As I describe in my "About the Lesson" video above, the "opener" to today's lesson is framed as a Mastery Problem for Mathematical Practice #1. This is the same problem as the opener to yesterday's lesson, and we've already spent some time talking about how to organize a complete solution to this problem.
I introduce the class and this problem, which is on the first slide of today's notes. I describe how the class will work, with completion of each task serving as a ticket to the next, before explaining why I'm asking everyone to start here. "Am I giving you this problem because I want you to practice addition?" I ask. "Of course not! I know that you all know what an odd number is, and yesterday you all demonstrated that you can find some of the possible solutions to this problem. I'm giving you this problem because I want you to be so perfectly organized that you're 100% sure your list is complete."
I leave students to finish this problem, because given time to really work through it, all students will eventually complete the list. I circulate and offer small, specific hints. For example, if I see that a student has 1, 5, 19 followed by 1, 9, 15, I'll ask if there are any possibilities in between these two. I also allows students to work together on this task, discussing the work and sharing good ideas. As students finish, however, I collect their work as a means for taking it "out of circulation" so no one else is tempted just to copy a complete solution from someone else (although I don't say that to kids).
Some students finished this problem during yesterday's class or overnight, so for them, it's straight into the next mastery problem.
When a student says they're done with the "At Odds!" problem, I collect their work, and I ask how sure they are that they have the whole solution. It's a nice chance to see how confident they are with the idea of organizing a list, and usually their work matches their demeanor (and when it doesn't that's also worth noting!).
I take the work, more because I want to take it "out of circulation" than anything, and I provide one of four versions of a mastery problem for SLT 5.1:
SLT 5.1: I can use guess and check to solve a problem with two or more unknowns.
There are four versions of the problem because my students sit in groups of four, and I don't want them to work together on this one. By now, they know that I use this strategy frequently enough, and my expectations are implicit in my use of four different problems.
This will be as far as some students get today. If that happens, it's ok, that's what I'm assessing, and one week into the unit, it would be a great outcome to see that everyone is confident with guess and check and ready to delve deeper into the algebra of graphing, and soon substitution, next week.
I remind students to refer to their notes or other problems they've worked on this week, and to remember that a complete solution by guess and check doesn't have to be too long. I urge students to look for patterns in their work, but other than that, I try not to help too much on these mastery problems.
At the end of class, I make sure to have collected at least this and the "At Odds!" problem from every student, and staple the work of each student together. What they produce today helps me plan for the next lesson, in which I'll group kids by what they were able to show me here.
The last slide of today's notes is provided as an optional scaffold. If students are really struggling with the guess and check problem, I'll project this exemplar at the front of the room for reference. Students saw this work yesterday, and I hope not to have to use it today, but just in case, it's ready.
The final "mastery" problem consists of a few parts, and is meant more to give students a chance to practice graphing systems and solving problems than to provide full evidence of mastery on SLT 5.2:
5.2: I can solve a system of equations by graphing, and I can interpret the intersection of two graphs in terms of a context.
When each student turns in their guess and check problem, I give them a sheet of a graph paper with the instruction to fold it in half. I also provide one system of linear equations, cut from an Infinite Algebra worksheet similar to last night's homework. "On the top half of the graph paper," I say, "I'd like you to create a perfect graph that shows the solution to this system. Show me when you're done."
Finally, I also use Infinite Algebra to randomly generate "classic" systems problems: finding the cost or quantity of two similar items like adult and student event tickets, or different kinds of food, or travel with and against a current. We'll dig into more of these problems soon, and part of the point here is to start giving students a little taste of what happens when graphing isn't easy. I tell them to define two variables, to write two equations, and then graph points on the back of their graph paper. Usually the students who get this far in today's work are game for attempting this task, and it serves as a nice springboard into next week's work.