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

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Exploring 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 drawings with another type of representation, called a front-right-top view.

Isometric Representation:

Front-Right-Top Representation

Activity 1: Exploring Front-Right-Top Views

TASK 1: Observe the different colors for the corner cubes.

Use the VIEW tool and the Rotation Controls to rotate the shape.

1. What are the Rotation Control settings to see a TOP view?

Turn off the 3D view by clicking on the 3D option. Does your front view match the one shown?

2. Repeat question 1 for a FRONT View and a RIGHT view.

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TASK 2:

1. Delete one cube from your picture. What do you notice about the FRONT-RIGHT-TOP view?

2. Continue deleting cubes.

What the fewest number of cubes you can delete to make the front view look different? The right view? The top?

3. Now start over by clicking the "Reload Figure" button.

What is the greatest number of cubes you can delete and still have the FRONT-RIGHT-TOP view look the same as for the original solid?

NCTM Standards and Expectations

Geometry 6-8

Use coordinate geometry to represent and examine the properties of geometric shapes.
Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.
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


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