This Warm-Up is set up to offer students the chance to either review prior knowledge or develop new knowledge. As students enter the room, I tell them that I want them to choose three problems to solve. I inform them that problems (1), (2) and (3) are review and problems (4), (5) and (6) are new. I tell the whole class that once they accomplished three problems of their choice, they could use a few minutes to ask questions about the two portfolio tasks they had been assigned so far.
I quickly circulate during the first few minutes of class to make sure that students had made appropriate choices. I motivate students who had mastered the material from the previous two days to skip the review problems. I ask students who had struggled to focus on the first 3 problems.
After a few minutes I encourage students to try to figure out problems 4 through 6. Some students complete the entire warm-up, but the class is able to move on after everyone has completed at least 3 problems.
Differentiation: Modified Warm-Up 3.docx
I tell all the students working on the modified warm-up to complete the entire warm-up. The previous day I had realized that for these students, figuring out the rule for a piecewise function was a real challenge because it was so abstract, so I asked them to focus on setting up the data table and the graph.
This lesson is a good example of “flipped lesson”. In fact, the series of lessons at the start of this unit are flipped in the following sense:
Traditional textbook lessons start with teaching skills explicitly, then give students a chance to practice. A few applications are tucked in at the very end of the section. In this unit I reverse this order in many of the lessons:
For today's lesson, the closing is the time to ask students to describe their steps in writing a function definition.
One benefit of this lesson is that it gives students a chance to practice finding the equations for linear models using a data tables. For some students, this task is still not easy. For these students, the closing is an opportunity to create a list of steps that somebody could use to find the rule for any piecewise graph. Writing processes is often a good way to internalize the algorithm.
The time allotted to this closing task can shrink or expand depending upon how much time you have. You can ask students to give a rough outline of the process, or you can ask them to give very detailed steps with an explanation of why they do each step. I like to allow time for at least one round of quick feedback, so I ask students to make an outline of steps independently, and then I quickly pair them with somebody else to compare their steps. This will eventually turn into a more formal assessment.