This list offers good places to begin looking for individual high school
lesson plans or materials on which to base them. For more sites, see our
page of
high school lesson plan collections, or
browse or search the Forum's
Internet Mathematics Library.
Selected High School Level Lessons
 3D Drawing and Geometry  Cathi Sanders
 A Math Forum Summer 1998 Institute project that uses examples of paintings, architecture, etc. to analyze different types of 3D drawings, and teaches students how to create them. Careers in 3D drawing that use these techniques, from architecture to movies, are also illustrated. Types include isometric, oblique, and perspective drawings. A drawing project for students is outlined and submissions are invited.
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 Building an Icosahedron as a Class Project  Frederick J. Wicklin
 A Teacher's Guide. This document describes how to build an icosahedron as a class project. The size is up to you. Stepbystep instructions are provided, as well as figures, diagrams, and templates.
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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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 Concurrency Points in a Triangle  Brakalova, Johnson, Scalzitti, Thornberry; The Geometry Center
 An interactive Webbased exploration designed to facilitate the teaching of triangle concurrency, both as an integral part of a geometry curriculum and as enrichment material. These pages can be used by individual students as a computer exploration, as classroom demonstration material, or as an alternative to a more traditional investigation of triangle congruency topics. Includes notes to students and teachers, and instructions for using the Geometer's Sketchpad in the activities. A final project created for Math 5337, Technology in the Geometry Classroom, at the Geometry Center, University of Minnesota.
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 Crystals:
Crystallography & Systems  Suzanne Alejandre
 A Math Forum Web Unit. Students studying polyhedra enjoy seeing the
structures as they occur in the real world. Crystalline structures can be
categorized into seven crystal systems: see photographs of beautiful
crystals or make paper models of crystals by printing out nets of crystals
and constructing the models. CrystalMaker software gives students experience
with ballandstick, spacefilling, wireframe, stick, dot surface cloud,
and polyhedral models of crystals. Also Java applets that show some of the
major forms for the hexoctahedralclass (symmetry 4/m3bar2/m) of crystals;
and links to Web sites about crystals.
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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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 Dueling Pinwheels  A Geometer's Sketchpad Activity  Cynthia Lanius
 Construction directions for rotations, translation, and reflection, with questions to explore and a demonstration sketch to download.
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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.
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 Euclid's Geometry: History and Practice  Alex Pearson, The Episcopal Academy, Merion, Pennsylvania
 A series of interdisciplinary lessons on Euclid's Elements, researched and written by a Classicist and hosted by the Math Forum. The material is organized into class work, short historical articles, assignments, essay questions, and a quiz.
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 Ferris Wheel  Jim King, University of Washington
 Physical devices can be modeled using dynamic geometry. A vital tool for moving objects around in the model are the isometries, or distancepreserving transformations. This model of a Ferris wheel provides a good example. A stepbystep description of how to model a Ferris wheel using translations and animation in Sketchpad.
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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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 Games on Graphs (MegaMath)  Nancy Casey; Los Alamos National Laboratory
 Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problemsolving situations and communicate the reasoning used in solving these problems. Graphs, stories and games provide scenarios for games that student can play on graphs. Also Three for the Money: The Degree/Diameter Problem, an unsolved problem for students to work on, and other games that can help students increase the range of possibility for games that they can invent on graphs. Big Ideas and Key Concepts include pages on Graphs; Properties of mathematical objects; Modeling; and Abstraction.
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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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 The Hot Tub: Interpreting Graphs  Cynthia Lanius
 Questions to answer about a graph... Notice the connection between the slope of the lines and the rate of change of the water depth. On what segments is the slope positive, and the water depth increasing? negative, and the water depth decreasing? On what segments is the slope 0, and the water depth is constant?
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 How Many Ways Can a Team Win a 7Game Series?  Kent Anderson; SCORE Mathematics
 Students discover how many ways a team can win a 7game series (NBA Finals, World Series, Stanley Cup) by accessing the Internet and then systematically constructing a sample space that lists all the possible ways. Aligned to the California State Standards. From the Schools of California Online Resources for Educators SCORE Mathematics Lessons.
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 If Only Nice Weather Could Last Year Round  Evan Glazer
 Students examine patterns and fluctuations in temperature data from cities around the United States, creating a model of the data to help predict the times during the year that these locations would be nice to visit.
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 It All Adds Up  A MayaQuest '96 Lesson Plan
 The Mayan mathematical system: base 20. Activities and discussion for primary and secondary grades, including converting from our base 10 to base 20, representing numbers in both systems and comparing length involved, and other discussion questions.
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 It's All Sewn Up! Grades 1012 (KQED/CELL)  Koistinen, LeBlanc; Math Online, KQED, San Francisco
 The clothing industry has grown tremendously in the last 25 years. In this lesson, students use the concept of linear inequalities and linear programming to maximize profit in the industry.
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 Just a Usual Day at Unusual School (MegaMath)  Nancy Casey; Los Alamos National Laboratory
 Students perform a play that takes place in a school where some of the students always lie and the rest always tell the truth. Terry, the protagonist, is trying to find out which students are which, but at the beginning, there is no way of knowing whom to believe. Can you figure out whom to believe in this play? With accompanying lesson plan and discussion questions.
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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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 Math, Baseball,
and the San Francisco Giants  Linda Uhrenholt; Pacific Bell Education
First
 By answering specific questions about travel expenses, food, tickets,
etc., students determine the cost of attending a Giants' game, the time it
would take to get there, etc. Guided questions and useful links to Internet
resources are provided for 15 activities, with concluding problems such as
itemizing your total expenses at the game, finding examples of math used in
baseball not touched on in the activities, and writing your own definition
of baseball.
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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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 The Most Colorful
Math of All (MegaMath)  Nancy Casey; Los Alamos National Laboratory
 Coloring is a profound mathematical topic with multimilliondollar
industrial applications. The problem presented here has been of interest to
mathematicians for over a hundred years. With a few crayons or markers and
some handdrawn maps, students can quickly find themselves grappling with
the fourcolor map problem. Activities,
Background Information, Evaluation.
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 New Ideas about
Knots  Nancy Casey
 Things Nancy Casey discovered after writing the basic MegaMath
information about knots.
Topics include: Tangled up pictures of tangled up ropes; Knot coloring
puzzles; Knots and counting; Pretzel knots.
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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 (Philadephia 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 Java script 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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 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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 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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 The Right Time: An Investigation of a Clock's Angles  Jon Basden, Highland Middle School
 A twoperiod lesson plan in which students think through the process of
determining how many times in a 24 hour period the hands of a clock will
form a right angle, drawing from a variety of problemsolving methods to
solve the problem. They may wish to use a spreadsheet.
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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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 Scaling: Grades
710 (KQED/CELL)  Koistinen, LeBlanc; Math Online, KQED, San Francisco
 In this lesson, students gain an understanding of the concept of
similarity as it applies to geometric shapes and solids, and extend their
understanding to other similar objects. They are introduced to the concept
of scaling, and ratio and proportion, and how it applies in many industries.
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 Soma Cube
Central  Jon Basden, Highland Middle School
 Students review the concepts of solid geometry, then try to determine
all of the ways that they can join no more than four cubes at their faces in
an irregular manner. The seven ways that one can join four or fewer cubes in
an irregular manner make up the pieces of the Soma Cube. After the students
discover the seven ways, they actually create Soma Cubes in class, exploring
geometric figures including cubes using the seven pieces, recording their
solutions, and trying to create their own puzzles.
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 Stressed Out:
Slope as Rate of Change  Cynthia Lanius
 It's the night of the big game. You're in the locker room. The coach is
pumping the team up. "Now, I know you people are nervous. That's okay, in
fact, that's what we want. You're going to perform better on the court
(stage) if you're a little nervous." Does the graph shown confirm what the
coach told you? Write a statement that describes performance as stress
increases... This lesson introduces basic knowledge and skills important to
a study of functions in algebra and lays the groundwork for calculus.
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 Studying
Polyhedra  Suzanne Alejandre
 What is a polyhedron? A definition and a Java applet to help in
exploring the five regular polyhedra to find how many faces and vertices
each has, and what polygons make up the faces. Also links to a page of
information about buckyballs,
stories written by students after studying polyhedra, other sites with
information about regular polyhedra, and other sites with information about
Greece and Greek mathematicians.
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 Survey Results 1999: LITES Data Collection Unit  Jon Basden, Highland Middle
School
 Students use scientific methodologies to analyze information about the
characteristics and preferences of the students in their class to make
predictions about the students in the other classes. After finishing the
research on the students in their own school, they use data gathered from
classes in online partner schools to conduct similar analyses, and draw
conclusions related to the geographic locations of those schools. Five
phases are provided, with links to sites on the Web for more ideas.
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 Taking Stock 
Donlan, Post, Christman; Happy Valley School District, Santa Cruz, CA
 A multigrade project focusing on the stock market with participants in
grades 5 through 12 from California to New York to Florida, including up to
50 schools per session (fall or spring) across the country. The integrated
thematic project begins with 6 activities and worksheets available for
downloading from the site: Understanding the Stock Page; Fractions of a
Dollar; Stock Symbols; Profit and Loss; Corporate Research; and Persuasive
Letters.
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 Tessellation
Tutorials  Suzanne Alejandre
 A series of tutorials that teach students how to tessellate (somewhat in
the style of the art of M.C. Escher) using HyperCard for black and white
and/or HyperStudio for color, ClarisWorks, LogoWriter, templates, or simple
straightedge and compass. The tessellation lessons include units
incorporating rotations and glide reflections, a section called "Where's the
Math" that elaborates on some underlying geometric principles, comments
contributed by others, and samples of
student work.
more>>
 Three for the
Money: The Degree/Diameter Problem (MegaMath)  Nancy Casey; Los Alamos
National Laboratory
 Students can understand and work on an unsolved problem in mathematics.
There is a good chance that this problem can be solved by someone who spends
enough time experimenting with it. The only skills required to work on it
are the ability to draw dots and connect them with lines, and the
understanding of four ideas related to graphs: degree, diameter, planarity,
and size. With ideas for discussion.
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 Tour of Symmetry
Groups  Lori Thomson; The Geometry Center
 A Web unit that covers Types of Symmetry (Translation, Reflection, Glide
Reflection, Halfturn, Combinations); Symmetry in Frieze Groups (Patterns,
Groups, Lengthwise and Crosswise Symmetry); Using Kali to Explore Frieze
Groups (with beginning and advanced exercises and pattern galleries); and
Symmetry in Wallpaper Groups.
more>>
 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.
more>>
 The Twelve Days
of Christmas  Judy Brown
 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.
more>>
 The Twelve Days
of Christmas and Pascal's Triangle  Judy Brown
 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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 Untangling the
Mathematics of Knots (MegaMath)  Nancy Casey; Los Alamos National
Laboratory
 Fundamentals of knot theory for a wide range of levels  a variety of
activities for exploring knots made from pieces of rope. Students can make
and verify observations about knots, classify them, combine them, and find
ways to determine if two knots are alike. The activities outlined here can
be combined to form a single lesson about mathematical knots, or a larger
investigative unit that extends over a longer period of time. Key concepts
include knot theory, topology, operations, and proof.
more>>
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