I overheard multiple conversations between students who noticed the rate of change both sped up and slowed down. They were convinced they were doing it wrong. That's the kind of dissonance I'm looking for!
I base all of the trigonometric functions/ratios in the unit circle. We use this activity as an anchor for our future discussions about all sorts of things: the graph of sine and cosine, how we create triangles within the circle, and even sine being the distance from the xaxis and cosine the distance from the yaxis. I overheard multiple conversations between students who noticed the rate of change both sped up and slowed down. They were convinced they were doing it wrong. That's the kind of dissonance I'm looking for! Here is a complete write up of the lesson.
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Original problem by Robert Kaplinsky. I use the problem directly after we learn about special right triangles in Geometry (454590 and 306090). Lot's of great overlap between Algebra and Geometry here. Lot's of great opportunities for students to present different solution methods.
We spent a day working on a fun task from the MARS Team. Here is the only setup:
After spending 30 minutes or so working on this problem in groups, we ran out of time. Meh. We planned on starting class the next day talking about our ideas for solution methods. Normally, with two minutes left of class, they line up at the door like cattle. Some of the students weren't done with the problem yet. I didn't do a very good job posting about activities as I did them this year. I'm working through a new Algebra 1 curriculum (I'm not impressed with it) and I'm trying to rethink how I do formative assessment. My activities aren't changing much this year, the amount of time we spend doing activities and experiments feels about right. I guess that's a good thing. Here's an activity we do at the beginning of our unit on linearity: cup stacking. I took this idea hook line and sinker from Dan Meyer and Andrew Stadel. Rather than do this as a 3 ACT lesson, I use it as a chance to get students out of their seats and talking to one another.
We begin by giving 5 styrofoam cups to every pair of students. Then I show a picture of me getting my height measured at my doctor's office (in cm). They have to figure out how many cups tall I am. We also almost always need to come to an agreement about how to measure the cups. Quick setup and clean up and almost complete engagement. You can't ask for much more than that. This activity helps students solidify their understanding of the new vocabulary identifying the angles created by a transversal between two lines. To make it a weebit more interesting, we also look at transversals across nonparallel lines. 
Andrew Busch
I teach Math and Programming at Summit Middle School in Boulder, CO. Categories
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