Kal-el has been doing a lot of skateboarding.
Something he has been practicing a lot lately are 180 flips getting ready to work up to a 360 flip. If you have no idea what I'm talking about here is a video of how to do a 360 flip on a skateboard.
Kal-El has been avoiding geometry lately, but all of this flipping has led to a lot of talk about 180's and 360's. Sometimes when he has a failed attempt my husband will say, "hmm, that was more like a 120 kiddo." Kal-El asked us, "What do all those numbers mean." Now what I said will sound like I was putting him off, but what it really is is a very calculated maneuver. "It's geometry. You have to know a lot about geometry to skateboard. Those numbers are second grade geometry." Now that part about second grade is not really true. In a Montessori environment a child could easily do this work prior to second grade or may not get to it until later. I knew that if he thought it was "second grade" work he would want to do it immediately (as any self-respecting first grader would).
Sure enough, yesterday I heard the school bell ringing in the middle of the afternoon. I peeked in the school room to find Kal-El sitting at the table with his hands folded and paper set out. He said "I want you to teach me about all those geometry numbers in my skateboarding right now."
I pulled out the Montessori protractor, the fraction circles, and pulled up the appropriate page in the Keys of the Universe elementary geometry album. I have three elementary geometry albums. The reason I chose the KotU album is that it has all of the stories in it. In this case I needed the story about the Babylonians and how the circle came to be divided into 360°. Hint: it has to do with a close approximation of how many days it takes the Earth to revolve around the Sun. This is another example of how Montessori education works...Kal-El personal interest led to a geometry lesson that led to a history lesson that linked to an astronomy lesson that stemmed from the First Great Lesson in the first place. Fun!
This was a good time to learn some circle vocabulary while we were at it. After I read the story about the Babylonians, I explained how the Montessori protractor works according to the album script. I told Kal-El that the distance all around a circle is called the circumference. I quickly pulled a figure of a little man out of our miniatures and Kal-El had the man walk the circumference of the circle.
Next I explained that if the man only walked a portion of the circumference the portion he walks is called an "arc" and that when skateboarders refer to a 180 or a 360 they are measuring the arc they made (according to central angle). We put a smaller fraction piece in the protractor and I used poster putty to add a little skateboard to the miniature man's feet. We put the man along the first side of the angle and Kal-El had the little man do flips to the other side of the angle so he could observe that the outside foot was traveling along the arc.
It popped into my head that this was a good time to explain how a drafting compass works. I put a little dot next to one of the miniature man's feet to represent the stationary foot. Then, I pinned a pencil (with my hand) along side the man's other leg. I showed Kal-El on a piece of paper how if I made the man do a flip on his skateboard while I held a pencil there it drew an arc on the paper. I showed him that if the many did a 360 on his skateboard it drew a complete circle. Obviously I couldn't take a picture of this because I was in the middle of making a miniature man do a skateboard trick while I was pinning a pencil to his leg... BUT! Here is a picture of Kal-El enjoying repeating my trick with the little man without the pencil to retrace the circle on the paper.
Afterward I pulled out the drafting compass and pointed out that the man's two legs were like the two legs of this compass. The compass leg with the pin makes a dot on the paper when you use it just like the dot I drew near the man's stationary leg. The second leg has a pencil strapped to it just like I did with the man.
Kal-El experimented with drawing some circles and arcs with the compass.
Kal-El still needed more practice with the protractor and needed to learn how to notate degrees so I invented a little game off-the-cuff. I pulled out a bunch of different-sized pieces from the fraction circle drawers. I told Kal-El that a bunch of skateboarders were having a 180 competition and this pieces represented the arc of each skateboarder's attempt. His job was to measure each piece, notate the measurement below, and determine the winner.
After finding results for the pieces I set out Kal-El replayed this game on his own many times for about ten minutes. Then I changed the game to a 360 competition and showed him how we could use multiple fraction pieces to represent bigger arcs.
We have plans to continue this work to talk specifically about angles rather than arcs and have some fun ideas how to keep that angle work linked to skateboarding!