Moving into the final week of class, I've already established all of the lesson structures that will be employed over the next few days. There will be one more day of work in the computer lab, and another group problem solving session. Mostly, I will provide as much time as possible for students to complete the work of their choice. As I describe in this video, that's what the next three lessons are all about.
Daily openers will help students review for the final exam, and they may frame the work if kids decide that they need more practice on a given topic.
To learn more about the open-ended work time that's happening here, take a look at the first lesson of this unit, where I frame the unit and explain that work request forms that continue to be available to students. For further framing, check out the fourth and fifth lessons of this unit, where I share some of my ideas about finding and creating assignments and providing space for students to get what they need.
I prepare all sorts of assignments for students, but I don't break my back to do so. To save time and to try out new stuff, I'll try out new assignments that I've found online, make photocopies of old textbook pages, or just use good old Kuta Software. I'm not sharing these resources here, because they're all borrowed or stolen, but just telling you about how I engage in the work of finding what's right for my kids. I don't know what I'd do if I didn't have the math teacher twitter-blogosphere and two dozen algebra textbooks from across the decades to supplement what my school provides.
On a final note, I strongly recommend throwing on some good music during work time. The right tunes can take what's already a hive of optimism and make it divine.
Today's opening review task cuts to the chase by giving students the chance to check what they know about slope-intercept form. Students are given four linear equations, all in slope-intercept form, and asked to graph them on the same axes.
I do not say much about this opener. Instead, I post it for students to see, and I circulate for a few minutes to make sure that everyone is getting started. Then I use this task as an "Entry Ticket" that students must complete before they're allowed to move on to whatever they do next. I say, "Finish this task as quickly as you can, and come show me when you're done. You and I will work together to decide what you should work on today." I take a seat at the desk I've set up at the front of the room (which I describe here), and I wait for students to come to me.
This strategy works when I know that all students can complete a task - or at least come very close - with little help from me, and it allows for a really nice checking strategy. When students come up to show me what they've got, I take a look at their work. If there are errors, I pick up my pen and I write the equations of the lines that the student actually graphed. I show the student what I've written, saying, "here's the equation that you graphed - can you see how it's similar to the original?" I give them a moment to think and then I ask what has to change.
The kids are never completely wrong. Their errors always have something to do with swapping a + or - sign, inverting the slope, or (sheesh!) forgetting which axis is the x and which is the y. With this feedback in hand, I send students back to create a second draft of their work. In the end, students have learned another example of what studying looks like.
When the work is done right - after one or more visits to my workbench - we consult about they should do next. They either tell me about the assignment they're currently working on, or they grab a copy of something new.
On the second day, the opening review task is a classic sort of "overtaking problem" that can be solved in a few different ways. As they get started, I remind students about the structure of their final exam, and I say that one of the problems on the group section will be similar to this.
Like the mixture problems of a few days ago, these problems incorporate the fundamental skills of creating equations, as well as the more advanced skills involved in solving a system of equations. As I discuss with the kids, these problems can be solved by guess and check or by creating a table, but as we've discussed throughout the year, both of those strategies ought to lead to algebraic methods, for which I provide these notes.
In contrast to how I treated the previous opener, standing back and giving kids space to get the work done, I am very hands-on with this one. I push the pace a bit, and elicit as much thinking as I can from students while getting the problems done. Some students will keep up, and for them this will be a confidence builder. Others will know they could use some practice, so when they get to work, they'll choose to work on a few more problems like these.
The third in this series of review openers is about the graph of a quadratic function. I expect students to remember how to answer these questions, or at least to able to consult with their notes and their neighbors to make sure that they get each part done. I review the format of the final exam - "you'll do one hour of individual work, and one hour of group problem solving," I say - and then I tell students that on the individual section of the exam, they'll see a series of questions very similar to these. They'll be given the graph of a parabola and they'll have to answer a few questions about it.
On the first slide, students are given a graph and asked to give the roots, the vertex, the equation for the axis of symmetry, and the equation of the parabola. Like yesterday, I push the pace on this slide. I try to get students to say the answers aloud, and then I give them just a few moments to ask questions or take a few notes.
I put up the second slide and tell students that this is one options for getting started today. "If you feel like you could ought to brush up a little on your knowledge of quadratic functions, then this is a great place to start," I say. "Otherwise, you can jump back into the work of your choice. Let me know right away if you have questions about this or any other assignments." Then I start buzzing around the room, taking questions, and work time is underway once again. As class continues, I'm likely to answer student questions by writing and talking about notes like these. In any work session like this, there are all sorts of possibilities for what can happen. If I see that a few students have questions about the same topic, I'll teach an impromptu mini-lesson.