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![]() ![]() 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. That show us how many times we've added.I had great ambitions to do a lot of schoolwork this summer. We start out on the first item in the sequence, then work out how many times we have to add our constant to get to the final item. This is what we do when we divide by the difference. More generally, for each hop you take, the number of hops is always one less than the number of squares you've been standing in. You have to hop 4 times to get from your initial position in the first square to your final position in the fifth square. Then from the second to the third: 2 hops. You hop from the first to the second: 1 hop. Imagine there is a line of 5 squares on the ground. You have to add one because you're working out how many items there are in the series by counting how many hops it takes to get from the first to the last. ![]() ![]() ![]() The latest Recoverit 10.0 application can run on Windows and Mac OSX operating systems. 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It could also use some more hotkeys for navigating between fleets/colonies on the strategy screen, etc. + I like the UI feel, reminded me a bit of Galactic Imperium II/Endless Space - very seamless but it needs a few more polish to ensure the info I need to make a decision is provided to me on the same screen on which I have to make that decision. Right now it looks headed to be a nice "light" 4x space game, but doesn’t have the meat on the bones or polish (yet) to compete with Sword of the Stars I and Distant Worlds (my current top of the heap space 4x strategy games) However, I think it does need some more polish and a few round of patches - and I hope that the developer's track record with Star Drive 1 was not an indicator of things to come with Star Drive 2. It certainly gave me the one-more-turn itch and I am glad to see (as others have mentioned) the incorporation of so many concepts from past 4x space strategy games. I was finally able to put some time into this last night. 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So I guess what I'm saying is that a well loved game that SD2 is being compared to has this same problem in spades, but was still a good and fun game. Amusingly, the 3rd choice was so bad that I don't recall what it was. I don't mean "not as good", I mean "you missed out on a core technology, you are now dead".īecause of the nature of exponential growth, the early choices were the most important, and if you choose something that didn't support that growth (say, missile bases over autofactories) you would simply be overwhelmed by an opponent who grew bigger faster than you, no matter how good the missile bases were for defense at the time you got them (and they weren't very good anyway). ![]() For single player, you could do whatever you wanted, but in multiplayer, many early choices were death sentences. I don't disagree with this sentiment, but MooII had many "clear winners" at various tech levels. ![]() Freyland wrote: Also, if the game has a must-have tech above all others, the developer is doing it wrong. ![]() |
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