Symmetry: A First Grade Exploration

This week I was able to learn a tremendous amount from the first graders about how to best structure a lesson on symmetry.  As a librarian, my first tool is usually a book.  I startedscreen-shot-2016-09-30-at-1-00-18-pm this lesson by sharing the book, Let’s Fly a Kite by Stuart Murphy and illustrated by Brian Floca.  This sweet book introduces, without even mentioning the mathematical term, symmetry.  A brother and sister discover it as they make a kite, drive to the beach and enjoy a picnic lunch.  Their stealthy babysitter teaches them about dividing things in half and how different lines can make equal and unequal parts.

After reading the book, we quickly viewed some images on the screen to talk about the ‘big’ mathematical word, symmetry and how things can be symmetrical.

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Next, I explained that I had a challenge for them today.  Using ONLY 2 x 4 and 4 x 4 Legos in a variety of colors, they needed to build one half of a design with their partner.  (Our Lego wall is over 28′ long, so each student could effectively have their own blue ’tile’ to build on.  You could do the same thing with baseplates.  Because my laptop has a Brick Book Cover, I actually used my laptop case to ‘build’ an example.



As I taught the lesson throughout the day, I constantly tweaked it. At first I had students building with dozens of Lego bricks and it became far too abstract for their partner to try to re-create.  There were some students who used a ‘different’ line of symmetry than the one that I had ‘intended’ for them to use.screen-shot-2016-09-30-at-2-15-20-pm

For example, my own initial example was WAY TOO hard for first graders.

By the end of the day, I had decided that the central concept, symmetry, was being polluted by the massive amount of bricks the kids had at their disposal.  So, I quickly sorted the Lego bricks and put 12 bricks of the same shape and color in two different bags.  Then, each ‘group’ got a corresponding bag.  Then the challenge became, with the same 12 bricks, can you make half a design and then have your partner mirror it?  This was far more successful and a whole lot more fun for both the kids and I.  In the end, the kids connected to the work they had done in art around the same concept and that was the goal all along!


Harmonograph Explorations

Several months ago, I saw an image on Facebook that got my mind reeling.  The photo was of what looked like a giant string art project created on a grassy area.  Amy Hartman posted the image on the STEAM Art Educator’s page.  String art example

I wrote a detailed blog post about the projects we’ve done for years and how the image above inspired me to collaborate with fourth-grade classroom teachers and our math facilitator at the end of the school year.

I didn’t, however, have time to write about another tangent I began to explore with my students.  The whole idea of lines and the beauty that arises out of their mathematical principles got me looking into the idea of pendulums being used to create art.

After looking online at various designs, my colleague Josh Burker’s simple design seemed to be the perfect way to introduce the concept to my students.  I had some scrap lumber on hand from our wagon project earlier in the year, so I laid out a design similar to Josh’s only a little bit bigger.

IMG_1196The harmonograph design had a few changes from its original.  I added the wheels to make it easier to move around and I replaced the strings with a chain to make it easier to change the length.  The last enhancement was the addition of a sheet of steel.  This allowed me to use magnets to hold the paper in place.

IMG_1204The tape dispensers act as weights.  By moving the weights around, the pendulum swings at different frequencies and creates unique designs.

IMG_1198The students  helped me create a pen holder that solved the problem of ‘wobble’ as the surface moved under it.

IMG_1197A completed drawing.


Detail of the above completed drawing.

We learned an awful lot about creating art with a harmonograph.  We found that ‘gel’ pens were the most effective type of drawing instrument.  We also learned that glossy paper, particularly the ‘old’ photo paper that we once used to print photos on inkjet printers, seemed to work exceptionally well; the surface creates less friction and allows the pen to glide more smoothly over its surface.


The longer the pen is allowed to swing, the more intricate the designs.



This was the result of several evolutions.

Because I’m always seeking to make connections, I started exploring how we could link technology to this exploration.  I was not disappointed.  There were several phenomenal iOS apps that allow the user to experience using a harmonograph without having to change paper or pens.  My favorites are:


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Harmonograph ToyScreen Shot 2016-07-20 at 12.32.17 PM

There are even a few online examples that are fun to explore:

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The virtual harmonograph on the Chrome Store is elegant and simple to use.

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Of course, because I am a total library geek, I dug in and found some FASCINATING articles about some of the first designs that were created in the 1880’s.  There is a mindblowing collection of writings and designs on the Historical Society of Pennsylvania by John Andrew.  He explored the connection of sound frequencies and how they are represented.

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My next exploration is going to be creating my very own version of a two pendulum harmonograph.  The image on the left is from one of the most comprehensive resources for those who want to understand the beauty and mathematical principles behind harmonograph creations, Walking Randomly.



If you are curious about making your own harmonograph, here are some instructions from 1920 that will show you exactly how to make your own!