Illuminations: Spatial Reasoning Using Cubes & Isometric Drawings: Part 3 -- Other 2D Representations -- Front-Right-Top

Spatial Reasoning Using Cubes & Isometric Drawings: Part 3 -- Other 2D Representations -- Front-Right-Top


Building from the Front-Right-Top Views

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

Part Two explored isometric drawings as one way to represent a 3D shape. In this activity you will compare isometric drawing with another type of representation called a front-right-top view.

Below are some sets of FRT views. Click on the button below to use the drawing tool to try to construct isometric drawings that match each set of FRT views. Then copy each drawing onto isometric dot paper.

Hint: It might help to keep the FRT Tool open while you draw!

Teacher Reflection
 

1. Do you think the front-right-top representation contains all the same information as an isometric view?

2. In the previous activities you saw that sometimes two solids have the same FRT view but different isometric views.

Do you think it is possible for two solids to have the same isometric drawing, but different FRT views? If so, create an example using the drawing tool. If not, convince a partner why.

3. For what applications might a FRT view be more useful than an isometric view?

For what applications might an isometric view be more useful?

Explain your thinking in both cases.

NCTM Standards and Expectations
 
Geometry 6-8
  1. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.
  2. Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.
  3. 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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