# Monthly Archives: November 2014

## Motivating 1/x

We’re deep in a functions unit in FST (year two of a decelerated Algebra 2 course), and I love it. I love the concept of a relationship that takes inputs and produces outputs. I love visualizing functions with graphs. I love that functions feel natural and intuitive. I’m trying hard to share this enthusiasm with my students. They’re doing well with it so far, and it’s interesting to see how they think about functions.

Last class, I wanted to introduce f(x) = 1/x. I love this function. I love the discussions about division by zero and division by really large numbers and how the graph represents those ideas visually. My colleague shared a fun investigation with me, and I am so glad that I tried it out. At first I was hesitant because I know that I don’t explain directions well, but I focused on being very explicit and modelling each step. The kids investigated the breaking point of spaghetti. I wish I had some photos, but the students placed a dry spaghetti noodle over the edge of the table and hung a paper cup on the end of the noodle and added pennies one by one until the noodle snapped. The fun factor was definitely there- the kids enjoyed predicting when it would snap and liked watching the pennies crash to the floor.

Besides being fun, the activity modelled the function effectively. The kids recorded their data (length of spaghetti vs number of pennies), and I used Desmos to display some class data.

VoilĂ , a hyperbola. The investigation gave the kids a good understanding of how the function behaves and why the graph looks the way it does. In retrospect, I should have done more of a “Noticing and Wondering” activity with the graph, but instead I just asked some questions like “What happened as the length of the spaghetti got longer?” and “What happened if the length of the spaghetti was really small?” which probably did too much of the thinking for them, but oh well.

Filed under FST / Algebra 2, fun, graphing, group work

I came home from school on Tuesday and told my boyfriend that I wasn’t going back. Of course, I was overreacting to one bad day, and after a good night’s rest, I went to school as normal the next morning. The rest of the week went great, so there you go. It’s so easy to focus on the negative and forget the positive that I have to continually remind myself of what’s going well in my classroom, or I’d never make it.

Last week, my administration granted me the privilege to watch an experienced colleague teach a class. I watched a Biology class that was so well taught that I left feeling inspired. I used to think classroom management was my biggest issue, but after watching that lesson, I realized that time management might actually be my biggest problem. I wasn’t managing time at all. (That sounds crazy, but it really shouldn’t surprise me. I won “Most Likely to be Late to their Own Funeral” in high school. The clock in my car is always set to a random time. I never rush anywhere or feel a sense of urgency.) For example, I used to set the kids off on a task with absolutely no time-frame. I guess I thought that every kid had to finish before moving on.

To avoid wasting so much time, I need to keep things moving fairly quickly. I need to set time limits on activities. I can’t have kids messing around because they think they have the rest of the class period to accomplish something that really only needs 10 minutes of concentrated effort. I need to have tasks for kids who finish early, and I need to recognize that there’s not enough time to wait for 25 kids to each discover something on their own. One thing that has been effective for me is to have a list of two things that students need to accomplish within a given time-frame, with the second item being one that doesn’t require all students to get to before moving on.

Lessons learned there for sure, and that’s a good thing. Other good things: Had a good 1-1 conversation with a student who acts out in my class and likes to challenge me. Two students I’ve been trying to get a hold of for awhile finally came in after school to take missing tests and even waited 10 minutes extra for me because I was in a meeting that went long. Did a a fun investigation in FST (blog post coming soon, hopefully). Taught some algebra-heavy topics in Geometry and no one threw a fit, including me.

Did a long problem in Geometry, and at the end a student pointed out “that answer doesn’t make sense”. She was right, it didn’t, but I couldn’t see a mistake in my work. I stepped back and told everyone to try and find the mistake. Finally, one of my favorite delinquents (he’s not really) piped up, and said “The point is labelled wrong in the diagram. It should be (1,0) not (0,1).” Dang it, a typo on the handout. But all was well because I got to model mistake-making in front of my students. Then I had to go through and basically re-do the entire problem which was also good because the students got to see it again and hopefully understand better.

Oh yeah, and I’m the advisor of the newly formed snowboard and ski club. Held a brief meeting in my classroom after school just to see how many people were interested, and within a few minutes, my room was packed. It was awesome. One of my Geom kids has stepped up as the student leader of the club, which is exactly what I needed.