In the last video we got some practice adding what we could consider smaller numbers. For example, if we added 3 plus 2, we could imagine that if maybe I had 3 lemons-- 1, 2, 3. And if I were to add to those 3 lemons maybe 3 lime-- is it lime or limes? Well, 2 green lemons or 2 more tart pieces of fruit. How much tart, sour fruit to do I have now? Well, we learned in the last video we have 1, 2, 3, 4, 5 pieces of fruit. So 3 plus 2 is equal to 5. And we also saw that that's the exact same thing as if we add 2 plus 3. And I think that makes sense because this is the same thing as starting with, maybe you have 2 lemons and you add 3 lime to it. You're still going to end up with 5 pieces of fruit. 1, 2, 3, 4, or 5. Just like that. So it doesn't matter what order you add in, you're still going to get 5. And this way of thinking about addition I view as the counting way of thinking about addition. The other thing we saw in the last video is the number line version and they're essentially the same thing. So we could draw a line. And all a number line is, it lists all of the numbers in order. It lists all of the numbers and you can actually go as high as you need to go. You could go up to a million, gazillion, trillion. We won't do that; I wouldn't have space or time in this video to do it. And you actually can go as low as possible. We'll start at 0, assuming-- in future videos I'll tell you about numbers smaller than 0. And maybe you can think about what that might mean tonight. But let's start at 0, and 0 means nothing. If I have 0 lemons, it means I have no lemons. So 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11-- let's go pretty high. 12. That way I can reuse the number line. 13, 14, I could keep on going, but maybe fourteen will be enough for this video. But let's use a number line for these addition problems up here. So in last video, just as a bit of review, you can view 3 plus 2 as starting at 3 and then adding 2 to it. Or going 2 greater than 3. And just going greater or adding on the number line is just moving to the right or moving up by 2. So let's move up by 2. I'll do that in this orange color. So let's go up by 2. So we started at 3 and we go up by 1. And then we go up by 2, or we're jumping, and we end up at 5. Which is exactly what we got before. If we have 3 lemons, we add one lemon, we have 4 lemons. We add another lemon, we have 5 lemons or lime or tart pieces of fruit, whatever you might want to say. And when you look at this version of it where you switched the order, we started at 2 and we're adding 3 objects to it. In this case, they were lemons or limes. So we're going to add 3 to it. 1, 2, 3. And just like we expected, we got the same thing. We got 5 again. Now what I want to do in video and hopefully this was just a bit of review, is I want to tackle harder problems. I want to tackle slightly larger numbers. And in this video I want to just give you practice dealing with the slightly larger numbers. And then in the next video we're going to dig a little deeper and think about what numbers even mean. But let's just get some practice understanding how do you actually do the addition problems with larger numbers? Let me write it in a nice, soothing purple color. Let's say I wanted to add 9 plus 3. Well, there's a couple of ways we could do it. We could draw circles again. We could say, let's see. Maybe I'll draw stars. 1, 2, 3, 4-- my stars are degradingg-- 5, 6, 7, 8, 9. That's 9 stars and then I add 3 stars to it. So I add 1, 2, 3 stars. And then if you were to count the total number of stars you would say, let me do that in a different color-- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. I now have 12 stars. So you would say that 9 plus 3 is equal to 12. If you looked at the number line you're starting at 9, maybe you have 9 stars and you add one star, two star, three stars to that. And you end up with 12 stars, which is the exact answer we got before. So you can do the same process when you start adding larger numbers, even though that now-- and I want to you to notice, the difference now is our answer has two digits in it. We'll talk more about digits in a future video, but all a digit is is a numeral. It has a 1 and a 2. That's what 12 is. I won't dig too deep into that right now. I think you're pretty familiar with the number 12. But what I want to do is, now what happens when you start adding more-- when you start adding two-digit numbers like this? For example, if I were to add 27 plus let's say-- I don't know-- plus 15. Now, if you had a lot of time on your hands and you didn't care about how people judged you, you could draw out 27 circles and then draw out another 15 circles and then count the total number of circles you had. And that would give you an answer. Or you could draw a number line. You could draw a number line that went all the way to know whatever 27 plus 15 is. So it's going to be this really, really large number, but that would take you forever. So what I'm going to do is show you a way to do this type of problem where you really just have to know your addition, almost have it memorized, or at least, if you don't have it memorized, be able to do something like this for relatively small numbers. And by doing it for the relatively small numbers, you can do the harder problems like this. So what you do, this is the fun part. You add, and I'll talk more about what this means in the future. You look at each of the digits. So we call this place, the rightmost place, we call that the 1's place. And why do we call that the 1's place? Because 27 is 20 and seven 1's. It's 20 plus 7. It's 20 plus seven 1's. You could view it as it's 20 plus 7 pennies. And this place right here is called the 10's place. Now why is it called the 10's place? I mean there's a 2 right there. It's the place that's called the 10's place. So putting a 2 here means two 10's. The number 20, that's two 10's. If I have one dime and you gave me another dime, I now have two dimes, and that's $0.20. So that's what the 10's place is. I don't want to confuse you, I just want to show you how to do these problems right now. We'll dig a little bit deeper in future videos. I just want to give you that idea. But the way to do these problems is you look at the numbers in the 1's place and add those up first. So you say, OK, I'm not going to worry about this whole thing right now. Let me just add the 7 and the 5. So I'm going to add the 7 and the 5. And if you don't know what that is-- hopefully you'll be able to do that in your head fairly shortly-- you could look at the number line. Let's look at the number line here. So if you add 7, if you take 7, and you add 5 to it. 1, 2, 3, 4, 5. We end up at 12. Or if you started at 5 and added 7, you'd also end up at 12. So let's write that down. We know that 7 plus 5 is equal to 12. So what we do is we say 7 plus 5 is equal to-- and now this is a new thing. It might be a little bit of a mystery, magical thing for you right now. And in future videos I'll explain to you why this works. We want to write the 12. 7 plus 5 is 12, but we just write the 2 here and we carry the 1. 12. 1 2. Well, we wrote the 2 there, but we put the 1 up here. And the reason-- I'll give you a simple reason for doing that right now. I'll give you a better reason in the future. Is that you only had space to put one digit here and 12 is a two-digit number, so we had to think of some other place to put that 1. If you really want to think about it even more, 12 is the same thing as 10 plus 2. That's the same thing as 12. So if we say 7 plus 5 that's the same thing as 12, which is the same thing as two 1's-- two pennies, plus one dime. Plus one 10. So we put that one dime in the 10's place. So we really just said 7 plus 5 is one 10 plus two 1's. Or one dime plus two pennies. If that confuses you just say, well, I just write the 1's digit of the 2 there and I carry the 1. And then you do the exact same thing in the 10's place. You add the 1 plus the 2 plus the 1. So 1 plus 2, let's do that on a number line. This is fun. So let's see. 1 plus 2. Let me do it in a vibrant color. Let me do it in this magenta. So we start at 1. We're going to add 2 to it. 1 plus 2. We take that 1 from our 12. 1 plus 2, so you go up 1, 2. You end up at 3. Then you're going to add up another 1. So you add another 1. You're going to end up at 4. So you ended up at 42. And this was pretty neat because we didn't have to draw a number line all the way to 42. And we'd didn't have to draw 42 objects. Just by knowing what 7 plus 5 was and by knowing what 1 plus 2 plus 1 was, we were able to figure out that 27 and 15 is 42. Let's do another example. Maybe I'll do a little bit of a simpler example. Let's say I had 78 plus 3. We do the exact same thing before. We just look at the 1's place only. So we look at 8 plus 3. What's 8 plus 3? Hopefully we can do that in our heads at this point. But let's just think about it. 8 plus 1 is equal to 9. 8 plus 2 is equal to 10. 8 plus 3 is going to be equal to 11. You could do that on the number line if it makes it easier to visualize for you. So 8 plus 3 is equal to 11. So what we do here, we just have 8 plus 3 is equal to 11. Put this 1 right here, put that there, and carry the other 1. Because 11 is one 10, one dime plus one penny. That's 11. And then we add the 10's place. 1 dime plus 7 dimes is equal to 8 dimes. So 78 plus 3 is equal to 81. And now there's one thing I want to show you. You don't always have to carry numbers like that. Only if the answer to one of these has more than one digit in it. 11 is a two-digit number. So for example, if I have 56 plus 2. Here I could just say 6 plus 2 is 8. Hopefully we're getting good practice at this. So 6 plus 2 is 8. And then, I don't have anything to add this 5 to, so I just bring the 5 down here. So 56 plus 2 is 58. Just like that. And this is one you actually could have drawn on the number line. It wouldn't have been too hard. So if you were to draw the number line like that, you know 0 would be way off to the left some place. But let's say I had 50. 49, you could keep going to the left, but you have 51, 52, actually let me start a little higher than that because I'm going to run out of space. Let me start at maybe 55, 56, 57, 58, 59, and I could go in both directions, keep going. But if we start at 56 right there and we add 2, we go up one, we go up two. We end up at 58. So just like that we're able to do that problem. I'll see you in the next video.