## Creating Tessellations

### Diane Bates

#### Description

Explore the history of tessellations; then use art and geometry to create an original tessellation.

#### Objectives

The student understands the geometric concepts of symmetry, reflections, congruency, similarity, perpendicularity, parallelism, and transformations, including flips, slides, turns, and enlargements.

The student predicts and verifies patterns involving tessellations (a covering of a plane with congruent copies of the same pattern with no holes and no overlaps, like floor tiles).

The student understands ways in which cultural characteristics have been transmitted from one society to another (e.g., through art, architecture, language, other artifacts, traditions, beliefs, values, and behaviors).

The student understands and uses information from historical and cultural themes, trends, styles, periods of art, and artists.

The student understands how knowledge, skills, and attitudes gained from the visual arts can enhance and deepen understanding of life.

#### Materials

-Computer with large screen TV or LCD
-Software for creating Tessellations
-INTRODUCTION TO TESSALATIONS (book)
-Pencils
-Scissors
-Tape
-Colored pencils, crayons, or markers
-Dot paper (square, triangular, hexagonal)
-Sketching grids (square, triangular, hexagonal)

#### Preparations

The teacher needs to:
Be familiar with tessellation software.
Provide copies of pattern continuations.
Provide lessons of flips, slides, and rotations.
Provide copies of dot paper.
Provide copies of sketching grids.

#### Procedures

1. Provide background information (history, uses, and types of tessellations) to the students. Two ways to accomplish this are as follows:

a. Use tessellation software or tessellations you've created in conjunction with a large screen TV or LCD. Give the whole class an introduction to tessellations that includes examples, history, types, and an overview of how to use the software to create tessellations.

b. Another great source for this type of information is the book INTRODUCTION TO TESSALATIONS (available from Dale Seymour Publications). This book provides a great introduction and also has ideas for activities, dot paper masters, and sketching grid masters. Two other books in the same series that are useful include TEACHING TESSELLATING ART and TESSELLATION TEACHING MASTERS.

2. After students have received an introduction, they practice continuation of an existing tessellation pattern. Examples are provided as attachments to this lesson plan (Hexagon Ex.doc, Square Ex1.doc, Square Ex2.doc, Square Ex3. doc, Triangle Ex1.doc, and Triangle Ex2.doc). Make enough copies for students to choose the pattern that they want to complete. Students are not only required to complete the pattern but also color it.

3. Students then need instruction on how to flip (reflect), slide (translate), and rotate (turn) figures to create tessellations. Three sources for lessons of this type include the following:

a. Tessellation software (such as TesselMania! Deluxe) has classroom ideas, lesson plans, and student handouts to be used in conjunction with the software. A computer with a large screen TV is ideal for use with these lessons to instruct the entire class at one time.
b. The books listed above are excellent sources for ideas and lessons.
c. -The Scott Foresman-Addison Wesley Middle School Math- series have lessons on transformational geometry. An example is Course three (8th grade), pages 593-617.

4. The culmination of the lesson is for students to create an original tessellation that is graded using a rubric (attached file Tess Rubric.doc). A copy of the rubric is given to the students before they begin their original design so that they know the grading criteria. Their original designs can be created on dot paper or sketching grids (examples provided with attached files Hexagon Dot.doc, Square Dot.doc, Triangle Dot.doc, Square Sketch.doc, and Triangle Sketch.doc). The original design must use a flip (reflection), slide (translation), or rotation (turn) or a combination of the three. The original design can also be created using the tessellation software. One problem with using the tessellation software is allocation of time. If only one computer or one copy of the software is available in the classroom, then students would have to share class time or come in before school.

5. Depending on the level of the students, Escher-like tessellations can be taught and created during the first unit or as a second unit. The books described above and the TesselMania! Deluxe software both have detailed sections on creating M. C. Escher-like tessellations.

6. Original designs can be scanned and submitted via the Internet to the -World of Escher- contest (http://www.worldofescher.com).

#### Assessments

Each student will create an original tessellation that will be graded using a Rubric (attached file)

#### Extensions

This unit can be extended to include elements of art and history.