Technology Lesson Plan Competition

Elissa Biskner

Eastern Hills High School

Topic: Perspective Representation of Three-Dimensional Figures

Subject: Geometry

Grade: 10, 11

Timeline: 1 day; 45 minutes

Content Objective: Perspective Views of Solids

Essential Understanding:

The learner understands:

· A three-dimensional figure can be represented by a series of three two-dimensional drawings.

· Volume and surface area of a three-dimensional figure can be calculated from a series of two-dimensional drawings.

The learner will:

· Create a series of two-dimensional drawings to represent a three-dimensional figure.

· Utilize software in order to build a three-dimensional figure, and convert the 3-D figure to two dimensions.

Essential Question:

1. What is the minimum number of two-dimensional drawings needed to

accurately represent a three-dimensional figure?

2. Given these two-dimensional drawings, what/how much information do you

know about the three-dimensional figure?

TEKS Correlation: d(1)(c); e(2)(d)

TAKS Correlation: Objective 7

District Curriculum Alignment: Geometry; Third Six Weeks Overview

Materials/Resources: Snapcubes; Computers with internet access; Paper; Pencil

Pre-Requisite Knowledge/Vocabulary:

• Students should know the definition of faces, vertices, and edges.
• Students understand the difference between two-dimensional and three-dimensional
• Students know what volume and surface area are and the formulas to calculate them.

Activities/Process:

1. Obtain Snapcubes from instructor.

2. Use snapcubes to build a multi-level three-dimensional figure. You must use at least 10 cubes but no more than 20 cubes to build your figure.

3. Open the website http://illuminations.nctm.org

4. From the “View by Type of Content” choose Interactive Math Tools.

5. Scroll down and choose Isometric Drawing Tool.

6. Build your snapcube shap on the computer.

Hint: Refer to the directions if you are having trouble.

7. When you think you have built your shape successfully on the computer, click on the eye.

8. Rotate your figure by sliding the bars for the X-Y Rotation; Y-Z Rotation; X-Z Rotation. During and after these rotations, does the figure you built on the computer match the one you built by hand? If yes, go on to step #9. If no, close the rotation window, click on the eraser button twice, then go back to step #6 to try again.

9. On a piece of paper, draw your figure in two-dimensions from the three different perspectives: top, front, and side.

10. Click on the eye again, then click in the 3-D box. You should see three two-dimensional drawings. Do your drawings from step#9 match the computer’s two-dimensional drawings? If yes, go on to step #11. If no, what needs to be corrected in your drawings? Correct your drawings and move on to the next step.

11. Click in the plan box. What are the numbers in the squares representing?

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Real World Application:

• Architects and Engineers need to be able to represent three-dimensional figures on paper. The plans for a three-dimensional figure are drawn by a series of two-dimensional drawings for the builders to read and interpret.
• Builders must be able to interpret and translate two-dimensional drawings into a three-dimensional structure.

Correlated Web Sites: http://illuminations.nctm.org

Enrichment Activity:

1. Find the volume and surface area of your snapcube figure.

2. Explain how you found the volume and surface area of the figure.

3. Switch computers with a friend. Looking only at the 2-D drawings and plan, try to build your friends figure.

4. Calculate the volume and surface area of your friends figure.

5. Can you calculate volume and surface area using only two-dimensional drawings from the three perspectives? Explain why or why not.