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.”
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.
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.
There are so many wonderful ways to merge math with art. What are you doing in your classrooms to help your students create "mathterpieces?" Please share your comments and ideas!