The Symmetry of It All

Valentines Day at our house is all about construction paper. Making hearts and cards and decorations take over free time. That excitement extends well beyond when the candy is all eaten. I’m all about short cuts and time savers after the holiday, so I show the kids that if they fold their papers in half then they only have to cut out half of the heart to get a full heart. Of course they ask why - the question that rules every house with preschoolers. So I explain and we veer off into an adventure about symmetry.

A heart is a symmetric shape. That means that one side is the exact same as the other side. Said another way, if you fold it in half on top of itself, the sides will match up. In the case of a heart, it is vertically symmetric. I refrain at this point to show them that it is not symmetric about a horizontal axis and I’m glad I did (we’ll get there in a second…)

“Is anything else symmetric” they both want to know. Rather than telling them, I ask them to sit down and grab a bunch of paper and a pair of kid-safe scissors each. Then I ask them to each pick a shape. Briana picks a rectangular prism so I first have to talk her down to a regular 2-D rectangle. Abigail picks the triangle. I pick a circle.

We all cut our shapes out, fold them and see if the shapes are symmetric. I tell them to allow for a tiny bit of mismatch due to the fact that our cuts aren’t perfectly straight lines.

We discover that the rectangle and the circle are symmetric “no matter what”, aka vertically and horizontally. The triangle is much more interesting. It is symmetric if you fold it side-to-side BUT if you fold the top down it is not!

This unexpected result, since we did the triangle last, has piqued the girls’ interest noticeably. They scan the room looking for triangular things that might “work right” like the rectangle and circle did. I let them search to their hearts content, folding papers, foam shapes, doll blankets, and everything they can find in a triangular shape. In the end they concede that the triangle is only horizontally symmetric.

Then they recheck the heart that they thought they knew all about and discover that it too is only symmetric about the vertical axis. They are literally jumping up and down with surprise. I am cracking up. You never know what is going to tickle their imaginations.

Now they want to try other shapes. We find that the square and the octagon behave but the pentagon has a triangle on it and that triangle ruins everything.

I ask them how they know if something is symmetric. They quickly answer, “Fold it!” What about you, are you symmetric? They touch their toes and laugh at Mommy. Of course not. But what about if you could fold sideways? You have one eye, arm, leg on each side. We think about it. “Oh no, Briana!” Abby exclaims. “We are…a…TRIANGLE!” I laugh. We are not triangular but we are only symmetric in one direction.

I tell them to draw a picture. Anything they want. Then fold the paper in half and only look at half of the picture. Cut it out and open it up.

Briana draws a girl in a dress.

Abby draws a star.

When the shape is cut out, we unfold it to see the symmetric versions of our drawings. See, you can make any shape symmetric on one axis if you draw half on a folded piece of paper and cut it out.

  

Then we try another couple of pictures each.

“Nope, the hand is not symmetric…unless we cut off the thumb” Bree tells me, cutting off her thumb (on the paper) to prove her point.

Briana then insists that I take a cute picture of her and her mannequin for my blog - nevermind that we are doing this before bedtime and she's in pjs. (Uh-oh, the kids are catching on! At least for now, they love looking at “Mommy’s stories about our activities on the computer”.)

Then we compound shapes – making a house out of a triangle and a square, an angel out of the girl and what started out as fire. We talk about the changes to symmetry.

Since we’re folding and cutting, I show the kids one last thing - paper dolls. Sort of. I never could make those things!

There is one thing that I want to highlight with this blog – you guys know by now that I advocate for directly and succinctly answering all of your kids’ questions, even if you have to look up the answers together. I want to add that an answer does not always have to be verbal. Demonstrations and activities that they can do themselves are many times the best way to answer a question. Just think, if I’d told the kids that some shapes are symmetric and some aren’t they would not have had nearly the grasp on the concept that they have by figuring that out themselves with some guidance.

<3 Pedigreed Housewife