Monday, February 17, 2014

"Murdering" Triangles

One of the biggest benefits of having two classes learning the same material at different paces is that I get to teach the same lesson twice but not one right after the other. This proved to be very helpful when going outside of my comfort zone and teaching a more hands on lesson/activity to help students learn the angle sum of triangles and then find a formula for the angle sum of other polygons. Initially when I did this activity with 2nd hour which is the students who are at level for seventh grade I found there were a few things missing which I thought could be helpful to students for the next time. It also just so happened that the first time through this activity I was observed by COE a second time. My coordinator thought this activity was very fun for the kids and even told me that he was able to learn something from the lesson he didn't know before. He thought the lesson was refreshing to see since it was so different from the lesson I had done the first time he observed me. He did suggest that I provide some sort of closure for the students, which I failed to provide for second hour and he felt that they might not have fully grasped what I wanted them to from the activity and a good way to gauge that would be asking them simply "So, what did we learn today?"

When I did this same activity with 3rd hour I knew that I wanted to provide more closure with the students and also have them help develop a formula we could use to find the angle sum of polygons. I figured since 3rd hour is the more advanced students they would need less guidance than my first class and would be able to come up with this formula with much less help than second hour would have needed (I didn't do this generalization with 2nd hour). Knowing how chatty 3rd hour can be and having the lesson on a Friday AND that Friday being Valentines day AND being the day I was observed by my content coordinator...well needless to say this activity was either going to be great and productive or a total flop.

While in the lesson I felt that though the kids were SUPER chatty, I was able to reign them back in and keep them focused enough to take from the activity what I wanted them to...

Funny side note: when I asked students to rip off the two angles of their triangles whose vertices they hadn't placed on the straight angle, many students responded by gasping and complaining that we were murdering triangles by doing such a thing. Thought that was something only math loving middle schoolers would come up with and had a good laugh with them about it.

The students asked lots of questions that I wasn't really prepared for, and I like to think that I think of nearly every question before going into the lesson but this really shouldn't have surprised me since this class is so witty and can come up with enough questions to fill an hour just full of questions. There were many questions that students asked about which I wish I had had more time to address and especially after meeting with my content coordinator and talking through how to answer the questions. I think I'd really like to take the time (if I have it) to go back and discuss with students WHY we can't/can divide the polygons into triangles a variety of different ways and have students explore different ways of dividing up our polygons and how to make those work (if possible). I'm hoping to spend some review time having students look into this along with go back and look at more variety of triangles to solidify our "proof" of the sum of the angles of every triangle equaling 180. I think next time I would also remove the last two polygons (lightning bolt and star) from the hand out until students had already gained a deep understanding of how to find the sum of the angles, then (especially with an advanced class) I might give them those last two polygons to find the sum of the angles as more problem solving types of questions to push the limits of their understanding.

The activity didn't go poorly by any means; it actually went very well there's just a few things I would like to change. With a little guidance from me the students were able to come up with a general formula for finding the angle sum of polygons at the end of the lesson. Which my students before weren't able to do and didn't have the time to do. At the end of the lesson as I was passing out the worksheet with a reflection and take home piece, I had students cover with me possible answers they could have for their reflection piece on what they learned from the activity. By doing this I was able to get all the students involved and thinking about the lesson along with gauge their comprehension of what we'd just done and know if they were taking away from the lesson what I wanted them to. This wasn't something I did with 2nd hour and was really helpful because I realized how much my students had taken away from the activity and even though they were chatty they really learned a lot from the activity and had a lot of fun.

There are definitely ways that I could shorten or extend this activity based on how in-depth I want my students to explore and how much I think my students can handle. But overall I think for my first time stepping outside my comfort zone and doing an activity with students I was able to create an activity that engaged students, was fun, and had them learning and taking away from the activity exactly what I wanted them to.

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