Background – World Wide
 Two main systems of measurement
 Metric System
 Based on the number 10
 U.S. Customary System
 Based on halving or doubling units
Background – World Wide
 What countries besides the U.S. have not
adopted the metric system?
 All countries have adopted the metric system,
including the United States. However, in nearly all
countries people still use traditional units. For a
country to switch to metric is a process that
happens over time. Only 3 countries in the world,
have not officially adopted metric as their primary
system of measuring.
Background – World Wide
Myanmar
United States
(formly known
as Burma)
Liberia (Settled by
free-men and former
enslaved blacks after
America’s Civil war.
Three countries have not officially adopted the International System of Units
as their primary or sole system of measurement: Liberia, Myanmar, and the
United States.
https://www.youtube.com/watc
h?time_continue=15&v=kDPSVGH
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Place the Zero end of your rule at the end of your object, usually on
the left side.
Place the Zero end of your rule at the end of your object, usually
on the left side. Make sure the end of the ruler is flush with your
object, and use your left hand to hold it in place
1” = 1 INCH
1’ = 1 FOOT
1 CM = 1 CENTIMETER
1 INCH= 2.54 CENTIMETERS
1 MILLIMETER=0.1 CENTIMETERS
1 MILLIMETER = 0.0393700787
INCHES
0
1
The distance is representing a full inch.
The full inch is divided into two sections.
The number of sections determines the denominator.
Notice the line height.
0
1
1
2
Each half inch section is divided into two sections.
Notice the line height. It’s getting smaller.
Remember the number of sections determines the denominator.
0 What will the denominator be for the new lines?
1
2
1
Each half inch section is divided into two sections.
Notice the line height. It’s getting smaller.
0
The denominator is 4 because of the 4 sections
created by the new lines.
1
4
2
4
=
1
2
3
4
1
Each forth inch section is divided into two sections.
Notice the line height. It’s getting smaller.
0
The denominator is 8 because of the 8 sections
created by the new lines.
1
8
1
4
1
2
3
8
5
8
3
4
1
7
8
Each eighth inch section is divided into two sections.
Notice the line height. It’s getting smaller.
The denominator is 16 because of the 16 sections
created by the new lines.
0
1
2
1
4
1
8
3
8
3
4
5
8
1
3
5
7
16
16
16
16
9
16
11
16
1
7
8
13
16
15
16
You now know all the fractions on a common school
ruler.
But how can you tell the fractions just by look at the
line heights?
0
1
1
2
1
4
1
8
3
8
3
4
5
8
1
3
5
7
16
16
16
16
9
16
11
16
7
8
13
16
15
16
PAY CLOSE ATTENTION NOW
0
You can tell what the fraction is for each line by
covering the lines up.
1
PAY CLOSE ATTENTION NOW
Cover the lines up.
0
1
PAY CLOSE ATTENTION NOW
NOW expose the first set of lines.
HOW many sections are created?
0
1
2 sections. That tells me the denominator
0
1
2
Count by odd numbers for the numerator.
Remember the 2 sections. That tells me the
denominator.
0
1
1
2
Expose the next set of lines.
The number of sections created tells me the denominator.
0
1
1
2
4
4
Count by odd numbers for the numerators.
0
1
1
4
1
2
3
4
Expose the next set of lines.
The number of sections created tells me the denominator.
0
1
1
2
1
4
8
3
4
8
8
8
Count by odd numbers for the numerators.
0
1
1
8
1
4
1
2
3
8
3
5
8
4
7
8
Expose the next set of lines.
The number of sections created tells me the denominator.
0
1
1
4
1
8
16
1
2
16
3
3
8
16
4
5
8
16
16
16
7
8
16
16
Count by odd numbers for the numerators.
0
1
1
4
1
8
1
16
1
2
3
16
3
3
8
5
16
4
5
8
7
16
9
16
11
16
7
8
13
16
15
16
You try it.
Expose the first set of lines.
0
1
What is the denominator?
0
1
The denominator is 2.
Now what is the numerator?
0
1
2
The numerator is 1. It’s the first odd number.
Now try the next set of lines.
0
1
1
2
The denominator will be 4.
The numerators will be 1 and 3. Count by odd numbers.
0
1
1
2
The denominator will be 4.
The numerators will be 1 and 3. Count by odd numbers.
Now expose the next set of lines.
0
1
1
4
1
2
3
4
What will denominator be?
The numerators will be? Remember, count by odd numbers.
0
1
1
4
1
2
3
4
The denominator will be 8.
And the numerators will be 1,3,5 and 7.
Now expose the last set of lines.
0
1
1
8
1
4
1
2
3
8
5
8
3
4
7
8
What will denominator be?
The numerators will be? Remember, count by odd numbers.
0
1
1
8
1
4
1
2
3
8
5
8
3
4
7
8
The denominator will be 16?
The numerators will be? 1,3,5,7,9,11,13 and 15. Remember,
you count by odd numbers.
0
1
1
4
1
8
1
16
1
2
3
16
3
8
5
16
3
4
5
8
7
16
9
16
11
16
7
8
13
16
15
16
Why do we count by odd number?
Remember math class and reducing fractions.
We only have odd number in the numerators because an
even number could be reduced.
0
1
1
4
1
8
1
16
1
2
3
16
3
8
5
16
3
4
5
8
7
16
9
16
11
16
7
8
13
16
15
16
All the red fractions can be reduced. Do you see any patterns?
0
1
1
8
1
1
4
1
2
3
8
5
8
3
4
7
8
2 3 4 5 6 7 8 9 10 11 12 13 14 15
16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
Following Directions Lesson
 Take out a
clean sheet of
notebook
paper and
something to
write with.
 Place it in front
of you on your
desk.
Following Directions Lesson
 Fold your
paper in half
vertically.
Following Directions Lesson
 Open your paper up
and place it holes to
the top on your
desk.
 Draw a line all the
way down the
crease on the paper.
 “DO NOT WRITE
ON THE DESK!!”
Following Directions Lesson
 Fold the paper in
half the other
way,horizontally.
 You can see my
line because I
used a Sharpie
Marker and it
bled through the
paper.
Following Directions Lesson
 Open the paper up
with the holes to
the top.
 Draw a line from
the center of the
paper to the
margin closest to
you.
Following Directions Lesson
 Fold the paper
like you had it last
, horizontally.
 Then fold it over
again in the same
direction as you
folded it last.
Following Directions Lesson
 Open the paper
up.
 Draw a line on
each of the
creases half
way to the
bottom
margin.
 Then fold your
paper back up
like you last
had it.
Following Directions Lesson
 Fold the paper
over one more
time in the
same direction
as your last
fold, making it
even more
slender.
Following Directions Lesson
 Open the paper
up.
 Draw lines on
the four creases
half as long as
the last lines
you drew, or ¼
of the way to
the bottom
margin.
Following Directions Lesson
 Draw small lines
on our paper in
between each of
the lines already
on your paper and
the left and right
edges.
 Make the lines
extend down and
be half as long as
the last lines
drawn.
Following Directions Lesson
 Next, draw lines on
the left and right
edges all the way
down below the
margin, half way
between the margin
and the bottom of
the paper.
 And in case you
haven’t already
figured it out, we are
making a ruler.
Reading a Ruler
 Now all you
have to do is
count the lines
as you go from
left to right.
1
3
5
2
7
9
6
11
13
10
4
15
14
12
8
0
16
Reading A Ruler

By counting
you realize
that you have
16 equal parts
to an inch.
 Next you
show each
number as a
fraction or
portion of the
total number
16.
1/16 3/16 5/16 7/16
2/16
6/16
4/16
9/16 11/16 13/16
15/16
10/16
14/16
12/16
8/16
0
16/16
Reading A Ruler
 Next, you must remember from math that a
fraction should always be expressed in lowest
possible terms.
 1/16 for example is in its lowest form, it cannot be
reduced any farther.
 2/16 however, can be reduced.
2 is the numerator (top number in a fraction)
16 is the denominator (bottom number in a
fraction)
Reading A Ruler
 2/16 can be reduced by 2. This means that both 2
and 16 are divisible by 2.
 2 divided by 2 = 1
 16 divided by 2 = 8
 Therefore our reduced fraction will be 1/8.
Reading A Ruler
 Now lets take 3/16, will it reduce?
 I bet that someone said yes!
 Some people look at the three as the numerator
and the six in the sixteen (denominator) and
automatically think that this fraction will reduce.
However, it will not reduce.
 3/16 is already in its lowest terms.
Reading A Ruler
 Next, lets look at 4/16. Yes it will reduce. There
are two ways to reduce fractions like this one. If
you’re a math wiz, you might say that 4 will go
into 16. If you do, you are right. You can divide the
numerator into the denominator. This is the
quickest of the two ways, but you can divided both
the numerator and the denominator by 2, twice.
You have to be careful to get fractions like this one
into lowest possible terms.
Reading A Ruler
 The easiest way to deal with 4/16:
 4 divided by 4 = 1
 16 divided by 4 = 4
 Your reduced fraction is ¼.
Reading A Ruler
 The other way to deal with 4/16 is:
 4 divided by 2 = 2
 16 divided by 2 = 8
 Your fraction is 2/8, but is it reduced to lowest
possible terms? NO, you have to reduce again.
 2 divided by 2 = 1
 8 divided by 2 = 4
 Your reduced fraction is 1/4
Reading A Ruler
 Now that you know how to reduce these
fractions, you finish reducing the rest of the
fractions on your ruler.
Reading A Ruler

Now Check
your fractions
against these
correct
answers.
1/16 3/16 5/16 7/16
1/8
3/8
1/4
9/16 11/16 13/16 15/16
5/8
7/8
3/4
1/2
0
1
 Now that you know
how to use a ruler,
here are some short
cuts for you.
 As you have noticed,
the lines are different
lengths on the ruler.
 As we go across one
more time pay
attention to the line
length and the
denominator
associated with it.
Reading A Ruler
1/16 3/16 5/16 7/16
1/8
3/8
1/4
9/16 11/16 13/16 15/16
5/8
7/8
3/4
1/2
0
1
Reading A Ruler

Did you notice
a trend?
 The longest
lines were of
course whole
numbers.
0
1
Reading A Ruler

The second
longest line is
1/2.

The third
longest line
has a
denominator
of 4.
1/4
3/4
1/2
Reading A Ruler


The fourth
longest lines
always have a
denominator
of 8.
The shortest
lines always
have a
denominator
of 16.
1/16 3/16 5/16 7/16
1/8
3/8
9/16 11/16 13/16
15/16
5/8
7/8
Reading A Ruler
 Now let’s look at
the whole ruler.
Can you tell me
what would be
the correct
measurement for
the letter A.
 The answer is
5-7/16.
 You start at the
whole number
and you add the
calculated
fraction to the
whole number to
give the correct
distance.
A
5
6
Reading A Ruler






What is the correct
measurement for the
letter A.
The answer is 103/16.
What is the correct
measurement for the
letter B.
The answer is 103/8.
What is the correct
measurement for the
letter C.
The answer is
103/4.
A
10
B
C
11
Reading A Ruler





Now you know how to read a ruler and deal with the
fractions involved.
But these are measurements, and have to be
expressed as measurements. Write the following 15/16
notes on your paper.
This standard ruler is to be expressed in inches or in.
or “. Example: 1 ½”
12 inches is equal to 1 foot or ft. or ‘. Example 4’ 1 ½”
Three feet is equal to 1 yard or yd.
Reading A Ruler
 See if you can tell the measurements of the
objects on the following screens for a quick
quiz.
 On the back of your paper title it
Measurement Quiz and number from 1 to 5.
Measurement Quiz
1.
Measurement Quiz
2.
Measurement Quiz
3.
Measurement Quiz
4.
Measurement Quiz
5.
Measurement Quiz Answers
 The answers to the quiz are:
1. 6 - 7/16”
2. 3 – 11/16”
3. 5 – 5/8”
4. 4 – 7/8”
5. 11 – 9/16”