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Welcome to the presentation on level two addition.

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Well I think we should get started with some problems, and

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hopefully as we work through them, you'll have an

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understanding of how to do these types of problems.

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Let me make sure the pen tool is correct.

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Let's say I had 11 plus 4.

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So first you'd say hey, Sal, 11 plus 4, I don't know how to

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add two-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 how to add

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one-digit numbers and you can use something called carrying

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to solve the whole problem.

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Then we'll actually try to visually represent it to show

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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 is you first look

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at the right-most digit on the 11.

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We call this the ones place, right?

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Because this 1 is 1, and we call this the tens place.

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I know I'm going to confuse you a lot, but that's when

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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 1 and you add it to the number right below it.

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So 1 plus 4 is 5.

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You knew that, right?

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You know that 1 plus 4 is equal to 5.

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That's all I did here.

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I just said this 1 plus this 4 is equal to 5.

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Now I go to this 1.

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This 1 plus -- well there's nothing here other than a plus

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sign and that's not a number.

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So this 1 plus nothing is 1.

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So we put a 1 here.

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And we get 11 plus 4 is equal to 15.

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Just so you know that this system actually works, let's

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actually draw it out in a couple of different ways

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just to give you the intuition of 11 plus 4.

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So if I had 11 balls -- one, two, three, four, five, six,

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seven, eight, nine, ten, eleven.

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That's eleven, right?

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

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So one, two, three, four.

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So now all we have to do is count how many total circles

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or balls we have now.

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That's one, two, three, four, five, six, seven, eight,

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nine, ten, eleven, twelve, thirteen, fourteen, fifteen.

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I don't recommend that you do this every time you do

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a problem because it'll take you a long time.

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But hey, if you ever get confused, it's better to take a

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long time than to get it wrong.

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Let's think about another way of representing this, because

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I think different visual approaches appeal in different

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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 but

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you're going to see it now.

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And a number line, all I do is I draw out all

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the numbers in order.

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

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can get to 15 -- 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.

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And so on.

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And these arrows mean that the numbers keep going

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in both directions.

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I know this is a little early for you to learn this, but

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actually the numbers can actually keep going to the

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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 -- let me see where 11

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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 increase 11 by 4.

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

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right, 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 15.

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Once again, this takes a long time, but if you ever get

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confused or you forget what 1 plus 4 is, although I don't

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think you should, 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 28 plus 7.

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8 plus 7 -- I'll tell you, frankly, even to this

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day, I sometimes get confused with 8 plus 7.

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If you know the answer then you already know how to do this

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problem, you can just write whatever the answer

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is down here.

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But let draw it on the number line, because I think a little

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bit of more basic addition practice isn't unwarranted

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at this point.

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So we could do out with the number line again.

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8 plus 7.

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I'm not going to start at 0, I'll start at like 5, because

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if you keep going you'll get to 0 eventually.

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So let's see 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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It'll keep going all the way to 100 and 1,000 and a

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million billion trillion.

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So what are we doing?

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We start at 8 because this is 8 plus 7.

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We want to figure out what 8 plus 7 is.

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So we start at 8.

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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's 15 shows up again.

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So 8 plus 7 is equal to 15.

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Over time as you do practice, I think you'll memorize these

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that 8 plus 7 is 15 or whatever, 6 plus 7 is

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13 or any of these.

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

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line 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 plus 7 is 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 five 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

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this works and maybe you might even kind of have an intuition

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because the 1 is in the tens place, and this is

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the tens 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

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2, and you get 35.

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Because 1 plus 2 is equal to 3, right?

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So you're done.

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35.

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You might ask, well, does that make sense that

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28 plus 7 is 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 plus 7 we know is 15.

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And I don't know how comfortable we are

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with higher numbers.

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But 18 plus 7 -- so look at this pattern.

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8 plus 7 is equal to 15.

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18 plus 7 -- you're probably saying, Sal, where are you

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getting the 18 from, but take my word for it.

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18 plus 7 is 25.

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28 plus 7 is equal to 35, which is the one that we just did.

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This is a check mark.

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If you kept going, you said 38 plus 7, that

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actually equals 45.

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So you might see a little pattern here, and then you can

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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

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believe me is you say OK, 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 a larger little bit -- the number a little bit larger.

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Let's do some more problems, and I think we'll

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do a couple more.

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Let's do it a little faster because you might get what

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we're doing here now.

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Let's do a hard one.

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Let's do 99 plus 9.

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So what's 9 plus 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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That's a fair way to do it, although you should

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eventually kind of know it.

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9 plus 9 it turns out is 18.

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

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And now you just say 1 plus 9.

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Well you know what 1 plus 9 is.

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1 plus 9 is equal to 10.

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So there's nowhere to carry this 1, so you write the

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whole thing down here.

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So 99 plus 9 is equal to 108.

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Let's do one more problem.

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Let's say 56 plus 7.

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Well what's 6 plus 7.

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Well 6 plus 7 is 13, right?

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If you get confused, draw out everything again.

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And then you get 1 plus 5.

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1 plus 5 is 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 two addition problems.

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Have fun.

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