They noticed patterns in parts (a) and (b) and were able to explain why the derivatives of (c) and (d) were the same as (a). Part (e) went better than expected and generally confirmed their conjectures. The results from parts (f) and (g) were confusing for many and I found that it was helpful to rewrite the question and get them to write the answer in the same form in order for them to see the pattern still held. They got stuck trying to do part (h) from first principles so needed to find the derivative another way.
At this point we stated the power rule as a group and turned to proving it. In the past, I have gone through the proof with my classes and many students' eyes have glazed over as they completely tuned me out. This time I gave them the expansion of x^n - a^n, we talked about how many terms there would be in part of it and let them try the proof. At least one group in each class finished the proof on their own! And all groups made good headway with it which helped them stay engaged when I showed them the full thing. I think they thought it was kind of cool!
I gave them two more questions after the proof:
The first was no problem and the second was done incorrectly by almost 100% of groups. We stopped there for today and I asked them to write down a summary of what they had learned. I didn't do anything else to close the lesson as I felt like it wasn't needed.
Here is the sequence for tomorrow:
Overall I thought today went well. I have done enough of this type of work with students that I was very comfortable and my students were great. There were a few times when I took a marker (there was only one marker/piece of chalk for each group) and handed it to a particular student, but in general they took turns doing the questions. Those not writing the solutions were watching what was going on, looking for errors. There were some good discussions going on today, but I anticipate more tomorrow due to the nature of the questions. There were some groups that would call me over to check their work, but they got a lot of "What do you think?" and "Convince me" and "Are you sure?" so I suspect that will diminish as we continue. I had to ask a few students to put their phones away, but it was not really an issue. They all did math and were all thinking and even those who came in knowing the power rule learned something new.