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Lesson Plan
Science and Mathematics Initiative for Learning Enhancement (SMILE)

Smile: Polyhedrons

For Teachers 9th - 10th Standards
This in-depth paper examines the idea of convexity. Euclid's Elements, the first geometry textbook, assumed convexity without mentioning the term.
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Activity
Wolfram Research

Wolfram Math World: Space Filling Polyhedron

For Students 9th - 10th Standards
This MathWorld site shows pictures of polyhedra which can fill space. A discussion of these figures follows.
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Handout
University of Georgia

University of Georgia: Inter Math: Platonic Solids

For Students 9th - 10th
This site gives a description of platonic solids along with a visual representation of each of the five platonic solids. At the bottom of the page are links to cut-out-templates for each of the platonic solids. Be sure to follow the...
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Activity
University of Cambridge

University of Cambridge: Nrich: Skeleton Shapes

For Students 3rd - 8th Standards
At this one page website a variety of polyhedra are shown. The challenge is to create the skeleton for each polyhedron and identify the needed materials. You can check your solution right at the website.
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Whiteboard
ClassFlow

Class Flow: Three Dimensional Figures

For Teachers 6th - 8th Standards
[Free Registration/Login Required] This flipchart describes the characteristics of polyhedrons and asks students to classify figures according to the number of vertices, faces, and bases of the figures.
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Activity
National Council of Teachers of Mathematics

The Math Forum: Polyhedra Nets Paper

For Students 9th - 10th Standards
Contains six examples of polyhedra nets (cube, tetrahedron, octahedron, dodecahedron, icosahedron, cubosctahedron).
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Handout
CK-12 Foundation

Ck 12: Geometry: Polyhedra Study Guide

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] This study guide reviews how to classify polyhedra, Euler's formula, and regular polyhedra.
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Activity
University of Saskatchewan (Canada)

University of Saskatchewan: Geometry

For Students 9th - 10th Standards
The University of Saskatchewan's Department of Mathematics and Statistics provides high school students with online tutorials and exercises on what they deem some of the most important topics in geometry: Triangles, and Circles and Other...
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Website
University of Wisconsin

University of Wisconsin: Exploring the Nanoworld: Teaching Modules

For Teachers 9th - 10th
A collection of lesson plans and student handouts on teaching students about the "nanoworld."
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Handout
National Council of Teachers of Mathematics

The Math Forum: Ask Dr. Math: Faq, Geometric Figures

For Students 9th - 10th Standards
This page brings you to a table of contents of three-dimensional figures. Selecting a figure will bring you to a page defining and illustrating the figure with applicable formulas listed.
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Handout
Cool Math

Coolmath: Coolmath4kids: Polyhedra Gallery

For Students 9th - 10th Standards
A gallery of complex polyhedra with descriptions and characteristics.
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Unit Plan
Cuemath

Cuemath: Platonic Solids

For Students 9th - 10th
Learn more about platonic sold geometry, understand the platonic solid names, view some solved examples, and try your hand at some interactive problems.
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Unit Plan
Cuemath

Cuemath: Square Pyramid

For Students 9th - 10th Standards
A comprehensive guide for learning all about square pyramids with definitions, properties, examples, and practice questions.
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Unit Plan
Cuemath

Cuemath: Tetrahedron

For Students 9th - 10th Standards
A comprehensive guide for learning all about tetrahedrons with definitions, properties, formulas, examples, and practice questions.
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Unit Plan
Cuemath

Cuemath: Prism

For Students 9th - 10th Standards
Explore the world of prisms in this mini-lesson by learning what are prisms, definitions with shapes and examples, the difference between regular, irregular, right, and oblique prisms, the surface area of a prism, and the volume of a...
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Lesson Plan
PBS

Wnet: Thirteen: Ed Online: Virtual Polyhedra

For Teachers 9th - 10th Standards
Students explore polyhedron's through technology and paper/ pencil constructions.
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eBook
Mathigon

Mathigon: Geometry: Polygons and Polyhedra: More on Polyhedra

For Students 9th - 10th Standards
This lesson focuses on polyhedra other than the platonic solids; these include an Archimedean solid, a polyhedron made up of different kinds of regular polygons, that looks the same from every direction. There are 13 different...
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eBook
Mathigon

Mathigon: Geometry: Polygons and Polyhedra: Platonic Solids

For Students 9th - 10th
A Platonic solid is a polyhedron made up of only one kind of regular polygon, that looks the same from every direction. (In other words, the same number of faces meet at every vertex.) There are only five different Platonic solids:...
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Study Guide
Oswego City School District

Regents Exam Prep Center: Platonic Solids

For Students 9th - 10th
Did you know that the five regular platonic solids (tetrahedron, octahedron, icosahedron, cube, and dodecahedron) were thought to represent earth, air, fire, water, and the universe? This chart shows an image and provides a description...
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Handout
Oswego City School District

Regents Exam Prep Center: Pyramids

For Teachers 9th - 10th
What is a pyramid? Find a definition, example images, and formulas for finding the volume and surface area of a pyramid if given base and height measurements. Includes a very brief look at a pyramid in Egypt and its measurements.
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Graphic
Other

Showroom: All Uniform Polyhedra

For Students 9th - 10th
This site has pictures and information on many different types of polyhedra.
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Instructional Video
Khan Academy

Khan Academy: Intro to Nets of Polyhedra

For Students 4th - 6th Standards
Learn about the nets that represent 3D solids. [6:48]
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Activity
Annenberg Foundation

Annenberg Learner: Geometry 3 D Shapes: Platonic Solids

For Students 9th - 10th Standards
Learn about platonic solids, a special type of polyhedra. Read a definition, make three-dimensional models using printouts, and play with an interactive animation, which will show you the faces, vertices, and edges on platonic solids:...
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Activity
Varsity Tutors

Varsity Tutors: Hotmath: Graphing Calculator Practice Problems Areas and Volumes

For Students 9th - 10th Standards
Practice using your graphing calculator for area and volume problems. If you get stumped or if you would like to check your work, then select the View Solution button, which is located directly under each problem.

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