Lattice Multiplication is a great multiplication strategy for students who struggle with the standard algorithm. If you have a student who is learning how to solve multi-digit multiplication problems, then the lattice method is for you!
Many students need help with multiplication tricks and strategies when they are first learning how to multiply multi-digit numbers. In this video, I will show you how to set up the boxes for lattice multiplication for a 2-digit by 2-digit multiplication problem.
Transcript
Hi my name is Beth from My Tutoring Bee, and today we are going to be doing a redo of one of my oldest and most popular videos: How to do Lattice Multiplication
Okay so we’re going to work on this multiplication problem 271 * 43 and I chose a three-digit by a two-digit number so that I could really show you how to set up our boxes that we’re going to use for our lattice multiplication because we have a three-digit number by a two-digit number.
I want to create a rectangle that has three squares or rectangles inside of it by two squares so I’m going to go ahead and start off with a nice big rectangle here, and as you can see, I’m using graph paper. I really like to use graph paper for a lot of different kinds of math problems but it really makes setting up these boxes easier.
So as you can see, I’ve got two long rectangles going this way that’s going to be for my two-digit number, and then I’m going to split it up this way into three sections so something like that and you can get really detailed with it and count out the squares if you want to.
But I’m going to just go ahead and set it up like that. All right and so this is for my three-digit number going across the top here and my two-digit number going across the the the side. So let’s go ahead and write those numbers in. So I’ve just got 271 going across and then 43 on the side all right so with lattice multiplication we’re going to be kind of working diagonally once we get all of our numbers built in here.
So what I’m going to do, I’m going to go ahead and X out this top left corner and the bottom right corner and some students like to put in dots here on all of the other corners that were the lines cross.
So you can do that that just kind of helps to line it up because we’re going to draw some diagonal lines through all of these boxes and so let’s go ahead and do that, and I would recommend using some kind of ruler or straight edge to do this. So I’m starting at the at any dot that’s in the upper right hand corner and going all the way through and past my bigger rectangle and it should extend out beyond down here, below as well as over there to the side on the left.
You don’t have to be super long but just enough we’re going to be writing some numbers in the in this area here outside, so that’s why we want them there. Okay so we’ve got all of our boxes set up so now we’re going to start multiplying and in my original video that I did 10 years ago on this, I got so many comments about how long this method takes to set up all the boxes and how confusing it is. I think that this method does take a little bit longer than the standard algorithm; however this can be a really great visual tool for students who are struggling with that standard algorithm it really gives them the scaffolding that they need to know
where to put all of the different numbers.
Okay so here we go – what we’re going to do is we’re going to multiply any of these numbers on the outside side and the sections where they meet is where we’re going to put their product. So let’s go through a couple of examples.
One of the great things about this lattice multiplication method is that you can start in any box that you want to; you don’t have to go in a specific order. So
you can start here with uh 1 and four let’s go ahead and do that 1 * 4 that
gives us four. Whenever we have a single digit product or single digit answer we do want to write it as two digits and put a zero or something in this place. Some people maybe like to put an X there, some people will just cross it out; I like to put a zero there.
We definitely want to put the four down in this lower little triangle of this square just so that it represents 04 and not 4 because that would be 40, so we want 04 here. Let’s go on to this box here so 7 * 4 that gives us 28, so since that’s a two-digit number we can just put each of those digits in each of the little triangles there. 2 * 4 that’s 8, so again a single digit number; we’re going to just go ahead and put a zero there as a placeholder and then the eight.
Now let’s drop down here to this box so we’re going to multiply 1 * 3 so that this is the area where those two match up so 1 * 3 is 3 again, a single digit number. So we’ve got the zero as a place for 7 * 3 gives us 21, so we’re going to put the 21 there, and then 2 * 3 gives us six, so we’re going to go ahead and put the six there.
Okay at this point I like to recommend to my students to go ahead and just cross out or scribble out these numbers on the outside of the rectangle the numbers that we use to multiply because we’re going to start adding these numbers and we don’t want these to accidentally get added in to what we’re about to do so just a little recommendation there we’re going to start over here in this section- this little triangle down here the very bottom right- and we’re going to add any numbers that we have inside our rectangle and then we’re going to put that sum outside here.
That’s why we have those lines extending out past the rectangle, so we’ve got just three in this section. So we’re going to go ahead and drop down a three down here. Actually we’re going to go ahead and drop a three down here all right so now
we’re in this section where we’re adding up 4 0 and 1, okay, so that’s going to go
down here. 4 + 0 is 4+ one more is five.
All right now we’re going to go to this section so see we’re just just like we do when we’re adding normally, we’re starting from the right and working our way left and and adding up all those numbers. We’re just kind of looking at it diagonally here. Some of my students call this sliding down the mountain, which I think is really cute, so you’re just going to slide down and count up all of those numbers and then put the sum here with this.
We’ve got 0 plus 8 + 2 + 6 well 8 + 2 is 10 and then 6 is 16 since we do have a two-digit number. Just like when we’re adding with the regular standard algorithm, we’re going to go ahead and write the six here and then carry the one up to the next place value.
All right now we’re going to add up all these numbers in this diagonal section, so we’ve got a 1 a 2 an 8 and a zero. 2 + 8 is 10 plus one more is 11 so we’re going to write down that: one and again carry that one over to the next to the next place value and then we’ve got 1 + 0 is 1.
All right and so we’re done; this is it, this is our product 271 * 4 43 = 11,653.
All right there you go! I hope you enjoyed this lesson on lattice multiplication. Please let me know what you think in the comment section below.
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Extra Credit
I also created a “sequel” using this method with larger numbers:
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