Illuminations: Geometric Solids and Their Properties

Geometric Solids and Their Properties

Getting to Know the Solids

 Students are introduced to some of the basic polyhedra. Students explore the shapes of the faces of these solids.

Learning Objectives

 Students will: analyze characteristics and properties of three dimensional geometric shapes name each of the faces of common geometric solids

Materials

 Geometric Solids Tool Various physical models of the geometric solids (optional)

Instructional Plan

Students should spend time spinning the geometric shapes below. They can see the controls to get to know the shapes. In a math journal or on a blank piece of paper, ask students to record what they discover about the shapes.

Each of the shapes is called a polyhedron, which means "many faces." (Note: Polyhedra is the plural form.)

Students may use the Geometric Solids Tool, which is identical to the following tool:

Instructions for Students

Choose a Shape:

• Click on the new shape button.

Rotate the Shape:

• Place the mouse pointer on the shape. Move the mouse while holding down the mouse button.

Color the Shape:

• Click on a color. Hold the Shift Key while clicking the mouse where you want to paint. You can paint a face, an edge or a corner.

Remove the Color:

• Click on the reset shape button.

See Through the Shape:

• Click the box by Transparent.

Change Shape Size:

• Use the mouse to move the blue lever.

Developing the Activity

It is expected that students will identify the solids as having flat sides and that they will say the first shape is made of pentagons, the second is made of lots of triangles, and the third is made of triangles but is different from shape 2, and so on.

They may tell you which is their favorite shape and why, and they may mention which shape is more familiar to them.

Be sure to have the students check the Transparent box so they can also view the shapes as transparent. Ask what information about the shapes they can see more easily in the transparent views.

It is very beneficial for students to work with solid models in becoming familiar with the properties of solids. If you have geoblocks or other geosolids, make them available to students.

Open-ended directions, such as, "See what you discover about the shapes. Share your discoveries with a friend," can be useful.

You can begin to derive some vocabulary from student dialogue. For example, a student might say, "There is a flat side." And the teacher could respond, "Yes, we call that flat side a face." The terms faces, edges, and corners are defined in the next lesson.

Questions for Students

 How are the shapes alike? [All have many sides. The sides are polygons. Three of the solids are made of triangles.] How are the shapes different? [The number of faces is different. The flat sides (faces) of one of the sames (the irregular polyhedron) are different shapes.] Find two shapes that are alike. Tell a friend about the two shapes. [Student responses may vary.] Find two different shapes. Explain how they are different. [Student responses may vary.]

Assessment Options

 Using the interactive geometry tool, students can rotate each shape to see all the faces. The suggested Questions for Students (above) are open-ended to allow for an assessment of students' knowledge of geometric vocabulary.

NCTM Standards and Expectations

 Geometry 3-5Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
 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

Activities

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