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 me make sure the pen tool is correct.
Let's say I had 11 plus 4.
So first you'd say hey, Sal, 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.
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.
So what you do with these types of problems is you first look
at the right-most digit on the 11.
We call this the ones place, right?
Because this 1 is 1, and we call this the tens place.
I know I'm going to confuse you a lot, but that's when
everything looks easier later on.
So you look at this ones place, you say there's a 1 there.
You take that 1 and you add it to the number right below it.
So 1 plus 4 is 5.
You knew that, right?
You know that 1 plus 4 is equal to 5.
That's all I did here.
I just said this 1 plus this 4 is equal to 5.
Now I go to this 1.
This 1 plus -- well there's nothing here other than a plus
sign and that's not a number.
So this 1 plus nothing is 1.
So we put a 1 here.
And we get 11 plus 4 is equal to 15.
Just so you know that this system actually works, let's
actually draw it out in a couple of different ways
just to give you the intuition of 11 plus 4.
So if I had 11 balls -- one, two, three, four, five, six,
seven, eight, nine, ten, eleven.
That's eleven, right?
So that's 11 and we're going to add 4 to it.
So one, two, three, four.
So now all we have to do is count how many total circles
or balls we have now.
That's one, two, three, four, five, six, seven, eight,
nine, ten, eleven, twelve, thirteen, fourteen, fifteen.
I don't recommend that you do this every time you do
a problem because it'll take you a long time.
But hey, if you ever get confused, it's better to take a
long time than to get it wrong.
Let's think about another way of representing this, because
I think different visual approaches appeal in different
ways to different people.
Let's draw a number line.
I don't know if you've seen a number line before but
you're going to see it now.
And a number line, all I do is I draw out all
the numbers in order.
So 0, 1, 2, 3, 4, 5, 6 -- I'm doing them small so I know I
can get to 15 -- 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.
And so on.
And these arrows mean that the numbers keep going
in both directions.
I know this is a little early for you to learn this, but
actually the numbers can actually keep going to the
left below zero as well.
I'll leave you to think about that.
But anyway, so let's go back to this problem.
So we have 11, so let me circle 11 -- let me see where 11
is on the number line.
11 is here, right?
This is 11.
And we're adding 4.
So when you add, that means we're increase 11 by 4.
So that when you increase we're going to go up the number line,
right, or we're going to go the right on the number line
because the numbers are getting bigger.
So we'd go 1, 2, 3, 4 -- bam.
We're at 15.
Once again, this takes a long time, but if you ever get
confused or you forget what 1 plus 4 is, although I don't
think you should, then you could just do it this way.
Let's do some maybe harder problems now.
Let's do 28 plus 7.
8 plus 7 -- I'll tell you, frankly, even to this
day, I sometimes get confused with 8 plus 7.
If you know the answer then you already know how to do this
problem, you can just write whatever the answer
is down here.
But let draw it on the number line, because I think a little
bit of more basic addition practice isn't unwarranted
at this point.
So we could do out with the number line again.
8 plus 7.
I'm not going to start at 0, I'll start at like 5, because
if you keep going you'll get to 0 eventually.
So let's see 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18 and so on.
It'll keep going all the way to 100 and 1,000 and a
million billion trillion.
So what are we doing?
We start at 8 because this is 8 plus 7.
We want to figure out what 8 plus 7 is.
So we start at 8.
We're going to add 7 to it.
Let me change colors.
So you go 1, 2, 3, 4, 5, 6, 7.
Oh, that's 15 shows up again.
So 8 plus 7 is equal to 15.
Over time as you do practice, I think you'll memorize these
that 8 plus 7 is 15 or whatever, 6 plus 7 is
13 or any of these.
But in the interim it actually doesn't hurt to do this number
line because you actually are visualizing what's happening.
And you can do it with the circles as well.
So we know 8 plus 7 is 15.
So this is a new thing you're going to learn right now.
You don't write the whole 15 down here.
You write the 5 -- you write this five right here.
And then that 1, you carry the 1.
You put it up there.
I think in a future presentation I'll explain why
this works and maybe you might even kind of have an intuition
because the 1 is in the tens place, and this is
the tens place.
I don't want to confuse you.
So you have that 1 and now you add it to the
2, and you get 35.
Because 1 plus 2 is equal to 3, right?
So you're done.
35.
You might ask, well, does that make sense that
28 plus 7 is 35?
And there's a couple of ways I'd like to think about this.
Well, 8 plus 7 we know is 15.
And I don't know how comfortable we are
with higher numbers.
But 18 plus 7 -- so look at this pattern.
8 plus 7 is equal to 15.
18 plus 7 -- you're probably saying, Sal, where are you
getting the 18 from, but take my word for it.
18 plus 7 is 25.
28 plus 7 is equal to 35, which is the one that we just did.
This is a check mark.
If you kept going, you said 38 plus 7, that
actually equals 45.
So you might see a little pattern here, and then you can
just sit and think about this for a little bit if you like.
Maybe you pause the video.
Another way you could think about this if you still don't
believe me is you say OK, if I have 28, if I add 1 I get 29,
if I add 2 I get 30, if I add 3 I get 31.
If I add 4 I get 32.
If I add 5 I get 33.
If I add 6 I get 34.
And if I add 7 I get 35 again.
Right, all I did is I kept saying oh, if I had one more
I'll get a larger little bit -- the number a little bit larger.
Let's do some more problems, and I think we'll
do a couple more.
Let's do it a little faster because you might get what
we're doing here now.
Let's do a hard one.
Let's do 99 plus 9.
So what's 9 plus 9?
So if you don't know what it is, you can work it out
either using the number line or drawing the circles.
That's a fair way to do it, although you should
eventually kind of know it.
9 plus 9 it turns out is 18.
You put the 8 down here and you carry the 1.
And now you just say 1 plus 9.
Well you know what 1 plus 9 is.
1 plus 9 is equal to 10.
So there's nowhere to carry this 1, so you write the
whole thing down here.
So 99 plus 9 is equal to 108.
Let's do one more problem.
Let's say 56 plus 7.
Well what's 6 plus 7.
Well 6 plus 7 is 13, right?
If you get confused, draw out everything again.
And then you get 1 plus 5.
1 plus 5 is 6.
63.
And you might want to give yourself a bunch of problems
and I think you're also now, if you understand what we did,
ready to try the level two addition problems.
Have fun.