# ACOS Objective 8

Recognize geometric relationships among two=dimensional and three-dimensional objects.
• Drawing geometric figures when given specified components, including base and height
• Investigating properties and relationships among congruent figures
• Identifying geometric ideas in settings outside the mathematics classroom
• Using networks to represent and solve problems

ARMT Possible Points = 6 (MC, OE)
• The drawings of two-dimensional and three-dimensional figures may be included.
• The drawings of two-dimensional figures may be on a grid.
• A two-dimensional figure may be compared to the same two-dimensional figure, a different two-dimensional figure, or a three-dimensional figure.
• A three-dimensional figure may be compared to the same three-dimensional figure, a different three-dimensional figure, or a two-dimensional figure.

Sample problems from Item Specs

Teachers' Labs
This site from the Annenberg Channel provides teachers with a deeper understanding of geometry concepts. This lab divides activities into two broad categories. Activities about shape center on identifying properties of various shapes and measuring their dimensions (symmetry, coordinates, and proportion) . Activities about space focus on moving objects—or yourself—around in your imagination, and visualizing how things will look.

Webquest: It's All Greek to Me

Are you ready for some time travel? You've been selected to join us on an adventure through the ages, back to the time of the ancient Greeks. Along the way, you'll research the life and mathematical discoveries of Pythagoras. You'll also explore many three-dimensional solids known to the ancient Greeks and construct one of your own. Our time machine will be leaving soon, so pack your geometry tool kit and prepare to meet a geometry giant!

Greek Challenge 1:
First, write a short report on Pythagoras and the Pythagorean Theorem.
Greek Challenge 2:
Second, investigate and write a report on the platonic solids known to the Greeks.
Greek Challenge 3:
Third, create a presentation that includes both of your reports and a three-dimensional model of at least one platonic solid.
Math Content:real-life applications of geometry, Pythagorean Theorem, three-dimensional solids, symmetry
Technology Skills: research, Web page, PowerPoint® presentation, newspaper/magazine article, poster, or video.
Interdisciplinary: Language arts (writing a report), History (ancient Greece)

JavaGami is a free downloadable software environment for designing and building paper sculpture. Choose for a number of starting polyhedra, which appear in a 3D window alongside a corresponding "folding net" in a 2D window. Employ both built-in features and the embedded programming language to customize the polyhedron, stretching or shrinking the polyhedron along its axes, truncating it at vertices, or adding pyramidal caps to faces. After the user customizes the new shape, the software attempts to generate a folding net for it, and offers a variety of paint tools to decorate the folding net.

I need to print the documentation.

Fractals - An Introduction

The History of Tangrams
This PowerPoint was shared by someone at AMSTI 2007.