Rigid Transformations Design Project

To wrap up Unit 1: Rigid Transformations, I turned OUR’s Unit 1 Lesson 17, into a project. Here are some of their final designs displayed next to other patterns “from around the world”:

The Task:

Create a tessellation or rotational symmetry design and describe the mathematics within your art.

I emphasized that I wanted their designs to be gorgeous enough to blend in with the patterns already displayed on the wall. Normally, math class isn’t supposed to be about aesthetics  because, you know, true beauty lies in mathematical ideas and deep understanding, but I think it was appropriate in this case. Caring about the beauty of their work stressed three things: (1) the importance of precision (2) the interdisciplinary nature of patterns/designs (3) the authenticity of the project.

The Set Up:

For the warm up, we did a notice and wonder about M.C. Escher’s “Night and Day”. Talk of rigid transformations came up naturally.

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I shared a slideshow that defined tessellations and rotational symmetry and had a plethora of examples:

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Students chose which type of design they wanted to create and got to work. A few sketched their own designs, but most used pattern blocks to build and trace their designs.

In both classes there were a few kids who didn’t really get into the assignment, but they perked up when I showed them how to create a tessellation by cutting a design out of a square. Great examples from mathengage.org  can be found here.

After creating their designs they responded to this prompt:

Write a paragraph about your design. Include the following:

  • A general description of your tessellation.
  • A description of the transformations that take the pattern to itself.  Be sure to consider translations, reflections, and rotations.

I modeled how to draw and label points and lines on their designs using pencil, so that they could describe the transformations accurately.


I’m still not sure whether the project was mathematical enough.  I do think it required students to think about translations, reflections, and rotations in a slightly new way, and I liked that it was both accessible and open-ended. I was disheartened by how many students wrote subpar descriptions, but I guess it suggests that it was challenging for them to describe transformations accurately in a newish context.

Next time:

  • Set clearer expectations for the amount of time they have. The project took them much longer than I expected. They had an hour the first day, half an hour after they finished their unit test, and half an hour another day when we did small group rotations.
  • Go through a peer revision process or self-check against the rubric before submitting their final descriptions.
  • Maybe have them type their descriptions so they can be printed and added to the wall, or create an additional online gallery.
  • For a speedier project, maybe just build the shapes with pattern blocks, photograph, annotate and describe digitally?

Here are the rubrics I used, and here is the handout. Would love suggestions for how to make this more rigorous!

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