South Carolina ETV

South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

What a View! (Grades 4-6)

Master Teacher

Elizabeth Kelbaugh

Overview

This lesson will allow students to explore two- and three-dimensional geometric shapes, figures, and models and develop spatial sense by thinking about and representing geometric figures.

SC Math Standards Met

IV—Geometry and Spatial Sense

Strand B, C, and G

Learning Objectives

Students will:

be able to identify, describe, classify, and compare two- and three-dimensional geometric shapes, figures, and models according to their attributes
be able to identify different views of a three- dimensional object
develop spatial sense by thinking about and representing geometric figures

Materials

isometric dot paper
net drawings of several three-dimensional figures

ITV Series

Math Vantage: Spatial Sense Unit, "2D Visions in a 3D World"

Previewing Activities

Introduce the lesson by telling students that the lesson will deal with two- and three-dimensional figures. Ask, "What are the three dimensions?" (length, width, and depth)

If students have trouble naming them, show the first portion of the video with the narrator out- side in a large sculpture where she names them. Pause for a short discussion.

Focus for Viewing 1

To give students a specific responsibility while viewing, ask them to listen and look for techniques that help us make two-dimensional figures look like three-dimensional figures.

Viewing Activity 1

Start the video after the narrator is outside in a large sculpture. Pause after the train sequence when the narrator says, "Each car looks smaller than the car in front of it."

Ask students to name the techniques that help us make two-dimensional figures look like three- dimensional figures. (light, shadow, perspective, motion, and binocular vision) Lead a short discussion about these techniques.

Post-Viewing Activities 1

1. Engage students in a discussion about how math is used and how isometric drawings represent three-dimensional figures.

2. Have students practice isometric drawings on isometric dot paper.

3. After students complete Activity Sheet 1, in which they interpret isometric drawings, follow up with the next portion of the video lesson focusing on the use of point of view.

Focus for Viewing 2

To give students a specific responsibility while viewing, ask them to listen for an explanation of what makes up three-dimensional figures.

Viewing Activity 2

Restart and play the video through the segment featuring point of view. Pause after the different views of the can with the music, before the view of video games. Ask students, "What are three-dimensional figures made up of?" (shapes flattened into two-dimensional patterns called nets) "How does the shape of an object change as your point of view changes?"

Post-Viewing Activities 2

1. Engage students in a discussion about flattened two-dimensional patterns called nets and the different points of view.

2. Show students samples of nets and have them predict what three-dimensional figures they will make when put together.

3. Have students work in groups to cut out and put together nets to form models of several common three-dimensional figures.

Print out:

Activity 2A
Activity 2B
Activity 2C
Activity 2D

4. After students complete the activity, follow up with the next portion of the video lesson.

Focus for Viewing 3

To give students a specific responsibility while viewing, ask them to look for occupations and other activities that depend on interpretation of two-dimensional representations of our three-dimensional world.

Viewing Activity 3

Start the video with the video game racer. Stop after the ski divers. Ask students, "What occupations and other activities depend on interpretation of two-dimensional representations of our three-dimensional world?" (video games, computer-generated graphics, surgeon, air traffic controller, and ski divers)

Post-Viewing Activities 3

1. Engage students in a discussion about the importance of correctly interpreting two-dimensional representations.

Remind students of techniques that give clues, such as light, shadow, and perspective.

2. Have students write a news article or story about how interpretation of two-dimensional representations of our three-dimensional world affected someone.

Action Plan

1. Publish student stories and drawings in a class newspaper, class book, or on a Web page.

Extensions

1. Art: Investigate quilt design representing three-dimensional cubes that uses three colors of rhombi which form a hexagon (similar to isometric drawings). Have students make paper patterns or fabric quilt squares.

Additional Resources

"Pop Out Patterns" by Carol S. Gossett. AIMS Magazine (May/June 1995).
ITV Series: Math Vantage: Patterns Unit. The "Tessellations/Transformations" lesson has a segment on the three-dimensional cube in a quilt design.
"MATH Cube" activity by Dr. Evan M. Maletsky, Montclair State College (see Activity Sheet 3).

Activity Sheets (PDF)