Geometry, getting our groove back

It was a fabulous break, two full weeks plus three weekends. The snow came on strong right before break started and continued right into the first week, until we had a couple feet of beautiful snowpack. Then the sun came out. Bliss! So now we are back at school and trying to get back into the swing. Geometry meets first thing, and everyone is tired.

I meet them at the door, hand everyone a slip of paper as I welcome them back. Projected are instructions to write on the slip:

1) Your name

2) Something really fun you did over break

3) Name for a quadrilateral with two parallel sides

4) Definition of a kite.

They work on it while I take roll; I collect the slips and toss them on my desk. “OK, people, it was an awesome break and now we are back. I am glad to see you all. You have amazing Geometry knowledge in your heads but it may be kind of hard to access it after all the fun time off. You may not have thought about Geometry once over break and that’s fine; in fact, maybe I didn’t either. But now we are going to blow out the cobwebs so get ready.”

We are most of the way through a unit on special quadrilaterals. I grab the deck of cards (with a kid’s name written on each card) and shuffle, and fire up the slides. We play “Name it” where I project a general quadrilateral with some extra information, draw a card, and a kid has to try to specify what kind of figure it is. They have the right to pass, but are encouraged to make educated guesses, or give a partial answer.

I do everything I can to avoid revealing whether the kid is right or not. Clever Hans is always on my mind these days. “What makes you say that?” “How sure are you?” “Who agrees or disagrees?” I encourage dissent and try to make it OK, really OK, to be wrong. I’m trying to avoid the correct answer, said once. I notice several kids are making sketches to help figure these out, which is awesome but I wish more kids were. It can take a long time for the class to come to a consensus about a difficult slide. Once they do, next slide and next card.

By the time we get through all the slides (about 20) they are worked. I have everyone get up, stretch. Go to the bathroom if you need to or get a drink, but hurry. We are about halfway through an 80-minute block.

New topic: midsegment of a trapezoid. I explain what it is, show some examples and non-examples, make sure everyone gets the definition. “Okay, what can you conjecture about these things? Consider angles and segment lengths, go!” Usually I would make small groups with the cards but today I just go with who’s already close, waving them into clumps of four.

After 10-15 minutes I call them back to order and start asking groups to share. The things they need to know about the midsegment, they’ve pretty much figured out. Every group gets parallel to the bases and corresponding angles. Most get midsegment length average of the two base lengths. One group has figured out a way to prove it by chopping the trapezoid up to make a rectangle. Nice.

Okay, what if we take this trapezoid and shrink one base down to a point? We now have the midsegment of a triangle. What can you conjecture? They get it and some kids make pretty clear, convincing arguments. I think (hope) we have dodged the bullet of the right answer, said once.

Ten minutes left. Do the homework now and you won’t have to do it at home. Work with a friend, go! I grab the stack of entry slips and thumb through. I cruise around and connect with several kids about things they did over break. “You sledded down that? Epic!” “Glad you got to see your cousins. Where were they visiting from?” “You saw the King Tut exhibit. I’m so jealous!” I also help with the homework, a little. Then the bell rings. We’re back.


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We are all born into this world, and at some point we will die and that will be that. In the meantime, let’s enjoy our minds and the wonderful and ridiculous things we can do with them. I don’t know about you, but I’m here to have FUN.
-Paul Lockhart

In theory, theory and practice are the same. In practice, they are not.

-Yogi Berra


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