Suzanne's Mathematics Lessons

# Geometry

aligned to the NCTM Standards - Geometry: Grades 6-8
Bricks Activity
Classroom activity (also called the Masonry Problem; a variation on polyominoes) 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.

Cooperative group activity designed to reinforce the concept of area. Two examples of student work are available.

Chinese Tangram Puzzles (English version) || Rompecabezas 'Tangrams' Chinos (Spanish version)
In this activity from Frisbie Middle School's Multicultural Math Fair students solve puzzles using rotation, reflection and translation to fit all the pieces together.

Circle Designs
Includes some background on circles in Islamic cultures, and an activity exploring the geometry involved in some circle designs.

Crystals
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.

Nets of Crystals
Real World - Viewing Crystals
Systems of Crystals
Fractals
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.

Geometric Factoring
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.

Navajo Burntwater Designs (English version) || Diseños Navajo 'Burntwater' (Spanish version)
In this activity from Frisbie Middle School's Multicultural Math Fair students use translations and reflections to create symmetrical designs.

Paper Folding Activity
Students fold a sheet of paper (a manipulative) and also simulate folding using a javascript activity by Nathalie Sinclair (technology) to observe geometric relations. Students think about the angle measurements and the side measurements of the triangles in order to deduce the relations of the triangles. Ideas of similarity are investigated using both a manipulative and technology. Finally, students are asked to respond to questions in a paper/pencil activity.

Pirate Diamond Activity
Students use problem-solving strategies and then justify their reasoning: they pour using containers (manipulatives) and also simulate pouring using the ESCOT Runner software (technology) to determine whether they can produce eight units using only a six-unit container and a ten-unit container. After working through the first problem students are asked to respond to similar problems. Students explain one of those problems step-by-step in a paper/pencil activity.

Polyhedra in the Classroom
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.

Constructing Rectangular Prisms
HyperCard Animation
Paper Nets
Polyhedra Essay
Polyhedra on the Web
Polyhedra Speech
Using KaleidoTile
Regular Tessellations
A middle school lesson utilizing BoxerMath.com's Tessellation Tool Java applet to help students understand why equilateral triangles, squares, and regular hexagons tessellate regularly in the Euclidean plane.

A kinesthetic activity designed to develop group interaction and cooperation while working with constructing a large parallelogram, square, rectangle, rhombus and trapezoid using rope held by the participants.

Sonya's Symmetry (English version) || Simetría de Sonya (Spanish version)
In this activity from Frisbie Middle School's Multicultural Math Fair students use a manipulative to see and draw reflections.

Studying Mandelbrot Fractals
What is a fractal? A definition and a Java applet to help in exploring the Mandelbrot set, redrawing small areas to fill the fractal screen and noticing how the images compare. Also links to other sites with fractal information for middle-schoolers.

Studying Polyhedra
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.

Tangrams
An activity using tangrams to reinforce vocabulary of geometry. Links to other tangram sites included.

Tessellation Tutorials
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.

Four Types of Symmetry
Historical and Geographical Connections
Repeated Reflections
Regular Tessellations
Tessellate! - a Java applet written by the Shodor Organization
Tessellating - Using a Straightedge & Compass
Using Activity Pattern Blocks
What Is a Tessellation?
What Is a Tiling?
Using Kali (English version) || Usando Kali (Spanish version)
In this activity from Frisbie Middle School's Multicultural Math Fair students use an interactive 2D Euclidean symmetry pattern editor.

What is Area?
Collaborative group activity comparing area and perimeter using Hands-On Math software by Ventura Educational Systems but the ideas could be adapted to use with other software or a Java applet.

Back to Suzanne's Mathematics Lessons 2001