Here is the setup:
Students worked out expressions for length, width and area and for their rates of change before completing the following table.
It is always interesting to see who comes up with it quickly and who takes a little longer (often because they are trying really complicated things!).
Once I felt like the majority of students had found the pattern, I sent them off to their VNPS to work through today's sequence of questions.
The last of these asked them to come up with the product rule for three terms. I loved what some of the groups did. They extended the introductory activity to 3-D, added height and worked through the numbers again! (sorry that the picture quality is terrible)
Here's a group that came up with a conjecture for the product rule with three terms and tested it out. I would like to say they did this instead of asking me if they were right, but they did jump right to it when I said they should check it for themselves.
It was really exciting to see such fantastic work, at such a high level from all my students. I love how they trust that they will be able to tackle all the questions I give them and believe in themselves enough to try.
P.S. All of my planning is on one getting-bigger-by-the-day Word document. I'll post the whole thing at the end of the unit.