Usually I've tried to give the course some context -- we're going to find slope at a point and area under a curve: here's why we care. Last year, I built a given-the-velocity-find-the-distance activity. It was okay, and I'll probably use a revised version of it at some point in the year. (I've already videoed the speedometer on my new e-bike in preparation.)
This year, I'm going to jump right into limits. Here's may plan for the first two days or so.
Day 1 (30 minutes): First thing, a Which One Doesn't Belong (word doc link):
Since most (all?) of the students will not have done a WODB before, I suspect that (D) will be the overwhelming selection as the "right" answer. I'll need to use my sneaky teacher skills to get them to start looking elsewhere as well. No sweat.
Next, we'll do a Desmos Polygraph I made that will (I hope!) force them to start reaching for vocabulary they don't yet have. ("Teach us the right words!" they'll demand, "Teach us! Pleeeeeeease!")
That will likely finish the 30 minutes. It will feel half-done, but that's okay.
For homework, inspired by CalcDave's 8-year-old* (!) blog post, discovered via Sam Shah's also 8-year-old blog post, I've made a questionnaire of my own. I added a little more algebra to mine, and a little less get-to-know-you. (I've taught the majority of my students before, and I know most of the rest from other things.) I do need to test their mettle, so to speak, as I'd like to determine whether the AP pace and demands will work for them moving forward.
Day 2 will be a couple of Speed Dating exercises. We'll do the first one without hardly any guidance from me as to what a limit is. I will tell them how to read the statement ("the limit as x approaches 2 of f(x)") and make that part of the exercise, so that they get used to the language. Other than that, the'll need to figure out where the right answers come from. This is what I've taken from the #MTBoS philosophy: don't tell students anything.
After that's run its course, we'll regroup as a class and I'll answer any questions they have. Once that happens, we'll do the second speed dating exercise, this time (if all goes right) with a bit more comfort and success. Homework will be practicing limits by graphing, and then we can get into algebraic limits on day three.
And we're off..
*As a side-note, I keep waiting for a time when I don't look back 8 or 10 years and think, "Holy cow -- I had no idea what I was doing back then." So I'm assuming Sam and Dave have moved on to something that they feel is progress, while progress for me is moving into someone else's past. My past is open for occupancy. If only I'd blogged back then.
