## Exploring the Isometric Drawing Tool

• Lesson
6-8
1

Students explore using the isometric drawing tool and gain practice and experience in manipulating drawings.

This lesson, and the other lessons in this unit, use the Isometric Drawing Tool. Before using this lesson with your students, be sure to familiarize yourself with this tool and all of its features.

 Isometric Drawing Tool

To begin this lesson, ask students if they are familiar with isometric grids or isometric dot paper. (Some students may have also heard this paper referred to as "hexagonal grid paper.") If some students know what this paper is, allow them to share with their classmates. Then, ask when the paper is used. Students may express that the paper is used to draw three-dimensional objects, such as cubes.

Distribute a sheet of Isometric Dot Paper to each student, and place a transparency of one of these sheets on the overhead projector. Show students how this paper can be used to draw a cube by connecting some of the dots. (You may also want to shade one or two of the sides, to add perspective.) Ask students to create an object of their own by connecting some of the dots on their own. Tell them that their drawing should not just randomly connect dots; instead, it should represent a 3‑D object that could be built.

 Isometric Dot Paper

Tell students to open the Isometric Drawing Tool on their computers. For this lesson, students should work individually. (Alternatively, pair students so that they may share a computer; however, putting students into groups of three or more may impede student learning and should be avoided, if possible.)

Allow students time to explore the various features of the drawing tool. Give them a chance to practice building shapes. Encourage students to experiment with the various features and read through the Instructions. (In fact, you may wish to print the instructions, display them on the overhead projector, and walk students through the features of the tool step-by-step.)

Once students have become familiar with the tool, ask them to create the following figure on their screens. (Give them the following hint: Build the figure from front to back and from top to bottom, to assure proper alignment of the cubes.) It is important to tell students that the figure consists of eight red cubes below two blue cubes.

 When all students have built this figure, have them press the View button (the "eye").

This will open a separate window that allows students to rotate the figure in three dimensions. (Note that this new window may appear hidden below the current browser window, and therefore may not be visible to students. Students can bring the View window to the front by clicking on the icon in the taskbar at the bottom of the screen; or, they can minimize all of the other windows that are currently open.)

The best way to deal with the View window, however, is to reduce the size of the window in which the Isometric Drawing Tool appears. Then, place the View window to the right of the Isometric Drawing Tool window. This will allow students to work with both views visible simultaneously. When the windows are appropriately resized, students' computer screens should look something like this:

To ensure that all students understand how the tool works, ask them to build a figure that meets the follow requirements:

• The figure must have more than five cubes.
• Use at least two different colors.
• Some cubes should be hidden behind or below other cubes.

Allow students time to create their three-dimensional figures. Once they have completed their constructions, they can compare their figures with those of the students near them. There should be multiple solutions based on the requirements, and this is a good time for students to share their ideas with the class.

Students should practice moving the cubes around so they can count all of the cubes used to create the three-dimensional figure, especially those that are stacked or hidden. This can be done by using the Arrow to select and drag some cubes; alternatively, students can use the Unit Movement buttons:

 Arrow Button Unit Movement Buttons

As a task for students, require them to move the figures back to their original positions. That is, have them use the Unit Movement buttons to practice aligning the cubes. (As students proceed through this activity, they may become frustrated. To alleviate this frustration, require them to have the View window open side-by-side with the Isometric Drawing Tool; that way, they will be able to see the exact result of each move.)

If time permits, students may create additional shapes. Or, if students master the Isometric Drawing Tool quickly, you might consider moving directly to the next lesson in this unit.

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Questions for Students

1. What is one set of Rotation Control features that rotates the shape to another isometric view?

[X-Y Rotation, Y-Z Rotation, or X-Z Rotation.]

2. What features of isometric drawings did you use to decide the object had been sufficiently rotated?

[The values of each of the rotation control features indicate how far the object had been rotated. 3. Additionally, students can determine the proper rotation by inspection; that is, if they can see what they need to see, then the figure has been sufficiently rotated.]

### Finding Surface Area and Volume

6-8
Using the isometric drawing tool, students build three-dimensional figures and find the surface area and volume of each figure.

### Building Using the Front-Right-Top View

6-8
Students explore drawing the front-right-top view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the front-right-top view.

### Using Cubes and Isometric Drawings: Mat Plans

6-8
Students explore drawing a mat plan when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the mat plan.

### Do They Match?

6-8
Using three dimensional figures they have constructed, students determine when two isometric drawings can represent the same shape and explain their reasoning. Students will also determine what possible shapes might have the same isometric drawing and explain their reasoning.

### Are They Possible?

6-8
Students examine some isometric drawings that seem to be impossible and investigate one way Escher used to create these "impossible" figures.

### Learning Objectives

Students will:

• Explore and practice using the isometric drawing tool
• Explore polyhedra using different representations and perspectives