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In the last video
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we got some practice
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adding what we could consider smaller numbers.
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For example, if we added 3 + 2
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we could imagine that if
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maybe I had three lemons -- 1, 2, 3 --
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and if I were to add to those three lemons
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maybe two lime-- Is it lime or limes?
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Let's just -- Well, two green lemons --
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or two more tart pieces of fruit
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How many-- how much tart, sour fruit do I have now?
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Well, we learned in the last video
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we have 1, 2, 3, 4, 5 pieces of fruit.
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So 3 + 2 = 5.
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And we also saw that
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that's the exact same thing as if
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we add 2 + 3.
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And I think that makes sense.
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Because this is the same thing as
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starting with -- Maybe you have 2 lemons
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and you add 3 limes 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, 5.
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Just like that.
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So it doesn't matter what order you add in.
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You're still going to get five.
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And this way of thinking about addition
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I view as the counting way of thinking about addition
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The other thing we saw in the last video
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is the number line version
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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
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it lists all of the numbers in order.
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It lists all of the numbers.
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And you can actually go as 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.
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I wouldn't have space or time in 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 --
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In future videos, I'll tell you
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about numbers smaller than 0.
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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.
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I could keep on going
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But maybe 14 will be enough for this video
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But let's use a number line
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for these addition problems up here.
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So in the last video -- just as a bit of a review --
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you can view 3 + 2 as starting at 3 --
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and then adding 2 to it.
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Or going two greater than 3.
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And just going greater --
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or adding on the number line --
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is just moving to the right -- or moving up by two.
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So let's move up by two.
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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 three and we go up by one.
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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 three lemons
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we add one lemon, we have four lemons.
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We add another lemon, we have 5 lemons --
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or limes -- or tart pieces of fruit.
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Whatever you might want to say.
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And when you look at this version of it --
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when you switched the order --
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We started at 2
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and we're adding 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 three to it.
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1, 2, 3.
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And just like we expected,
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we got the same thing.
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We got 5 again.
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Now what I want to do in this video --
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and hopefully this was just a bit of a review --
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-- is I want to tackle harder problems.
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I want to tackle slightly larger numbers.
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And then in the next video --
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And in this video I want to just
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give you practice dealing
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with the slightly larger numbers.
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And then, in the next video
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we're going to dig a little deeper
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and think about what numbers even mean
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But let's just get some practice understanding
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"How do 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 + 3.
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Well, there are 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, I have --
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Maybe I'll draw stars. 1, 2, 3, 4 --
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My stars are degrading,
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-- 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
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the total number of stars, you would say --
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(Let me do that in a different color.)
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-- 1, 2, 3, 4, 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 + 3 = 12.
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It's equal to 12.
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If you looked at the number line --
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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
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and you add 1 star, 2 stars, 3 stars to that.
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And you end up with 12 stars.
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Which is the exact answer we got before.
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So you can do the same process when you start
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adding larger numbers, even though that now --
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And I want you to notice, the difference now is
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our answer has two digits in it.
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(And we'll talk more about digits in a future video.)
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But all a digit is is a numeral. Right?
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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 go into -- 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 --
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Now what happens when you start adding more?
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When you start adding
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two-digit 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 -- plus15. (27 + 15.)
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Now, if you had a lot of time on your hands
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and you didn't care about how people judged you
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you could draw out 27 circles,
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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
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went all the way to whatever 27 + 15 is.
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So it's going to be this really, really large number,
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but that wouldtake you forever.
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So what I'm going to do
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is show you a way to
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do this type of problem
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where you really just have to know your addition
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almost have it memorized, or at least
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if you don't have it memorized
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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
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what this 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
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we call that the ones place.
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And why do we call that the ones place?
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Because 27 is 20 and 7 ones.
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It's twenty plus seven.
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It's twenty plus seven ones.
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You could view it as it's twenty plus seven pennies.
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And this place right here is called the tens place.
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Now why is it called the tens place?
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I mean there's a two right there.
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It's the place that's called the tens place.
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So putting a two here means two tens.
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The number twenty, that's two tens.
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If I have one dime and you gave me another dime
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I now have two dimes, and that's twenty cents
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So that's what the tens place is.
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I don't want to confuse you
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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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But I just want to give you that idea.
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But the way to do these problems is
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you look at the numbers in the ones place
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and add those up first.
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So you say, OK, I'm not going to worry about
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this whole thing right now.
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Let me just add the seven and the five.
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So I'm going to add the seven and the five.
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And if you don't know what that is
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hopefully you'll be able to do that
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in your head fairly shortly
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-- 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 seven
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if you take seven, and you add five to it.
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-- 1, 2, 3, 4, 5 --
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We end up at twelve.
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Or if you started at five and added seven
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you'd also end up at twelve.
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So let's write that down.
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We know that 7 + 5 = 12.
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So what we do is we say 7 + 5 is equal to
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-- and now this is a new thing.
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It might be a little bit of a mystery
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magical thing 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 write -- we want to write the 12.
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7 + 5 is 12. But we just write the 2 here
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and we carry the 1.
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12. one, two
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Well, we wrote the 2 there,
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but we put the 1 up here, right?
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And the reason --
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(I'll give you a simple reason for 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
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and twelve is a two-digit number
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so we had to think of some
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other place to put that 1.
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If you really want to think about it even more
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12 is the same thing
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as 10 + 2, right?
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That's the same thing as 12.
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So if we say 7 + 5, that's the same thing as 12
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which is the same thing as two ones. Right?
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Two 1s. 2 pennies, plus 1 dime.
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Plus 1 ten. Plus 1 dime.
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So we put that 1 dime in the 10s place.
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So we really just said 7 + 5 is one 10 plus two 1s.
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Or 1 dime plus 2 pennies.
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If that confuses you, just write, just say,
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well I just write the 1s digit of the 2 there
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and I carry the 1.
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And then you do the exact same thing in the 10s place.
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You add the 1 plus the 2 plus the 1.
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So 1 + 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 + 2.
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Let's start -- 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 one.
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We're going to add two to it.
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1 + 2.
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We take that 1 from our 12..
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1 + 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 one.
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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, right?
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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 + 5 was
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and by knowing what 1 + 2 + 1 was
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we were able to figure out that
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27 + 15 = 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 + 3.
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We do the exact same thing as before.
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We just look at the 1s place only.
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So we look at 8 + 3.
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What's 8 + 3?
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Hopefully, we can do that
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in our heads at this point.
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But let's just think about it.
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8 + 1 = 9.
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8 + 2 = 10.
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8 + 3 is going to be equal to 11.
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You could do that on the number line
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if it makes it easier to visualize for you.
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So 8 + 3 = 11.
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So what we do here, we just have 8 + 3 = 11.
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Put this one right here, put that there
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and carry the other one.
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Because eleven is
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one ten -- one dime -- plus one penny.
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That's eleven.
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And then we add the tens place.
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1 dime plus 7 dimes is equal to 8 dimes.
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So 78 + 3 = 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
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has more 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 + 2.
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Here, I could just say 6 + 2 is 8. Right?
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Hopefully, we're getting good practice at this.
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So 6 + 2 = 8.
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And then, I don't have anything to add this 5 to.
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So, I just bring the five down here.
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So 56 + 2 = 58.
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Just like that.
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And this is one you actually
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could have drawn on 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,
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0 would be way off to the left some place.
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But let's say I had 50, no I think you'd have 49
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you could keep going to the left
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but you have 51, 52 --
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Actually let me start a little higher than that.
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Because I'm going to run out of space.
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Let me start at maybe 55, 56, 57, 58, 59 --
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And I could go in both directions -- keep going.
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But if we start at fifty-six right there and we add two
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We 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.