There are many different
addition strategies
and ways that we can
solve addition problems.
I'm going to cover just
a few of them today
and show you them with our
expression here of 146 plus 88.
I'm going to start by showing
you the count on strategy.
Sometimes we even call this
the number line strategy
or the open number line strategy.
When children are first starting
to learn to add, they
start by counting all.
So this is the first step.
So if I start by saying
what's five plus three?
Young children will often
start right over here
and start by counting with one.
So they'll go one, two, three, four,
five, six, seven, eight.
There's eight here.
Now as adults we know
that I already know I have five fingers.
I can just start on six
for this finger, right?
That's called the count on.
So first children learn by counting all.
Then they learn by counting on.
Then lastly they use something called
the break apart method.
And this is where they can say things like
"well, if I know eight plus six is 14,
then I know I can take two
from the six, make the eight
a 10 and get 10 plus four.
So they're really manipulating
numbers at that point.
So again, children start by counting all
then they count on,
then they break apart numbers
and use that to do their
addition strategies.
So the beauty of the count on strategy is
you can use an open number
line to show your work.
Now you might be thinking
what's an open number line?
It's basically a line
where I call them hops
where the we hop on it and
they're not proportionate.
So a giant hop could be
five, or it could be 100.
So they label it.
I'm going to first start by
taking 88 and starting there.
Know you can start at one 46 or 88.
So either at end,
so I'm going to start at 88
and I'm going to hop 146.
Now there are some students
that might think about hopping
to get to a friendly number.
There are some students that
might think about hopping
in terms of well, there's a 100 there
so let me hop that first.
But know that everyone's version
of friendly is different.
And this is what the
beauty of this strategy is.
So you're going to see
lots of different answers,
what I wouldn't want to see.
And sometimes I see this
in adults, not children,
by the way, is things
like I'm going to hop six
and give me 94.
That's not really like
how a child would think
because they're trying to
get to a friendly number.
They're trying to get to the easiest,
the path of least resistance.
So I'm going to guess a lot
of children would start by adding 100.
So let me do that here.
And I'm going to put a plus 100
so that I know that that's what I did.
And I know that I now have 188.
I know that if I'm thinking as an adult,
I can break it apart by
place value and add 40.
But I'm also thinking that
that's not really easy for me
to add by 40 because I don't
know what 188 plus 40 is.
I know that I've still got 46 to go here.
I think I'm going to get
to a friendly number.
So I think I'm going to
only hop two to get to 190.
So now I've got 44 to still go.
Okay, well now I can hop 10
and get to 200 really easily.
So I'm going to hop 10 again, notice
that my hops are not
proportional and that's okay.
Now I'm going to be at 200
and instead of 44 I now
have 34 left of my 146.
So now I can easily
actually I could easily
just hop 34 at this point
'cause I know that 200 plus 34 is 234.
So I'm going to have hop that last bit.
And I know that my answer is 234.
Let me show you starting at
146 and going that direction.
The beauty of this strategy is
that everyone's answer is
going to look totally different
and that's perfectly fine.
So now I need to add 88 for my hops
so I'm counting on 88 if you will.
So I'm looking
and I definitely even six
plus eight is hard for me.
I'm a second grader.
This is really difficult.
So I think I'm just going
to hop four to get started
so that I get to a friendlier number.
So I know that that will get me to 150.
Remember I've got 88 to go.
So now I only have 84.
Good job, I can hear
you in the background.
All right, now I know I can
get to another friendly number
and that's hopping 50
and I can get to 200.
So that will leave me with 34.
And then again, I could hop 34
and now I get my same answer of 234.
Again, there's so many different ways
that you're going to see
even this problem done
in practice amongst your students,
which is why it is super cool to watch.
Now let me show you the second strategy
which we refer to as partial sums.
This is really great for mental addition.
Here's what's cool about partial sums.
Chances are high you already do this one
you just didn't know it
was called partial sums.
So let's take a look again
we've got 146 plus 88 still.
Now we know the answer is 234.
We can do this mentally by
breaking apart our numbers
by place value.
By the way, this is only one way
that you can do partial sums.
I'm going to show you
another way in just a minute.
Instead of thinking of
this as 146 plus 88,
I'm going to think
of this as 100 plus I know
there's no hundreds in 88,
so that's going to give me 100.
Then I've got four 40 plus 80.
Here's where the make a 10
strategy comes in really handy
because if I know that
four plus eight is 12,
then I know that 40 plus 80 is 120.
Just to refresh your memory
the make a 10 strategy goes like this.
I can take, I see that this
eight is two away from 10.
So I'm going to take two
away the four, make this a 10
and now I can easily add
two plus 10, which is 12.
So I know that 40 plus 80 is 120.
Last, I have my one so
I have six plus eight.
Again, I can use the make a 10 strategy,
take two from here
so this was going to be four.
This becomes 10, four plus 10 is 14.
Now I can add these altogether.
I get 100 plus 120 is
220 plus 10 more 230.
I'm using the count on even
in my head, plus four is 234.
I just showed you the partial
sum strategy broken apart
by place value.
However, I want you to
know that's not always
the best way to do it.
Let me show you what I mean
for this example, I actually
want to use a different number
'cause I think it will help
to illustrate my point
a little bit better.
When I think about the
expression 52 plus 18,
some students are going to
want to break this 18 apart
into eight and 10.
And when they do that,
they can actually again,
make a 10 strategy, know
that 52 plus eight is 60,
60 plus 10 gives them 70.
So this is going to be a
lot easier for some students
than saying 50 plus 10 is
60 two plus eight is 10
60 plus 10 is 70.
Again, lots of different ways
that you can break numbers apart.
Nothing is really right or wrong.
It's really interesting
to hear students' thinking
and reasoning as they explain
why they chose the numbers that they did.
The strategy of breaking numbers apart,
either by place value or
sometimes like I did here
with my model.
We sometimes call that
the break apart strategy.
Just to give you better idea sums means
the answer to an addition expressions.
So partial sums is really
saying it's breaking
the numbers apart in a
way, but just so you know,
that is kind of what you
might hear in practice for
that sort of mathematical model.
The last strategy I want to show you today
is called modified addends
or the compensation model.
For this strategy I want to
write my numbers vertically
this is just easier for me.
So I'm going to write 146 plus 88.
And what I'm thinking about is,
I wish that this top number
was a friendlier number.
Like say it was 150, then
I wouldn't have to carry
so many times or keep regrouping, right?
So let me change it.
So I'm going to add four
and I now have 150 plus 88
and now I can easily add those.
I have eight 150 plus 80
gives me 230 so I have 238.
However, remember I added on this four
so now I need to take away that four.
So I'm going to subtract
it out from the end
and I get 234 for my answer.
What's cool about this strategy is
you can actually do it to addends.
So let me show you what that looks like.
I went ahead and changed our
problem just a little bit,
just so I could show you
how modifying addends
in some cases really proves helpful.
So I've got 146 plus 48.
Again, I'm going to make my
top addend friendlier number
by adding four.
And then I see that I'm
only two way from 50
so I'm going to also add to there.
This is going to give me 150 plus 50.
Hm, nice see what I did there.
Okay this is really easy to do in my head.
So now I know I have 200,
but remember I still need to subtract out
this four plus two which is six.
So I'm going to subtract six
which gives me 194 for my answer.
I hope this video is
giving you some new ideas
on how you can solve
addition problems even
in your own life.
In college, I worked at a beauty salon
and I was constantly having to do
the math behind tips for the hairstylist.
And so people would come up
to me and they would say,
"can you add on a 20% tip?"
And I had to learn how
to do that mental math.
And then I did it over and
over in practiced a ton
and got really good at percentages.
So you too can be great at math
with enough time put into it
and some great strategy.
So I want to really
recommend that you try some
of these strategies, force yourself
to use some of them and
see if you like them.
You know, it sure beats the air addition.
You know what I'm talking
about, where you do this.
And then you're like, okay,
I think I carry the one.
Oh, shoot but what was that number?
You've done this before, right?
It's not a good strategy.
So try some of these strategies.
I think you're going to have a lot
of fun as you experiment with them.
