When planning my first unit with sequences, I just assumed Recursive models would wait until Algebra 2. Last week, my students took their first benchmark for the year and what do you know, but a question about a recursive model.
F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
I’m struggling to see the difference in these 2 standards. As I look at examples, I feel they are much the same or at least co-exist within a problem.
As I watched students during their benchmark, I was aware of the recursive formula question. When I looked all of my classes results, only 38% got it correct. As I looked at their response distribution, most students picked an example that at least corresponded to the give sequence in some manner. However, one class in particular, response distribution was 35%, 18%, 29%, 18% which says to me they are unsure of the notation. The subscripts are throwing them off. Something I need to help them make sense of.
I briefly introduced recursive models Friday, but we worked with them more today. I had a student ask, so is this like a function of the term before it? Hmmm. Sort of. Yes. Across the board 3 of my classes are very strong in terminology and understanding functions. So this was a connection. I saw students eyes widen and they nodded at our discussion. Alrighty then. Let’s try another. And there ya go, the connection was made, they were able to “see” the process within the model.
I wrote 3 different models on the board.
1 minute, think to yourself: How are they alike? How are they different? Now, turn to a friend and share your thoughts.
1 minute, think to yourself: How do I know which model is which? What do you see/look at to help you decide? Now turn to a friend and share your thoughts.
So many good things shared. Its amazing how I can have 4 different ways of seeing something, but yet, each is beneficial somehow. Some of their comments: Two of them have a1(first term), some have d, some have r. But what I heard again and again – they all have (n-1) but the location is different. What does that location of n-a tell us? Once, its a factor for repeated addition, another its an exponent for repeated multiplication and the recursive, its a subscript for the term before.
So, their conclusion…the math is not hard. Knowing what the notation means makes it difficult.