NBI Post #2: Something That I'm Proud Of

Seems like the New Blogger Initiative has gotten started with a bang... my Google Reader is bursting at the seams and I'm seeing lots of new faces on Twitter. So here we go with entry #2. I chose the first prompt:

Find one worksheet or activity or test or unit or question or powerpoint slide or syllabus or anything that you are proud of. Share it.

I cheated because I couldn't pick just one, and had to settle for two that are very connected. So my favorite sequence of lessons to teach are on the topic of slope-intercept form of a linear equation. I feel like there's so much richness there, in terms of patterns, real-world applications, and connections to previous and future topics that I've always enjoyed teaching it. My main problem has been time constraints hitting against my desire to do a million different activities with this topic. Last year, this was the sequence that I used:

1) Introduce patterns that grow in a linear fashion. Students are in groups and need to predict the previous and the next figures in the pattern. Then, they need to explain the pattern - what changes? what stays the same? Then, they describe the 100th figure in the pattern and generalize to the xth figure. Repeat for a few more patterns that are still linear, but either grow faster or slower or start with a different number of tiles. We make a table showing the data (figure # versus # of tiles), graph it, and then all the awesomeness gets even more so when we start connecting and comparing all of the different representations and finally discuss the equation for each pattern and how it shows this information.

Intro to Slope-Intercept Form

I really like this activity because it is so group-focused - all I need to do is moderate the discussions, and all of the discovery and thinking comes from the students. The tasks are also low-entry and kids that maybe typically don't participate much seem to enjoy the visual patterns and predictions. I love days when I feel like the students are running the classroom and I see intrinsic engagement.

2) The next day, students complete a lab-type activity in groups, called "Linear Walks." They use motion detectors to visualize the relationship between time and distance and better understand why the graph of an equation in slope-intercept form looks the way that it does. This was adapted from the Discovering Algebra textbook, but I've seen versions of it in lots of places.

Linear Walks Lab

This is also a super fun day for me because there's such a clear connection for students between the algebraic reality (variables and equations and such) and what's actually going on in front of them. It's so clear why the graph of y = 0.5x + 2 looks the way that it does since it represents someone standing 2 meters away from the motion detector and increasing their distance by 0.5 meters every second. It also connects nicely to when we discuss point-slope form of an equation a few lessons later. An equation like y = 0.5(x – 1) + 2 now means that someone standing 2 meters away from the motion detector waited 1 second (so they lost 1 second of time, hence we subtract 1 from x) and then started increasing their distance by 0.5 meters every second.

I love that these two lessons make sense of an abstract concept like y = mx + b without memorization or "tricks," but rather through understanding of patterns and physical concepts like movement over time. It gives me a nice contextual handle to refer back to throughout the chapter: "If your graph represented someone walking, would their distance be increasing or decreasing over time?" "If your equation represented a pattern, how many tiles would it have started with?"

I'd love to hear how others teach this topic and if you have any feedback or criticism of these lessons.