Three Dimensional Shapes
http://cstlcsm.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—
•recognize, name, build, draw, compare,
and sort two- and three-dimensional
Analyze characteristics and properties of
shapes;
two- and three-dimensional geometric
•describe attributes and parts of two- and
shapes and develop mathematical
three-dimensional shapes;
arguments about geometric relationships
•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 threedimensional 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 = height
s = 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 pyramid
Right
Height of an oblique pyramid
Note: the height
is outside the
pyramid
Regular polyhedra (Platonic solids)
Tetrahedron
Hexahedron
Dodecahedron
Octahedron
Icosahedron
Extensions of this lesson
• There are only 5 possible regular
polyhedra. Can you explain why?
• Investigate Euler’s Formula
F+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.edu
http://cstlcsm.semo.edu/mcallister/mainpage