Simple Symmetry

I love to peruse education catalogs and check out all the latest and greatest resources that are out there, but sometimes I really wonder if people really buy all that stuff? I was perusing the other day and came across geometry mirrors, a math manipulative I’ve never even considered buying. “Watch students grasp the concept of symmetry as they use these plastic mirrors!” I immediately thought, “Kids don’t need a plastic mirror. They just need to make a symme-tree.”


First, you need to understand the basic principle of symmetry if you don’t already. For a lesson on what symmetry is, watch this video.  It can be used for you to better understand how to teach it, or even for kids to watch with you to teach them the basics.

Now take a piece of green construction paper and fold it in half the long way. While still folded, cut a simple tree shape. Because it’s folded in half you will be naturally be creating a symmetrical tree when you unfold it.  (You can make a pine tree with solid green or include brown construction paper as a trunk on a deciduous tree.)


Show your kids how any shape that can be perfectly folded on itself is symmetrical. Some shapes even have more than one line of symmetry (rectangles, diamonds. and squares are examples of this.)  Think about how many lines of symmetry a circle has! After each kid has their basic symmetrical tree, ask them to cut out other symmetrical shapes out of construction paper. If this is difficult for them to realize on their own, show them how they can fold the paper in half before cutting.




Do you really need the tree to teach this? Well, no. . . but there are an awful lot of new math terms out there to grasp and why not help out with this TREE memory trick?  Trust me, they won’t forget symmetry after this simple activity.


Have the kids draw one or more lines of symmetry on their shapes to solidify the idea.


Additional Layers:

  • Whenever possible, I love to have kids moving while learning. Go on a walk and find things that have a line of symmetry.  It may be street sign, a flower, an ant, or the rectangle of the sidewalk.  Let kids spot as many symmetrical shapes as they can.
  • The above lesson is dealing with symmetry in 2-D. Think about how symmetry works in 3-D. Get a ball and figure out what it would take to divide it symmetrically. (Hint: instead of using a LINE of symmetry, you have to find a SHAPE of symmetry.)
  • Talk about how symmetry and reflection are related.  And yes, it’s perfectly fine to use a mirror to teach this concept, just don’t waste your money on buying a “geometry mirror” when any mirror will do just fine!
  • Make a symmetrical painting.  Start by folding a sheet of paper in half.  Open it back up.  Put paint on one half, the fold it again to squish the paint on to the other side.  When you open it back up you’ll have a reflection.

Here is one we did of fireworks using dark paper and glitter glue:


Fireworks-Art-(2)And here is another one of a tree:


More From Layers of Learning:

If you liked this post, you might also like these other simple math ideas from Layers of Learning.

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