Modeling and Solving Equations

Adrianne: Hey there it’s Adrianne from Math for Middles. I’m so excited to be with you today. I thought I would talk a little bit about modeling equations and showing how we can help students with the multi step part of it. Because most of the students here at Math for Middles are visual spatial learners we use a lot of manipulatives to help them master these math concepts and we do simultaneous processing where we’re working with the models but we’re also writing the numbers out so they can see the connection.

Adrianne: So, first of all your student’s going to need to have some background information. We can’t do equations if we don’t understand what an equation is, what a variable is, and those are two concepts that’ll need to be talked about before you can reach this point. So, when I talk to a student about this we talk about what the goal is when we’re solving the equation. And our goal is always going to be to isolate the variable. And your student may not understand what this word isolate even means. You want to talk about that. Where have they heard this word before? What can they relate to? My mind always goes to isolate as in someone being in time out or in jail in single confinement in a little jail cell. That’s isolation, that’s being alone all by itself. So, that’s going to be our goal. That is always our goal when we’re solving equations.

Adrianne: And then, I tell the students, “Well the other thing we need to do is we need to figure out who’s messing with our X?” And so, I always type that out. “Who’s messing with my X?” And they love this and I say it kind of silly too. I say, “Who’s messing with my X?” And then they giggle and laugh. “No, really who’s messing with my X?” And in this case it’s this plus three, he’s messing with my X and that’s not good. So, now we need to identify how are they messing with my X. And we have that here, how are they messing with my X. Well, in this case it’s adding three. At this point we talk about how we need to do what’s called an inverse operation to make that three stop messing with my X. And inverse operations are super cool because they undo stuff. So, we’ve got to do our inverse operation.

Adrianne: Next, we’ve got to identify that this is adding three. So, the inverse of adding is subtracting. So, we’re going to need to take away three and do it from both sides. So, those are some of the things we start talking about. Then we start building it with our math manipulatives. So, let’s go ahead and do that. So, here we have X, we have our X plus three, one, two, three, and that equals … Let me get an equal sign here. That’s a plus. I keep doing that. There we go. Equals our eight. And then, we have eight single guys over here, one, two, three, four, and I’m going to make the work easy for me and I’m going to duplicate it. Okay. So, we’ve made it visually, X plus three equals eight. Going back to our questions who’s messing with our X? This guy, these three, these positive threes. How are they messing with it? Through addition. How am I going to undo it and make him stop messing around? Well, I’m going to do the inverse operation of subtracting three. So, we have one, two, three. Okay so that’s our next step.

Adrianne: As your student’s working you want to make sure that you’re showing each step. So, we have X plus three equals eight. That was our first step over here. And then, we said, “Oh positive three plus three is the one messing with my X and I’m going to undo it so I’m going to subtract three.” So, I put in three, negative three spots, that’s on this side. Okay. Now, I have to keep it even because this is an equation. If I’m messing with one side I’ve got to mess with the other side. So, I’m going to take this, duplicate it, bring it over here. Okay. So, now I subtracted three from both sides. Let’s show that. Minus three, and we’re going to put that on this side. Now, my students love this part about the digital manipulatives because there’s something super cool about this.

Adrianne: So, when we go like this it changes right here and it’s going to allow us to combine these together and our goal when we’re fixing that number that’s messing with our X is to get zeros or ones. And when I add three and I subtract three I’m going to get a zero. So, watch what happens when I click that button. It goes away. Wasn’t that awesome? So, on this side we have just X over here now. I subtracted it and then we have to do it over here on this side. So, I’m going to highlight all of this and I’m going to tell it to combine them. We’re going to add eight plus a negative three and it leaves us with one, two, three, four, five, and that’s how we walk through doing the equations simultaneous processing. And the students love watching those numbers collapse into each other with the software here which is awesome.

Adrianne: So, helping your student by using these manipulatives and writing the steps out at the same time on the other side is going to be key for helping them make and build that transition between the models which are super helpful and the abstract which is just the numbers. And I like to have these steps written out too at the top of the paper. Here’s our goal. We’re going to isolate the variable. We’re going to discover who’s messing with my X, how are they messing with my X, and then what inverse operation will make that number stop messing with my X. So, when we talked about inverse operations obviously we know that adding and subtracting go together. So, those are our inverses here and then we have multiplying and I can’t make a division sign on here so I’ll just do this and I’m going to fix it with my pen tool and we’ll make a little division sign. There we go. So, those are our inverse operations, adding and subtracting goes together, multiplying and dividing goes together.

Adrianne: Okay. I think that is enough for today. If you have more questions about modeling these equations let me know. The software that we’re using here is called Braining Camp. If you’d like to get in touch with that head over to ETA Hand to Mind and look for Braining Camp. It’s a digital manipulative that you can buy access to. They have a free trial as well. If you’ve got a child that’s struggling with making the connection from the abstract to what’s really happening reach out to us. We would love to help you. We work with students that have dyslexia, ADHD, dyscalculia, autism. And teaching in this way using the multi sensory method is what really helps move the needle. So, if you have questions for us or would like to get in touch with us make sure to head over to MathforMiddles.com, reach out via our contact button and we would be happen to help you. Thanks so much for meeting with me today we’ll talk soon.