Despite a few technology hiccups, things went well, evidenced by the few graphs on the gdoc as of now. Hopefully by tomorrow there will be more.
Observations: (Followed by deeper thoughts):
- Thank goodness I had them print up the blank graphs just in case, because that turned out to be the only reason we were able to proceed when there were tech problems. Always have a Plan B that doesn't involve tech.
- Not everyone was able to open the ggb file, (miss I don't have java) but every group had at least one person who could. Always group when you're using a fancy-schmancy tool.
- Needed to walk through it a bit at first, emphasizing that the graph they are building is of time vs height, not of the little green ordered pairs that follow the car around in the ggb file. Did I miss an opportunity to do another hint-troduction?
- In the last class, I started out by getting them to mark the various times out on the circle - where would 15 seconds be....etc. But I feel like that was sort of spoon-feeding. Although this group needs more pushing, plus NO ONE could open geogebra, so I had to screen share it and move the car around for them. I forgive myself.
- Didn't get to the second part (distance from wall) in most cases. That's fine, they can do that on their own tonight. GACK - Homework.
- In one class, no one used the checkbox that revealed the angles, probably because no one got that far, but also because this group very early on decided that it would be linear. And none of the points they graphed disproved that - they didn't have enough of them to see the curving part. But that's okay, part of learning what something is, is learning what it isn't.
- In the other class, everyone ended up clicking the checkbox to reveal the angle lines. Got the thrill of my life when I saw "OHHHH!! THAT HELPS A LOT!"
- Nevertheless, I don't think anyone saw the angle as being significant - to them it was more about cutting the circle up into sectors. But maybe once they sleep on it, that will be more obvious. Maybe I need to change that ggb so that instead of sector lines popping up, it's an arm that rotates, and they make it rotate via a slider. And it changes colour when it hits 30, 45, 60, etc. Hmm. I wonder how to do that. Great. How long is THAT going to take me to do?
- Most of them predicted that the curve would be linear, or piece-wise linear, or an absolute value function. I heard some talk of quadratic too. I neither confirmed nor denied. It's not about getting the right answer at this point, it's about seeing the circular motion, and about how they should check out their assumptions, and how a few points can make all the difference.
- Do we have to find the height for all the times you have in the table?
- Aren't the four compass points enough?
- Will it be a line?
- How can we find 5 seconds on the wheel?
- Why did you give us such a wide graph?
- Is there a rule for this type of graph?
- It's just going to repeat
- It looks like hills
- It looks like teeth
- This was fun!
We're going to look at all the graphs together. At this moment there is really only one that is correct and complete for the first cycle. They are going to tell me which one(s) are right. Then and only then will I show them this! And I will bring up angle as the quantity that interlocks with seconds. Then we'll start talking about the periodicity, etc, all those things I thought we'd get to today.