December 26, 2017

Snowflakes (Geometry Review)

My contained special ed class has been following the 8th grade IM curriculum. I decided last week that I would give them a midterm exam on units 1-3 in January which meant we'd need to start reviewing some of the ideas from the geometry units. Folding snowflakes the class before winter break seemed like a good place to start!

I begin each class by projecting an image and asking "How many?" To preview the lesson that day we counted with snowflakes:

(I found this on google images but the source is great - it includes instructions for these and more!)
Students counted snowflakes, holes, points, stars, hearts and snowmen (can you see them in the center snowflake? They're wearing top hats!). They used specifics like first, second and third snowflake as well as small, medium and large holes. They reasoned about totals and made comparisons and wrote equations. Have I mentioned that I love this routine for the rich mathematics and language it invites? Because I do love this routine.

After counting everything we could, it was time to start making our own! I googled something like geometry snowflakes and came across a pdf with an FBI copyright warning which I ignored for my class but I won't post it here. Instead you can have the version with a million ads, sorry. The instructions are the same and that link includes the helpful hint to make sure the smallest triangle is on the outside at the end. I'm glad I tried to make one before doing it with the class or we would have had some asymmetrical snowflakes round 1!

Here's where the geometry review came in. As I walked around the room checking everyone had folded correctly, we discussed a vocab word for each step. Step 1: line segment, Step 2: midpoint, Step 3: vertex, Step 4: name that triangle!, Step 5: congruent. I was impressed with how close to congruent most students angles were. Often when I've done origami in class before students struggle to line things up precisely but this set of instructions was quite accessible.

Once everyone had their folds done it was time to cut. I was surprised to find most of them had never done this before and were hesitant to make a cut. I’m glad I had made a few samples the day before and could fold them back up to show how I cut. Once they saw an example they hesitantly made a cut. It was cool to see that several students unfolded after their first cut to see what happened, then refolded and cut some more. The reactions of “did that cut do what I expected?” were great. Students were definitely invested and expressed enthusiasm or dismay about their creations.

After they finished cutting I asked them to notice and wonder about their own result. Then we gathered all the samples together to discuss notices and wonderings. They were able to name the base shape as a pentagon, describe methods to create stars on the inside and outside, and how to make a tree (one not pictured in the close ups had a tree in the snowflake, the small decorated trees were a happy accident when the para cut too much and her snowflake turned into 5 parts!). Then we discussed aesthetics - we seemed to like the ones with more paper cut out. Kids were eager to cut more of their first one or try again. Everyone who didn’t know where to start cutting the first time was eager to try something new out after our discussion!

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