In the last video we got some
practice adding what we could consider smaller numbers. For example, if we added 3 plus
2, we could imagine that if maybe I had 3 lemons-- 1, 2, 3. And if I were to add to those
3 lemons maybe 3 lime-- is it lime or limes? Well, 2 green lemons or 2
more tart pieces of fruit. How much tart, sour
fruit to do I have now? Well, we learned in the last
video we have 1, 2, 3, 4, 5 pieces of fruit. So 3 plus 2 is equal to 5. And we also saw that that's
the exact same thing as if we add 2 plus 3. And I think that makes sense
because this is the same thing as starting with, maybe you
have 2 lemons and you add 3 lime to it. You're still going to end
up with 5 pieces of fruit. 1, 2, 3, 4, or 5. Just like that. So it doesn't matter what
order you add in, you're still going to get 5. And this way of thinking about
addition I view as the counting way of thinking about addition. The other thing we saw in the
last video is the number line version and they're
essentially the same thing. So we could draw a line. And all a number line
is, it lists all of the numbers in order. It lists all of the numbers
and you can actually go as high as you need to go. You could go up to a million,
gazillion, trillion. We won't do that; I wouldn't
have space or time in this video to do it. And you actually can go
as low as possible. We'll start at 0, assuming-- in
future videos I'll tell you about numbers smaller than 0. And maybe you can think about
what that might mean tonight. But let's start at 0,
and 0 means nothing. If I have 0 lemons, it
means I have no lemons. So 0, 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11-- let's go pretty high. 12. That way I can reuse
the number line. 13, 14, I could keep on going,
but maybe fourteen will be enough for this video. But let's use a number
line for these addition problems up here. So in last video, just as a bit
of review, you can view 3 plus 2 as starting at 3 and
then adding 2 to it. Or going 2 greater than 3. And just going greater or
adding on the number line is just moving to the right
or moving up by 2. So let's move up by 2. I'll do that in
this orange color. So let's go up by 2. So we started at 3
and we go up by 1. And then we go up by
2, or we're jumping, and we end up at 5. Which is exactly
what we got before. If we have 3 lemons, we add
one lemon, we have 4 lemons. We add another lemon, we have 5
lemons or lime or tart pieces of fruit, whatever you
might want to say. And when you look at this
version of it where you switched the order, we started
at 2 and we're adding 3 objects to it. In this case, they
were lemons or limes. So we're going to add 3 to it. 1, 2, 3. And just like we expected,
we got the same thing. We got 5 again. Now what I want to do in video
and hopefully this was just a bit of review, is I want to
tackle harder problems. I want to tackle slightly
larger numbers. And in this video I want
to just give you practice dealing with the
slightly larger numbers. And then in the next video
we're going to dig a little deeper and think about
what numbers even mean. But let's just get some
practice understanding how do you actually do the addition
problems with larger numbers? Let me write it in a nice,
soothing purple color. Let's say I wanted
to add 9 plus 3. Well, there's a couple
of ways we could do it. We could draw circles again. We could say, let's see. Maybe I'll draw stars. 1, 2, 3, 4-- my stars are
degradingg-- 5, 6, 7, 8, 9. That's 9 stars and then
I add 3 stars to it. So I add 1, 2, 3 stars. And then if you were to count
the total number of stars you would say, let me do that in a
different color-- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. I now have 12 stars. So you would say that 9
plus 3 is equal to 12. If you looked at the number
line you're starting at 9, maybe you have 9 stars and
you add one star, two star, three stars to that. And you end up with 12
stars, which is the exact answer we got before. So you can do the same process
when you start adding larger numbers, even though that now--
and I want to you to notice, the difference now is our
answer has two digits in it. We'll talk more about digits
in a future video, but all a digit is is a numeral. It has a 1 and a 2. That's what 12 is. I won't dig too deep
into that right now. I think you're pretty
familiar with the number 12. But what I want to do is, now
what happens when you start adding more-- when you
start adding two-digit numbers like this? For example, if I were to
add 27 plus let's say-- I don't know-- plus 15. Now, if you had a lot of time
on your hands and you didn't care about how people judged
you, you could draw out 27 circles and then draw out
another 15 circles and then count the total number
of circles you had. And that would give
you an answer. Or you could draw
a number line. You could draw a number line
that went all the way to know whatever 27 plus 15 is. So it's going to be this
really, really large number, but that would
take you forever. So what I'm going to do is show
you a way to do this type of problem where you really just
have to know your addition, almost have it memorized, or at
least, if you don't have it memorized, be able to do
something like this for relatively small numbers. And by doing it for the
relatively small numbers, you can do the harder
problems like this. So what you do, this
is the fun part. You add, and I'll talk
more about what this means in the future. You look at each of the digits. So we call this place, the
rightmost place, we call that the 1's place. And why do we call
that the 1's place? Because 27 is 20 and seven 1's. It's 20 plus 7. It's 20 plus seven 1's. You could view it as
it's 20 plus 7 pennies. And this place right here
is called the 10's place. Now why is it called
the 10's place? I mean there's a 2 right there. It's the place that's
called the 10's place. So putting a 2 here
means two 10's. The number 20, that's two 10's. If I have one dime and you gave
me another dime, I now have two dimes, and that's $0.20. So that's what the
10's place is. I don't want to confuse you, I
just want to show you how to do these problems right now. We'll dig a little bit
deeper in future videos. I just want to give
you that idea. But the way to do these
problems is you look at the numbers in the 1's place
and add those up first. So you say, OK, I'm not
going to worry about this whole thing right now. Let me just add
the 7 and the 5. So I'm going to add
the 7 and the 5. And if you don't know what that
is-- hopefully you'll be able to do that in your head fairly
shortly-- you could look at the number line. Let's look at the
number line here. So if you add 7, if you take
7, and you add 5 to it. 1, 2, 3, 4, 5. We end up at 12. Or if you started at
5 and added 7, you'd also end up at 12. So let's write that down. We know that 7 plus
5 is equal to 12. So what we do is we say 7
plus 5 is equal to-- and now this is a new thing. It might be a little bit of
a mystery, magical thing for you right now. And in future videos I'll
explain to you why this works. We want to write the 12. 7 plus 5 is 12, but we
just write the 2 here and we carry the 1. 12. 1 2. Well, we wrote the 2 there,
but we put the 1 up here. And the reason-- I'll give
you a simple reason for doing that right now. I'll give you a better
reason in the future. Is that you only had space to
put one digit here and 12 is a two-digit number, so we had
to think of some other place to put that 1. If you really want to think
about it even more, 12 is the same thing as 10 plus 2. That's the same thing as 12. So if we say 7 plus 5 that's
the same thing as 12, which is the same thing as two 1's--
two pennies, plus one dime. Plus one 10. So we put that one dime
in the 10's place. So we really just said 7 plus
5 is one 10 plus two 1's. Or one dime plus two pennies. If that confuses you just say,
well, I just write the 1's digit of the 2 there
and I carry the 1. And then you do the exact same
thing in the 10's place. You add the 1 plus
the 2 plus the 1. So 1 plus 2, let's do
that on a number line. This is fun. So let's see. 1 plus 2. Let me do it in a
vibrant color. Let me do it in this magenta. So we start at 1. We're going to add 2 to it. 1 plus 2. We take that 1 from our 12. 1 plus 2, so you go up 1, 2. You end up at 3. Then you're going to
add up another 1. So you add another 1. You're going to end up at 4. So you ended up at 42. And this was pretty neat
because we didn't have to draw a number line
all the way to 42. And we'd didn't have
to draw 42 objects. Just by knowing what 7 plus 5
was and by knowing what 1 plus 2 plus 1 was, we were able
to figure out that 27 and 15 is 42. Let's do another example. Maybe I'll do a little bit
of a simpler example. Let's say I had 78 plus 3. We do the exact
same thing before. We just look at the
1's place only. So we look at 8 plus 3. What's 8 plus 3? Hopefully we can do that in
our heads at this point. But let's just think about it. 8 plus 1 is equal to 9. 8 plus 2 is equal to 10. 8 plus 3 is going
to be equal to 11. You could do that on the number
line if it makes it easier to visualize for you. So 8 plus 3 is equal to 11. So what we do here, we just
have 8 plus 3 is equal to 11. Put this 1 right here, put that
there, and carry the other 1. Because 11 is one 10, one
dime plus one penny. That's 11. And then we add the 10's place. 1 dime plus 7 dimes
is equal to 8 dimes. So 78 plus 3 is equal to 81. And now there's one thing
I want to show you. You don't always have to
carry numbers like that. Only if the answer to
one of these has more than one digit in it. 11 is a two-digit number. So for example, if
I have 56 plus 2. Here I could just
say 6 plus 2 is 8. Hopefully we're getting
good practice at this. So 6 plus 2 is 8. And then, I don't have anything
to add this 5 to, so I just bring the 5 down here. So 56 plus 2 is 58. Just like that. And this is one you actually
could have drawn on the number line. It wouldn't have been too hard. So if you were to draw the
number line like that, you know 0 would be way off
to the left some place. But let's say I had 50. 49, you could keep going to the
left, but you have 51, 52, actually let me start a little
higher than that because I'm going to run out of space. Let me start at maybe 55, 56,
57, 58, 59, and I could go in both directions, keep going. But if we start at 56 right
there and we add 2, we go up one, we go up two. We end up at 58. So just like that we're
able to do that problem. I'll see you in the next video.