I just spent an entire afternoon trying to wrap my mind around the IB Portfolio Type II Tasks. I found a fantastic podcast on Youtube that I am going to share with my kids: Part 1 and Part 2. What I really liked about this podcast is that the teachers walked through the technical aspect of the graphing program, as well as reviewed the rubric in parts relating to their thinking-out-loud about the sample task. I am going to assign as homework these two videos for my kids to watch at home, and then together I will go over it with them again in class, pausing every so often to go over the mathematical content and to allow them to install/run Autograph with my assistance. (There are some things that the video glosses over that the kids might find tricky to navigate on their own.)
It seems to me like many Type II tasks want the kids to "analytically" come up with their own equation, which can mean plugging in multiple points and solving the system of equations in order to find the coefficients, OR using what they know about the meanings of the coefficients (ie. amplitude or frequency) in order to construct the equation algebraically from the graph. Then, the tasks call for the students to either modify their equation to match additional data or ask them to generate (using technology) a different type of regression equation. The latter isn't always trivial to do, especially since sometimes the task gives them a fairly hairy form of equation to play with. And then, assuming that they can successfully do the mathematical modeling, they'll need to firmly link the asymptotic behavior of their regressed equation to the context of the problem, in order to examine whether that asymptotic behavior makes sense or if the modeling domain should be restricted only to the given set of data. In some cases, the kids may even need to have some background knowledge of the topic in order to properly discuss the asymptotic behavior.
In order for the kids to be successful, we'll need: 1 day of going through the basics of regression and rehearsing the technical aspects of the graphing software; at least 1 day of looking at different types of non-perfect numeric patterns, in order to figure out what type of regression is necessary (Some types are far messier than others; the IB tasks aren't messing around with simple quadratic or even cubic regression. It looks like I'll have to go into some fairly involving functions review with my batch of Grade 12's...); another 0.5 day of looking at asymptotic behavior.
Even though the task is going to surely be challenging, I think it's going to be really good for their mathematical minds to tackle this task. As a teacher, I really like how the IB Program has high expectations for all kids, because those are some very noble and worthwhile goals for us to shoot for in the math class!
(More to come about Type I tasks a few months from now...)