WEBVTT

00:00:00.316 --> 00:00:04.976
[Music] Welcome to Using a Number
Line to Teach Fractions.

00:00:06.056 --> 00:00:10.416
At Madison Elementary, an open number
line has become an invaluable tool

00:00:10.416 --> 00:00:13.316
for students to use with
addition and subtraction

00:00:13.316 --> 00:00:14.886
of whole numbers and fractions.

00:00:15.326 --> 00:00:20.206
An open number line is just an empty
line used to record mental strategies.

00:00:20.666 --> 00:00:24.976
With representations on the open number
line, students move beyond counting

00:00:24.976 --> 00:00:30.086
by ones, to taking leaps, decomposing
numbers, and using landmark numbers.

00:00:30.086 --> 00:00:35.496
Third-grade teacher Christian Skalstad
demonstrates how students might record

00:00:35.496 --> 00:00:41.346
on an open number line doing the
subtraction problem 437 - 265.

00:00:42.286 --> 00:00:48.386
And another example is they could solve
437 - 265 using the open number line.

00:00:48.876 --> 00:00:56.096
So they could start with 265 and count
up to 437 to find out the difference.

00:00:56.276 --> 00:01:03.956
So a student might start with 265 plus
10 gets them to a landmark number of 275

00:01:04.495 --> 00:01:10.646
and then add another 25 to get
to 300, always keeping in mind

00:01:10.646 --> 00:01:12.196
where they want to go and end up.

00:01:12.606 --> 00:01:18.006
Then they might add another 100 on
to that, which should get them to 400

00:01:18.056 --> 00:01:24.036
and then add on 37 to get to 437.

00:01:25.636 --> 00:01:28.016
So once they get to this
point, then they need to look

00:01:28.016 --> 00:01:33.776
and see how much it took to get
from 265 to 437, so they would start

00:01:33.776 --> 00:01:39.616
with 100 plus 37 plus 25 plus the 10.

00:01:40.466 --> 00:01:43.426
Some of the students who are more fluent
mathematically might be able to deal

00:01:43.426 --> 00:01:50.046
with the 37, others might break it
down into a 25 and a 10 and a 2.

00:01:50.456 --> 00:01:58.856
So they have the 100 plus the 25 plus
the 25 is 150, then they have the 10

00:01:58.856 --> 00:02:08.716
and the 10 which is 20 and 2 left,
150 plus 20 is 170 plus 2 is 172.

00:02:09.696 --> 00:02:14.246
An open number line with two scales
(double-scaled) becomes a tool

00:02:14.246 --> 00:02:16.196
for adding and subtracting fractions.

00:02:16.726 --> 00:02:21.336
Instructional math coach Sharon Leonard
demonstrates how students might use this

00:02:21.336 --> 00:02:25.216
tool calculating 1/4 + 1/5.

00:02:25.216 --> 00:02:29.136
We use the double open number line
quite a bit for fifth and sixth graders.

00:02:29.696 --> 00:02:33.156
Double open number line is a little
different than a regular number line

00:02:33.156 --> 00:02:37.266
in that it has fractions running across
the top and whole numbers running

00:02:37.266 --> 00:02:41.546
across the bottom so that children can
begin to see proportional reasoning

00:02:41.936 --> 00:02:43.396
and almost an idea of ratio.

00:02:43.936 --> 00:02:47.626
So they can use the double number
line for many things, for equivalents,

00:02:47.626 --> 00:02:50.066
for adding and subtracting fractions.

00:02:50.596 --> 00:02:56.276
One example might be, they were
given the equation 1/4 + 1/5.

00:02:56.276 --> 00:02:59.436
As we get further along, we will let
the children tell us what they would

00:02:59.436 --> 00:03:02.506
like for their whole number to be
represented on this number line.

00:03:02.556 --> 00:03:07.796
For this problem children will most
likely pick 20, so we'll try that first.

00:03:08.126 --> 00:03:10.856
And they will pick 20 because they
have done a lot of work with factors

00:03:10.856 --> 00:03:12.926
and they know that 4
and 5 are factors of 20,

00:03:13.636 --> 00:03:17.346
so see 1 would be here,
and 20 would be here.

00:03:17.456 --> 00:03:22.356
So they might first then say, "Well,
I am going to take my one-fourth here,

00:03:22.936 --> 00:03:24.746
and represent it with this jump."

00:03:25.076 --> 00:03:28.646
We also talk about how our open number
lines don't have to be to scale,

00:03:28.826 --> 00:03:29.916
they have to be approximate.

00:03:30.396 --> 00:03:34.926
So here is about one-fourth-our numbers,
however, have to be accurate-and

00:03:35.006 --> 00:03:38.936
if we were taking a bike trip, for
example, that was a 20-mile bike trip

00:03:38.936 --> 00:03:42.546
and we were one-fourth of the way,
we would have traveled 5 miles.

00:03:43.336 --> 00:03:47.536
So we have represented our one-fourth
and they might add on their one-fifth,

00:03:48.166 --> 00:03:53.446
and one-fifth of 20 would be 4
miles, which we will represent here,

00:03:54.256 --> 00:03:59.106
which gives us a total of
9 miles, so our fraction

00:03:59.346 --> 00:04:04.296
for 1/4 + 1/5 would be
9 out of 20 or 9/20.

00:04:05.036 --> 00:04:06.876
So they can complete their equation.

00:04:08.276 --> 00:04:11.626
Another student might use 100 as
the whole number that they wanted

00:04:11.626 --> 00:04:15.006
to work with, because they might
like working with percentages.

00:04:15.726 --> 00:04:19.286
So their number line still needs
to be about the same length

00:04:19.286 --> 00:04:24.206
so we can compare them in a minute
here, so here's 0, here's 100,

00:04:25.396 --> 00:04:27.916
and our first jump here at one-fourth.

00:04:28.666 --> 00:04:32.526
And now if we are thinking out of
100, our kids are pretty fluent

00:04:32.526 --> 00:04:35.686
with percentages and they would
be able to tell us that one-fourth

00:04:36.026 --> 00:04:42.316
of 100 is 25%, so they would be able to
put their 25 here, representing 25 miles

00:04:42.316 --> 00:04:47.026
if you were thinking of a bike course,
and then here's their jump of one-fifth,

00:04:47.456 --> 00:04:52.106
and one-fifth of a 100 is
20, for a total here of 45.

00:04:52.726 --> 00:04:56.136
The fraction might be 45 out of a 100,

00:04:56.916 --> 00:04:59.546
which leads to a great
discussion of equivalent fractions.

00:05:00.046 --> 00:05:02.466
Here we have 9/20, here we have 45/100.

00:05:03.756 --> 00:05:06.246
Are they the same or do
they have different values?

00:05:06.246 --> 00:05:08.376
And how can we discuss
that, how can we prove that?

00:05:08.856 --> 00:05:12.236
Sixth-grade students present
their solutions to a problem

00:05:12.236 --> 00:05:16.446
about Frank's Fresh Farm, where he
must decide whether he has enough gas

00:05:16.446 --> 00:05:17.596
for a trip he is planning.

00:05:18.346 --> 00:05:23.426
The problem presents information both in
miles and in fractions of a tank of gas.

00:05:25.416 --> 00:05:28.306
Students used a number of
visual representations,

00:05:28.306 --> 00:05:31.866
but most found the double-scaled
number line a useful tool.

00:05:32.696 --> 00:05:36.276
Notice how here students use
a double-scaled number line,

00:05:36.276 --> 00:05:40.516
with one scale representing the gas
gauge, and the other the miles traveled.

00:05:41.306 --> 00:05:43.196
In the investigation of this problem,

00:05:43.306 --> 00:05:47.136
students found that the open
double-scaled number line represents

00:05:47.186 --> 00:05:51.616
equivalence and is a useful tool for
addition and subtraction of fractions.

00:05:53.056 --> 00:05:56.806
To learn more about teaching fractions,
please see the additional materials

00:05:56.866 --> 00:05:59.976
on the Doing What Works website.

00:05:59.976 --> 00:06:00.000
[Music]