Today's opener is a twist on a lesson from last week, in which we looked at the role parentheses play in a two-step equation. Now, we'll compare what division looks like when it's the first step versus the second step in a two-step equation. Here are the two equations that comprise today's opener.
It is helpful to read these equations out loud as if they are number tricks. That way, when we solve the equation, we really just have to "undo" the trick by reading it in reverse. (This is an idea upon which I elaborate in tomorrow's lesson.) For example, the first equation is read: "Take a number, divide by 7, then subtract 2, and you'll get 10." It can be solved by reading it opposite and backwards as "Take 10, add 2, then multiply by 7, and you'll get the original number."
The second equation swaps the order of the two operations. "Take a number, subtract 2, then divide by 7, and you'll get 10" leads to the solution, "Take 10, multiply by 7, then add 2, and you'll get the original number."
This sort of thinking continues to give students a facility with inverse operations and the more complex algebraic moves that we'll make later in the year.
Review the Agenda
The key idea that I want to get across in today's lesson is that every one has room to grow in his/her linear equation-solving skills, and that everyone will improve through collaboration and perseverance. I point to today's agenda as we move on into today's work time. It's a brief agenda that frames our work like this: "Through COLLABORATION, everyone can level-up on their equation-solving abilities!"
I've previously distributed today's worksheet (see below) to some classes. Today, I make sure that everyone has it. The last part of the agenda tells students to "Pick an equation and make it perfect!" The key here is that everyone should be challenging themselves appropriately. Today's work is not about the grade, it's about building skills, and the majority of kids understand this. Therefore, it takes little prompting to get each student to choose an equation that's just beyond his/her perceived level of understanding and give it a try. The part where we try to "make it perfect" is the collaborative part, and the result is actually a pleasantly productive work environment.
Worksheet: SLT 1.1, Level 4 through 7
Before I get to that, here's a brief description of the handout. This is a Kuta Software Infinite Algebra worksheet that consists of six equations at each level from Level 4 (two-steps) through Level 7 (multiple steps, with fractions). In the instructions at the top of the pages, I tell students to show all work on a separate sheet of paper, and that I want to see all steps, because that's an indicator of perseverance, which is what I'm grading here. That's what I expect to see.
Collaborative Practice Time
Today's work might happen in small groups at tables, but often it's as a whole class. Sooner or later, each class reaches the point where everyone buys the idea that we're in this together and that the collaborative approach really works. Once this happens, there's no classroom management necessary: whenever someone goes to the board to share an example, everyone else is keyed in.
The ideal that I cultivate is for students to suggest examples and try them on the board. Each time this happens, we have an opportunity to critique someone's work collaboratively. We can critique the algebraic moves they've made, or we can critique the layout and the presentation. As a class, we suggest edits of both kinds. We also admire exemplary efforts and review how to check your work.
Two common suggestions I make about layout are to line up the equal signs (by the time I took this picture, kids had come a long way and I was getting especially picky), and to increase spacing between the lines, which reduces clutter and makes things easier to read.
It's important to see the context of our work here: students are not just doing busy work at any point. They are specifically targeting the type of equation they'd like to be able to solve, and then they're thinking critically about what they know and where they need help. By taking it one level and one equation at a time rather than bombarding them with practice, this approach gives students the chance to understanding what they're learning, because they must be able to name it in the first place.
In the back of everyone's mind should be the work that's underway on the Linear Equation Project. I am most proud when students begin to reference the properties applied at each step without my prompting. While one student is working at the board, other will be naming properties under their breath. It's really cool to see.
When everyone is involved today's class moves way too quickly! In order to summarize and debrief, I bring it back to our originally stated goal with the prompt:
How did you level up today?
I ask for students to jot their name and their answer on a separate sheet of paper, and I collect these as students leave. This is a great opportunity to gain more insight into how each student thinks about his or her own learning.