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Welcome to the presentation on level two addition. Well I think we should get started with some problems, and hopefully as we work through them, you'll have an understanding of how to do these types of problems. Let's see... Let me make sure the pen tool is correct. Okay.

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Let's say I had 11 plus 4.

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So at first you'd say hey, Sal, you know, 11 plus 4, 
I don't know how to add two-digit numbers yet.
Well there's a couple of ways we can think about this.
First I'll show you how all you have to know is 
how to add one-digit numbers and you can use something called 
carrying to solve the whole problem.
And then we'll actually try to visually represent it to show you 
how you could actually do this type of problem in your head as well.


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you'll have an understanding of how to do these types of problems. Let's see...

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Let me make sure the pen tool is correct. Okay.

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Let's say I had 11+4.

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So at first you'd say hey, Sal, you know, 11+4,

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I don't know how to add 2-digit numbers yet.

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Well there's a couple of ways we can think about this.

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First I'll show you how all you have to know is

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how to add 1-digit numbers

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and you can use something called carrying to solve the whole problem.

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And then we'll actually try to visually represent it

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to show you how you could actually do this type of problem

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in your head as well.

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So what you do with these types of problems

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is you first look at the right-most digit on the 11.

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We call this the one's place, right?

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Because this one is one, and we call this the ten's place.

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I know I'm going to confuse you a lot,

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but that's just so how everything looks--

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that's so everything looks easier later on.

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So you look at this ones place, you say there's a 1 there.

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You take that one and you add it to the number right below it.

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So 1+4=5.

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You knew that, right?

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Right? You know that 1+4=5.

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And that's all I did here.

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I just said this 1 + this 4 = 5.

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Now I go to this one.

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This 1+ -- well there's nothing here

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other than a plus sign and that's not a number.

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So this one plus nothing is one.

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So we put a one here.

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And we get 11+4=15.

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And just so you know that this system actually works.

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Let's actually draw it out in a couple of different ways

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Just to give you the intuition of 11+4.

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So if I had 11 balls -- 1, 2, 3, 4, 5, 6,

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7, 8, 9, 10, 11.

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That's 11, right? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

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Alright, I should do it like they do on Sesame Street,

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(singing) "1, 2, 3, 4, 5, 6, 7, 8, 9, 10-"

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Oh actually I think I messed up. It's 11.

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Anyway! It's early. I'm being a little ridiculous.

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Okay! So that's 11 and we're going to add 4 to it.

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So 1, 2, 3, 4,

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So now all we have to do is

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count how many total circles or balls we have now.

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That's 1, 2, 3, 4, 5, 6, 7, 8,

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9, 10, 11, 12, 13, 14, 15.

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15, and I don't recommend that you do this every time you do a problem

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because it'll take you a long time.

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But hey, if you ever get confused,

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it's better to take along time than to get it wrong.

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Let's think about another way of representing this,

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because I think different visual approaches

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appeal in different ways to different people.

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Let's draw a number line.

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I don't know if you've seen a number line before

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but you're going to see it now.

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And a number line, all I do is

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I draw out all the numbers in order.

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So 0, 1, 2, 3, 4, 5, 6 -- I'm doing them small

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so I know I can get to 15. 6 -- 7, 8, 9, 10, 11,

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12, 13, 14, 15, 16, 17, 18, and so on.

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And these arrows mean that

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the numbers keep going in both directions.

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I know this is a little early for you to learn this.

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But actually the numbers can actually keep

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going to the left below zero as well.

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I'll leave you to think about that.

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But anyway, so let's go back to this problem.

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So we have 11, so let me circle 11 --

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let me see where 11 is on the number line.

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11 is here, right?

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This is 11.

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And we're adding 4.

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So when you add, that means we're gonna increase 11 by 4.

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So that when you increase we're going to go up the number line, right?

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Or we're going to go the right on the number line,

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because the numbers are getting bigger.

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So we'd go 1, 2, 3, 4 -- bam!

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We're at fifteen.

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Once again, this takes a long time. But if you ever get confused

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or you forget what one plus four is,

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although I don't think you should,

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then you could just do it this way.

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Let's do some maybe harder problems now.

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Let's do, let's do 28+7.

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Okay. 8+7 -- I'll tell you, frankly, even to this day,

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I sometimes get confused with 8+7.

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So let's-- If you know the answer

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then you already know how to do this problem,

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you can just write whatever the answer is right here.

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But let's draw it out on the number line,

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because I think a little bit of more basic addition practices

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isn't unwarranted at this point.

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So we could do it with the number line again.

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8+7.

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And this time I'm not going to start at 0, I'll start at like 5,

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because, you know, if you keep going you'll get to 0 eventually.

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So let's see you get 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,

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16, 17, 18, and so on

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And it'll keep going to a hundred and a thousand

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and a million billion trillion.

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So what are we doing?

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We start at eight because this is 8+7.

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We want to figure out what 8+7 is.

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So we start at 8.

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And we're going to add 7 to it.

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Let me change colors.

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So you go 1, 2, 3, 4, 5, 6, 7.

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Oh, that 15 shows up again.

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So 8+7 is equal to 15.

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And over time as you do practice,

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I think you'll memorize these that 8+7=15 or
whatever,

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6+7=13 or any of these.

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But in the interim it actually doesn't hurt to do this number line

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because you actually are visualizing what's happening.

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And you can do it with the circles as well.

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So we know 8+7=15.

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So this is a new thing you're going to learn right now.

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You don't write the whole 15 down here.

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You write the 5 -- you write this 5 right here.

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And then that 1, you carry the 1.

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You put it up there.

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I think in a future presentation I'll explain why this works

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and maybe you might even kind of have an intuition

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because the 1 is in the ten’s place,

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and this is the ten‘s place.

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I don't want to confuse you.

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So you have that 1 and now you add it to the 2,

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and you get 35.

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Right? Because 1+2=3, right?

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So you're done.

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35.

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And you might ask, well,

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does that make sense that 28+7=35?

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And there's a couple of ways I'd like to think about this.

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Well, 8+7 we know is 15, right?

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And I don't know how comfortable

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you are with higher numbers.

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But 8+7 -- so look at this pattern.

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8+7=15.

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18+7 -- you're probably saying,

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Sal, where are you getting the 18 from, but take my word for it.

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18+7=25.

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28+7=35 which is the one that we just did.

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That is a check mark.

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And if you kept going, you said 38+7,

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that actually equals 45.

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So you might see a little pattern here,

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and then you can just sit and think about this for a little bit if you like.

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Maybe you pause the video.

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Another way you could think about this, if you still don't believe me, is

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you say, okay, if I have 28, if I add 1, I get 29.

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If I add 2, I get 30. If I add 3, I get 31.

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If I add 4, I get 32.

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If I add 5, I get 33.

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If I add 6, I get 34.

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And if I add 7, I get 35 again.

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Right, all I did is I kept saying oh, if I had one more

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I'll get larger a little bit -- the number a little bit larger.

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Let's do some more problems,

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and I think we'll do a couple more.

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Let's do it a little faster

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because you might get what we're doing here now.

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Let's do a hard one.

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Let's do 99+9.

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So what's 9+9?

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So if you don't know what it is, you can work it out

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either using the number line or drawing the circles.

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And, you know that's a fair way to do it,

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although you should eventually kind of know it.

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9+9 it turns out is 18. 9+9 is equal to 18...so 9+9...

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and you put the 8 down here and you carry the 1.

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And now you just say 1+9.

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Well you know what 1+9 is.

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1+ 9=10.

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And so there's nowhere to carry this 1,

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so you write the whole thing down here.

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So 99+9=108.

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Let's do one more problem.

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Let's say 56+7.

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Well what's six plus seven.

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Well 6+7=13, right?

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If you get confused, draw out everything again.

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And then you get 1+5.

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1+5=6.

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63.

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And you might want to give yourself a bunch of problems

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and I think you're also now, if you understand what we did,

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ready to try the level 2 addition problems.

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Have fun!