Perhaps the most frustrating day yet, although it wasn't necessarily due to the lesson. The openers (pdf) - which I thought they should be able to do fairly quickly and easily - stumped them. Completely. Even #1, which they seemed to think was simple on Friday, was a problem for many of them.
Opener #2, which I thought was an "easy" dimensional analysis problem (because I realized that they were getting lost in the really long ones I had been giving them), wasn't. It appears as though speed (miles per hour, kilometers per hour) is not as straightforward for them as I thought it was (they don't get that distance should go in the numerator, time in the denominator). I need to do a better job of checking my assumptions at the door.
Then opener #3, which were the same problems they were supposed to do for homework over the weekend, except I specifically asked them to find k today, were a mystery to many of them as well. I think that after going over all the openers, as well as today's lesson, they understand them much better, but today felt like I was starting over at square one.
Then the lesson (pdf) was looking at direct and indirect variation via the gear ratios on a bike. Following Friday's lead (which I'm still not sure I want to do), I structured it out the wazoo. (Interesting - Firefox recognizes "wazoo" as spelled correctly, but not "pdf.") I brought in my bike, borrowed a stand from another teacher at school, and stepped them through how far the wheel turned for one turn of the pedals when in different gears. I pre-counted the teeth on the gears I was going to use and pre-filled in that part of the table, so the students could just concentrate on how far the wheel went each time. I had students volunteer to come up and turn the pedals, catch the tire, and write the number of wheel revolutions in the table, but other than that I led them through it. Again, I think there was value in doing this today, but I was still doing too much of the thinking.
For homework for Wednesday I gave them what I was anticipating would be a fun, but not too tough, problem involving Lance Armstrong and the Tour de France (although now I wonder), and had them finish the last two steps of the bike variation activity.