Illuminations: Spatial Reasoning Using Cubes and Isometric Drawings: Part Two -- Solid to Isometric -- One to Many

Spatial Reasoning Using Cubes and Isometric Drawings: Part Two -- Solid to Isometric -- One to Many

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

When is a cube not a cube?

In this interactive geometry investigation students will explore polyhedra using different representations and perspectives for three dimensional block figures.

Learning Objectives

Students will

Analyze characteristics and properties of three dimensional geometric shapes and develop mathematical arguments about geometric relationships
Use visualization, spatial reasoning, and geometric modeling to solve problems

Materials

Computer and Internet connection

Instructional Plan

In Activity 2, we explored strategies for deciding when two isometric drawings could represent the same shape. This investigation will explore what possible shapes might have the same isometric drawing.

Complete the questions in the following three tasks.

Task 1: In the drawing tool window below, use the View Tool "3D" feature to find a view of the image that looks just like the one to the right.

1. How many cubes appear to be in the blue shape?

2. How many cubes are in the shape below?

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Task 2:

Use the button below to see another possible shape. As in Activity 1, use the View Tool to match the drawing to the cube above.

3. How many cubes are in this shape?

Task 3:

Look at the following isometric drawing.

4. How many cubes do you actually see in this drawing?

5. Click on the button below to see this object with the drawing tool.

Use the rotation controls to view the shape from other perspectives.

Count the actual number of cubes in this shape.

Teacher Reflection

1. Think about your answers to the three tasks.

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?

2. How do you decide what a given isometric drawing is supposed to represent?

3. What additional information might you provide to specify a particular shape?

NCTM Standards and Expectations

Geometry 6-8

Use coordinate geometry to represent and examine the properties of geometric shapes.
Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.
Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.


		1 period
		NCTM Resources Principles and Standards for School Mathematics


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