MATERIALS:
Per Group (of four students):
• A set of three-dimensional wooden or plastic shapes. Set should include one each of the following: a cube, a square pyramid, a cylinder, a cone, and a sphere and a variety of prisms such as a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, or an octagonal prism.
• Scissors
• Tape
• One set of building materials. (Provide each student group with one set of materials. Choose from the items listed below.)

• Recording Sheets: Alike and Different and Constructions

Per Teacher:
• A set of three-dimensional wooden or plastic shapes. Set should include one each of the following: a cube, a square pyramid, a cylinder, a cone, and a sphere and a variety of prisms such as a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, or an octagonal prism.

Per Group:
• Computer with Internet access or computer with PC/TV adapter or projector.
• VCR Tape of Invasion of the Polygons
• Television with VCR
• Chart Paper
• Pencils
• Paper

PREP FOR TEACHERS:
Prior to teaching this lesson:
1. Bookmark the web sites: http://www.illuminations.nctm.org; http://www.greatbuildings.com/gbc.html and http://www.nps.gov/nama.
NOTE: The teacher should try the activities on each website and print copies of the items featured on the web pages to use when instructing students.
2. View the tape: Invasion of the Polygons

Preparation for the hands-on component of the lesson:
1. Make copies of the student recording sheets: Alike and Different and Constructions.
2. Prepare chart paper for the class discussions.
3. Students should also have prior experience with two-dimensional figures before this lesson.
4. Important Geometric Terms: cube, pyramid, prism, cylinder, sphere, cone
• Polyhedra (singular, polyhedron): Solids whose faces are polygons.
• Polygon: A closed two-dimensional figure that is made up of line segments that intersect only at their end points.
• Faces: Polygonal regions that make up the surface of a solid.
• Edges: The line segments created by the intersection of two faces of a solid.
• Vertices (singular, vertex): The points of intersection of two or more edges.

When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

INTRODUCTORY ACTIVITY:
Day One: 50 minutes

Step 1. Introduce lesson topic to students by telling students, “In math class we have had the opportunity to examine and explore shapes only in two-dimensions. Two-dimensional shapes lie flat and are sometimes called flat or plane shapes. We can draw these shapes on paper and they are often represented in books. Today we will enter the world of three-dimensional shapes. Three-dimensional figures can stand up – they have height.”

Step 2. Allow students to brainstorm a list of two-dimensional shapes. (The list may include: circles, triangles, squares, rectangles, circles, pentagons, hexagons, etc.) Show students the three-dimensional figures. Choose one solid and ask students to describe the solid. Ask questions such as: “How is the solid like the flat (2-D) shapes: How is it different? Can you make this solid using some of the two-dimensional shapes?” As a class, list the similarities and differences between two-dimensional and three-dimensional shapes. Discuss the class findings.

Step 3. Divide students into groups of four. Provide each group with a three-dimensional figure. Instruct students to compare the three-dimensional figure to one or more two-dimensional shapes. Each group will use the Alike and Different recording sheet to list all the things that the shapes have in common and all of the things that are different. Allow groups to share their findings. Examples of student responses may note that “a cube is similar to a square because it is made up of squares”, etc. At this time introduce the terminology: faces, vertices, and edges. Use one solid as an example and show students the faces, vertices, and edges.

Step 4. Instruct each group to trace the faces of their solid and list the two-dimensional shapes used to “construct” the solid. Allow students to cut out the tracing of the faces and use these flat shapes and tape to reconstruct the solid figure. Instruct each group to write a description of their solid that includes the following information: name of the solid, number of faces, vertices, edges, and the flat shapes used to make the solid. Use chart paper to record each group’s findings. See example:

Step 5: Use the class computer with PC/TV adapter, a projector, or allow students to work in small groups to log on to http://www.illuminations.nctm.org. Click on I-Math Investigations and scroll down to the section for grades 3 – 5. Students will use the Exploring Geometric Solids and Their Properties i-Math Investigation. Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students that they will have the opportunity to examine virtual models of the three-dimensional figures. Instruct students to use the “Counting Parts of Solids” section to locate the faces, vertices, and edges of the virtual figures. Ask students, “Is there a relationship among the faces, edges, and vertices of a solid figure?” Allow students to share their findings. NOTE: It is important that the teacher highlight the features of the interactive investigation for students prior to the independent student activity. Allow students to share their findings with the entire class.

LEARNING ACTIVITIES:
Day Two: 50 minutes

Step 1. Allow students to review the discussion from the previous day’s lesson. Use the recording sheets, class lists, and other student recordings to help students with the review process.

Step 2. Divide students into groups of four. Distribute a set of three-dimensional wooden or plastic figures and a set of building materials to each group. Ask each group to select one three-dimensional figure from the set of solids. Instruct students to work cooperatively to construct one of the faces on their solid. Discuss the characteristics of the plane (flat) shape they created. “How many vertices (corners) does the shape have? How many edges (sides)? Were you able to create non-square rectangles? If yes, how? Can you make triangles that aren’t equilateral?”
NOTE: Students will have to use their problem solving skills to discover that the straws can be cut to varying lengths to create non-square rectangles and triangles with sides of varying lengths. Students can also mix coffee stirrers with toothpicks to create these shapes.

Step 3. Instruct students to use the building materials to construct as many three-dimensional models of the solid figures as they possibly can. Tell students that if they find any solids that cannot be created, to make a list of those solids. Ask students to complete a Constructions recording sheet that tells the number of vertices, edges, and faces for each solid they construct. Questions to ask students: “What building material did you use? How many toothpicks are stuck in each gumdrop (marshmallow, etc.)? Is the number the same for every vertex? How can you “see” the faces of the solid? How is your model like an x-ray?”

Step 4. Allow students to display their constructions placing the constructions next to the appropriate three-dimensional figure. If time permits, allow each group to take a “gallery walk” to view the constructions. Ask students if there were any figures that they weren’t able to construct. If so, ask students to group those figures together. Students should place the cone, sphere, and cylinder together. Ask students, “How are the figures you were able to build different from the ones you could not build?” Student responses may include “the cone, sphere, and cylinder have circular shapes.” “These shapes don’t have edges (sides) or vertices (corners).”

Step 5. Insert the video, The Eddie Files with Kay Toliver, Geometry: Invasion of the Polygons into your VCR. Provide your students with a FOCUS FOR MEDIA INTERACTION. Ask students to watch the video segment and note the geometric term Mrs. Toliver uses with her students to describe the colored shapes. START the tape at the beginning where Mrs. Toliver shows the students the three-dimensional colored figure. PAUSE the tape after the students look at the three-dimensional models and list the polygons used to make each polyhedron. Check for comprehension. (Students should state that the plane (flat) figures used to construct the three-dimensional models are all models of polygons.) The students should conclude that the figures they were able to make are all polyhedra, so the cone, sphere, and cylinder are not polyhedra.
NOTE: Students could make a chart labeled: “Polyhedron/ Not a polyhedron” to help illustrate their findings.

CULMINATING ACTIVITIES:
Step 1: Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students that polygons are everywhere in the environment. Ask students to watch the video segment and list the polygons that Eddie finds at the construction site. FAST FORWARD the tape to the segment that shows Eddie at the construction site talking to the construction workers. PLAY the tape until Eddie leaves the construction site completing his visit with the construction workers. STOP the tape. Check for comprehension. Students should note that the building was made up of many polygons such as a rhombus and a parallelogram. Take students on a short walk around the playground to locate polygons and polyhedra in their school environment.

Step 2. Use the class computer with PC/TV adapter, a projector, or allow students to work in small groups to log on to http://www.greatbuildings.com/gbc.html and http://www.nps.gov/nama. Students will examine photos of landmarks and buildings to discover the presence of polygons and polyhedra in real-life objects. Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students to complete the following task for each website they visit:
• Identify the name of each solid figure they find and tell where it is located in the picture and how it is used. Example: I found part of a sphere in the Jefferson Memorial. It’s used as a roof.
• Keep a record of the shape they found and a picture of the whole structure to show the shape in context. (Students can record in several ways: use the copy image feature of their web browser to save pictures, print pictures directly from Web pages, make rough sketches or outlines.)
Questions to ask students may include: “Of what does the shape of that building remind you? What shape does the top of that monument look like? Do you see part of a figure in that building? How would you describe the shape of that roof? Do any of these buildings remind you of buildings in your neighborhood, city, etc.?”

Step 3: Assessment Procedures
• Teacher Observation
• Class Participation
• Student performance on the class activities.
• Student work will be evaluated based on the successful completion of all assigned tasks and the completed recording sheets for all activities.

CROSS-CURRICULAR EXTENSIONS:
LANGUAGE ARTS:
• Instruct students to create an alphabet book of geometric terms. Students must include illustrations for each term used in their alphabet book.
ART/MATHEMATICS:
• Allow students to read literature books such as The Patchwork Quilt, Eight Hands Round: A Patchwork Alphabet, or Sam Johnson and the Blue Ribbon Quilt. Students should observe the quilt squares and list the polygons used to create each square. Students can use construction paper, glue, and scissors to create their own original quilt squares. Students should describe their quilt squares by listing the polygons they used to create their quilt square.

COMMUNITY CONNECTIONS:
• Invite an architect to visit your class and tell the students about the designs used for buildings he/she has designed. Encourage the guest to point out the polygons present in the building design.

• Invite a contractor to visit your class and tell the students about the types of building materials used to construct buildings. Encourage the guest to tell students how he/she uses certain shapes and designs such as tubing to make a structure stronger. For example, most buildings have a square or rectangular base. Help students relate building design to the constructions they created in the learning activity.

STUDENT MATERIALS:
See attached: Student Materials include:
• Alike and Different Recording Sheet (  PDF )
• Constructions Recording Sheet (  PDF )