Long Division with Sequence Buttons

Hi, there. It’s Adrianne from Math for Middles. So excited to have you with me today. Today I wanted to talk about long division. Now, this is a topic that I’m visiting with one of my students right now, so I thought it would be helpful to talk about it in general with everybody.

My student gets completely overwhelmed with long division, and actually doesn’t see the point in why we even need to master long division, when you carry around these handy dandy things called calculators. But there is a point to the madness, and learning the skills, because it lends itself to learning higher levels of math, learning how to follow sequences of steps, and the like.

So, I’m gonna show you just the basics today. So, with basic division, the idea behind division is we have a group, and we’re trying to create different groupings. So, I have nine strawberries, and I’d like to put them into two groups equally. So, we have to keep sharing, and each group has to have the same amount in them. Let me show you.

So, obviously we can drag these over, one for you, one for me, one for you, one for me. And my circles are obviously not big enough. But we’re just gonna keep sharing until we run out. So far each group has four. Uh oh. I don’t have enough to make another group. And so, this is our remainder. Now, we could cut it in half and then we would share it equally. And most kids know this intuitively, right? I can break this cookie and share it with my friend, and we each get a half.

So, that’s really important. But it becomes tricky when we’re doing much larger quantities. Doing the one for me, one for you is really simple, great, fantastic, basic division. But what happens when we get bigger quantities like this? This is 312. And each bundle of sticks that you see here represents the quantity of ten. And all together, we have 312 items. Well, then it becomes a whole ‘nother story to try to do the one for me, one for you idea.

And so, long division is handy when we’re trying to make groups of objects. And our students need to master the skills behind doing that. Now, a lot of teachers like to use partial products. But ultimately our goal is to arrive at the traditional algorithm for long division because it’s efficient and it’s effective, and we do not make as many errors.

So, why don’t we do 312 divided by two, together? And I wanted to show you the multisensory way. So, with multisensory way, we have what’s called sequence buttons. Now, sequence buttons help us keep track of the steps for long division. The very first thing we do, is we start by dividing, then we multiply. Subtract, compare, bring down.

So, I’m gonna talk about each of those things with you. Let’s go ahead and get started, and then I’ll talk a little more about the language behind that. And our goal is to get to the point where the student only needs to have these symbols out to the side to help them remember how to do the steps. But we also give them more detail in the beginning.

So, I’m gonna change my pen to pink, so you can see really easily. So, we start here with the first digit all the way to the left. Which, first and foremost will be confusing, because we’re used to starting at the far right. But in long division, we always start at the left. And the first question we ask ourselves is, “I have three. Do I have enough to make a group of two?” Yes. So, that’s our first step in division. How many groups can I make? “Well, I can make one.” Then we multiply one times two, is two.

Next step is subtract. My brain. Then we finish subtracting, there’s one left over. Then we compare. That’s the step. “Do I have enough to make another group of two?” And some students get to this step and they see that there’s more than how many groups they were making, which is a trigger to go back and make a bigger group.

But in this case, we have not enough to make another group. So, what do I do? Well, I bring down the next quantity. And so, now I have 11. So, we start again with our steps back up here, at divide. How many groups of two can I fit inside of 11? Well, I can fit five. Step two, I’m gonna multiply five times two, is ten. Now, third step. Subtract. And we have one left over. Compare. “Do I have enough to make another group?” Nope. I need to bring down. We have two.

How many groups of two are in 12? There are six. I put a six up here. Six times two is 12. And I subtract. And I have zero. Do I have enough to make another group of two? No. Do I have any more numbers out here? No. Then, I’m all done.

There are 156 items inside of my two groups. And we actually use a grid like this to keep our work neat and orderly because bad hand writing can lead to lots of errors, which is a problem.

So, let’s do it again and I’ll show you with the steps written out this time.

So, here we have 416 divided by four. How many groups can I make? That’s the first question. Then I write that amount of groups on the top line, and we multiply. Then we subtract. Then we compare. Do I have enough to make another group? Yes, or no. And if it’s no, then I’m gonna bring down the next number to make another group.

So, let’s run through it. Starting right here at this very first digit, do I have enough to make a group of four? Yes. One times four, is four. Subtract. Zero. Alright. Now, time to compare. Do I have enough to make another group? Nope. I’m gonna bring it down. One. And then I ask myself again, how many groups can I make? I only have one, can I make another group? The answer is no in this case. Now a lot of students would just move on and bring down that six. But we have to practice the fact that we’re gonna put a zero up here, and we zero times four, we cannot skip this step. We have one. Then we do the compare again. Do I have enough to make another group? No. Now I can pull down the six. How many groups of four in 16? There are four.

Four times four is 16. And we have a zero. So, that’s how we work through it with our students, and we practice it again and again. And we want it to get to the point where the student has just these buttons to look at. And they can do it independently and write those buttons on the paper when they see a long division problem.

Students are gonna be doing this, also, in higher grade levels, six, seven, eight, when they’re trying to make decimals. And so, it’s a really important skill to practice because a lot of schools are not going to allow the student to use a calculator. And also, students can typically enter into the calculator incorrectly. And so, we wanna make sure that they understand how to do the long division way. And having this grid is really helpful for our students, and helps them to really grasp what’s happening here.

So, if you’ve got questions for me about this, I would love to help. We would love to work with you over at Math for Middles. Head over to madeformath.com to learn more. Feel free to leave me comments below the video. And we’ll talk again next week.

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