# Polyhedra in the Classroom

### Suzanne Alejandre

Tessellation Tutorials || Magic Squares || Suzanne's Math Lessons

As part of the Rialto Unified School District, Frisbie Middle School was using the Glencoe instructional materials to teach mathematics. The unit presented here uses the objectives found in Unit 14 of Glencoe's Interactive Mathematics, but the activities have been designed so that students can take extra time on specific mathematical ideas. This unit works well if the class can regularly go to a computer lab with Internet access and/or if the classroom has computers with Internet access.

## Student Activities

 Introduction to Polyhedra Rectangular Prism: A cooperative group activity to construct perfect rectangular prisms. Paper Nets Print out nets and construct six paper models of polyhedra. KaleidoTile Learn how a tiling is built up from reflections of a single tile, reflect a triangle, and explore Euclidean and spherical symmetry groups. KaleidoTile Handout A chart of the questions used by groups of students working with KaleidoTile. KaleidoTile Software Download the software (free) from the Geometry Center. Buckyballs Links to Web sites with information on Carbon-60 (buckyball), a real world example of a polyhedron. Paper Net of a Buckyball Print out the net and construct a model of a buckyball. Extra Credit Buckyball Speech Challenge students to stand and speak about buckyballs. Crystals Information on real world polyhedra crystalline structures. Systems of Crystals Information on the seven crystal systems with links to photographs of examples. Paper Nets of Crystals Print out nets and construct paper models of the polyhedra that are crystals. CrystalMaker Interactive Crystallography HyperCard Polyhedra Animation Use HyperCard (Macintosh) to show polyhedra in motion. Students draw polyhedra and rotate their figures. Elephant Puzzle Print the puzzle and challenge the students to fold the net so that the elephant parts fit together correctly. Cube Coloring Problem Problem-solving using manipulatives. Another Cube Coloring Problem Painted Cube from nrich.maths.org Polyhedra Speech Challenge students to stand and speak about their polyhedra models. Journal Entry Students describe polyhedra on the Web, using journal writing to process their learning. Polyhedra on the Web Links to Web sites with beautiful models of polyhedra. Polyhedra EssayAssessment of what the students have learned about polyhedra.

### Objectives

Unit 14 is the second of six units for 8th grade students. The Unit objectives are:
• to introduce the students to the concepts of surface area and volume while focusing on the importance of measurement.
• to teach the relation between surface area and volume and apply this in various settings.
My specific objectives for the unit are:
1. Students will calculate the surface area of a rectangular prism.
(
NCTM Grades 6-8 Standards Geometry and Measurement)

2. Students will name the characteristics (number of edges, faces, vertices, and the shape of the face) of 6 specific polyhedra: the cube, tetrahedron, octahedron, dodecahedron, icosahedron, and cuboctahedron.
(NCTM Grades 6-8 Standards Geometry and Measurement)

3. Students will use the writing process to demonstrate understanding of the characteristics of polyhedra.
(NCTM Grades 6-8 Standards Communication)

4. Students will verbally describe polyhedra.
(NCTM Grades 6-8 Standards Communication)

5. Students will explore polyhedra in the real world through crystalline structures and "buckyballs."
(NCTM Grades 6-8 Standards Connections)

### Assessment

Students are assessed as they complete each activity. Group participation points are given if the students have been actively engaged in their group activity. Individual completion points are given as the activity or assignment is completed. Points are given to students who stand and give a speech on one of the polyhedra. The Polyhedra Essay is the final unit assessment. To receive full points on the essay all of the components of the essay must be addressed.

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