Let's Tessellate
 
Overview of Lesson

Students will create tessellating designs using congruent polygons after learning about M.C. Escher.

Lesson Objectives

Texas Essential Knowledge and Skills (TEKS) for Math

Math TEKS for grades 6-8 (2) Students build foundation of basic understandings in (among many things) patterns, relationships, spatial reasoning and measurement.

Resources and Materials

• examples of M.C. Escher’s work
• (Available for check-out through The Grace Museum) Escher Bowl – Take 5 Print
• Math in the Real World of Design and Art by Shirley Cook
• Discovering Great Artists by Mary Ann F. Kohl and Kim Solga
• Tessellations: the History and Making of Symmetrical Designs by Pam Stephens
• index paper in a variety of colors but lots of white
• small lined index cards
• _ inch grid paper
• pencils
• white rubber erasers
• See Thru rulers
• Tape
• colored pencils or markers
• poster paint, brushes, water, palettes, paper towels

Vocabulary

Tessellation - a special kind of design made from shapes that fit together.

Congruent - having the same shape and size. In tessellation designs, congruent polygons fit together like jigsaw puzzle pieces, repeating various patterns.

Background and Activity Instructions

Show a checkerboard. This is a simple tessellation made of squares. What other congruent polygons fit together perfectly? (diamonds, octagons, rectangle, triangles) There are also weird shapes that tessellate. A man who liked to make these weird and wonderful designs was M.C. Escher. Have you ever heard of him? Escher grew up in Holland in the first part of the 20th century. While studying art and traveling in Europe he discovered that he liked the geometric designs made by Moorish artist in Spain and northern Africa. Show page 11 in Pam Stephens’ book. Show some of Escher’s designs. Show Escher Bowl. What is the congruent shape that is repeated? Now show page 13 in the Stephens book. How is this quilt like the other tessellating patterns? There are 3 types of tessellations: translation, rotation and reflection. We will stick to the simplest: translation, which repeats in a side-to-side and top-to-bottom pattern of congruent shapes. See page 34 for descriptions of rotating and reflecting tessellations.

1. Give each student a 3 X 5” ruled index card. Tell them to measure and cut a 2” square from it.
2. Next, draw a simple line on the top and left edge. Cut these out.
3. Tape the top cut out to the bottom edge and the left edge cut out to the right edge. This will be your pattern.
4. Draw a 6 X 10 inch rectangle on the grid paper. Divide this rectangle into 15, 2 inch squares. Copy the pattern or template into each block. Try out a color scheme using colored pencil or markers. If the student likes the design, he may proceed to the last step. If not, encourage redesign.
5. Lightly recreate the grid on white or colored index paper. Lightly add the pattern and paint using knowledge of the color wheel.