1. Three Dimensional Shapes http://cstl- csm.semo.edu/mcallister/mainpage Cheryl J. McAllister Southeast Missouri State University MCTM – 2012

2. 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.

3. 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

4. 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

5. 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 Analyze characteristics 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;

6. 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

7. 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.

8. 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.

9. Prisms

10. 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.

11. Triangluar Pyramid

12. 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)

13. Height and slant height h = height s = slant height

14. 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.

15. Height of a right pyramid Right

16. Height of an oblique pyramid Note: the height is outside the pyramid

17. Regular polyhedra (Platonic solids) Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron

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

19. Where to find directions http://www.auntannie.com/Geometric/PlatonicSolids/

20. Another method - Folding nets This is what a tetrahedron looks like if you flatten it out.

21. Thank you! cjmcallister@semo.edu http://cstl- csm.semo.edu/mcallister/mainpage