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Math Meets Art: Symmetry Self-Portraits

By Genia Connell on May 9, 2013

Symmetry is one of my favorite parts of our geometry unit. We always begin by looking for symmetry in the world around us. The perfect book to begin my lessons on symmetry is Seeing Symmetry by Loreen Reedy. It opens my students’ eyes to symmetry that surrounds them in letters, words, nature, and even architecture.  After reading this book, my students love to design their own geometric animals, flowers, and buildings.

Beyond drawing the symmetrical butterfly, however, I like to show my students exactly how symmetrical they are. In order to do this we create symmetrical self-portraits, an activity that uses precise measurement to get beautiful results. Below, you’ll find the directions I had my students follow to create their “other half.”

Materials

• Closeup photo of each student
• 8.5 x 11 white paper for printing
• Paper cutter
• 9 x 12 white construction paper
• Glue sticks
• Rulers
• Shape templates (optional)
• Crayons and colored pencils for coloring.

Step-by-Step Directions

Step One: First, I took a closeup photo of each student. It’s best to take it straight on, making sure the head isn’t tilted to the left or right.

Step Two: Next, I downloaded the photos from my camera and resized them in Microsoft Word so that they took up most of a full page. Once they were resized, I printed them in color.

Step Three: Using scissors, I cut out each head. Having the head trimmed makes it easier to find the line of symmetry for the next step.

Step Four: Using the paper trimmer, I cut each photo in half, straight down the middle. I used the middle of the student’s nose to help me find the halfway mark on each student’s face.

Step Five: Students glued their half-heads onto a piece of 9 x 12 white construction paper.

This next part involves some modeling. Once you show the students how to measure, most can do it with ease.

Step Six: Using the ruler, students pick a starting point and measure how far it is from the line of symmetry. Then they measure that exact same distance on the opposite side, marking the spot with a dot.

For example, Eiki started with his eye. He measured and learned that the inside corner of his right eye was 1.25 cm from the line of symmetry. This helped him know that his left eye must also be 1.25 cm from the line of symmetry. So he measured 1.25 cm and made a dot there. Next he measured the distance from the center to the outside corner, making a dot on the opposite side.

Step Seven: Students continue to measure and mark dots all around the perimeter of their heads. Once they have generated a good amount of dots, I tell the class that they have made themselves into a dot-to-dot drawing and it is time for them to connect the dots! Once the dots are connected, they can really start to see their image emerge.

Step Eight: Next, students began coloring their portraits.

Step Nine: For the final step, students added a background of their choosing. Many used shape templates or rulers to draw symmetrical shapes and patterns. Getting the background symmetrical proved to be the trickiest part for my students, and I will definitely model this step more next time.

Symmetry Meets Technology

My class loves the free app Symmetry Lab Basic. This app quickly became a favorite during all the indoor recess we had over the cold winter months. Students use the touchscreen on the iPad to draw creative, symmetrical, kaleidoscope-like works of art.

On the desktop computers, my students enjoyed all the features of Polygon Playground that not only allowed them to create symmetrical shapes, but also introduced them to tessellations.

One of the easiest ways to show symmetry is through snowflakes. My students enjoy making them out of paper, but it is much faster (and neater!) to make them on the computer with Make a Flake.

Books to Try

Thank you so much! Very good study of symmetry in art!

Wonderful activity Genia! I was just thinking about my art teacher who introduced us to symmetry and thereby Math without even our knowing that. A self portrait is a great way to get the kids to stay interested. Thanks!

Hi! I just wanted to give you an update on this project! As you know, I did the first picture in August when school first began and had great results. Well, just the other day we did them again for open house and displayed the pictures site by side! Seeing how much they grew both physically and in their ability to do this project was AMAZING! My students loved it and were just as surprised as I was! My parents loved it as well! Thank you again for sharing this idea. It is one that I plan to do every year!

Hi! I just wanted to let you know that I just did this project with my students as a beginning of the school activity! It was awesome and the pictures were great! After a couple lessons about symmetry and having them find the line of symmetry in shapes, letters, nature etc, I had them practice drawing objects...then themselves! I was really amazed at how well they did considering the school year has just begun...day 4 to be exact! I modeled how to use the ruler to measure, but they were not really ready for that so I had them use rulers to make sure their facial features lined up.

Thanks again for posting such a great activity! I will be doing this again for years to come!

Anna

This activity is AWESOME!!!! I'd love to do it at the beginning of the year for class portraits! What do you think?

Thanks, Anna! My 3rd graders did this a little later in the year, but if your students are ready to tackle it earlier, I think this would make a great beginning of the year activity! ~Genia

Amazing activity- and making their own self portrait kids will love this activity

Thanks, Roxan! They were all very proud of their finished products!

A fabulous write-up of how to do the symmetry portrait activity. Thanks so much for mentioning my book Seeing Symmetry! Off to pin this article!

Outstanding activity. Thank you for all of your time posting in such detail. Can't imagine how much time your posting takes. Thank you so for your sharing at this very busy time if the year. Anxious to try this with my class and share with teaching team!

The portrait is a great idea! Thank you for the app recommendation too. I have the Math Art book, and do projects from it every year. For some really cool symmetry puzzles, check out Dr. Gordon Hamilton's math website called MathPickle! http://bit.ly/10JxYWf