Fraction Bars are a
part to whole
area model
for fractions.
A common model
for many years
has been pies or pizzas.
One set
of Fraction Bar activity mats
has both of these models
pies
and bars.
One advantage
of the fraction bars model
is that it can be used
for measurement.
and also
for locating fractions on a number line.
These two ideas
will be illustrated in this video.
Let's began
using fraction bars to measure the length
of 
some objects.
The length of this pencil
is longer than
seven parts out of twelve.
We've got to increase the uh...
number of shaded parts. Okay this looks like we
have it here.
The uh...
this pencil is approximately
the same as the length as nine out of
twelve
parts of a fraction bar,
so we'll say its length is
nine-twelfths bar,
or nine-twelftgs of a bar.
Let's look at a longer pencil here.
We'll try ten,
ten out of twelve, that's not quite as long
enough.
Let's use eleven out of 
twelve.
Sometimes you have to do a little bit of rounding here, this is a little more than eleven out of
twelve, but you can see that is less than
half of the next space.
So we're going to say that 
the length of this pencil
is eleven
over twelve bars,
almost a whole bar.
Next we will measure with the bars
to construct a number line.
This is the beginning of the number line
from zero to two.
And between zero and one,
there one, two, three, four, five, . . .
twelve parts.
This length from zero to one
is the same length as
one whole bar,
so we can use the shaded amounts
of the orange bars to write the numbers
under the marks on this number line.
Since two parts of this bar are shaded,
the shaded amount represents the fraction two-twelfths.
So we can write two
twelves
beneath this mark.
Now a common mistake for some students is
to think the fraction for this mark
should be three twelfths, they count the marks,
one, two, three,
but it's the spaces
we need to count.
And the shaded amounts of the fraction
bars can help us to remember this.
So we can continue to use the shaded
amounts of  
fraction bars
to write other numbers between zero
and one.
Four parts shaded, this is going to
be the fraction four
twelves,
now we'll just continue along here, this is
going to be
six-twelves, we'll do every other mark here,
this is eight-
twelfths, ten-twelfths
now eventually we're going up here to where we have a whole bar,
twelve -twelfths.
And instead of writing twelve-twelfths here, we write "1" because this is
one whole bar.
Now we can continue to use fraction bars
to get the
numbers for marks between one and two.
So this mark here
is going to be
one hold bar and two-twelfths. We're going to write one and two-
twelfths.
Now this number is a mixture of the whole number one and the fraction two-twelfths.
Now we can continue as before, and we write the
mixed numbers one
one and four-twelfths,
one and
six twelfths,
one and
eight-twelfths,
one and ten-twelfths,
and eventually we're going to have two whole bars
and because of that we write the number 
"2" rather than one and twelfth over twelve.
And this is only the beginning of the number
line,
and it can be extended 
to three bars, four for bars, and so forth.
This activity
will help students
connect the region model
for fractions to the more abstract
number line model.
Now a fraction bar has 
a length of six inches,
and this two-bar number line has a length of
twelve inches.
And this fits onto a standard eight and one-half
 by eleven sheet of paper.
Now this is a black line master from the grades 5 to 8
Fraction Bars Teacher's Guide.
And these can be run off for students so
that each student can form their own
number line
by writing in the 
fractions and mixed numbers.
Let's use the number line for a
few more measurements.
Again just a pencil that has a length of
more than one and two-twelfths, its almost one
and three-twelves,
very close.
So rounded off
the length of this is going to be
one and three-twelfths bars.
Another things that's common in the classroom is the 
standard sheet of paper.
This length is one and five-twelfths bars.
The length of
one and ten over twelve.
Now you can also convert these measurements into inches, because each space on the orange bars
is a half an inch, so you've got one inch
from zero to two over twelve,
and uh...
you can see that this is going to be
eleven inches, which is
an eight and one-half by eleven inch 
sheet of paper.
Now working in pairs, students can use two of the number lines
to measure larger objects.
Let's look at a game from fractionbars.com that uses mixed numbers.
In Fraction Darts,
we will select the option of one player,
a difficulty level of one,
and type the player's name.
The height of the dart board is mixed
numbers that goes from 
one and four-ninths to 
four and one half.
The player approximates the location of
a balloon,
types in a number,
press Throw Dart.
Nice shot!
In this lesson
we introduced
measuring,
mixed numbers,
and the fraction number line.
The number line
is a common model for fractions
but it is more abstract
than the region model.
In the activity in his video,
we showed that students can build
a fraction number line
by using the more familiar
region model.
This connection of 
 region model
to the number line model
helps students to see what fractions go
with the points on the line.
