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In the last video we got some practice adding what we could

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consider smaller numbers.

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For example, if we added 3 plus 2, we could imagine that if

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maybe I had 3 lemons-- 1, 2, 3.

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And if I were to add to those 3 lemons maybe 3 lime--

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is it lime or limes?

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Well, 2 green lemons or 2 more tart pieces of fruit.

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How much tart, sour fruit to do I have now?

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Well, we learned in the last video we have 1, 2, 3,

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4, 5 pieces of fruit.

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So 3 plus 2 is equal to 5.

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And we also saw that that's the exact same thing

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as if we add 2 plus 3.

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And I think that makes sense because this is the same thing

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as starting with, maybe you have 2 lemons and you

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add 3 lime to it.

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You're still going to end up with 5 pieces of fruit.

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1, 2, 3, 4, or 5.

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Just like that.

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So it doesn't matter what order you add in, you're

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still going to get 5.

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And this way of thinking about addition I view as the counting

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way of thinking about addition.

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The other thing we saw in the last video is the number

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line version and they're essentially the same thing.

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So we could draw a line.

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And all a number line is, it lists all of

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the numbers in order.

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It lists all of the numbers and you can actually go as

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high as you need to go.

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You could go up to a million, gazillion, trillion.

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We won't do that; I wouldn't have space or time in

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this video to do it.

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And you actually can go as low as possible.

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We'll start at 0, assuming-- in future videos I'll tell you

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about numbers smaller than 0.

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And maybe you can think about what that might mean tonight.

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But let's start at 0, and 0 means nothing.

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If I have 0 lemons, it means I have no lemons.

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So 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11--

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let's go pretty high.

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12.

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That way I can reuse the number line.

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13, 14, I could keep on going, but maybe fourteen will

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be enough for this video.

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But let's use a number line for these addition

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problems up here.

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So in last video, just as a bit of review, you can view 3 plus

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2 as starting at 3 and then adding 2 to it.

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Or going 2 greater than 3.

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And just going greater or adding on the number line is

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just moving to the right or moving up by 2.

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So let's move up by 2.

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I'll do that in this orange color.

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So let's go up by 2.

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So we started at 3 and we go up by 1.

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And then we go up by 2, or we're jumping,

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and we end up at 5.

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Which is exactly what we got before.

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If we have 3 lemons, we add one lemon, we have 4 lemons.

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We add another lemon, we have 5 lemons or lime or tart pieces

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of fruit, whatever you might want to say.

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And when you look at this version of it where you

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switched the order, we started at 2 and we're adding

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3 objects to it.

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In this case, they were lemons or limes.

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So we're going to add 3 to it.

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1, 2, 3.

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And just like we expected, we got the same thing.

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We got 5 again.

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Now what I want to do in video and hopefully this was just a

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bit of review, is I want to tackle harder problems.

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I want to tackle slightly larger numbers.

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And in this video I want to just give you practice

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dealing with the slightly larger numbers.

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And then in the next video we're going to dig a little

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deeper and think about what numbers even mean.

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But let's just get some practice understanding how do

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you actually do the addition problems with larger numbers?

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Let me write it in a nice, soothing purple color.

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Let's say I wanted to add 9 plus 3.

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Well, there's a couple of ways we could do it.

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We could draw circles again.

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We could say, let's see.

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Maybe I'll draw stars.

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1, 2, 3, 4-- my stars are degradingg-- 5, 6, 7, 8, 9.

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That's 9 stars and then I add 3 stars to it.

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So I add 1, 2, 3 stars.

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And then if you were to count the total number of stars you

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would say, let me do that in a different color-- 1, 2, 3, 4,

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5, 6, 7, 8, 9, 10, 11, 12.

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I now have 12 stars.

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So you would say that 9 plus 3 is equal to 12.

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If you looked at the number line you're starting at 9,

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maybe you have 9 stars and you add one star, two

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star, three stars to that.

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And you end up with 12 stars, which is the exact

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answer we got before.

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So you can do the same process when you start adding larger

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numbers, even though that now-- and I want to you to notice,

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the difference now is our answer has two digits in it.

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We'll talk more about digits in a future video, but all

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a digit is is a numeral.

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It has a 1 and a 2.

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That's what 12 is.

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I won't dig too deep into that right now.

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I think you're pretty familiar with the number 12.

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But what I want to do is, now what happens when you start

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adding more-- when you start adding two-digit

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numbers like this?

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For example, if I were to add 27 plus let's say--

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I don't know-- plus 15.

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Now, if you had a lot of time on your hands and you didn't

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care about how people judged you, you could draw out 27

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circles and then draw out another 15 circles and then

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count the total number of circles you had.

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And that would give you an answer.

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Or you could draw a number line.

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You could draw a number line that went all the way to know

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whatever 27 plus 15 is.

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So it's going to be this really, really large

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number, but that would take you forever.

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So what I'm going to do is show you a way to do this type of

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problem where you really just have to know your addition,

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almost have it memorized, or at least, if you don't have it

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memorized, be able to do something like this for

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relatively small numbers.

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And by doing it for the relatively small numbers,

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you can do the harder problems like this.

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So what you do, this is the fun part.

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You add, and I'll talk more about what this

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means in the future.

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You look at each of the digits.

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So we call this place, the rightmost place, we call

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that the 1's place.

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And why do we call that the 1's place?

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Because 27 is 20 and seven 1's.

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It's 20 plus 7.

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It's 20 plus seven 1's.

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You could view it as it's 20 plus 7 pennies.

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And this place right here is called the 10's place.

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Now why is it called the 10's place?

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I mean there's a 2 right there.

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It's the place that's called the 10's place.

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So putting a 2 here means two 10's.

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The number 20, that's two 10's.

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If I have one dime and you gave me another dime, I now have

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two dimes, and that's $0.20.

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So that's what the 10's place is.

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I don't want to confuse you, I just want to show you how to

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do these problems right now.

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We'll dig a little bit deeper in future videos.

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I just want to give you that idea.

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But the way to do these problems is you look at the

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numbers in the 1's place and add those up first.

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So you say, OK, I'm not going to worry about this

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whole thing right now.

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Let me just add the 7 and the 5.

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So I'm going to add the 7 and the 5.

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And if you don't know what that is-- hopefully you'll be able

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to do that in your head fairly shortly-- you could look

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at the number line.

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Let's look at the number line here.

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So if you add 7, if you take 7, and you add 5 to it.

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1, 2, 3, 4, 5.

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We end up at 12.

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Or if you started at 5 and added 7, you'd

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also end up at 12.

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So let's write that down.

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We know that 7 plus 5 is equal to 12.

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So what we do is we say 7 plus 5 is equal to-- and

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now this is a new thing.

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It might be a little bit of a mystery, magical thing

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for you right now.

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And in future videos I'll explain to you why this works.

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We want to write the 12.

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7 plus 5 is 12, but we just write the 2 here

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and we carry the 1.

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12.

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1 2.

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Well, we wrote the 2 there, but we put the 1 up here.

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And the reason-- I'll give you a simple reason for

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doing that right now.

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I'll give you a better reason in the future.

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Is that you only had space to put one digit here and 12 is a

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two-digit number, so we had to think of some other

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place to put that 1.

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If you really want to think about it even more, 12 is the

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same thing as 10 plus 2.

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That's the same thing as 12.

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So if we say 7 plus 5 that's the same thing as 12, which is

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the same thing as two 1's-- two pennies, plus one dime.

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Plus one 10.

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So we put that one dime in the 10's place.

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So we really just said 7 plus 5 is one 10 plus two 1's.

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Or one dime plus two pennies.

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If that confuses you just say, well, I just write the 1's

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digit of the 2 there and I carry the 1.

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And then you do the exact same thing in the 10's place.

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You add the 1 plus the 2 plus the 1.

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So 1 plus 2, let's do that on a number line.

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This is fun.

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So let's see.

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1 plus 2.

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Let me do it in a vibrant color.

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Let me do it in this magenta.

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So we start at 1.

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We're going to add 2 to it.

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1 plus 2.

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We take that 1 from our 12.

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1 plus 2, so you go up 1, 2.

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You end up at 3.

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Then you're going to add up another 1.

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So you add another 1.

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You're going to end up at 4.

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So you ended up at 42.

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And this was pretty neat because we didn't have to

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draw a number line all the way to 42.

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And we'd didn't have to draw 42 objects.

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Just by knowing what 7 plus 5 was and by knowing what 1 plus

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2 plus 1 was, we were able to figure out that

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27 and 15 is 42.

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Let's do another example.

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Maybe I'll do a little bit of a simpler example.

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Let's say I had 78 plus 3.

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We do the exact same thing before.

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We just look at the 1's place only.

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So we look at 8 plus 3.

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What's 8 plus 3?

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Hopefully we can do that in our heads at this point.

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But let's just think about it.

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8 plus 1 is equal to 9.

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8 plus 2 is equal to 10.

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8 plus 3 is going to be equal to 11.

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You could do that on the number line if it makes it easier

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to visualize for you.

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So 8 plus 3 is equal to 11.

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So what we do here, we just have 8 plus 3 is equal to 11.

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Put this 1 right here, put that there, and carry the other 1.

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Because 11 is one 10, one dime plus one penny.

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That's 11.

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And then we add the 10's place.

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1 dime plus 7 dimes is equal to 8 dimes.

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So 78 plus 3 is equal to 81.

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And now there's one thing I want to show you.

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You don't always have to carry numbers like that.

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Only if the answer to one of these has more

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than one digit in it.

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11 is a two-digit number.

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So for example, if I have 56 plus 2.

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Here I could just say 6 plus 2 is 8.

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Hopefully we're getting good practice at this.

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So 6 plus 2 is 8.

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And then, I don't have anything to add this 5 to, so I just

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bring the 5 down here.

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So 56 plus 2 is 58.

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Just like that.

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And this is one you actually could have drawn on

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the number line.

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It wouldn't have been too hard.

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So if you were to draw the number line like that, you

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know 0 would be way off to the left some place.

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But let's say I had 50.

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49, you could keep going to the left, but you have 51, 52,

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actually let me start a little higher than that because I'm

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going to run out of space.

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Let me start at maybe 55, 56, 57, 58, 59, and I could go in

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both directions, keep going.

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But if we start at 56 right there and we add 2, we

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go up one, we go up two.

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We end up at 58.

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So just like that we're able to do that problem.

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I'll see you in the next video.