Three Dimensional Shapes

http://cstl-csm.semo.edu/mcallister/mainpage

Cheryl J. McAllister Southeast Missouri State University

MCTM – 2012

While I am talking…

• Select a color(s) of construction paper you like• Select a circle making tool of your choice• Draw circles with at least a 1 inch radius, but

no more than a 2 in radius.• You will need at least 4 circles, but 8 will be

the best.• You may have to take turns with the tools.

Geometry Standard for Grades Pre-K-2

Instructional programs from prekindergarten through grade 12 should

enable all students to—

In prekindergarten through grade 2 all students should—

Analyze characteristics and properties of two- and three-dimensional geometric

shapes and develop mathematical arguments about geometric relationships

•recognize, name, build, draw, compare, and sort two- and three-dimensional

shapes;•describe attributes and parts of two- and

three-dimensional shapes;•investigate and predict the results of

putting together and taking apart two- and three-dimensional shapes.

http://www.nctm.org/standards/content.aspx?id=26846

Geometry Standard for Grades 3-5

Instructional programs from prekindergarten through grade 12 should

enable all students to— In grades 3–5 all students should—

Analyze characteristics and properties of two- and three-dimensional geometric

shapes and develop mathematical arguments about geometric relationships

•identify, compare, and analyze attributes of two- and three-dimensional shapes and

develop vocabulary to describe the attributes;

•classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes

such as triangles and pyramids;

http://www.nctm.org/standards/content.aspx?id=26814

Geometry Standard for Grades 6-8

• Instructional programs from prekindergarten through grade 12 should enable all students to—

• Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

• Expectations: In grades 6–8 all students should— • precisely describe, classify, and understand relationships

among types of two- and three-dimensional objects using their defining properties;

• understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects;

The activity today is one of many, many ways to get students thinking about and exploring 3-

D figures

• Can be used to review vocabulary• Can teach students to use construction tools

such as compass and straight edge• Can be used to teach some math history• Can be used as an art activity to decorate the

classroom

Polyhedron (polyhedra)

• A three dimensional figure composed of polygonal regions (called faces) joined at the sides (edges). The point where edges meet is called a vertex.

Polyhedra are often categorized by their shapes

• Prisms – composed of two bases (which are congruent polygons), joined by parallelograms (called lateral faces).

• Pyramids – composed of 1 polygonal base and lateral faces that are triangles that meet at a single point called the apex.

Prisms

Other info about prisms

• Prisms are often named for the shape of the bases

IF the lateral faces are rectangles, then we have a right prism. IF the lateral faces are not rectangles, then we have an oblique prism.

• The height (or altitude) of a prism is the perpendicular distance between the bases.

Triangluar Pyramid

More info about pyramids• Pyramids are often named by the shape

of the base. • The height of a pyramid is the

perpendicular distance from the apex to the base.

• The slant height of a pyramid is the distance from the apex along a lateral face of the pyramid, perpendicular to the opposite edge of the face. (see next slide)

Height and slant height

h = heights = slant height

More facts about pyramids

• IF the apex is over the center of the base, then the pyramid is a right pyramid, if not, then the pyramid is oblique.

• IF the base of the pyramid is a regular polygon, then the pyramid is said to be a regular pyramid.

Height of a right pyramidRight

Height of an oblique pyramid

Note: the height is outside the pyramid

Regular polyhedra (Platonic solids) Tetrahedron

Hexahedron Octahedron

Dodecahedron Icosahedron

Extensions of this lesson

• There are only 5 possible regular polyhedra. Can you explain why?

• Investigate Euler’s FormulaF + V = E + 2

Where to find directions

• http://www.auntannie.com/Geometric/PlatonicSolids/

Another method - Folding nets• This is what a tetrahedron looks like if you

flatten it out.

Thank you!

cjmcallister@semo.eduhttp://cstl-csm.semo.edu/

mcallister/mainpage