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

3-D Drawing and Geometry - Cathi Sanders

A Math Forum Summer 1998 Institute project that uses examples of paintings, architecture, etc. to analyze different types of 3-D drawings, and teaches students how to create them. Careers in 3-D 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. more>>

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. Step-by-step instructions are provided, as well as figures, diagrams, and templates. more>>

Classification of Patterns - Brown-Herbst, Donnelly, Stratton, Anderson-Nielsen; The Geometry Center

Materials about symmetry and classification of repeating patterns for students in grades 7-10 using wallpaper patterns, to be used as either an introduction or a review: a classroom-ready source of information. A final project created for Math 5337, Technology in the Geometry Classroom, at the Geometry Center, University of Minnesota. more>>

Concurrency Points in a Triangle - Brakalova, Johnson, Scalzitti, Thornberry; The Geometry Center

An interactive Web-based 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. more>>

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 ball-and-stick, space-filling, wire-frame, 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. more>>

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. more>>

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. more>>

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. more>>

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 cross-section, 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 Borsuk-Ulam 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. more>>

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. more>>

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 distance-preserving transformations. This model of a Ferris wheel provides a good example. A step-by-step description of how to model a Ferris wheel using translations and animation in Sketchpad. more>>

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. more>>

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 problem-solving 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. more>>

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. more>>

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. more>>

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 problem-solving situations, and communicate the reasoning used in solving these problems. Key concepts include Infinity, Transfinite arithmetic, and One-to-one correspondence. more>>

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? more>>

How Many Ways Can a Team Win a 7-Game Series? - Kent Anderson; SCORE Mathematics

Students discover how many ways a team can win a 7-game 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. more>>

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. more>>

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. more>>

It's All Sewn Up! Grades 10-12 (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. more>>

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. more>>

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. more>>

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. more>>

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. more>>

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. more>>

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 non-spatial 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. more>>

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. more>>

The Most Colorful Math of All (MegaMath) - Nancy Casey; Los Alamos National Laboratory

Coloring is a profound mathematical topic with multi-million-dollar 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 hand-drawn maps, students can quickly find themselves grappling with the four-color map problem. Activities, Background Information, Evaluation. more>>

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. more>>

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. more>>

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. more>>

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. more>>

The Right Time: An Investigation of a Clock's Angles - Jon Basden, Highland Middle School

A two-period 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 problem-solving methods to solve the problem. They may wish to use a spreadsheet. more>>

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 step-by-step, 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). more>>

Scaling: Grades 7-10 (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. more>>

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. more>>

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. more>>

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. more>>

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. more>>

Taking Stock - Donlan, Post, Christman; Happy Valley School District, Santa Cruz, CA

A multi-grade 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. more>>

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. more>>

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." more>>

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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