Monthly Archives: December 2014

‘Twas the day before break…

My goal for my Geometry classes today was to be as mathematically productive as possible, given that it was the last day of classes before break. The plan was to review the last assignment, take the quizlet (what my department calls formative assessment), do an extension problem, then make a Koch Snowflake if there was still time.

The extension problem was the “Shortest Path Problem” which I highly recommend.

Shortest path problem

It turned out to fit perfectly with what we’re learning right now. It also sparked some rich conversations and good reasoning, and everyone could at least venture a guess, even if they didn’t really know what to do to figure out the exact shortest path.

This plan was carried out differently in each of my three Geometry classes. In the first class, I reviewed several problems and concepts, kids followed along, asked questions, the usual. They took the quizlet. I passed out a half-sheet with the scenario typed out on it. I didn’t include a diagram, thinking that the kids should make the diagram. That was a mistake because the wording isn’t exactly clear, so some kids drew the tent and camper on opposite sides of the river and all sorts of random things. So I had to draw the diagram up on the board for everyone, which slightly killed the magic, but at least we were all on the same page.

A few kids calculated the distance of a path, but not the shortest, and then wanted to be done. I needed a way to motivate them to keep working. In a rare moment of brilliance, I decided to keep score. I announced “Jesse found a path that’s 1,518 feet, can anyone beat that?”. Then I’d write the student’s name and their shortest path on the board. It became a competition to see who could find the shortest path. I let things linger too long in my first class because a few students were really getting into it and asking wonderful questions like, “how do you know that’s 450 feet” and “can you show me how you got that”. So unfortunately several kids had checked out, but at least everyone did something with the problem.

In my other two classes, I skipped the homework review and went straight to the quizlet because there was no way they were going to sit and listen to me blah blah blah about their homework problems on dilations and scale factors. In my first afternoon class, student behavior dictated that decision. In my second afternoon class, I asked them what they wanted to do, and almost everyone said, “let’s just take the quizlet”. So in those classes, there was plenty of time to do both the shortest path problem and the Koch Snowflake.

This time I just asked them to read the problem on their own, and then I read it aloud and drew the diagram as I read so everyone started out with the correct diagram. In one class several kids said they didn’t know what to do to get started, so I said “guess and check” or “if you were the camper, where would you go if you wanted the shortest distance”. This was an excellent starting point for those kids.

The snowflakes were fun too. We saw the Sierpinski Triangle this year, so I brought that up again as a reminder of what a fractal is, but then said that the fractal they were about to make was going to be more holiday-themed. I gave everyone some triangle graph paper to help them with their triangles. At first I thought maybe I’d have them construct the equilateral triangle, but using the graph paper was a good call.

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Filed under fun, Geometry

The teacher learns

I’m getting better at making my expectations clear. Giving quick, short directions right away and repeating them until all students are with me sounds obvious, but it’s easy to move on without some kids and then you never really get them back.

Always be one step ahead of the kids. Pass out and explain the next task to the kids before they start their quizlet so that kids who finish early have something to do.

I freaking love warm ups. Haven’t figured out a system for them yet though. Should I preprint the questions on a half sheet? Should I grade it? I think the answer is probably yes to both of those questions, but I don’t love the idea of using more paper or having more things to grade.

Graphic organizers are great. A few phrases in a few boxes is more writing than we usually do in math class. They work on it individually, then in groups, then I solicit answers and go over it as a class.

That reminds me: cold-calling = awesome. I have cards with student names on them that I use. Open ended questions or questions with more than one right answer (give me one of the transformations we’ve talked about) are best.

I’m almost half-way done with my first year! The lows have been low, but the highs have been high, and I keep reminding myself just to be better than I was yesterday. Always learning.

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Filed under classroom management, productive struggle

Functions. Also, snowboarding.

Two things are occupying my mind right now: functions and snowboarding.

First, functions. Just finished up the unit on functions and transformations in FST (2nd half of an extended Alg2 course) , and I’ve been reflecting on what was good and what was bad.

The good? Using Desmos and sliders to see the effects on the graph. Doing a simple but effective investigation on f(x)=1/x. Color-coding graphs of transformations when there are multiple happening at once.

Could be better? I didn’t start color-coding until we were transforming sine and cosine. Kids like colored pencils and picking out what color to use. Next time I’m going to start doing this right away. I also did a function wall project where the students had to transform a function and add it to the wall (see picture). This was OK but I waited until the day before the test and had them do all at once. I should have had them add to the wall gradually, as we did each function.

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The bad? My review day. I feel like I didn’t do much of a summarizing activity. I threw the function wall project at them and then gave them a practice test. Not the most helpful. Next time I’d like to culminate the unit with a final summary. Maybe some sort of writing activity or graphic organizer.

What else? Curriculum. The curriculum I was given just confines the idea of functions and their transformations to one unit, which is ok, but I’m intrigued by the idea of examining the functions and their transformations one by one, a la Greg Waddell.

On to snowboarding. I had the crazy idea to start the snowboard and ski club at my school. It turns out the idea was popular enough that I’m taking 30 kids to a ski hill on Friday. Organizing everything and collecting money has been annoying (I don’t have the patience for record keeping, unfortunately), but it should be a really fun trip. I’m glad so many students are interested, and I’ve had two students step up as leaders. It’s been a good experience so far, and we haven’t even hit the slopes yet!

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