Math Poem

Writing a poem about math can be beneficial to students, especially if they are creative and enjoy writing poetry.  It can make them see math in a different light and is generally a new way of looking at abstract ideas.  However, for students who don't enjoy writing poetry (I would say >50% of students fall into this category) it can further alienate them from math - the opposite of the desired effect.  Also for my own classes I need to take into account my own interests and strengths, neither of which is poetry.  Unfortunately my attitude toward poetry is beyond simple apathy - I actively dislike poetry.  If I were to assign this in a classroom I don't know if I could mask my distaste for the assignment I am giving, and when it comes to questions or marking I would be lost and disinterested.  I like the idea of connecting math to other areas, but I would pick something I have more personal interest in so that I can at least model interest in the assignments I am giving out.

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.

Fermi Problems - Lesson Plan

Learning Outcomes: Be confident in making estimations, understand error in estimation, problem solving.

Hook: Fermi brief introduction and story about estimating TNT in atomic bomb.  Talk about in everyday life when we use estimation: tipping, tax, time, distances (driving).

Pretest: How many 10-dollar bills would it take to cover the surface of Canada?  Answer:950 trillion!

Lesson: Understand the problem -> Think of a plan -> Carry out the plan
Go through the example and how we would solve it using those three steps.

Activity: In groups of 3-4, hand out one problem to be solved by the group in the same way we have just shown.  Each group will have basically the same problem, but one group has access to computers, one has access to calculators only, one has no computer/calculator, and one has limited information from the problem. 
Question: How many songs does a radio station play per week?  Groups 1-3 will be told it is a classical station.
After 5 mins, have groups share their answer and how they got it.  After they've all shared talk about error and which group they think was closest in their estimation.

Post-Test: Assign a few problems for homework.

Summary/Conclusion: Scientists often look for Fermi estimates of the answer to a problem before turning to more sophisticated methods to calculate a precise answer. This provides a useful check on the results: where the complexity of a precise calculation might obscure a large error, the simplicity of Fermi calculations makes them far less susceptible to such mistakes. (Performing the Fermi calculation first is preferable because the intermediate estimates might otherwise be biased by knowledge of the calculated answer.)