# MEC Base Ten Block Addition

Speaker (woman):

We have been working to add three-digit numbers – both with our base-ten blocks and when writing out the problem like this.

On-screen: [(Problem is recorded vertically): 273+152.]

But I’ve noticed that some of us are having trouble with adding when we need to regroup or make trades. So today I am going to show you how to do this addition problem, 273 plus 152, using base-ten blocks to help us understand what each of the numbers we are recording means.  Our blocks will help show us when we regroup, and we will be able to see what is happening at each step when we solve an addition problem like this.

On-screen: [Screen shows one flat worth 100; one rod worth 10; one small cube worth 1.]

Remember, we have used base-ten blocks before.  This is a flat. It is worth one hundred. This is a rod. Rods are worth ten; and ten rods are equal to one flat. This is a small cube. Small cubes are worth one; and ten small cubes are equal to one rod.

So, when we do an addition problem using the base-ten blocks, the first thing we need to do is build the first number. In this case, our number is 273. I’ll start with the hundreds, and because I have two hundred, I will take two flats.

On-screen: [Screen shows two flats worth 100 each; seven rods worth 10 each; three small cubes worth 1 each.]

I will have 100, 200. Next, I need seven rods because there are 7 tens or seventy. This makes 210, 220, 230, 240, 250, 260, 270. And, finally, I need three small cubes to give us 271, 272, 273. So, that’s our first step. We have made this first number, 273, with our base ten blocks.

Next I’m going to build the second number so that I can see what I'm adding to 273. The second number is 152.

On-screen: [Screen shows 3 flats worth 100 each; 12 rods worth 10 each; 5 small cubes worth 1 each.]

So I’m going to need one flat for 100. I will need five rods for my five tens. This makes 110, 120, 130, 140, 150. And I have two small cubes that I’m going to need because I have two ones. So I have 151, 152.

So just like in our written problem we have 273 and we have 273 with our blocks plus 152. And we have 152 with our blocks.

Now that both of my numbers are built with the blocks, I can begin to combine the blocks that are the same. I am going to watch to see when I have enough blocks that I could trade.

I could start by combining any of the pieces that are alike, but I like to start with the little cubes because they’re the smallest. And, you know, when I make trades, I’m trading ten smaller things for one larger thing. So, I am going to start with my ones place and with my small cubes. And I am going to see how many cubes I have when I combine that. When I do, I have three, four, five. Five small cubes. Now I need to see if I have enough to make a trade. Hmmm, I remember that when I have ten small cubes, I can trade them in for a rod, but I only have five small cubes. I know that is not enough to trade so I’m finished with my small cubes and I want to record that in my written problem.

When I look at this in my written problem, I added the three ones to the two ones and I got five ones. I can write this in my ones column.

Next, I move on to my tens place. My rods are my groups of ten, so I am going to add my rods now. When I do this I have 7, 8, 9, 10, 11, 12. I have twelve rods. Hmmm. I know that twelve rods are equal to one flat and two rods because one flat is ten rods.

Instead of having all these rods, I can make a trade. I can line them up nice and close and I can check to make sure that my trade will be equal. Instead of twelve rods, I can have one flat and two rods. I know it’s the same, even though it looks different because one flat is the same as ten rods and I can even check that. So, I am going to make my trade now.

On-screen: [(Problem is recorded vertically): 273+152= 5 (part of answer). Screen shows 4 flats worth 100 each; 2 rods worth 10 each; 5 small cubes worth 1 each.]

Now I have one flat and two rods.

Let’s look at this in our written problem. When I look at my tens place, I have seven tens plus five tens.

This is the same as the seven rods and five rods that we added together over here.

I know that seven tens plus five tens is equal to twelve tens. So that would be ten tens, or one hundred, plus two extra tens. I am going to need to write this very carefully.

I am going to put my two tens in my tens column…these two tens here in my tens column.

On-screen: [(Problem is recorded vertically): 273+152= 25 (part of answer). Screen shows 4 flats worth 100 each; 2 rods worth 10 each; 5 small cubes worth 1 each.]

Looking at my base ten blocks I’ve written down these two rods, but I still need to record this flat.

Because the flat is worth 100, I look at the hundreds place. Here I write a one above the hundreds column to show that I have one hundred from my trades.

On-screen: [(Problem is recorded vertically): 273 (with 1 written above the 2) +152= 25 (part of answer). Screen shows 4 flats worth 100 each; 2 rods worth 10 each; 5 small cubes worth 1 each.]

So let’s review that, because sometimes people get confused about where this one comes from and this one and why we write it like this, but it’s really just a way of recording our trades.  When I added my tens I had twelve tens. There were enough tens to make a trade. So, I traded ten of the tens for a hundred, or this flat. Once I traded, they weren't tens any more, there was one hundred, so I recorded the one up here in the hundreds column.

I still had two tens, so I recorded that in the tens place of my sum.

Remember that the reason that the one got recorded up top is that we haven't counted it in our sum yet. We've just traded it for a larger place value.

OK, so let’s look at where we are now. We have five small cubes and two tens.

Now I am going to combine my flats. I have the flat that I got when I traded, I have the two flats here from our first number, and I have the one flat from our second number so I have 1, 2, 3, 4 flats. Or 100, 200, 300, 400.

On-screen: [(Problem is recorded vertically): 273 (with 1 written above the 2) +152= 25 (part of answer). Screen shows 4 flats worth 100 each; 2 rods worth 10 each; 5 small cubes worth 1 each.]

In my written problem, I can do the same thing. In my hundreds column I have the one hundred that I regrouped, the 200 from my first addend, and the 100 from my second addend. So, I have 100, 200, 300, 400.

I can record the four in the hundreds place to represent 400. So my answer in my written problem equals 425.

On-screen: [(Problem is recorded vertically): 273 (with 1 written above the 2) +152= 425. Screen shows 4 flats worth 100 each; 2 rods worth 10 each; 5 small cubes worth 1 each.]

Let’s double check our blocks and make sure that we have the same thing over there.

I have 100, 200, 300, 400, 410, 420, 421, 422, 423, 424, 425. I have 425 as my answer in my written problem and in my blocks.

Using these base ten blocks is really helpful with addition problems that require regrouping because I can see exactly what is happening when I make trades. Remember when we are working on our 3-digit addition problems, we want to start with our smallest parts, our ones, and then move to our tens, and then move to our hundreds. Anytime we get ten of something, we can make a trade and this will help us keep the same value of the blocks, even though they might look a little bit different. Remember it is also important to record the trades carefully in the written problem. When we use our blocks to show the problem, we can easily add numbers together, and we can see how the numbers look in the written problem.

End of MEC Base Ten Block Addition video.

Video duration: 9:54