Translation and transformation have continued to prove extremely difficult for my classes. Even my strongest students have been struggling. I'm still trying to work out what is making it so hard to understand (if anyone has insight on this, I'd really love to hear it). I think they are starting to get the hand of it, but for mastery, we'd need at least another full week, and that is time we just don't have - especially for something that is only tangentially in the standards.
I did incorporate the idea of texting in lesson 14, to introduce what I'm calling "translation notation". We're not talking about vectors or anything like that, but I wanted to give them an efficient way to describe the translations and calculate with them. The kids thought it was really funny; I did play it up, calling it "math chisme" (gossip) and pretending I was texting it under my sweatshirt to my friend. You wouldn't want to type out that whole sentence, right?
Anyway, here are the files from this week.
Lesson 12 (Horizontal Shift) Keynote Quicktime
Lesson 13 (Translation and Transformation Practice) No Keynote for this one
Lesson 14 (More Translation and Transformation) Keynote Quicktime
Thursday, November 20, 2008
Saturday, November 15, 2008
I've been really good about my timing all year, until this lesson... I wasn't able to finish it in any of my classes. We almost got to the end of the Keynote, and didn't have any time for independent practice. But that's why I don't really create more than one lesson at a time - so I can adapt as needed. Well, that and it takes a huge amount of time, and keeping afloat is what it's all about. I'm still not sure why this lesson took so long; some students were tearing through the class notes, figuring it out on their own and finishing before we even go there. And some students were struggling to keep up. I know it's always kind of like that, but we are working with a very visual representation right now, and it has shifted some of the dynamics of the classes.
Coming soon will be horizontal shift, but not horizontal stretch. I don't want to overload them, and the standards in Algebra 2 really only require that students be able to graph things like f(x) = a(x - h)^2 + k, or to say how one vertex form parabola got shifted to another one. They can learn horizontal stretch in pre-calculus with the trig functions. At least this will give them a good foundation for the tedious work of grinding through f(x) = -2sin(3x-pi/2)+5.
Lesson 11 (Vertical Shift / Stretch)
Lesson 11 Keynote
Sunday, November 09, 2008
We have Veterans' Day off on Tuesday, but we still have school on Monday. Would have been nice to get a four-day weekend. How many absences do you think we might have tomorrow? I decided to do a review lesson, both because my students are really struggling with graphical analysis stuff, and because I don't want to move ahead with potentially many students gone. Hopefully that doesn't happen. But there are at least 4 teachers who are taking a personal day, so...
I found a site with some good resources on understanding domain and range graphically, and have included some of those animations in this lesson's Keynote.
Lesson 10 (Graphical Analysis Practice)
Lesson 10 Keynote
Thursday, November 06, 2008
Here are the latest files... more work with domain and range (which continues to stump some students) in interval notation form, and my favorite, solving equations and inequalities graphically. These are very challenging concepts for students, even though they don't seem like they would be, compared to some of the other material. But Keynote really shines through for clearly showing how this works.
Lesson 8 (Domain and Range)
Lesson 8 Keynote
Lesson 9 (Analyzing Graphs)
Lesson 9 Keynote
Students were asking why we have to learn interval notation. I was going on about ease of communication and writing things more simply, but I wasn't getting anywhere until one student piped in with this gem: "Oh, it's just like texting". As soon as she said that, the rest of the class produced a collective "ohh...". Why didn't I think of that? I used it in the following class, and it worked well.
Monday, November 03, 2008
I went back and forth on whether or not to spend time on this, and in the end I decided to go with it. It will be helpful to students who go on to pre-calc and beyond, and it gives us a good opportunity to review solving linear inequalities and to keep working on finding domain and range of graphs. Plus, it's good to have a lesson every once and a while that is pretty easy for students to master right away - someone said today, "This is the easiest thing we've learned in like 50 years!".
Lesson 7 (Interval Notation)
Lesson 7 Keynote
Sunday, November 02, 2008
I know my posts have grown dull of late. Or maybe just functional. Hopefully the files remain helpful to you all. Enjoy that extra daylight savings hour!
Lesson 5 (Operations on Functions)
Lesson 5 Keynote
Lesson 6 (Operations on Functions in Multiple Representations)
No Keynote for this one... it was an extended class activity that we did on halloween; I handed out a chocolate kiss to each student in the group each time the whole group finished a round. For my costume, I was La Calavera Matematica de Michoacán.