Illuminations: Using Cubes and Isometric Drawings

# Using Cubes and Isometric Drawings

In this interactive geometry investigation, students explore polyhedra using different representations and perspectives for three dimensional block figures. In addition, students will examine area and volume concepts for block figures within this context.

### Math Content

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
• Create three dimensional shapes using the isometric drawing tool and represent these shapes as isometric drawings
• Find the surface area and volume of various polyhedra created in this unit

### Individual Lessons

Lesson 1 - Exploring the Isometric Drawing Tool

Students explore using the isometric drawing tool and gain practice and experience in manipulating drawings.

Lesson 2 - Do They Match?

Using three dimensional figures they have constructed, students determine when two isometric drawings can represent the same shape and explain their reasoning. Students will also determine what possible shapes might have the same isometric drawing and explain their reasoning.

Lesson 3 - Building Using the Front-Right-Top View

Students explore drawing the front-right-top view when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the front-right-top view.

Lesson 4 - Mat Plans

Students explore drawing a mat plan when given a three dimensional figure built from cubes. Students also explore building a three dimensional figure when given the mat plan.

Lesson 5 - Finding Surface Area and Volume

Using the isometric drawing tool, students build three-dimensional figures and find the surface area and volume of each figure.

Lesson 6 - Are They Possible?

Students examine some isometric drawings that seem to be impossible and investigate one way Escher used to create these "impossible" figures.

### NCTM Resources

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