In this lesson we'll connect the green
decimal
squares for hundreds to a decimal number line for hundreds, and
use this number line to measure objects
more precisely. This number line
has the decimals for tenths that were labeled
in the previous lesson .1, .2, .3,
up to .9, and also mixed decimals.
For example, .4
was located by using the square with
4 parts shaded out of 10.
The shading ends at this point, and we label this point,
.4. Notice that the Green Square for .40
has the same amount of shading as a red
square for
.4. So when we place the green square
with 40 shaded parts out of 100 on the number line,
this shading stops at that point .4.
So either the decimal .4 or the
decimal .40
can be used to label this point. The
green decimal square
is divided into 10 equal columns
and each column has 10 small parts or 10
small squares. The number line
from 0 to 1.0 also his 10 small parts,
0 to .1, .1 to .2,
.2 to .3, and so forth, and each of these parts
has 10 small parts. So the decimal
for every green square with 100 parts
will correspond to one of the hundred parts from 0 to 1.0.
For example, the decimal for one part
out of 100 is point 01.
The point 01
is the decimal for the first of these points, for the first of these the 100 points
from 0 to 1, and this point which we label
.01.
Let's look at the decimal placement for the
square with 45 parts shaded out of 100.
To find the point for the decimal .45 on the number line,
we go to .4, count of five more spaces,
one, two, three, four, five,
and that point is going to be here, point 45.
So the last column of the square for .45
has 5 parts shaded, half of the column is shaded,
and we went to .4 and went halfway from .4 to .5
to locate the point on the number line
for .45.
Let's locate
the points on the number line for a few
mixed
decimals. 1.83
is the mixed decimal for one whole
square
and 83 parts out of 100. So we go to 1.0 for
one whole square, and then go to 1.8,
80 more spaces, and then count off three more spaces
to get the point for the mixed decimal
1.83.
Let's look at the point for 2.58.
 
This is the mixed decimal for 2 whole squares and 58 parts out of 100.
Then we go to the point for 2.0 for 2 whole squares,
then go to 2.5 for fifty more parts out of 100, and then go
eight more spaces to get the point
for the mixed decimal 2.58.
We can use the spaces of this number
line to measure length.
The length of this pencil is very close to
1.85 units. So its length
to the nearest hundredth is 1.85
units. In the previous lesson,
we use the decimal number line for tenths.
We found that the length this paper clip was
between .2
and .3 units, but closer to .3 units.
Now we can see its length is very close
to .27 units. So is length
to the nearest hundred is .27 units.
Students can each be given hundreds
number line to measure objects.
For example, the width of this standard
sheet of paper is more than 2 units,
more than 2.1, and 2.15 units
to the nearest hundredth. And its length
is more than 2.7
and 2.77 units
to the nearest hundred. In the first
three lessons
we have used two different models for
decimals.
We used the region model with squares divided into 10,
100, and 1000 equal parts. The
second model
was number lines, and you may have seen
something
for the first time. We showed a
connection
from the concrete region model to the
more abstract number line model.
