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Grade 8:  The Learning Equation Math

31.02 Nets and Skeletons

3icon.gif (4368 bytes)

Measurement

Refresher pp 52-3

Learning Outcomes:

The student will:

First we need to understand the vocabulary:

Representation Example(s)

Definition/Explanation

solid pillars, butter 3-D object with a filled interior
shell milk container, cereal box 3-D object with an empty interior
net cardboard box prior to assembly flat diagram that can be folded to create a 3-D solid - shows faces
skeleton example:  hydro tower 3-D frame that shows the edges and vertices of an object

 

Next we need to look at some examples:

3-D Object Net Skeleton
Definition

flat diagram that can be folded to create a 3-D solid - shows faces

3-D frame that shows the edges and vertices of an object

prisms (triangle to decagon) Prism

construct the skeleton of a prism and a pyramid using straws and joiners

triangular prism Solids and Nets

Use dot paper to draw the skeleton of a triangular prism.

tri_prism.gif (1846 bytes)

rectangular prism Solids and Nets

Use plain paper and a ruler to draw the skeleton of a triangular pyramid.

cube cube_net_sml.png (28862 bytes)

Make a skeleton model of a cube using strips of cardboard fastened with paper clips.

cube2.gif (2045 bytes)

Pentagonal prism pent_net.gif (1423 bytes) pent_prism.gif (1923 bytes)
Hexagonal prism

hex_net.gif (1832 bytes)

hex_prism.gif (1848 bytes)
Cylinder

cylinder_net_sml.png (33177 bytes)

Using playdoh (or plasticene or marshmallows) and toothpicks, or straws and pipe cleaners (or cord or elastic thread) make a skeleton 3-D model of a cylinder.

cone Cone Net

conenet1.gif (1174 bytes) conenet2.gif (1200 bytes)

conenet3.gif (1420 bytes)

 

Using playdoh (or plasticene or marshmallows) and toothpicks, or straws and pipe cleaners (or cord or elastic thread) make a skeleton 3-D model of a cone.

Square Pyramid square_pyramid_sml.png (37371 bytes)

Construct the skeleton of a square pyramid using plastercine and tootpicks.

Pentagonal Pyramid pentagonal_pyramid_sml.png (39408 bytes)

Construct the skeleton of a pentagonal pyramid using marshmallows and tootpicks.

 

Review:

Dr. Gee's 3-D Lab

3-D Animations

These are great interactive activities.  If you visual the animations as empty, the object is a shell, because a filled interior represents a solid.

Complete list of Animations:  Eric Weisstein's World of Mathematics List of Animations

Prisms Pyramids Other

Prism - triangular to decagonal

Triangular Prism

Pentagonal Prism

Hexagonal Prism

Cube

Octagonal Prism

Pyramid - triangular to hexagonal

Square Pyramid

Pentagonal Pyramid

Cylinder

Cone

 

Enrichment:

Complete list of Animations:  Eric Weisstein's World of Mathematics List of Animations

Cube Dissection -- from Eric Weisstein's World of Mathematics - views

Möbius Strip -- from Eric Weisstein's World of Mathematics

 

Key Terms:

net, skeleton, polygon, cube, cylinder, face, prism, pyramid, transformation

Prerequisite Skills:

 

 

Information included in this lesson

Exploring Transformations:  Grade 7 Lesson 33.03

 

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Comments to:  Jim Reed
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