Teacher: All right. Good morning, class. We’ve been working on linear equations, and today, what I want to do is, I want to share some bar models for equations, and they give us a way that we can visualize the equations that we’ve been working on. You can look at them, kind of see the structure, and it can give you some ways to think about how we solve those equations.

All right. Let’s go to one and I want to see if, actually, some students can come on board to help me come up with this next one. I want to go ahead and have six Xs, but here, let’s see, we can add any small number that you want, and then we’re going to have it all equal to some large number. I’m hoping for a student who might be willing to come up and help me figure out this problem. We’ve got 6x plus some–I’m going to ask you for a smaller number here and then equal to some larger number there.

Do I have a volunteer who might be willing to come help me on board?

Student: Does it matter what number I pick? 

Teacher: You can pick any number you want. For this one, I’m looking for a smaller number in the first slot and then a larger number in the last slot.

Student: 2 there, and do 24. So, I would subtract the 2 to make it equal to 6x equals 22. Then, using the bar graph he showed us, I would make the bars.

Teacher: Nice.

Student: Which those are all equal to X.

Teacher: Yes. We will definitely pretend those are all the same X bars.

Student: Then, I would also have one large bar that would be equal to 22.

Teacher: Sure.

Student: Then, I would figure out how to get rid of the six as equally as I could.

Teacher: Yes. Really, what we’re doing now is we’re clearly gonna divide the 22 into those Xs. We can do that. I have it a little bit here too, then that’s perfect. I laid out these Xs just like you did, and I had this–what ended up being–I didn’t know you were going to have, but this little two hanging out here is equal to the whole number. 

Then, you did a nice job. You really brought into like, let’s just really focus on those six Xs, and then if we start dividing it into pieces we can figure out what the one X is. Thank you so much.

Over different lessons I try to bring different students up to just have a variety of voices and people sharing up front. Some students really enjoy being up there. Some don’t love it as much but I try to work with them, and what’s fun is to try to incorporate them into the part of teaching and making their ideas part of the lesson.