Title: A Multifaceted Activity, A Polyhedra Icosahedron (20 sided figure)

Grade level:  5+

Time: 2-10 periods of 20-40 minutes

Curriculum concepts: see unit 4

Corresponds with National Art Standards: see unit 1

Corresponds with National Math Standards: see unit 1

Lesson objectives: Students will learn the basic geometric shape of equilateral triangles, icosahedron, tetrahedron; they will be able to identify them and their unique mechanical property of strength,  identify functional aspects of the geometrical shapes listed; learn about rotational symmetry; learn about graphic design by creating horizontal, vertical and alternating patterns and study their motion and how distortions occur; learn that art is made from shapes and that some shapes occur naturally, are invented by humans, and have specific names and sometimes, purposes.

Background information and motivation:  It is commonly thought the Principal of Twisting and Release was first used by ancient Greeks to power catapults, which tossed heavy stones great distances. 

Although this is made of one piece of paper, when properly constructed, it can support a heavy book without being crushed.  An icosahedron’s structural qualities are demonstrated by explain triangulation.  The triangle is a shape used to make things (like bridges and buildings) that need to withstand a lot of weight or force.  They spread out the force so it is not focused at one point, causing something to break or fracture. 

The zoetrope is one of several animation toys that were invented in the 19th century.  They have the property of causing the images to appear thinner than their actual sizes when viewed in motion through the slits and were precursors to animation and films.

This multifaceted project incorporates elements from several academic areas. It requires varied tasks and satisfies artistic, technical and hands-on personal preferences while providing success for students of all artistic skill levels

Integration areas:  This project combines geometry, structure, physical science, graphic design, animation, motion, mechanical free-hand drawing with catapult mechanics.  It is an icosahedron, a geometric figure with 20 triangles made of equilateral triangles, therefore, it is a multifaceted lesson.  It has three distinct surface areas consisting of five triangles and a central band of ten triangles.

Materials:  18" x 24" Paper, ruler, a sharp edged instrument or scissors, coloring utensils-crayons, markers, etc., tape, string, glue, pipe cleaner, T-square and a 30-60 degree triangle (optional)

Vocabulary: Polyhedron, icosahedron, zoetrope, rotational symmetry, torsion, static, stationary, tetrahedron

Procedure:

1. Trace the notched template pattern of triangles with 3” sides.  Cut it out being careful to leave the hems.  The hems will not be seen and are not decorated.

2. Design, draw and color the surfaces, possibly with the form of motion in mind since the static drawing will look different in motion.  One end will have generally vertical lines or alternating color circling the structure, the other will have horizontal lines that waver. The middle can be designed freely by the student, using simple geometric and free forms, or elaborate representational drawings. Drawing skill is not a necessity and the outcome is a mystery until the icosahedron is in motion.

3. Score the edges.  Hold ruler on line.  Hold the knife like a pencil.  Press with sharp edge along lines (or teacher will do it to ensure sharp, crisp straight lines). Fold edges to make a creased form.  The ends are assembles first.  Starting at one end, each hem is glued to its neighbor from the inside.  The form begins to take shape as the ends come together.  The center follows automatically.  The last two hems of each end should be left unattached.  This will also leave two unattached hems in the center creating three openings that are connected end to end. A pipe cleaner axle with looped ends (bend and twist the loops around a pencil) is inserted into this opening. The three edges of the opening are then glued together.

Assessment and/or evaluation:  Students write an essay on the project including the information learned in Math Journal.  Students read it to students or parents; demonstrates the properties discussed, such as strength, by putting a heavy book on it. (see also Culmination)

Optional variations: 1. Add catapult torsion using string threaded through each loop of the pipe cleaner. Tie ends together. Hold the ends, stretch the string and spin the icosahedron. As it spins, the string loops twist around themselves. Pull gently and release, the string will unwind and rewind. Each pull and release keeps the icosahedron in motion, animating the surface designs. The horizontal lines move up and down the surface, the colors in the vertical pattern optically mix and the shapes and colors in the center mix and move. 2. Hang the Polyhedra from the ceiling.   3. Leave out the string or coloring.  4. Prepare the shape ahead of time or have the student actually use the template.  5. Make a tetrahedron with four triangles   6. Attach other shapes from the other lessons to Icosahedron.

A zoetrope, a forerunner of films, acts like the Icosahedron.  Look through the slits to see the movement of the picture inside as it spins.

References:  Adapted from  Strazdin, R. (2000, May), Icosahedrons:  A multifaceted project. Arts& Activities, 127 (4), 38.

Examples: see http://www.randisart.com/kid's%20page.htm

Culmination Units 1-5:  Invite Parents.  Everyone views the display of drawings and projects, Icosahedron Mobile (or Combination of Shapes Mobile) in a gallery style exhibit in the classroom or school’s hallways.  Students may  share their poems by reading them out loud or matting them on a nice background to posting them on the wall; add pictures or decorations with crayons, colored pencils or pens. 

References

Adejumo, Christopher O.

(2002).  Five ways to improve the teaching and understanding of art in the schools.  Art Education. Reston:  Sep

2002. Vol. 55, Iss. 5;  pg. 6, 6 pgs

Baicker, K.

(2004, April). Origami math. Instructor, 113(7), 41.

Kellah M Edens,   Ellen F Potter.

(2001). Promoting conceptual understanding through pictorial  representation. Studies in Art Education, 42(3), 214-233.  Retrieved July 31, 2008, from Research  Library database. (Document ID: 72375071).

Gayle Cloke, Nola Ewing,  Dory Stevens. 

(2001). The fine art of mathematics, Teaching children Mathematics, 8(2), 108-110. Retrieved August 8, 2008, from

Research Library database. (Document ID: 83776531).

Jensen, Eric.

(2001). Arts with The Brain in Mind, Reston,  Alexandria, Viginia, USA

Naylor, M.

(2006, March). Do you see a pattern? Teaching Prek-8, 36(6), 38.

Strazdin, R.

 (2000, May), Icosahedrons:  A multifaceted project. Arts& Activities, 127 (4), 38.

References:  Adapted from  Strazdin, R. (2000, May), Icosahedrons:  A multifaceted project. Arts& Activities, 127 (4), 38.