Learn about Basic Addition

Khan Academy Presents: Introduction to addition. Multiple visual ways to represent addition.

Welcome to the presentation on Basic Addition. I know what you’re thinking. “Sal, addition doesn’t seem so basic to me.” Well, I apologize. Hopefully by the end of this presentation or in a couple of weeks, it will seem basic. So let’s get started with - I guess we could say some problems. Well, let’s say I start with an old classic. 1+1 and I think you already know how to do this but I’ll kind of show you a way of doing this, in case you don’t have this memorized or you haven’t already mastered this. You say, “Well, if I have 1 - let’s call that an avocado. If I have one avocado and then, you were to give me another avocado, how many avocadoes do I now have? Well let’s see, I have two avocadoes. So 1+1=2. Now, I know what you’re thinking. That was too easy. So let me give me you something a little bit more difficult. Now, like the avocado. So I might stick with that theme. What is 3+4? This is a think a more difficult problem. Well, let’s stick with the avocadoes. And in case you don’t know what an avocado is, it’s actually a very delicious fruit. It’s actually the fattiest of all the fruits. You probably didn’t even think it was fruit even if you ate one. So, let’s say I have three avocadoes. And let’s say you were to give me four more avocadoes. So let me put this four in yellow, so you know that these are the ones you’re giving me. So, how many total avocadoes do I have now? 7 avocadoes. So 3+4=7. And I am going to make another way of thinking about this. It’s called the number line. And actually I think this is how I do it in my head when I forget. If I don’t have it memorized. So a number line, I just write all the numbers in order and I go high enough just so I could—all the numbers I’m using are kind of in it. So, you know the first number is zero which is nothing, maybe you don’t know, well now you know. So, we’re saying 3+4. So let’s start at 3. So I have 3 here. And we’re going to add four to that three. So all we do is we go up to the number line or we go to the right on the number line four more. That was—all we did is we just increased it by one, by two, by three, by four and then we ended up at seven. And that was our answer. We could do a couple of different ones. We could say, what if I actually—what 8+1 is. 8+1; well you might already know it. You know plus one is just the next number but if we look at the number line, you start at 8 and you add one. 8+1=9. Let’s do some harder problems. And just so you know if you’re a little daunted by this initially, you can always draw the circles. You can always do the number line and eventually overtime, the more practice you do, you’ll hopefully memorize this and you’ll do these problems in like half a second. I promise you. You just got to keep practicing. Let’s say I want to draw the number line. And actually I have a line too, so I shouldn’t—keeping all those ugly looking lines that I have been giving you. Look at that. Look at that; that’s amazing. Let’s see. Oh yeah look at that. Okay. So, that’s a nice looking line I’ve done. I feel bad to erase it later on. So let me draw a number line. So let’s do a hard problem. What is—I would do it in different colors now. 5+6. So if you want, you could pause the video and try this. You might already know the answer and the reason why I say this is a hard problem is because the answer has more numbers than fingers. So you can’t necessarily do it on your fingers. So let’s get started with this problem. Actually my phone is ringing but I’m going to ignore the phone because you’re more important. Okay. Let’s start at the 5. So we start at the five. And we’re going add six to it. We’re at 11. So 5+6=11. Now, I am going to ask you a question, what is 6+5? Well, we’re going to have to see that—can you switch the two numbers and get the same answer? Well let’s try that. I am going try it in a different color, so we don’t get all confuse. So let’s start at 6, right? Ignore the yellow for now and add 5 to it. Oh, we get to the same place. And I think you might want to try this on a bunch of problems and you’ll see it always works out, that is doesn’t matter what order you—5+6 is the same thing as 6+5. And that make sense. If I have five avocadoes and you give me six, I’m going to have 11. If I have six avocadoes and you give me five, I am going to have 11 either way. Let’s do a couple—since this number line is so nice, I want to do a few more problems using it. Although, as I use it, I am sure I’ll just continue to confuse you because I’ll write so much on top of it but let’s see. I’ll use white now. What is 8+7? Well, if you can still read this, 8 is right here, right? We’re going to add 7 to it. We go to 15. 8+7 is 15. So hopefully that gives you a sense of how to do this types of problems and more than—I guess this—and you’re going to learn multiplication a little bit but these types of problems are—when you’re getting started of in mathematics, this kind of require the most practiced and to some degree, you have to start memorizing them but overtime, you know, when you look back, I want you to remember how you feel while you’re watching this video right now. And then I want you to watch this video in like three years and remember how you felt when you’re watching it now. And you’re going to be, “Oh my God. This was so easy because you’re going to learn so fast.” So anyway, I think you have an idea if you don’t know the answer to any of the addition problems that we give in the exercises, you can press the hints and it will draw circles and then you can just cut up the circles or if you want to do it on your own so you get the problem right, you could draw the circles or you could draw a number line like we did in this presentation. I think you might be ready to tackle the addition problems. Have fun.