Illuminations: Spatial Reasoning Using Cubes and Isometric Drawings: Part One -- Exploring the Isometric Drawing Tool

Spatial Reasoning Using Cubes and Isometric Drawings: Part One -- Exploring the Isometric Drawing Tool


Building A Shape

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

One way to draw 3D (three dimensional) objects is to use a triangle grid called an isometric grid.

Activity: Building A Shape

1. Think about how you would build the figure shown using real cubes.

How many cubes are required?

2. Now use the drawing tool below to "build" the figure.

Click on the CUBE button and click the mouse where you would like a new cube.

Start from the back and work your way forward.

How many cubes did you use to build the figure?

Hint: Use the SELECT button to move cubes around so that you can count all the cubes.

[Instructions]

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. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
  
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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