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


Mat Plans

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 you will compare isometric drawing with another type of representation, a mat plan. A mat plan is a top view of a solid, with the number of cubes appearing in each vertical column displayed in the corresponding box.

Isometric Representation:

Mat Plan

Activity 3: Drawing Mat Plans

Look at figures A and B below.

A. B.

Questions:

1. Sketch a mat plan for each figure on paper. What do you notice?

2. Click on each image above to view it using the drawing tool, and then click on the View Tool.

Were your mat plans for the figures correct? If not, what do you notice now about the mat plans?



Activity 4: Building from a Mat Plan

Below are some mat plans. Click on the button below to use the drawing tool to try to construct isometric drawings that match each mat plan. You should try to make several different drawings for each mat plan, if possible. Transfer at least one of your drawings for each mat plan onto isometric dot paper. [Hint: It might help to keep the View Tool open while you draw!]

Teacher Reflection
 

  1. In the previous problems you saw that sometimes two different solids have the same mat plan. Can you think of some restrictions you could place on solids so that mat plans are unique?

  2. When might mat plans be more useful than isometric drawings or FRT views? When are they less useful? Why?

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