In this lesson we will look at a number line
for tenths of a decimal. The number line model
is more abstract than the region model
that we used for decimals in
lesson 1. With this lesson we show how
students can use a
region model to develop the number line
with understanding. This blank decimal
number line can be reproduced for students.
Students will noticed that his
four whole numbers numbers, 0, 1.0, 2.0, and 3.0,
and there are 10 spaces between each pair
of numbers.
Let's place a decimal square for .3 above
the number line,
so that the shading begins
above the zero point. Students know of the decimal for this square
is .3 and this helps
to show where .3 Is written on the number line.
Without making this connection from the
area model to the number line,
students often incorrectly will count the marks
on the number line starting at 0,
1, 2, 3 and think .3 should be written
at the end of the third mark. A few more
square can be selected.
Let's just illustrate the location for.9.
We start the shading is zero.
Now in this case students know that
the decimal for this square is .9, and so
that tells us that .9
goes at this point. Students can fill in
the rest of the decimal points from 0 to
1
I by using the shaded amounts of squares as
needed.
Here we see the decimals for tenths
written in between 0 and 1.0.
1.0 on this number line
can be illustrated and placing one whole
shaded square on the number line
to represent one whole. This will be
helpful to students
who see the pattern .1 .2 .3 and so
forth .8 .9
and think the next decimal here for
this point should be point 10
or .10. To show that the decimal for
this point is not .10,
we can use the green shaded square
with one column shaded, and students know
the decimal for this square
is .10, and the shading does not contain
you up to this point. So
this square shows that the decimal for this
point
here, in addition to being called .1
could be call .10.
Now one use of the number
is measuring length. So we will line up a paper clip here,
starting at the zero-point. The length of this
paper clip is more than .2 units and less
than .3 units,
but closer to .3 units. So the
length of the paperclip
rounded to the nearest tenth is .3 units.
Some objects are too long to measure
from 0 to 1.0. For example,
the length of this pen
has a length greater than 1.0,
so we will extend the tenths
from 1.0 to 2.0. Let's place the decimal
square
for .4
above the line so the shading starts
at 1.0.
Since we have a length of
one, from 0 to 1.0,
and now we have four more tenths, we can write
1.4 beneath the mark at the end of the shading for
.4. the number 1.4
is a mixture of the whole number 1
and the decimal .4, so it is
called
a mixed decimal. More squares can be used as needed
to get the mix decimals from
1.0 to 2.0,
and from 2.0 to 3.0. Here is the number line
completed
in mixed decimals in tenths from zero to
3.0. Now we can measure longer object,
such as the pen we looked at
a few minutes ago. Now we can see that its
length is
more than 1.3, less than 1.4, but
closer to 1.3 than 1.4, so in this case will
round down
and say the length of the pen to the nearest
tenth
is 1.3 units.
Students can measure objects such as the
length of
a pencil, or the dimensions of a
desk,
or book, or sheet of paper. In this lesson
we used the area model, decimal squares,
to make sense when labelling points
on a number line. We used the number line
to measure objects, more applications of decimals, and
introduced rounding in a natural way.
The pen we measured had a length greater than 1,
and this provided a reason to extend the number line,
and to introduce mixed decimals. When math concepts,
such as those used in these two lessons,
namely decimals,
number lines, rounding, and mixed decimals,
can be introduced in a natural, to
answer questions and provide information,
then the students will have a better feeling
for mathematics.
