It’s always fun to do something unexpected in the classroom, and to watch the kids’ reactions. It’s especially gratifying when the event furthers a curricular goal, or makes subject matter more palatable to the students. I remember one day in middle school where we math students weren’t particularly engaged in the material, and the teacher’s attempts to salvage the class weren’t working. She was a fine teacher, and we were normally motivated learners, but it was just one of those days where things didn’t click. She sighed, scrapped the lesson, and took out a large book of M.C. Escher drawings. While most of the students had seen some of his work before, the tessellation pictures were the ones we focused on. We marveled at the intricacy and precision of his work, and before long were discussing different types of symmetry and what types of shapes could and couldn’t be used to produce tessellations. It wasn’t the lesson the teacher had originally intended (or even wanted) to teach, but she did what gifted educators everywhere do: she took the class pulse, decided to change tactics by introducing something novel to the class, and wound up still delivering math content in a way that was memorable and valuable.
Tessellations are neat things. They’re created when a specific shape is multiplied and repeated over and over, until it covers the entire surface of a plane without any gaps in the pattern. Tessellations are sometimes also known as “tiling,” and can occur in nature as well as being a man-made product. The repeated shapes shown on brick walls, soccer balls, honeycombs, and the sections of an orange, for instance, are all examples of tiling, or tessellations. The use of tessellations as a decorative motif has been traced to the ancient Sumerians, who some 4,000 years ago decorated the walls of temples and other buildings with elaborate repeated patterns. It’s a fine blending of mathematics and visual art – a fairly rare combination – and can be a great topic to engage students who usually don’t like math. The trick is to consistently emphasize the mathematical properties of tessellations, and how they in turn make the artistic properties possible.
Tessellations can be taught across the curriculum and to a variety of age groups. Younger students can use pattern activity blocks to emphasize patterns and symmetry while working on their problem-solving skills. Older students can calculate distance using individual tile measurements, explore the different types of symmetry on a plane, and figure out which shapes tessellate and which ones don’t. All ages can create their own tessellations, using either simple shapes like triangles and squares or more complex irregular shapes. Tessellations can be studied in the art classroom, and in science by examining symmetry in nature, such as in animals and plants.
This week I’ve highlighted three hands-on tessellation lessons with activities for a variety of ages. Please be sure to read Peggy’s companion column where she discusses how to use these resources and others in the classroom. We’ll also be featuring several new lessons and resources on this topic each day throughout the week on our Facebook and Twitter pages, so be sure to take a look.
Exploring Tessellations
Subjects: Geometry, Art
Grade: K-2
In these activities, students learn about tessellations and how to create them. They learn to tessellate with one shape, two shapes, and finally with three dimensional (3-D) shapes. This lesson was produced by the Geometry Playground at Exploratorium, a museum of science, art, and human perception located in San Francisco, California. The Exploratorium offers a host of materials for educators, including lesson plans.
Medieval Tessellations
Subjects: Geometry, Art, World history
Grade: 6-8
The major focus of this lesson is to surreptitiously introduce the teaching of math concepts across the curriculum. Students will each produce a tessellation of original design that effectively uses shape, pattern/repetition and color to create a "beastie" inspired by bestiaries of the Middle Ages. This lesson is a produce of the Incredible Art Department at Princeton Online, and offers a plethora of materials for art teachers, art students, parents, homeschoolers and artists.
Let’s Tessellate
Grade: 9-12
This lesson is a hands-on, technology-based project that will take place in the classroom and computer lab. Students will discover which regular polygons tessellate the plane by constructing polygonal tessellations. Students will also use a spreadsheet to calculate the area and perimeter of the polygons. This lesson was produced by the Alabama Learning Exchange (ALEX), an education portal that provides lesson plans, education-related podcasts, best practices, and Alabama professional development activities. Lessons are aligned to Alabama Content Standards.
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