It turns out too many of my students STILL could not successfully work linear and angular speed problems. You'd see this look of abject fear in their eyes if you even showed them such a thing. While I was stressing about it one morning when I couldn't sleep, I remembered an old conversation with a science teacher that mentioned using little cards that the kids could manipulate and turn around and change one unit into the other.
I made up 6 little cards (I fit 4 x 6 on one sheet of colored regular paper) of approximately the colors above (color coded), and handed them out to the students. In about 30 minutes or so, we worked through 4 or so problems of graduating difficulty. At the end it looked like all of them could successfully switch from one set of units to the other. We'll see on Monday. Next time, with more prep, I may even have homework for them on this day!
My problems in order:
1. 200 in/min to convert to miles/min.
I made up some picture of me on a bike and what I was doing yesterday and had them write this down in their notes with a big space between the first and last statements. Then their pencils went down, and they were to pick the appropriate cards in the appropriate orientation to do the conversion, and "place them so I know you know what you're doing".
At first only 40% or so had the right cards in the right orientation. It was easy to walk around the room and spot check and ask if the inches canceled or if you got inches squared. Then they had to transfer that to their notes, and we discussed how how to put the numbers in the right places. Some kids still resisted writing the units, and they invariably put the "12" or the "5280" in the wrong places. We fixed that.
2. 10 mi/min convert to in/min.
Same process. This one was a kid's name riding a unicycle with the appropriate goofy picture. It also helped that the final answers came out really unrealistic - cause for more laughs and stories.
3. # feet/sec convert to miles/hour
Now there was some whining, but we talked about doing distance first, then time. They got it. (power walking? tricycle?)
4. #rotations/sec convert to feet/hour
(Human wheel like in cirque du soleil? Again a kid's name, and radius needed)
Anyhow, I think there was much joy in linear-speed-ville at the end. Hopefully, this will translate to understanding and accuracy on problems.