This is the lesson I intended to use for evaluations--you know what I mean--the lesson you plan to do in the next week and a half that you think will make you look the best. Things didn't go 'terrible' but neither did we actually get to the cool part of the lesson either.
In our study of similar figures, I use Math Assessment Project's: Floodlight Shadows. It does an excellent job progressing with a relatively simple group task (#2) involving similar triangles and then switches things up asking what happens to the length of the shadow when the football player moves (#3). The second question asks for a solution of an instance. The third question asks for a general solution method... a proof. All the resources you need are in the link.
Okay, but we gotta back up. I have two sections of Geometry this year--3rd and 6th periods. My Principal decided to come for my second section. I'm thinking "Sweet! I'll get some practice in." I had all sorts of grand ideas about how things were going to play out. Today I need to show off my mad teaching skills. It didn't happen.
Turns out the homework assignment from the night before ate most of my class period today. Now, in my Algebra 1B class this would have been horrid. In my Geometry class it's usually only frustrating to me--I have an agenda people!--everyone else seems cool with it.
Turns out the homework assignment from the night before ate most of my class period today. Now, in my Algebra 1B class this would have been horrid. In my Geometry class it's usually only frustrating to me--I have an agenda people!--everyone else seems cool with it.
 | Quick aside: sometime this last Fall I stumbled across a post by @edcampOSjr about his classroom redesign. I stole a little nugget about a classroom microphone kids can drop when they nail a problem. In my school, Geometry leans heavily towards proofs. Because I want students to be constantly evaluation both good and bad proofs, we have lots and lots of student presentations of solution methods. I introduced the mic just before Christmas break. I'm too cheap to buy a real broken mic of eBay so we make do with a toy mic. We've had to piece it back together after some rather dramatic mic drops but it still does the job. |
In 3rd period, as students asked questions on problems, other students volunteered to present their solution methods. Hands were raised. Students called on each other. Mics were dropped. Laughter. Shouts. 10 minutes on the task (up through #2). Whatever, I felt brilliant.
In 6th period, I gave the students a choice, we could either go over questions at the beginning of class and have a small start on the Floodlights task or we could start the Floodlights task and go over the homework the next day. Secretly, I hoped they would choose the lesson. We put it up to a class vote and they decided to check the homework. Okay, if things go like they did earlier in the day everything will be fine. As students asked questions on problems, ...crickets. Having them volunteer was sooo much harder than usual. Having them ask each other questions was like pulling teeth. It was akin to losing 2 months of classroom culture-building overnight. Sigh.
In 6th period, I gave the students a choice, we could either go over questions at the beginning of class and have a small start on the Floodlights task or we could start the Floodlights task and go over the homework the next day. Secretly, I hoped they would choose the lesson. We put it up to a class vote and they decided to check the homework. Okay, if things go like they did earlier in the day everything will be fine. As students asked questions on problems, ...crickets. Having them volunteer was sooo much harder than usual. Having them ask each other questions was like pulling teeth. It was akin to losing 2 months of classroom culture-building overnight. Sigh.
6th period ended their homework discussion with 15 to 20 minutes left of class. I pulled out the big honking white boards and set them to work on the task. One or two groups were ready by the time class ended but not enough for a classroom discussion. Homework was to complete task #2.
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We started off day 2 with a quick discussion about solution methods for #2 in the task, the length of the football player's shadows if he stood in the middle of the field. Every group had a solution method. Every group used proportions. It was a short discussion.
Then we upped difficulty level. What would happen to the football player's shadow when he walked towards one of the floodlights? Would the total length of both shadows stay the same or change?
Many groups attempted to extend their previous solution method using proportions. It worked for a couple of them but there is a lot of symbolic manipulation involved. At least half the groups who tried using proportions got stuck.
The actual lesson from mathshell.org has sample solution methods for students to evaluate after they've attempted the task. Last year I used them. This year I wanted to give it a little more time. I had them printed off, just in case. I stopped the groups with 10-15 minutes left of class the second day. In both of my classes, I had one group that either didn't complete a solution method or didn't have a promising plan of how to get one.
With our last 10 minutes of class, students presented solution methods. One group had a solution so elegant they received applause from the class (6th period). They dropped the mic with wide grins.
Homework was to revise a solution method they'd seen in class. I'm not very good at having students revise their work. I figured this was as good a time as any. We rework drafts over and over in English and History. We do experiments over and over again in science. Why not in math? I asked for complete sentences, diagrams, etc. We'll see.
Next year I'm going to split the task slide and give #3 it's own slide. Having #2 and #3 on the same page gave away too much about where I wanted to go. Some students had already attempted #3 at home the night after day 1 and controlled the discussion in their groups for too much of the time on day 2.
The actual lesson from mathshell.org has sample solution methods for students to evaluate after they've attempted the task. Last year I used them. This year I wanted to give it a little more time. I had them printed off, just in case. I stopped the groups with 10-15 minutes left of class the second day. In both of my classes, I had one group that either didn't complete a solution method or didn't have a promising plan of how to get one.
With our last 10 minutes of class, students presented solution methods. One group had a solution so elegant they received applause from the class (6th period). They dropped the mic with wide grins.
Homework was to revise a solution method they'd seen in class. I'm not very good at having students revise their work. I figured this was as good a time as any. We rework drafts over and over in English and History. We do experiments over and over again in science. Why not in math? I asked for complete sentences, diagrams, etc. We'll see.
Next year I'm going to split the task slide and give #3 it's own slide. Having #2 and #3 on the same page gave away too much about where I wanted to go. Some students had already attempted #3 at home the night after day 1 and controlled the discussion in their groups for too much of the time on day 2.
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