So let's talk about bar models. A bar model
is something you can use to solve a math problem.
It helps you organize the information you
have, visually, so you can see what you have,
and what's missing, and maybe some things
you can try. You know, in math, we use models
of all kinds. When you think of the word "model,"
you might be thinking of, like, someone who's
just ridiculously good looking for a living,
you know, like your teacher. But, you know,
a model is also just a small version of something.
You know, like a model airplane, or a model
of the solar system. A model is just something
we make that represents something else, and
in math we do that all the time. So the essence
of the bar model method is using spatial equality,
which you can see not coincidentally in an
equal sign. The top bar is the same as the
bottom -- they take up the same amount of
space -- they have spatial equality. In a
bar model, we're going to use, you know, the
things that we know, the parts of things,
to compare or calculate the total or the missing
amount in the other bar. You know, having
that right in front of you, once you see exactly
what you have or don't have, makes it pretty
intuitive to figure out what you're supposed
to do. If only everyone did that, you know,
use what you know to solve problems. Don't
just make stuff up like that one weird kid
on the playground. You know, math, maybe more
than any other subject, requires us to be
abstract thinkers at a very early age, whether
we're ready for it or not. And, you know,
some ways of dealing with that are to use
lots of hands-on manipulatives. And if you
don't have that, hey, grab a bar model. So
in this example, if we know that top bar represents
a total of ten, then the bottom bar, which
is spatially equal, again, "spatial" is the
space it takes up, then the bottom bar is
also equal to ten units and we can divide
the bar into equal parts and label them from
one to ten. You can also represent that equality
with other things, like tally marks. You can
put then dots in there. Or you can do it more
abstractly with the numbers. Whatever best
suits your skill level. If you have the total
value of a bar, which in this case is ten,
and then you have a part or a piece, in this
case it's three, then we're going to use the
equality of the bars -- they should both be
equal -- they should both be ten. We're going
to use that to find the difference, or the
missing part. And you can use whatever strategy
you're best at. You can count up, you can
subtract. The missing part here is seven.
Seven and three together make ten. And the
bar model, what's great about it, is it adapts
with your skill level. As your number sense
grows and you know how to break apart and
put together numbers without drawing things,
you'll begin to instantly recognize the missing
parts. When you have a total of ten and you
have five, then you know that other piece
has got to be five. Or if you have six, it's
going to be four.Or if you have seven, you're
going to need three. Or if it's eight, you're
going to need two. And if it's nine, you're
going to need one. The bar model strategy
is also called "part part whole." And in most
problems you'll be looking for the whole,
or total, or the largest or final amount,
and assigning that label and value, if you
have it, to the top bar. And then below you
would put the parts that are going to make
up that whole or total and largest and final
amount. If you have all the parts, like here
you have twelve and six, then you are going
to put them together to find the whole. Twelve
plus six is going to give you the total, which
is eighteen. There may be other problems where
you know what the total, the final amount,
is. Let's say you have one 
hundred and twenty 
and then you know one of the parts is 80.
We're going to use what we have, we're going to take away eighty from the total, one hundred twenty, to find the missing part.
The difference is forty. And that eighty and forty together equal one hundred twenty, which is the whole.
And then in some of the problems you'll be dealing with equal groups, but it's just as easy.
and 
then 
you know 
one 
of 
the parts 
is eighty.
