Fermi Problems - Reflection

Doing a lesson in 15 minutes is difficult to say the least, and when we began to notice we were running out of time the first thing that got cut was any explanation of what we were doing and how it relates (in general) to mathematics.  We should have planned more how we were going to present the material in a more in-depth way to ensure we did not run out of time.  I think we planned very well what we we going to teach, but not enough of how we were going to teach it and exactly how long each part would take.  This is especially important in a short lesson, but is also applicable to lessons in a real class where I often remember teachers running out of time when they were only halfway done their lesson.  The only other thing I would have done differently in our presentation was to give a clear outline of what we were going to do and why.  I don't think we made our goals for the lesson very clear to everyone and some students were left not really knowing where the lesson was going or how it applies to mathematics.  Perhaps even giving an additional problem for the groups to work on that involved Fermi estimations and integrated other more traditional mathematics that they are used to seeing.  That might have really highlighted the applications of estimating and the importance of it in all areas of mathematics, and given the students a reason why they should care about Fermi problems (other than they're cool).
A few of the good things we did that I would not change were: including a small group assignment, giving an interesting "hook" in the beginning with a small historical anecdote, and leaving time in the end to hear all of the groups' answers.  If there had been more time I would have liked to have had a class discussion about Fermi problems and the different answers each group came up with.  Also, having all four groups working on a slight variation of the same problem really worked for our presentation and I think made the lesson more interesting than if all four groups had just competed for the "correct" answer.