I am a Elementary Ed and Math major. This is part of an assignment.
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I teach 9th grade Algebra and the topic of fibonnacci sequence actually came up naturally. In fact, that's what I would suggest. We want to stir kids' curiosities. I was teaching arithmetic and geometric sequences just last month. Those are the two types mentioned in the Common Core. In all my classes, someone always asked if there was another "type" of sequence. That's when I threw up a list of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21,... and then asked students to come up with a way to find the next term. This was really fun. I asked if students figure it out, they should only tell me the next term and not give away the rule (this way, every student will be encouraged to find the pattern on their own). My students treated the task like a riddle. I didn't give any hints, and it was fun to watch students go "OMG I GET IT!".
On a side note, Common Core wants us to teach how to write explicit and recursive formulas. Since my students learned how to write formulas recursively, it was easy for them to write a recursive formula for a Fibonacci sequence as a_n=a_(n-1)+a_(n-2).
I always use Fibonacci when discussing recursive formulas. Many students have seen it before but not seen it written as a recursive formula. Either way it is a great example of how they work and is definitely more fun and beneficial if the students have to figure out the pattern themselves and come up with the way to write it out as a formula. I always encourage them to use words too if the symbols are too confusing at first. Have fun!
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