Common Issues with Linear Equations Transcript

Speaker 1: Alright, guys. Yesterday we did a pre-assessment and we studied those. I actually met with other 8th grade Math teachers in the district and their students were taking the same one, and we came up with a game plan. Today’s lesson was the first part of our formative assessment lesson, solving linear equations in two variables. We’re going to work on a problem today called Cash Registers and it kind of would make sense if I gave you some time to work on it by yourself so you know what heck is going on. I’m going to give you 10 minutes to get a feel for the question and work on it the best you can.

Yesterday after school, several colleagues around the district that also teach 8th grade Math and I got together to discuss our pre-assessments that we had given our students, and we discovered that a lot of our kids had the same misconceptions. What that allowed me to do is make my groupings for today.

The next thing I’m going to have you do is take this paper, your pencil, your calculator, find your group, arrange your desk. Go quickly. Here at Turkey Foot Middle School, we kind of do our test corrections in a similar fashion, so the students are used to this model of being placed with students that have the same overall misconceptions. So they can have rich discussions and they feel more empowered to argue their point.

Your goal is to produce a better answer than you did individually.

Speaker 2: Everybody try your equations. Plug in the X and Y for the 4x + Y =70.

Speaker 3: I got 3, 9, and 2, 6.

Speaker 2: Yeah, that’s what I got, too.

Speaker 4: What is 4 times the number of quarters plus the dollars?

Speaker 5: But 12 quarters [?].

Speaker 6: I messed up and I accidentally said 4 quarters instead of 4 times [?].

Speaker 1: They had roughly about 10 minutes to take care of that. And then I introduced some student work, other students not in our class, so they may have felt a little more apt to criticize because they’re not their classmates.

This set of questions is my expectation. They’re kind of laid out on the paper but I’d like to go over them quickly. So the first thing you’re going to do is correct any mistakes that you see, correct their work. What do you like about the student’s work? And you’re going to have four. What method did the student use? Like algebraic or…?

Students: Substitution, graphing.

Speaker 1: Substitution, graphing, table, elimination. Alright, things of that nature, that’s the expectation there. Is the student’s work clear? Is it accurate? Is it efficient? What errors did the student make and how can they improve their work? Please be specific. Alrighty, so let’s analyze Ms. Ava.

Speaker 7: These right here, she doesn’t have [?] because she didn’t have the numbers that she used from over here. She didn’t even use the numbers.

Speaker 8: I don’t think it’s accurate because she never really got the answer. She never got it correct. She would’ve been close.

Speaker 9: We can say it’s somewhat accurate and somewhat not. We can say it is accurate because she’s on the right track.

Speaker 8: Say it’s kind of accurate?

Speaker 1: They got to see different approaches to the problem and which ones might be more effective than others. And when it wasn’t them doing the problem themselves right then and they’re looking at somebody else’s work, they could say, “Oh, they made this mistake, they made that mistake. I don’t like how they organized this.” It kind of gave them a reference point about how to make their own work better.

Speaker 8: I’ll put that it should be [?].He attempted to use the elimination.

Speaker 1: Could I have your attention for a moment, please? I have not given you Joe and Mia’s work yet, so that will be the first thing we analyze tomorrow. Same kind of process that you’re doing today. Please stack up all of your papers. Make sure that the one on top has one of your group member’s names on it so when I collect your packet I’m going to be able to get it back to you tomorrow. Alright guys, you are excused.

Do you recall when we left yesterday we were looking at some student work and I promised that you would have two more folks to look at. We have Joe and we have Mia. If you are not finished with Ethan, that is where you start.

Yesterday I let them spend some time on what methods did the students choose, where their mistakes were and so forth. And then today they looked at two other student’s work that was a little more difficult.

Student: You know what he did wrong? He substituted Y as this.

Student: I think he didn’t multiply that by 4 and that by 3.

Student: Yeah, he just kind of put it down there.

Student: Yeah, he just multiplied that part and that part.

Student: You can see if all the student’s work that we’re correcting, they all make the same mistake. You can like hard wire it into your brain, “Don’t make this mistake and make sure you go back over your work,” because I think it was Ethan, one of the problems, he didn’t go back and recheck it. So he got the entire question wrong even though he did his processes right.

Student: Multiply the entire problem by 3 when you multiply by 3?

Student: It should’ve been 12y instead of 5y.

Student: Then he should have put parentheses around it.

Student: Yeah, he could have put parentheses right here and just put 3 there to make it neater.

Student: She’s got y = 50, but then there’s a bunch of “y =” everywhere, so you don’t really know what her answer is.

Student: Yeah. There is y = 66, there is y = 50, there is y = 10.

Speaker 1: The big benefit of these formative assessment lessons is we do give them the ability to argue things out. And yes we can clarify, but we will not tell them the answer. They’re going to have to come up with it on their own.

Okay, ladies and gentleman, even though we briefly talked about these yesterday, I want to make sure everybody is thinking together. So what did we think about Ava?

Student: She’s wrong.

Speaker 1: She’s wrong, but why?

Student: Because she gave it all up halfway through.

Speaker 1: She gave up. How many more steps would Ava have needed to get to the solution?

Student: Six.

Speaker 1: Six more. What about Ethan? Where was his mistake?

Student: When he had the equation, he didn’t multiply them by 1 by positive, 1 by negative, to cancel out one of the variables.

Speaker 1: Okay, so he didn’t get anything to cancel out and I think what method was he trying here?

Students: Elimination.

Speaker 1: Elimination.

I really think that they learned a lot throughout the lesson and they’re going to show growth on their post-assessments.

Raise your hand if your team says Ava is the most efficient. Alright, what about Ethan? Is he the most efficient? Ooh, you guys liked Ethan. That’s interesting. What about Joe? You guys liked Joe? What about Mia? Interesting. I would bet you guys like Ethan because he was using elimination. Is that it?

So now they have a reference point. Is this like Ethan’s work? Is this like Joe’s work? Is this like Mia’s work? Or is this good work? And I think they’ll know that now.