As has happened several times earlier in this course, today's opener is about patterns. I think it's important to note that today is a Monday, and that every class this week will follow roughly the same structure: we will open with some problems about patterns, and then proceed to practice solving linear equations.
The first three questions are similar to those I've asked before, both on openers and on patterns quizzes, and as I circulate I'm looking to see that students are gaining confidence on problems like these. I encourage students to talk to each other about these problems, to check each other's work, and to consult previous notes if they need help. After a few minutes, I invite students to the board to post their solutions to these first three.
The question for problem 3b is new. Rather than finding the value of a given term, I ask students to figure out where in the pattern the number -130 will show up. "What term will it be?" the question asks. We compare this question to the previous one, which asks for the value of the 300th term. We've already seen that the 300th term is -1150, so I ask students to estimate where -130 will fall. We note that the first few terms are 46, 42, 38, and so on, steadily decreasing by 4's. I write a few student estimates on the board: the 100th term, the 25th term, the 50th term, etc. Then, we develop the equation: -4n + 50 = -130, where n is the number of this unknown term. Here is an equation that the class can solve by committee, even if individual students will need help. I elicit the steps: we have to subtract 50 from both sides of the equation, then divide by -4, which yields n = 45. I ask if this sounds reasonable, and we compare it to the estimates students have made. Then we plug 45 into the original pattern rule and see that it works.
I summarize: "This week, we're going to practice solving linear equations. This is an example of a linear equation. Today we'll start getting into this work."
Two weeks ago, when I initially introduced the Number Line Project, I shared with the class a graph representing completion rates for the first project and the first problem set of the year. At that time, I presented everyone with a goal: on our new project, everyone should improve, and I want to see more people handing in the work. We spoke about hard work and the ability to improve over the course of the year. Today, I share the same graph, with added bars for the Number Line Project that was collected on Friday: Do these 9th graders hand in their work?. "Look at your growth!" I say, "I would say that we're achieving this goal!"
The data backs up a growth mindset, which I've been working to cultivate in this class since Day 1. But don't forget that we're also talking about data representations. This is very important. When kids ask, "Why is Period 4 lower?" then we can talk about assumptions. Would percentages be better? "Maybe that's what I should use," I muse out loud.
What comes next is establishing a norm of revision and a culture of quality, which will be a major focus over the next few weeks. We will work to see what great work looks like, in addition to just handing stuff in!
In order to continue framing the work we'll do this week, I distribute this week's homework sheet. It's a little different from previous editions; now the structure of these weekly homework sheets are established, they can take on a variety of forms.
The front lists textbook assignments each night, and vocabulary that students should look up in their books. The vocabulary consists of terms will use as we start to talk about the properties that allow us to solve equations, which will happen at the end of this week and continue into next.
The back is a list of linear equation levels, and a place for students to track their progress.
For four days this week, I lean pretty heavily on Kuta Software to generate an "infinite" number of linear equations to solve. Yes, we'll be skill drilling this stuff, but there's an element of game design that makes it just compelling enough that kids are willing to do it. That, and they've been working on projects for the first few weeks of school, and some of them are actually relieved that the class has taken this turn.
What I set up for today's class is an introduction: ten problems each at "Levels" 1, 2, and 3, which are outlined on the back of this week's homework sheet in the previous section. Level 1 consists of one-step equation with addition and subtraction, Level 2 is one-step equations with multiplication and division, and Level three is mixed one-step equations that include negative numbers. I invite students to skip directly to Level 3, but that if they get stuck on anything, they should go back and practice on Levels 1 and 2.
This provides us with baseline data, and it's as much for my students as it is for me.