## Exploring the Isometric Drawing Tool

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 unit with your students, be sure to familiarize yourself with this tool and all of its features. Note that this tool is mobile, so students may use their tablets to access the 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. If no students have heard of this paper, share this information with them.

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.

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.)

Read through the instructions of the tool. (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.)

As a class, have each student create the following figure on their screens. (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 Inspect tab.

This will allow students to rotate the figure in three dimensions. Students' computer screens should look something like this:

Go through each function in the Create and Inspect mode. Use the sliders to move cubes such that hidden ones are shown. After the figure is put back together, use the rotation tool to also show cubes that are hidden.

Next, ask students to refer to their own isometric drawing they created at the beginning of the class. To ensure that students are familiar with the tool, ask students to modify their drawing such that:

• The figure has more than five cubes.
• The figure uses at least two different colors.
• The figure indicates that some cubes are hidden behind or below other cubes.

Now, have students try and replicate their drawings using the isometric drawing tool. Once they have completed their constructions, have them check the constructions of the student seated next to them. Ask students to make sure that their classmate's drawings satisfy all three requirements. There should be multiple solutions based on the requirements, and this is a good time for students to share their ideas with the class. Circulate the room and help guide students who have not met all the requirements. Students can use the Print button in the Inspect mode to share their constructions with the class. You can also collect this as a form of assessment.

As a task for students, ask them to shift 5 cubes in their classmate's construction. Require students to move their own figures back to their original positions. That is, have them use the x-Axis, y-Axis, and z-Axis Sliders to practice aligning the cubes. (As students proceed through this activity, they may become frustrated. To alleviate this frustration, have students look back at their sketch and also use the Inspect mode for comparison.)

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.

Assessment Options

1. Ask students to print out their isometric constructions & turn it in with their sketch. Compare the two to see if students were able to create their intended constructions.
2. Circulate the room to see how efficiently students can move the cubes back to their original position (after their classmate has moved 5 of their cubes). Take note of students who may need additional help in the next lesson.

Extensions

Rather than an extension, it is recommended that you move on to the next lesson in this unit, Do They Match?

Questions for Students

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

[x-Axis Rotation, y-Axis Rotation, or z-Axis Rotation sliders.]

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. 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.]

Teacher Reflection

• How did using technology change students' level of engagement?
• How would you modify this lesson for low-level and high-level achievers?
• What other tasks could be done as a form of assessment or extension?

### Using Cubes and Isometric Drawings

6-8

Explore polyhedra using different representations and perspectives for three dimensional block figures.

### 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.

### 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.