I really liked the idea of the scavenger hunt today to introduce Fibonacci numbers. Because it involves such a bizarre assortment of items, I think the students will come to class with anticipation, wanting to find out what the items all have in common. However, some of these examples were easier to understand than others. I spent a good ten minutes counting scales on a pineapple, and I am still not convinced that it has anything to do with Fibonacci numbers! So I think I would go through all of the examples and determine which ones I thought were the most relevant. I would also be sure to introduce the bee example because I found that to be the most amazing display of the Fibonacci numbers in nature.

I definitely think that I will introduce Fibonacci numbers and Pascal’s triangle in my high school classes. I would probably teach about the Fibonacci numbers during a unit about series or patterns. In my number theory class, we spent a full day looking at the Fibonacci numbers in continued fraction expansions. I don’t know if I will ever tackle continued fractions in my high school classroom, but if I do, then I can incorporate the Fibonacci numbers and the scavenger hunt during that unit. Pascal’s triangle should definitely be discussed when talking about the Binomial Theorem. I know many people who still do not know how to solve (x+y)³ without multiplying it out first. If they were taught Pascal’s Triangle and spent a day doing activities about it, I don’t think they would ever forget how to expand a binomial.

I think that the most important thing to consider when covering these two topics is to show that they are relevant to mathematics. That can only be done by including these activities in a context where they belong. Taking a break between two units by doing an enrichment activity on Pascal’s Triangle does not show any sort of connection between mathematical topics. These connections within mathematics are exactly what the NCTM Standards are trying to address. I don’t see the point of doing an activity just to do it unless the students are able to see what it pertains to in the class they are taking. All in all, I think Fibonacci numbers and Pascal’s Triangle are two topics that are not stressed enough in high school mathematics and should be looked at using fun and educational activities such as the ones provided in class. However, there needs to be a clear-cut reason for why it is being taught, and it must fit into the flow and cohesiveness of the course.