Today's lesson is the last one before the two-day Unit 6 Exam. I didn't plan anything special for this lesson. I simply expected to have the same sort of "review and work period" that typically happens near the end of each unit. For this unit in particular, that sort of open-ended-choice work time has played an important role for the past two weeks. For the Algebra 1 course that I'm sharing with you here on BetterLesson, I thought about omitting this lesson entirely, and just mentioning the option of adding a "buffer day" to follow the previous lesson. As it turned out, what happened today was a little different than what I expected, and I want to share a bit about it here.
A work period still fits perfectly, and an additional buffer day beyond might be totally necessary as well. Students had the option to continue with the work of their choice, and some quietly progressed towards their own goals. Most of my students and I left that script today, however, and we spent the entire class working together through some guided practice on factoring & finding roots.
These topics feel different to kids at this point, and it's important to help kids notice that. No matter what everyone has done over the last few days (and there has been a lot of room for each student to follow their own pathway), we got together and worked with each of today's functions as a team. For some students, this was a review and a confidence builder. For others, it was the moment that everything clicked.
At the end of the day, being able to do polynomial arithmetic - including factoring, in its different forms - is central to what kids need moving forward. Every student achieves mastery at a different time and in a different way, and this lesson gives kids room to acknowledge what they've learned and what they haven't, and to continue build their own context for how the key ideas of this unit fit together.
Keeping in mind what I've shared above, here's a snapshot of what actually happened in class today. The opener, which is on the first slide of the lesson notes, follows the same fast-paced template as it did yesterday. When the late bell rings, I say, "In two minutes, I'll put the solutions up." Everyone scrambles to get going, and everyone does as much as they can.
After two minutes, I post the answers, which are on the second slide. I make sure to emphasize what the verb "factor" means. "One way to factor a quadratic expression is to do what you see here," I say emphatically. Students check their work, and we spend a few moments generalizing about the use of positive and negative signs.
Then we dig deeper into the thought process behind factoring each expression. I ask for volunteers to share how they thought about each problem, and I write their words on the board. Then I remind everyone that they're allowed to bring a one-page "cheat sheet" to tomorrow's exam. I say that combining an example problem with a sentence or two about the thinking behind the problem can be a great strategy for constructing a useful cheat sheet. Many of my students need help developing strong study skills, but they're eager to practice as they make cheat sheets, which help provide a more focused approach to "studying," which is such an open-ended word that even successful adults define it very differently.
I tell everyone that I have more review problems, but that if they're already engaged in getting some work done, then they should do that: either way works! I was surprised and excited by how many students wanted to engage in a whole-class discussion of these other review problems, which are on the fourth and fifth slides of the lesson notes.
On both slides, the prompt is to find the roots of each function, a task that gets more difficult with each one. We moved fluidly between individual practice and group discussions. I tried to stay out of the way as much as possible, but I also jumped in quickly when kids ask for help. When we were done finding the roots, kids took the lesson into their own hands. They wanted to find the axis of symmetry and the vertex of each of function, so we worked together to do that. After that, we graphed a few of these functions, labeling the key points. That took us through the entire lesson, and I loved the vibe the whole time. Neither of these ideas were scripted, but what could be finer?
Whatever happens, the key today is to help students notice that stuff "suddenly" feels easier! Say to kids, "Hey, you can factor now! How did you learn that?" It's so important to help students recognize the fruits of their labor.