Tom Schersten: Have you ever been told that when you add, you have to start on the right side? Well, it’s not true. The commutative property of addition says very clearly we can add in any order we want to. This video is going to show you how, when you understand place value, you can add a column of two digit numbers faster mentally than you can keying them into a calculator.

Please take a look at the problem that I have written down here. I have five two-digit numbers that I’m going to be adding, and I’ve also put out base ten blocks next to each one so we can clearly see that when we have 27, this 2 represents 20.

I’m going to start adding on the left side with the tens, and when I do that, I see that I have 20, 30, 40, 50, 60, 70, 80. I have 80 from the tens column.

I’m now looking over in the ones column, and I see that if I put my 3 with my 7, I can make another 10. If I put my 1 with my 9, I can make another 10. So, I have my 80, but in the ones column, I have some hidden 10s that make me 90, 100, and we have five left over, so the answer is 105.

Now, this is a really nice example where I have some friendly numbers, but let me show you another example. I still have five two-digit numbers. This time the numbers are not quite so friendly, but after I count the tens, I’m going to come to the ones column. When I’m adding with the tens first, instead of the ones, I’m using the commutative property of addition, and when I break numbers apart and recombine them into others, I’m using the associative property of addition.

What I’m going to do when I get to the ones is I’m going to put two of the ones from the 5 up with the 8 to make a 10, and I’m going to use 3 of these ones with the 7 to make a 10. So when I count this up, I’m going to get a 10, 20, 40, 50, 70, 80, 90, 96, 97, 98, 99. Notice all I’m doing is counting by tens, and then counting by ones.

The next video is going to extend this to three and four digit numbers.