Illuminations: Using Cubes and Isometric Drawings

Using Cubes and Isometric Drawings

Do They Match?

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.

Learning Objectives
 
Students will:
  • Construct three dimensional figures
  • Determine when two isometric drawings can represent the same shape
  • Determine what possible shapes might have the same isometric drawing
  • Explain their reasoning

Materials
 

Instructional Plan

Task 1

In this task, students will determine when two isometric drawings can represent the same shape.

Project the following images for the students to see:

A.
B.
C.

Below you will find a PDF which you can project or make into a color overhead transparency.

Do They Match? Image Do They Match? Image

Students should do the following:

  1. Predict which pairs could be drawings of the same object.
  2. Draw the figures using the Isometric Drawing Tool.
  3. Use the View tool and rotation controls. Determine whether or not their predictions were correct.
  4. For the pairs that could represent the same object, list the Rotation Control values they used to verify their answers.
  5. For the pairs that could not represent the same object, explain why.

Students can work in pairs to create isometric drawings and three dimensional figures for their partner to repeat the above steps.

Task 2

In this task, students explore what possible shapes might have the same isometric drawing.

Using the Isometric Drawing Tool, students should build the following figure:

Ask students how many cubes appear to be in the blue shape. Students can use the View tool to explore different perspectives of this figure.

Next, students should open another applet (by pressing Ctrl+N) to create the same shape, except that one of the top cubes will be missing. Students can compare the views of both of their figures. What do they notice about the isometric drawings for each? Can they build two more shapes that have the same isometric representation?

Students can work with their partners to repeat this task as needed.

Questions for Students
 
(Possible solutions are shown in italics.)
  • What strategies do you use to tell if two drawings can represent the same object? (Using different views to look at the drawing from different perspectives)
  • When is it difficult to decide if two drawings can represent the same object? (If you only have one perspective or view from which to see the object)
  • Thinking about Task 2 from today's lesson, what can you say about the possible shapes that have the blue isometric drawing as a possibility? Is there a minimum number of cubes in the shape? a maximum number of cubes? (4 is the minimum; 8 is the maximum)
  • What additional information might you provide to specify a particular shape? (any "gaps"; orientation or proximity of the cubes, etc.)
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

 Activities
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