Day 1: take notes on what imaginary numbers are. Boring, but it is a topic that always gets the students riled up. Their feather get ruffled once they know that their 7th grade teacher was mistaken when they were told "you can't take the square root of an negative number." in one such instance I got to pull out my Star Wars quotes and tell a student to "let go of their hatred." Most of the students thought imaginary numbers were kind of cool, some thought I was making it all up and playing a trick on them, and unfortunately some through it was the dumbest thing ever and they should be learning something "useful."
On day two i show most of this video, and put it in the context of a robotic arm rotating to pick things up at various points.
Then we get to the good stuff. I give students a little packet and have them do the top problem, they double check with me and if they did it right and get a quick "yep" or "not yet," they get to crumple up their paper and shoot it from the free throw line if they're correct, otherwise they have to keep working on the problem. There is only get the one shot per correct answer and if they miss then they have to go fetch their shot and put it in by hand. For all but one of my hours this was a great alternative to a worksheet, and I really saw them asking each other how to get the answer. Who knew throwing the piece of paper would be such a great motivator?!
The questions increase in difficulty, making for great differentiation. Students can go at their own pace and can know that they are right before continuing. The pace is fast, and I was relatively surprised at how hard students tried on something that they had just the previous day been questioning the relevance of.
Here is the template, just photocopy it in order and put the staples in and you'll be ready to go after its cut up, no need to organize the booklets.
