 
If you teach fractions you heard about
teaching fractions on a Number Line.
Students struggle with fractions because
they don't see them as numbers they see
them as magical symbols we learn about
in math class
and research shows us that when we use
Number Lines to teach fractions
we help students understand that
fractions really are numbers and they
behave like numbers.
In this lesson today we're going to
assume students know something about
unit fractions, 1/3, 1/8
and that they know something about
representing fractions on a Number Line
and we're gonna use that to represent
larger fractions on a Number Line.
Our first example will be 2/8. To do this
activity we're gonna use Fraction Towers,
will use an open Number Line that will
mark, and then we've got a marker for
doing our marking on the Number Line.
As you distribute materials to students,
think about having them work in groups
so that they can hear each other's ideas
and share information back and forth
and remember that you'll need to take
some time to think about how you're
going to manage the materials,
distributing things out,
talking to students about using them
appropriately, and that practical
of teaching with manipulatives. My first
question for students is
what's 1/8? Can use the tools you have in
front of you to represent 1/8?
Some of them will do that by grabbing
this 1/8 piece and saying here it is.
Guide them towards the Number Line and
have them think about
could mark a whole? Because 1/8 has to be one-eighth of something
so I mark my beginning and end of my
zero in my one
and then I can think about where's 1/8 than
that set
line up my pieces and mark my 1/8
on the Number Line. Once I've done that
and students understand that place
that's the review part, where's 2/8s? Where with that fall on the number line
some students will take two 1/8 pieces
and use that to mark lininig it up at
zero again.
While other students will take their
same 1/8
piece and move it over a step and then
land at the same spot.
Have them to think about what they've
done here
as they go from 1/8 to 2/8. They've moved
two steps along their Number Line
or they've added one 1/8 piece
to a second 1/8 piece. You can ask them to
represent that work as an addition
sentence
and you'll hopefully see something like
this 1/8 plus 1/8
equals 2/8. You can have your students
continue the activity with
other eights fractions or they can work
with a different fraction.
We might think in a second example
about marking fifths. I'm gonna demonstrate
this model using
virtual manipulatives. If you've got an
interactive whiteboard in your classroom
this is the tool you can use
for that. We'll have the same idea of our
unit
with 0 and 1 and if I wanna mark
3/5
I'll take that 1/5 peace and
counted along three times
labeling each step until I get to
3/5
as my mark. I can think about
3/5 then
as 1/5 plus 1/5 plus 1/5
Your goal in this lesson is to help
students see fractions as numbers
that they understand when they build 2/8
they're taking one 1/8
piece and counting on to a second or
3/5
one 1/5 counting on to a second and a
third.
By using concrete models we help
students understand that fractions
really are numbers.
They have a place on the Number Line we
modeled it and marked it
in our activity here and they behave
like numbers.
1 inch plus 1 inch is 2 inches. 
1/8 plus 1/8
is 2/8. They work the same way
the activities are the same kind of
model and that help students understand
that these are just a number we write in
a different way.
When we write fractions we use a couple
of digits at 2 and 8
we use a line segment. When I write a
large number
I might use a comma. When I write a decimal use a dot.
Fractions really are a single number,
they live in one place on the Number
Line
and these kinds of materials can help
students understand that.
