In the next class, we will start by reviewing the homework in a different manner than normal. We'll do the more traditional "I'll put the answers on the overhead, and we will go through it together to see if there are any questions" instead of my new homework review process . This is because the homework is long and has lots of short questions, and it is the review sheet for the day's quiz. I hope that reviewing the work this way today will be effective.
After the review, we will have a team challenge that is worth points on the quiz - not extra credit, but the normal, quotidian kind - 9 out of the 50 points. Teams will be given three 3-point problems, one at a time. They can work in their teams, use notes, and ask me a total of 3 questions for the whole activity. When they agree to a solution, they all sign off on that sheet and turn it in to me, getting the next problem in return. If anyone talks to a different team, they will lose 1 point from their score. I think that these rules will help keep them focused on their work and helping their teammates.
Problem 1: Given a piecewise function, make a graph
Problem 2: Given a graph of a piecewise function, determine the equations. (My hope is that they can work this out on their own, though they haven't gone in the backwards direction yet. They can use one of their 3 questions here, of course)
Problem 3: Given a graph of two lines that are not crossing, but clearly will cross, determine the exact point of intersection. (To do this, they have to determine the function of each line, and then solve the system algebraically. I think there will be a lot of confusion here, but if they ask me a good question, they should be able to proceed).
I haven't tried something like this before, so we'll see how it goes.
We'll then take a few minutes where I show them the answers and deal with any last minute questions. The class will then have the last 30 minutes to take the quiz.
The homework will focus on determining the functions of given piecewise graphs, along with review of solving absolute value inequalities and equations in preparation for the upcoming lessons in which we will solve these same problems graphically.