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


Another View

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 this activity we will examine how an object has many different isometric drawings or views by rotating the shape. The isometric drawing tool lets you rotate your shape as if it were real.

A solid shape has already been constructed in the drawing tool for you. Click on the VIEW tool. Choose the "Rotation Controls" option and use the sliders to rotate the shape.

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

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

3. On isometric dot paper, record a new view of the shape.

You may find it useful to color one or more of the cubes to help you keep track of the shape.

Now Try This

1. Use the drawing tool to create your own shape. Make a drawing of your shape on isometric paper.

 

2. Imagine that you are on the side of your shape and another person is standing on the other side of the object.

What are the Rotation Control values that shows what the person might see?

Record these values with a drawing of this view on isometric dot paper.

3. If someone was lying down and looking up at your object from below, what do you think they would see?

Record these values with a drawing of this view on isometric dot paper.

4. How do values in #2 and #3 differ from the original values? You can use "Reset View" to get the original values.

NCTM Standards and Expectations
 
Geometry 6-8
  1. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.
  2. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.
  3. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
  4. Use coordinate geometry to represent and examine the properties of geometric shapes.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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