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Math Forum Web Units and Lessons

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The World Wide Web opens interesting possibilities for educational materials through its combination of hypertext, interactivity, multimedia, and communication at a distance, particularly since users can construct their own Web contributions. The Math Forum is committed to being a resource built upon the activity of the teachers, students, and researchers who use it.

We have experimented with the use of the Web for instruction and with involving Forum users in the creation of materials for the Internet classroom. Here are some examples:

"Adventures in Statistics"
A preprint of a paper by teachers Tom Scavo and Byron Petraroja to appear in "Teaching Children Mathematics," which describes a mathematics project involving fifth grade students and the area of classrooms, including measurement, graphing, computation, data analysis, and presentation of results.

Algebra and Calculus via Sketchpad
Exploring equations for lines, parabolas, and tangents using the Geometer's Sketchpad. By Forum Teacher Associate Ruth Carver.

Building Models of Surfaces
The Forum is interested in the use of physical models as aids in understanding 3-Dimensional surfaces. Swarthmore College student Joan Hoffmann has created some how-to pages for building surfaces that appear in multi-variable calculus.

Chameleon Graphing
Two Web units by Ursula Whitcher, introducing The Coordinate Plane for elementary and middle school students, and Lines and Slope for middle and early high school students. With the help of Sam the Chameleon, learn to find points on a number line and graph points in the coordinate plane; then graph lines and learn to visualize slope with Sam's sister, Joan.

Exploring Data
Pages for finding and displaying data sets, designed to support workshops on statistics given by the Math Forum for the Urban Systemic Initiative. Included are: links by level to relevant statistics Standards; lesson plans for collecting, analyzing, and/or displaying data; sources of data sets, general information, courses, and statistics software on the Web; and an "Oceans of Data" page with a data set (diving records) to download, instructions for making a ClarisWorks or Excel graph, suggested questions for discussion, and related 'ocean links' (NOAA, SeaWifs, tide tables).

Factoring Through Geometry & Algebraic Factoring
A collection of lessons on factoring from Forum Teacher Associate Suzanne Alejandre. Using algebra tiles, students find a geometric basis for factoring and connect this to the familiar algebraic process. Also Designs With Circles: the geometry and harmony of circles.

Famous Problems in the History of Mathematics
History of mathematics presented through some famous problems, with exercises and their solutions. The problems include "The Bridges of Konigsberg", "Famous Paradoxes", and "The Problem of Points."

Geoboards in the Classroom
A unit for teachers from Tom Scavo that offers suggestions for using geoboards to explore the length and area of two-dimensional geometric figures. The Introduction includes pages that describe materials needed, offer discussion and activities for investigating length and area (in particular Pick's Theorem), and provide sample pages of dot paper to print out. Five lesson plans focus on lines, squares, rectangles, parallelograms, and right triangles, and a short bibliography rounds out the unit.

Geometry Through Art
Lesson ideas, facilitation suggestions, lists of materials needed, and handouts to photocopy. Artist/Educator Norman Shapiro focuses on the student as investigator, learning through doing, and using perception to stimulate the motivation for more developed concepts and language. Art is one of the intrinsically interesting applications of geometry and these pages provide a wonderful way in to this topic for children and adults alike.

Introduction to Vectors
Supplementary material to help students with their first encounter with vectors, and an experiment in the pedagogical possibilities of the WWW which allows nonlinear use of documents of all types, and of Geometer's Sketchpad, which has internal possibilities for unveiling, animating, and tabulating, in addition to its dynamic capabilities. From Gene Klotz, Director of the Math Forum.

An experiment in using the World Wide Web to illustrate the intuitive notion of limits in functions of two variables. Written by Gene Klotz and Swarthmore College student Ethan Magness.

Magic Squares
This unit by Forum Teacher Associate Suzanne Alejandre is designed for middle and older elementary school students, and includes classroom activities for four different squares: Lo Shu, Sator, Dürer, and Franklin, demonstrating number complexity and symmetry. Links and suggestions for history, geography, and writing activities for teachers interested in interdisciplinary work are included.

Math to Build On
Johnny and Margaret Hamilton's book covers much of the basic math used in the construction trades and gives us practice in its application. We offer a few sections to show some possibilities for alternative introductions to these fundamental concepts.

Pascal's Triangle
A Web unit designed to support workshops given by the Math Forum for the Urban Systemic Initiative. Read about the history of Pascal's triangle and learn to construct it; see 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.

Perspective Drawing, Moebius Strip, Polyhedra, and Spreadsheets
Mathematics and ... (art, things to make, spreadsheets) from Jan Garner.

Polyhedra in the Classroom
This unit by Suzanne Alejandre introduces the concepts of surface area and volume while focusing on the importance of measurement. Students calculate the surface area of a rectangular prism; name the characteristics (number of edges, faces, vertices, and the shape of the face) of 6 specific polyhedra (cube, tetrahedron, octahedron, dodecahedron, icosahedron, and cuboctahedron); demonstrate their understanding of the characteristics of polyhedra; and explore polyhedra in the real world through crystalline structures and 'buckyballs'. All objectives are coordinated with the NCTM Standards.

Primary Math Activities - Varnelle Moore
Lessons designed to engage young children in math activities. Interactive, manipulative-based projects, technology, paper/pencil practice, literature connections, and teacher support extension ideas are included in each unit. See Introduction to Geometry and Introduction to Measurement, with beginning concepts in geometry (describing shapes, making patterns, building shapes, rotational symmetry, and line symmetry), and Introduction to Fractions.

Regular Tessellations
Suzanne Alejandre at the Math Forum has developed a middle school lesson using's Tessellation Tool Java applet to help students understand why equilateral triangles, squares, and regular hexagons tessellate regularly in the Euclidean plane. In addition to alignment to NCTM Standards and a step-by-step guide, the Teacher Lesson Plan links to Math Forum resources such as: Information and Lessons, Problems of the Week, Teacher2Teacher, and Ask Dr. Math. A Student Page is also available.

Secondary Math Units
These pages by Margaret Sinclair provide units for grades 9-10: Data Collecting in the Classroom, Algebraic Problem-solving using Spreadsheets (a unit that emphasizes moving from numerical to symbolic representation), and a newspaper review unit on the Skydome; and grades 11-12: Three Days in the Lab (Sketchpad assignments for seniors when lab time is short); Linear Transformations using Spreadsheets; Show and Tell for Big Kids (investigating math using computers when you have limited lab time); and Investigating Functions Using Spreadsheets (with an emphasis on Microsoft Excel).

Tangent Planes
An experiment in using the World Wide Web to illustrate the intuitive notion of the tangent plane to a graph of a function of two variables. Written by Math Forum Director Gene Klotz and Swarthmore College student Ethan Magness.

A unit by teacher Tom Scavo for grades 4 through 6 that uses tangrams to compute the area of polygons without employing formulas. The terms 'congruent' and 'similar' are introduced, and students construct their own tangrams, find the areas of tangrams, and learn to calculate the area of any polygon constructed from tangrams.

Tessellation Tutorials
A series of tutorials by Forum Teacher Associate Suzanne Alejandre that teach students how to tessellate (somewhat in the style of M.C. Escher) using HyperCard or HyperStudio, ClarisWorks, LogoWriter, templates, or simple straightedge & compass. These tessellation lessons include units incorporating rotations and glide reflections, a section called "Where's the Math" that elaborates on some underlying geometric principles, Historical and Geographical Connections, comments contributed by others who have enjoyed using this tutorial, and samples of student work.

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