I would definately set up the tables in section 5 with the first row labeled “n” and the second row labeled “Sn” – again to reinforce that this is just a linear or exponential function with the first row being the independent variable. It also adds a little variety to a page full of words. I think this reinforces what you have already stated about these just being linear or exponential functions. On parts 3 & 4 you may want to provide a table or part of a graph and ask them for the 40th term or something. I have a couple of items for consideration. I like the tiled diagrams at the start – especially where you can visually see a squared term and a linear term. But I like the idea that we can use sequences to talk about growth/rate of change… So maybe that might be an interesting way to go about end behavior of rational functions? And then we can analyze the quotient of the sequences… Or something. & series as our second unit, when we do rational functions, we can treat something like (2x^2-5x+1)/(-3x^3-1) as two sequences (the top polynomial sequence, and the bottom polynomial sequence). One thing I thought of that might be cool is that now that we’re doing seq. But I’m learning how to be less teacher-centered and this is something I know I have to practice doing (even if I do it poorly for a (long) while). I’m excited/nervous to see if I can make it work in class… some group, some individual, some homework… Mainly I’m worried about debriefing and having that go smoothly and not take AN INSANE AMOUNT OF TIME and going over everything. Thanks! I’m pretty proud of it, but we’ll see how it goes once I actually USE it. But I understand I am giving them A LOT of scaffolding with which to do it. I’m liberally defining problem solving as having students deal with situations they have never dealt with before, and generalizing from those situations. I’m super nervous, but we’ll see if this is an experiment that fails or not. But I think there is so much depth and abstract thinking that can be brought out of a unit properly done. From what I’ve heard from teachers everywhere, sequences and series always get short shrift in precalculus classes because they come at the end of the year. Usually I think classes do this whole unit in single week, and there’s no way we’ll be done with it in that time. Lastly, yes, I know this is a long packet. Huge thanks in the creation of this goes to who went through a lot of it page by page and gave excellent suggestions! Precalculus guru! Also I included a few blogposts at the end of the document which I stole wholesale from or adapted in my own way. The packet with my teacher notes, and the packet without my teacher notes. Students are asked to conjecture and defend their conjecture at various times. There are connections drawn to graphs, and to a few geometric visualizations of sequences and series. The motivation for sequences comes out of a series of IQ-test-ish puzzles, and the motivation for series comes out of a lottery problem. The last thing I have to say is that although it may look pretty traditional (the questions), try to think about the packet if you were a student and you were in a class going through it. I’m not great at the former, but I’m definitely getting better at the latter. I guess what I mean to say is: these packets/worksheets that I tend to create don’t make kids like/love math, but it does get them to think about math. To put it out there: I would never say that what I do is inherently engaging for my kids. It also gets at almost all the standard things in a sequences and series unit (except for recursive equations, which I threw out). It’s simply a scaffolded way to help kids think in an increasingly abstract way. This is the first time I’m creating an entire guided unit. Those of you who know me know that I am a pretty traditional teacher, and I have gotten in the habit of creating guided worksheets as a structural backbone for a lot of my classes. I like that we’ll be doing it early in the year, because I want them to see immediately that we are not going to be focusing on plug-and-chug but real thinking. Our department is also trying to integrate more problem solving in the curriculum, and so I tried to make this unit involve as much problem solving as possible. The other teacher and I have decided to totally mess around with the ordering of topics, and we put sequences and series as the second unit. It’s a new course for me: Advanced Precalculus. Instead I started, abandoned, and restarted a unit for a course that I’m teaching next year. I had great ambitions to do a lot of schoolwork this summer.
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