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


Do They Match?

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 Activity 1, we saw that a shape can have more than one isometric drawing. When do two isometric drawings represent the same shape? How can we decide?

Directions: Look at each pair of images below.

1. Which the pairs do you think could be drawings of the same object?

Record your conjectures before continuing on.

2. Now click on the images to see them in the drawing tool.

Use the View Tool and "Rotation Controls" options. Were your guesses correct?

3. For the pairs that could represent the same object, list the Rotation Control values you used to verify your answer.

For the pairs that could not represent the same object, explain why.

A.
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B.
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C.
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Teacher Reflection
 

  1. What strategies do you use to tell if two drawings can represent the same object?

  2. What difficulties did you encounter trying to use the tool to answer the questions?

  3. When is it difficult to decide if two drawings can represent the same object?

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