1. You’re Flat Out Right! Mary Brill August 21, 2006 Web Worthy Works MAED 591 Instructional Protocol: This PowerPoint lesson plans comes equipped with appropriate animations and settings to use in the classroom. Each slide may be printed as a guided notes, however answers must be removed prior. Students should be able to work in small groups. (No more than three per group) Objectives: Students should be able to… 1. Differentiate between two- and three-dimensional objects 2. Define face, vertex, and edge. 3. Understand and implement Euler’s Formula

2. You’re Flat out Right! Summary “You’re Flat Out Right!” introduces to students a new way of looking at three-dimensional objects. This interactive lesson comes with guided notes, a few short response questions requiring prior knowledge of polygons, and online Java Applets to differentiate from the everyday paper and pencil practice. Students will discover the relationship certain polyhedrons hold and why they are so special and important in our world. As a follow up lesson, given ample time, students could research the different needs/uses for such knowledge that they discovered throughout this lesson. These real-life revelations will hopefully encourage further discussion. Standards NCTM Standards Geometry: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Use visualization, spatial reasoning, and geometric modeling to solve problems MST Standards Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.

3. You accidentally left your soccer ball out in the yard. Before you could save it, your older brother ran over it with what he calls, his “BIG daddy MACK, four wheeler.” When he ran over the ball, a few of the seams ripped open, so that, when spread out, the “ball” could lay flat. What do you suppose it would look like? Draw a sketch below. Brill buster

4. Sometimes in mathematics we study ideas that are abstract and difficult to see, but polyhedra can be seen! Crystals are real world examples of polyhedra. The salt you sprinkle on your food is a crystal in the shape of a cube. Brill break through Would you say the soccer ball is two dimensional or three dimensional? Three Dimensional is correct! Because the soccer ball is something we can pick up, we consider it to be 3-D. What types of figures make the soccer ball? Polygons, or more specifically, pentagons. Polyhedra

5. Check Your Answers What is a polyhedron? A polyhedron is a 3-D solid whose faces are polygons joined at their edges, and each edge is connected at a vertex. What is a polyhedron For each polyhedron below outline, shade, or circle each edge, vertex, and face.

6. Euler in action PolyhedronFaces (F)Vertices (V)F + V =Edges (E) Tetrahedron4486 Cube681412 Triangular Prism 55108 Rectangular Pyramid 55108 Complete the chart below. What do you notice about the relationship between the faces, vertices, and edges of a polyhedron? Euler Formula F + V – E = 2