White/Yolk Theorem (how any two regions of the plane can be equally divided  a specific case of the BorsukUlam Theorem, with a proof of the Theorem included), spherical geometry, and embryo calculus (exponential growth and the number e). Each module offers interactive Java components and additional references. Part of the Chickscope project at the Beckman Institute. Also available at http://new.math.uiuc.edu/eggmath/.
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 Fractals: Definition & Activities  Suzanne Alejandre
A Math Forum Web Unit. Includes definitions and descriptions of fractals, links to pages on the Sierpinski triangle, the Koch edge, the Peano curve, the Lorenz attractor, and the Dragon curve; and more links to fractal sites on the Web.
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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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 The Golden Ratio  Blacker, Polanski, Schwach; The Geometry Center
Introduction to the Golden Ratio and Fibonacci Sequence. Instead of simply supplying definitions and asking the student to engage in mindless practice, students work through several activities to discover the applications of the Golden Ratio and Fibonacci Sequence. With Geometer's Sketchpad activities. A final project created for Math 5337, Technology in the Geometry Classroom, at the Geometry Center, University of Minnesota.
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 The Hand Squeeze: A Data Collection and Analysis Class Experiment  Cynthia Lanius
An experiment: measuring the amount of time that it takes for a hand squeeze to pass around a circle. Record, graph, and analyze the data, and make predictions about the time it would take for more people/greater distances.
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 Hotel Infinity (MegaMath)  Nancy Casey; Los Alamos National Laboratory
Will a hotel with an infinite number of rooms always have a vacancy? Students develop number sense, use numbers and number relationships in problemsolving situations, and communicate the reasoning used in solving these problems. Key concepts include Infinity, Transfinite arithmetic, and Onetoone correspondence.
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 Introduction to Fractions for Primary Students  Varnelle Moore
A Web unit designed to introduce young children (K2) to beginning concepts in fractions: equal parts, divide and shade, parts to whole, and writing fractions. Each lesson includes an interactive, manipulativebased project, technology, paper/pencil practice, and literature connections. Helpful links and teacher support extension ideas are also provided including alignment to NCTM Standards.
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 Introduction to Measurement for Primary Students  Varnelle Moore
A Web unit designed designed to engage young children in a series of activities where they measure and describe the attributes of integer bars: building houses, short vs. tall, designing bridges, measuring using integer bars. Each lesson includes an interactive, manipulativebased project, technology, paper/pencil practice, and literature connections. Helpful links and teacher support extension ideas are also provided.
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 Locker Problem  Suzanne Alejandre
A classroom activity (also called 1000 Lockers) aligned to the NCTM and California Standards, to be explored through the use of manipulatives and a ClarisWorks spreadsheet. Students then look for patterns and write the answer algebraically. The problem: imagine you are at a school that still has student lockers. There are 1000 lockers, all shut and unlocked, and 1000 students. Suppose the first student goes along the row and opens every other locker. The second student then goes along and shuts every other locker beginning with number 2. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.) The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this continues until the thousand students have followed the pattern with the thousand lockers. At the end, which lockers will be open and which will be closed? Why? A teacher lesson plan is provided.
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 Machines That Eat Your Words (MegaMath)  Nancy Casey; Los Alamos National Laboratory
An introduction to the concept of finite state machines, and how they are used to design computer systems that will recognize patterns. A finite state machine is an imaginary (or abstract) machine that is used to study and design systems that recognize and identify patterns. The idea of a finite state machine is a powerful one that has many applications in computer science. Mathematics as Problem Solving, Mathematics as Communication, Mathematics as Reasoning, and Mathematical Connections are critical items throughout the NCTM Standards. They appear at every level because they form the core of what it means to do mathematics.
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 Magic Squares: Math, History, Geography  Suzanne Alejandre
Designed primarily for middle school and older elementary school students, this Math Forum Web unit includes classroom activities for four different squares: Lo Shu, Sator, Dürer, and Franklin, three of them demonstrating increasing complexity using numbers, and one made up of letters, with number and symmetry questions and links and suggestions for history / geography / writing activities for teachers interested in interdisciplinary work. Includes directions for building magic squares, definitions, discussion of some special properties of magic squares, a Java applet, and links to other magic square Web sites.
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 Mathematics of Cartography  Cynthia Lanius
A map is a set of points, lines, and areas all defined both by position with reference to a coordinate system and by nonspatial attributes. These pages discuss how maps are used, give examples of different kinds of maps, and cover map history and math topics  lines, points, areas, coordinates, etc., in particular scale, coordinate systems, and projection. Also Problems, Resources, Careers in mapmaking, Teachers' Notes, and References.
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 The Million $ Mission  Cynthia Lanius
You have your choice of two payment options on your new job: 1. One cent on the first day, two cents on the second day, and double your salary every day thereafter for the thirty days; or 2. Exactly $1,000,000. (That's one million dollars!) What's the best choice? Includes pages on exponential growth and patterns, links to exponentials on the Web, questions, and teachers notes.
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 No Matter What Shape Your Fractions Are In  Cynthia Lanius
Students explore geometric models of fractions and discover relations among them, reinforcing their knowledge of fractions by using online pattern block activities. The lessons are designed for students to work independently or with guidance from the teacher. Lessons should be printed so students can draw and color the appropriate shapes. Teachers notes are included.
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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; carry out interactive investigations in JavaScript or the Geometer's Sketchpad, and explore this famous triangle through lesson plans that feature questions, answers, discussion, and student worksheets.
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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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 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 materials on the Internet. Recognizing that math curricula for students in these grades is most often built around the manipulation of tools such as pencils, compasses, and rulers, the designers of this site have endeavored to teach the same concepts without relying on the physical acuity of the student. Activities involve finding the shortest path between two cities or how many people can board your plane, flying a herd of buffalo to the prairies, learning to fly a rescue helicopter and how planes lift, knowing when an overcast sky is really overcast, flying a kite, and planning a flight around the country. Teachers are invited to register their classes.
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 Rectangle Pattern Challenges  Cynthia Lanius
Examine different stges of rectangle patterns, and describe what you must do to get from one to the next. Observe the designs looking for patterns. Use the symmetry of the design to help you count. Organize your information into a table. On square grid paper create your own design, showing at least 3 stages. It must have at least two lines of symmetry, and it must follow a regular numerical growth pattern. On a separate sheet of paper, fill in the calculations in a table like the one shown. Teachers notes are included.
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 River Crossing (Math Exploration Quilt)  Rik Littlefield; Hanford School
You want to cross a river to reach a point exactly opposite where you are currently standing. Explore this problem stepbystep, encountering the following basic ideas: 1) Pythagorean theorem; 2) time = distance / speed; 3) distance = time * speed; 4) sums and differences of distances; and 5) the arcsine function for right triangles (which we didn't really need to solve the problem, just to get the angle expressed in a familiar way).
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 TableTop Earthquakes  John C. Lahr
A demonstration of seismology for middleschool teachers and students that can be used to augment lessons in earth science (faulting, elastic rebound, plate motions), physics (forms of energy, elasticity, friction, magnetism, waves), math (graphing, logarithms, probability), social studies (hazard mitigation), and geography (global distribution of earthquakes).
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 Traffic Jam Activity  Suzanne Alejandre
A classroom activity (also called Hop, Skip, Jump) aligned to the NCTM and California Standards, to be explored through large movement experience, manipulatives, and an interactive Java applet. Students then revisit the activity, look for patterns, and write the answer algebraically. The activity: there are seven stepping stones and six people. On the three lefthand stones, facing the center, stand three of the people. The other three people stand on the three righthand stones, also facing the center. The center stone is not occupied. Everyone must move so that the people originally standing on the righthand stepping stones are on the lefthand stones, and those originally standing on the lefthand stepping stones are on the righthand stones, with the center stone again unoccupied. A teacher lesson plan is provided.
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 The Twelve Days of Christmas and Pascal's Triangle  Judy Brown, DIMACS and The Math Forum
A lesson in which, using Pascal's triangle, students find the number of items given each day in the song, "The 12 Days of Christmas."
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 The Twelve Days of Christmas  Judy Brown, DIMACS and The Math Forum
A lesson in which students find the number of items given each day in the song, "The 12 Days of Christmas." This project is designed to be used as a warmup activity during the 12 days preceding Christmas.
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 UBUYACAR  Maricopa Center for Learning and Instruction
An online problembased learning manual for students that poses the question: "You are interested in purchasing a new vehicle. What should your annual salary be to afford the car you want?" Students move through a problemsolving process. A Tutor's Manual coaches the teacher in his or her role as facilitator. The manuals are also available in PDF format. Part of Maricopa Community College's Problem Based Learning (PBL) site.
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