Nets and Drawing for Visualizing Geometry

ObjectiveObjectiveTo make nets and drawing of three-dimensional figures

Name of the section

Section Objectives

Materials Needed

• Graph paper• Isometric drawing paper• Straight Edge

Essential Understandingand Definition

• Essential UnderstandingEssential Understanding for this section: You can represent a three-dimensional figure using special drawing techniques.

• DefinitionDefinition: A netnet is a two-dimensional diagram that you can fold to form a three-dimensional figure. A net shows all of the surfaces of a figure in one view.

Identifying a Solid from a Net

•Watch the net to the left fold into a cube.

•The net below it folds into the cube shown beside it.

•Each “cube” net has how many squares (sides)?

– six

•These are two examples of a net for a cube.

•How many ways are there to arrange six squares so that they make a cube?

Finding all the nets

Your job is to find all the different cube nets that are possible. (Two are provided for you!)

• each time, you must use all six tiles • if two tiles touch, they must border along

a full side Draw each of your solutions on graph

paperLet me check to see if it is one we

have not done yet.Color it, cut it out and tape it together.

Cube Nets Answer

13 4

56 7

8

9

2

Talk about it

• What properties are common to all nets?

• What type of nets will not work? Why not?

• Without folding, is there a quick way to tell if a net will fold into a cube?

• How can you tell if two nets are identical?

Sides of the Net

• Let’s go back to theoriginal net. Which letters will be on the top and front of the cube?

• AA, CC, E E, and FF all share an edge with DD when you fold the net, but only two of those sides are visible n the cube shown.

• AA wraps around and joins with D D to become the back of the cube.

• BB becomes the left side. FF folds back to become the bottom.

• EE folds down to become the top of the cube. CC becomes the front.

C

E

C

E

Got it?

• Given this net folds into this cube, which letters will be on the top and right side of the cube?

B

E

C

Drawing a Net from a Solid

• Package designers use nets to design boxes and other containers like cereal boxes.

• What is the net for the rectangular prism formed by the box.

• Label the net with its dimensions.9”9”

12”12”

2.5”2.5”

Drawing a Net from a Solid

• Why is the actual box not a net?

9”9”

12”12”2.5”2.5”

Got it?

• What is the net for the figure?

• Label the net with its dimensions.

• Is there another possible net for the figure? If so, draw it.

• Wolfram animation

Isometric Drawing

• Definition: An isometric isometric drawing drawing shows a corner view of a three-dimensional figure. It allows you to see the top, front, and side of the figure.

• You can draw an isometric drawing on isometric dot paper.

• The simple drawing of a file cabinet here is an isometric drawing.

Visualizing Geometry

• A net shows a three-dimensional figure as a folded-out flat surface.

• A net shows three-dimensional figure using slanted lines to represent depth.

Isometric Drawing

• What is an isometric drawingof the cube structure?

• Draw the front edges• Draw the right edges• Draw the back edges

Got it?

• What is an isometric drawing of the cube structure?

Going in reverseCan

we take a three-dimensional

isometric drawing and draw the three

two-dimensional views?

top front

right

Solid lines show visible edges.

Dashed lines show hidden edges.

The isometric drawing shows the same three

views.

Orthographic Drawings

• What we just viewed were orthographic drawings.

• Definition: An orthographic drawing is another way to represent a three-dimensional figure.

• An orthographic drawing shows three separate views: a top view, a front view and a right-side view.

Get it?

• What is the orthographic drawing for this isometric drawing?

Classwork and Homework

Exit Card

1. Tell whether the figure is isometric, orthographic, a net or none.