A NEW Way to Teach Symmetry. It’s called Silk.

As a former geometry teacher, I remember teaching students about line and rotational symmetry using images such as hearts, stop signs (octagons), stars, equilateral triangles, and even the alphabet (T, I, A, M, N, etc…) — see figure below.  So when I stumbled upon Silk (www.weavesilk.com), I was intrigued at the possibilities of having students create symmetries of their own to learn the concept.

Can you identify the symmetries in the example above?  Which color(s) has line symmetry and which color(s) has rotational symmetry?  What kind of line symmetry (vertical, horizontal) and rotational symmetry (45°, 90°, 180°) do they have?  Notice how the yellow and gray silk designs have both line (vertical and horizontal) and rotational (180°) symmetry while the purple silk design only has line (vertical) symmetry.

If you turn off the “Mirror across center” option in Silk, you can make symmetrical drawings that are more difficult to identify.  If you also select “No rotational symmetry” on the slider, you can create a drawing with no symmetry.  Click “Share” to connect to social media or copy a link to your drawing.

So, what could you do with this in your class?

Here are some ideas of how STUDENTS can use their symmetrical drawings created with Silk.

• Share them via a blog, Google Slides, Google Classroom post, or Padlet.  Students can comment or analyze each others’ creations to identify the symmetries.
• Each student can make a slide presentation with 2 sections, one for line symmetries and one for rotational symmetries.  Identify each drawing in the line symmetry section as having vertical and/or horizontal line symmetry with an explanation of why.  Do the same in the rotational symmetry section including the degrees of rotational symmetry for each example.
• Make the drawings an image background in Google Drawings on which the student can draw lines and add text boxes to explain the symmetry in their drawing.  They can share their drawings with the teacher and/or fellow students directly via Google Classroom, insert it into a Google Slides presentation or download it as an image file and share it via Padlet, Pinterest, or other sharing applications.  If the teacher shares a Google Slides presentation with the whole class, students can add their images and explanations to it so that they could learn about symmetry from their peers.  Then, students can give feedback (critique or even correct) their classmates’ work.
• Students can download their drawings of symmetry to create questions.  These questions can be asked via a Google Forms quiz which they can link to on Google Classroom, Padlet, TodaysMeet, or other sharing applications for their peers to answer.

Here are some ideas of how TEACHERS can use Silk.

• Demonstrate line and rotational symmetry by drawing each type and discussing the properties of each type.
• Create symmetrical drawings as displayed above with multiple colors representing various types of symmetry.  Ask students to identify the symmetry for each color.
• Share this Google Slides presentation using Google Classroom so that each student gets a copy.  The students can add drawings that fit the title of each slide.  For example, students can use 2-fold rotational symmetry (as Silk calls it) to demonstrate 90° rotational symmetry.  Students can submit their Google Slides presentation via Google Classroom.
• Create drawings to put on a quiz using Google Forms or some other online quiz application such as Socrative, Formative, or Kahoot!
• Use the Desmos Graphing Calculator to overlay a coordinate plane on top of your drawing and then show how the relationships between symmetry and slope.  Here is an example.  Students can discover the appropriate slope for the line of symmetry and then discuss why it works.  Discuss this using polar coordinates as well.
• Challenge: Have students figure out how to create 45° rotational symmetry by combining drawings with 90° rotational symmetries.

The possibilities are truly endless.  I highly recommend you give students an opportunity to explore and create with this tool.  It definitely ups the fun factor and highlights the influence of symmetry on art.  Check out this simple Google images search for “symmetry in logos” for more examples of this.  If you think of a novel way to use this tool, please share it in the comment section below.  Thank you and enjoy!