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K–12 teaching and learning · from the UNC School of Education

Tessellations with M.C. Escher

This lesson familiarizes students with tessellations, designs created by images placed against each other with no empty spaces. It also introduces the work of M. C. Escher. It can be used in conjunction with math lessons in geometry.

A lesson plan for grades 6–8 Visual Arts Education

By Judith Riddle

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Learning outcomes

Students will:

  • identify and appreciate the work of M. C. Escher.
  • construct a tessellation and use it to create a pattern in which there are no empty spaces.

Teacher planning

Time required for lesson

80 minutes

Materials/resources

  • Reproductions of tesselations by M. C. Escher
  • Squares or rectangles of stiff paper or tagboard, 3″x 5″ maximum size
  • Tape
  • Scissors
  • 12×18″ drawing paper
  • Crayons or markers
  • Pencil

Technology resources

Computer with Internet access (optional)

Pre-activities

Introduce the Dutch graphic artist M. C. Escher, 1898-1972. Show the Escher reproductions and discuss how Escher uses the tesselations to fill the plane, that there is no foreground or background, and the space is completely filled with the design.

Activities

  1. Give each student a piece of tagboard. It can be a square or a rectangle.
  2. Have the students color one side of the tagboard so that they know which side is the top.
  3. Starting at one edge of the square or rectangle, draw a shape from the edge, into the space, and out to the edge again.
  4. Cut this shape out and tape to the opposite edge of the shape without turning it or flipping it over.
  5. Then cut the entire shape in half and tape the uncut edges together making sure the colored side is on top. This is the template for the tessellation.
  6. Use this template to fill the plane with the shape, which interlocks with itself like puzzle pieces fit together.
  7. The shapes can then be colored with crayons or markers.

Assessment

The pattern should cover the entire plane with no spaces between the shapes or overlapping anywhere.

Supplemental information

Examples of tessellations by Escher are helpful to illustrate the principle to students.

Examples of tesselations done by other students can be a motivational help. The students are quite intrigued and like to figure out how they were done.

Related websites

How to Make a Tessellation http://www2.spsu.edu/math/tiling/2.html

Student Tessellations http://mathforum.org/alejandre/students.tess.html

Tessellation Tutorials
http://forum.swarthmore.edu/sum95/suzanne/tess.intro.html

The M.C. Escher Pages
http://users.erols.com/ziring/escher.htm

M. C. Escher Pictures of Tessellations Optical Illusions Art Prints
http://www.johnshepler.com/posters/escherpictures.html

Comments

This lesson can be modified to add more technical information such as types of symmetry used in tessellation: translation, glide, rotation, and reflection. A subsequent lesson can be done attempting tessellations that are representational, as in Escher’s fish or bird tessellations.

North Carolina Curriculum Alignment

Visual Arts Education (2001)

Grade 6

  • Goal 1: The learner will develop critical and creative thinking skills and perceptual awareness necessary for understanding and producing art.
  • Goal 3: The learner will organize the components of a work into a cohesive whole through knowledge of organizational principles of design and art elements.
    • Objective 3.04: Recognize and discuss the value of intuitive perceptions in the problem-solving process.
  • Goal 4: The learner will choose and evaluate a range of subject matter and ideas to communicate intended meaning in artworks.
    • Objective 4.05: Recognize and discuss the personal imagery and style of various artists.
  • Goal 6: The learner will reflect upon and assess the characteristics and merits of their work and the work of others.
    • Objective 6.01: Describe various purposes for creating works of visual art.
  • Goal 7: The learner will perceive connections between visual arts and other disciplines.
    • Objective 7.01: Identify connections, similarities and differences between the visual arts and other disciplines.

Grade 7

  • Goal 1: The learner will develop critical and creative thinking skills and perceptual awareness necessary for understanding and producing art.
    • Objective 1.01: Expand knowledge for organizing and creating art.
    • Objective 1.04: Understand and discuss that ideas from reality and from fantasy may be used to create original art.
  • Goal 3: The learner will organize the components of a work into a cohesive whole through knowledge of organizational principles of design and art elements.
    • Objective 3.05: Explore and discuss the value of experimentation in the problem-solving process.
  • Goal 4: The learner will choose and evaluate a range of subject matter and ideas to communicate intended meaning in artworks.
    • Objective 4.05: Explore how artists develop personal imagery and style.
  • Goal 7: The learner will perceive connections between visual arts and other disciplines.
    • Objective 7.01: Explain connections, similarities and differences between the visual arts and other disciplines.

Grade 8

  • Goal 1: The learner will develop critical and creative thinking skills and perceptual awareness necessary for understanding and producing art.
  • Goal 3: The learner will organize the components of a work into a cohesive whole through knowledge of organizational principles of design and art elements.
    • Objective 3.05: Apply diverse experimental solutions in problem-solving.
  • Goal 4: The learner will choose and evaluate a range of subject matter and ideas to communicate intended meaning in artworks.
  • Goal 7: The learner will perceive connections between visual arts and other disciplines.
    • Objective 7.01: Interpret and analyze connections, similarities and differences between the visual arts and other disciplines.