ACTIVITY 11

Tessellations: Where Art, Math, and Insects Meet

Teaching Objectives:

1. Students will identify six basic geometric shapes: circle, rectangle, square, triangle, octagon, pentagon (or any angular shape the teacher would like to cover).
2. Students will understand the concept of tessellation.
3. Students will design puzzles with pieces that tessellate.
4. Students will create an artistic work employing tessellation.
5. Students will be introduced to the artwork of M. C. Escher and his use of tessellations and insects in his work.

Materials Needed:

• Examples of M. C. Escher's art in which he used tessellation and insects; use the Internet or art books; there are also many M. C. Escher products on the market including coloring books, calendars, puzzles, T-shirts, and wrapping paper.
• Examples of mosaic artwork
• Cardboard or paper geometric shapes: circle, rectangle, square, triangle, pentagon, hexagon, and octagon.
• Manila envelopes
• Poster board (optional)
• Black and colored construction paper
• Puzzles containing pieces with geometric shapes. DaMert Company (1609 Fourth Street, Berkeley, CA 94710) produces triangular-shaped puzzles with triangular-shaped pieces, two of these puzzles have insect themes.

Procedure:

Discuss these geometric shapes with the students: circle, rectangle, square, triangle, pentagon, hexagon, and octagon.

Define the term tessellation with the students:

• Tessellate: make of small squares or blocks, or in a checkered pattern (1)
• Tessellate: to form into or adorn with mosaic (2)
• Tessellation: mosaic; esp.: a covering of an infinite geometric plane without gaps or overlaps by congruent plane figures of one type or a few types (2)

The web sites Alexsandra's Tessellations and Totally Tessellated have examples of tessellations in art work.

See if the students have dictionaries with different ways of stating these definitions.

Have the students draw circles on a sheet of paper. Ask the students to look at these circles and determine why circles by themselves cannot tessellate.

Discuss the works of M. C. Escher and how he combined tessellation and ordinary insects to create works of art. Would the pictures have been as interesting without the insects Escher involved in them?

Have commercially-created puzzles available in the room for students to attempt.

Ask the students to demonstrate tessellation by drawing a picture of an insect or insects which the students then cut into a puzzle with geometric-shaped pieces. Older students might want to glue their pictures to a piece of poster board before cutting out the puzzle. Have the students place the puzzle pieces in a manila envelope and allow the students to share their puzzles with each other.

Using the black construction paper as a "frame," have the students cut colored pieces of paper in geometric shapes and design a mosaic picture which employs tessellation. Challenge the students to work the shape of an insect into the mosaic that they create with these colored pieces of paper.

Supplemental Activities:

Ask the students to research the life and works of M. C. Escher. Encourage them to use the Internet as well as printed sources.

Have the students look through art books and find works of art that have insects in them. For example, the book I Spy Two Eyes: Numbers in Art has two such pictures and the book I Spy a Lion: Animals in Art has one. This activity will introduce the students to great works of art and at the same time test their powers of observation.

Ask the students which shape bees use to make honeycomb. Does a honeycomb tessellate? Build a honeycomb of bee facts. Use the Honeycomb Worksheet and have the students place a bee fact in each section. Cut out each student's honeycomb and put them together in one large honeycomb on a wall or bulletin board.

(1) Thorndike, E. L., and Barnhart, Clarence L. Thorndike-Barnhart Student Dictionary. Updated version. Glenview, Illinois: HarperCollins, 1997.

(2) Merriam Webster's Collegiate Dictionary. 10th edition. Springfield, Massachusetts: Merriam-Webster, Incorporated, 1996.