These are the notes that I used to introduce function notation after our wrap-up discussion on lesson 1.4. As you can see, I only got through the first example, but I think that’s fine.
Almost all of my students had never before seen the formal mathematical concept of “function”, nor had they seen function notation, so this lesson was really just about planting some seeds in their brain that still need a lot of time to mature.
When writing the function recursively, I said f(d) is the “current” and wondered aloud what the “next” would be. I wish I could remember all of the ideas they shot at me, and I wish I had the time to analyze the thinking behind those ideas, because they were all over the map!
I hope some students try to write their recursive equation using function notation when we do lesson 1.5. It’ll be interesting to see if the knowledge transfers to a geometric sequence.