## #4 The power of understanding place value when adding 3- and 4-digit numbers

Date: *May 6th, 2015*

By: *Tom Schersten*

**Tom Schersten**: This video is going to show the power of understanding place value when adding three- and four-digit numbers. Please take a look at the example that I have here: 375 add 256. I’m going to start adding on the left side, because I know that that stands for 300, and this is 200, and that makes 500, altogether.

When I look at my tens column, I see that I have enough tens to make another 100. I’m going to take 30 from my 50, and put it with the 70, to make another 100, and I will actually trade those in for another 100. Then I see that I have 620, but when I get to the ones column, I have enough ones to trade for another 10, and when I trade in 10 ones, for another 10 stick, I have 631.

All I’ve done is to count by hundreds, then count by tens, and then count by ones.

Let me show you a larger example. This is an example of adding two four-digit numbers. Again, when I add them, I’m going to start adding with the thousands.

I’m going to count to see how many thousands there are, but before I write it down, I’m going to look and see if there’s any more hidden thousands in the one hundreds column. When I add up my hundreds, before I write it down, I’m going to check my tens column, to see if I have any hidden hundreds, and before I write down my tens number, I’m going to check my ones column, to see if it has any hidden tens.

When I add this up, I’m starting with the 4,000, plus the 3,000, makes 7,000. But before I write down the 7,000, I’m checking to see that I have enough hundreds here to make another 1,000. I’m going to use three of the hundreds from the 500, to put with the 700, to make another 1,000, and now I have a total of 8,000.

When I use three of these to make another 1,000 there, I only have two hundreds left. I’m not writing down a 200 yet, because I want to check and see if I have any hidden hundreds in the tens column, which I don’t, so I’m writing down the 200.

I’m coming to the tens column, and I see that I have 50, my 30 and 20 is 50, but before I write it down, I’m checking my ones column, and I see that I have enough ones to make another 10, and two leftovers. I’m going to have a total of six tens, and two ones left over.

During the last few videos, we have been taking numbers apart, and recombining them, to make numbers that were much easier to do computation with. The next video is going to show you a structure whereby kids can use base 10 blocks to model the kind of thinking they have for adding and subtracting two-digit numbers with regrouping. Thank you.