This activity went very well in the beginning. Students jumped very easily from working on the concentration data to identifying and writing down the proportional relationship. They then seemed to feel quite comfortable with the conjecture in Q4 and testing their conjecture further in Q5. It was a huge surprise to me then as to how much they struggled in Q7. Many students who had seemed very comfortable with the ideas when starting with data seemed unable to go in the other direction with the simple assertion from us that this was always true. I spent quite a bit of time in class talking about the conclusion that we were working from (that if a rate of change equation was of a certain form then the original relationship was exponential) and what we could infer from the rate of change equation given that conclusion. Given more time it might be good to insert something between that conclusion in 6 and the question in 7.
Students struggle greatly with the synthesis questions if they are trying to work through the original activity via pattern finding so it is a good time to try to highlight the importance of understanding the meaning of these rate of change equations.