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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.
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.
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)
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.
Extensions of this lesson
• There are only 5 possible regular polyhedra. Can you explain why?
• Investigate Euler’s FormulaF + V = E + 2