When I saw that the teacher's guide allowed 60 minutes for this activity I thought there was no way. I thought we would get through it quicker...haha! We didn't even finish and we had OVER an hour. This activity helps the students to explore and HOPEFULLY discover the rule for dividing powers with the same base. I love it! It is really revealing the lack of number sense that my students have. The questions are not really that difficult...that is why I thought we would breeze right through.
I have allowed myself to "sit" on this activity and not rush it because I really believe it might help to cement the concept. I am going to be absent tomorrow from my classes and I have some good exploration worksheets on exponents to leave for my students. However, it has reminded me how blessed we are to have found a book that combines the exploration with the context. Someone had a wonderful imagination!
**Update 3/7/15** Original post was made 3/16/15
This year when I taught this lesson I took the time to help the students to explore #2. I did not let anyone blurt out an answer when we first started looking at it. I have been using the random integer generator on the TI-83 (which is awesome but I just now figured out how to do it!!) to call on students. In my classes I just happened to call on students who were unsure of what to do so I just asked them to start by making a guess. I told them to tell me a number of ounces of cake and a number of ounces of beverage and then I showed them how to "test" their answer to see if this would give an answer where Alice's height was multiplied by 8. Then I randomly called on more students. The first 3 students guessed more beverage than cake (ugh!) so I asked the next student to make a "conjecture" on whether or not more beverage than cake would EVER allow Alice's height to be multiplied by 8. My 2nd class arrived at the correct number of ounces much faster than my 1st one did but I feel that modeling to the students how to "guess and check" was valuable. I am always telling them not to ever erase their guesses. I want them to learn to look back over the ideas that didn't work in order to help them to identify new theories that might work!! Anyway...the day I taught this lesson this year I felt really good about what we had accomplished:)