Spatial Reasoning Using Cubes and Isometric Drawings
Part Three: Other 2D Representations -- Mat Plans

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!]






Reflections:

  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?

Click here to go to the next step of the investigation.


Front-Right-Top I
Front-Right-Top II
Mat Plan
Back to Overview



Last updated: April 16, 2003

© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use

The mission of the National Council of Teachers of Mathematics is to provide the vision and leadership necessary to ensure a mathematics education of the highest quality for all students. The NCTM Illuminations Web site is devoted to providing Internet resources to improve the teaching and learning of mathematics in grades pre-K through 12. The views expressed or implied on this Web site, unless otherwise noted, should not be interpreted as official positions of the Council.