Illuminations: Geometric Solids and Their Properties

# Geometric Solids and Their Properties

## Making A Shape Jacket

 Students identify which geometric solids can be made from given nets. Students also create nets for common geometric solids.

### Learning Objectives

 Students will: analyze characteristics and properties of three dimensional geometric shapes and develop mathematical arguments about geometric relationships use visualization, spatial reasoning, and geometric modeling to solve problems identify which geometric solids can be made from given nets create nets for common geometric solids

### Instructional Plan

Begin the lesson by asking students if they are familiar with shape jackets. Based upon their experiences in this unit, they should be able to identify what a shape jacket is.

Pose the following questions to students.

Look at these two jackets. Which solids do you think they match?

 Jacket number 1 Jacket number 2

The above images are available on the Shape Jackets overhead.

Students should recognize that both jackets form triangular pyramids.

Next, introduce the formal geometry terms. A jacket for a geometric solid that can be folded to create the surface of the solid is called a net. A net is a way of representing a polyhedron in two dimensions. (A net is a two-dimensional figure with indicated lines for folding that folds into a three-dimensional polyhedron.)

For this part of the activity, students should work with a partner. Look at the cube. Ask students to plan how they will make a net for a cube.

Students can use grid paper to make their nets. They should fold their nets to create a cube, making sure that an actual cube is formed.

Students should make nets for other solids, such as rectangular prisms, triangular prisms, and square pyramids.

### Assessment Options

 Students can use the Cube Nets Tool. Students click on a net to identify whether or not it will form a cube.

### Extensions

 Students can create nets for some of the more complex geometric solids, such as the octahedron, dodecahedron, icosahedron, and an irregular polyhedron.

### NCTM Standards and Expectations

 Geometry 3-5Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes. Build and draw geometric objects.
 Applet generously provided by L. O. Cannon, James Dorward, E. Robert Heal, and Richard Wellman (Utah State University, www.matti.usu.edu). The USU MATTI project is supported by the National Science Foundation (award number 9819107). Copyright 1999.

1 period

### NCTM Resources

Principles and Standards for School Mathematics

### Activities

 More and Better Mathematics for All Students
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