I asked each group to just tell me which one they thought didn't belong - those are the blue check marks below. Then I asked for reasoning, which is in red. Lots of students told me that the bottom left did not belong because it didn't have an x-intercept. I found this very interesting. We had a conversation about what the arrows at the ends of the line mean and whether that line would eventually cross the x-axis. I asked them all to continue to think about reasons why top left and bottom left did not belong. The 2nd round of reasons are in brown.
I then randomly paired them to work on the Tying Knots activity. I struggled with how much to scaffold this one. I have done it in a very scaffolded way in the past and wanted to get away from that while still providing a context for what they were doing. It was not a roaring success. One group did get right to work and were doing an awesome job. But so many other just sat there wanting to be told what to do and where to write it. I assume this is of my own doing, as I have given them structured handouts for much of the semester. To be fair, some were confused by the context and couldn't (didn't want to?) get past that. This is the handout they got today. I am going to work on it some more now... back in a few minutes. Here is the new version. I hope this will be clearer and help provide a lower entry point.
Here is some data collection going on:
Each pair got one of 5 different thicknesses of rope. They had trouble with things like understanding that it shouldn't matter how you place the knots along the rope and figuring out how to calculate the diameter of the rope. I feel like I need to get them to think about what they are doing more before they actually start, but I am unsure how to do that.
Here is some of their data:
One group started on their second rope today so we will need to continue this tomorrow. The goal is to then find a relationship between the diameter and the rate of change so that we can extrapolate to a thicker rope. And then we will solve systems with the ropes. Today's class was disappointing - I hope tomorrow's will be better.