Introduction
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This lesson was developed by Northside Teachers as part of the Region 20 TIFTECH Training Program.

The lesson explores the relationship between mathematics and art through tessellations.  Students are exposed to the history of tessellations and tilings and learn about M. C. Escher and his works.

Content Area, Grade Level

This lesson is appropriate for high school students in art or in geometry.

Texas Essential Knowledge and Skills (TEKS) addressed by this lesson include:

Geometry 111.34    The student uses properties of transformations
                              and their compositions to make connections between
                              mathematics and the real world in applications such
                              as tessellations or fractals.

§117.52. Art, Level I.

                    (1) Four basic strands--perception, creative expression/performance, historical and
                    cultural heritage, and critical evaluation--provide broad, unifying structures for
                    organizing the knowledge and skills students are expected to acquire. Students rely
                    on their perceptions of the environment, developed through increasing visual
                    awareness and sensitivity to surroundings, memory, imagination, and life
                    experiences, as a source for creating artworks. They express their thoughts and
                    ideas creatively, while challenging their imagination, fostering reflective thinking,
                    and developing disciplined effort and problem-solving skills.

                    (2) By analyzing artistic styles and historical periods students develop respect for
                    the traditions and contributions of diverse cultures. Students respond to and
                    analyze artworks, thus contributing to the development of lifelong skills of making
                    informed judgments and evaluations.

• The students will define the term tessellation and demonstrate their understanding of the term by identifying what shapes will tessellate.
• The students will create their own tessellation.
• The students will relate the geometric basis of tessellations with the creations of M C. Escher.
• The students will critique their project and their knowledge by producing a self evaluation.

   The entire lesson can take up to three weeks to implement.  However, teachers are encouraged to use any aspect of the lesson that fits into their curriculum.

    Days 1 - 3 are used for internet research on the definition, history, and the creation of tessellations.

    Days 4 - 14 are used for the creation of the tessellation, adding the color and highlights to the pattern, and matting the final project.

    Day 15 is used for the self evaluation.

Resources Needed
 

• Internet access for all students in order for them to research the topic.
• Art supplies listed as part of the student page.
• Either an art teacher or a geometry teacher can successfully implement this lesson. A team approach utilizing the teacher expertise from both areas would be the ideal situation.

    Students must be able to construct their basic tessellation shape using a straight edge and a compass.

Evaluation

    The success of this lesson can be evaluated by the student projects, their introductory paper, and their self evaluation.  The projects should demonstrate geometric symmetry as well as creativity and aesthetic appeal.

Conclusion

    This lesson will introduce the students to the connection between mathematics and art.