background – world wide two main systems of measurement metric system based on the number 10 ...

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

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.

United States

Myanmar (formly known as Burma)

Liberia (Settled by free-men and former enslaved blacks after America’s Civil war.

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

The distance is representing a full inch.

0 1

The full inch is divided into two sections.

The number of sections determines the denominator.

Notice the line height.0 1

2

1

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.

What will the denominator be for the new lines?0 1

2

1

Each half inch section is divided into two sections.

Notice the line height. It’s getting smaller.

The denominator is 4 because of the 4 sections created by the new lines.0 1

2

1

4

1

4

34

2=

Each forth inch section is divided into two sections.

Notice the line height. It’s getting smaller.

The denominator is 8 because of the 8 sections created by the new lines.0 1

2

1

4

1

4

3

8

1

8

3

8

5

8

7

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

4

3

8

1

8

3

8

5

8

7

16

1

16

3

16

5

16

7

16

9

16

11

16

1316

15

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

2

1

4

1

4

3

8

1

8

3

8

5

8

7

16

1

16

3

16

5

16

7

16

9

16

11

16

1316

15

PAY CLOSE ATTENTION NOW

You can tell what the fraction is for each line by covering the lines up.

0 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.

0 1

2

1

Remember the 2 sections. That tells me the denominator.

Expose the next set of lines.The number of sections created tells me the denominator.

0 1

2

1

4

4

Count by odd numbers for the numerators.

0 1

2

1

4

1

4

3

Expose the next set of lines.The number of sections created tells me the denominator.

0 1

2

1

4

1

4

3

8 8 8 8

Count by odd numbers for the numerators.

0 1

2

1

4

1

4

3

8

1

8

3

8

5

8

7

Expose the next set of lines.The number of sections created tells me the denominator.

0 1

2

1

4

1

4

3

8

1

8

3

8

5

8

7

16

16

16

16

16

16

16

16

Count by odd numbers for the numerators.

0 1

2

1

4

1

4

3

8

1

8

3

8

5

8

7

16

1

16

3

16

5

16

7

16

9

16

11

16

13

16

15

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

2

1

The denominator will be 4.

The numerators will be 1 and 3. Count by odd numbers.

0 1

2

1

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

2

1

4

1

4

3

What will denominator be?

The numerators will be? Remember, count by odd numbers.

0 1

2

1

4

1

4

3

The denominator will be 8.

And the numerators will be 1,3,5 and 7.

Now expose the last set of lines.

0 1

2

1

4

1

4

3

8

1

8

3

8

5

8

7

What will denominator be?The numerators will be? Remember, count by odd numbers.

0 1

2

1

4

1

4

3

8

1

8

3

8

5

8

7

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

2

1

4

1

4

3

8

1

8

3

8

5

8

7

16

1

16

3

16

5

16

7

16

9

16

11

16

13

16

15

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

2

1

4

1

4

3

8

1

8

3

8

5

8

7

16

1

16

3

16

5

16

7

16

9

16

11

16

13

16

15

16

2

All the red fractions can be reduced. Do you see any patterns?

0 1

2

1

4

1 4

3

8

1

8

3

8

5

8

7

16

1

16

3

16

5

16

7

16

9

16

11

16

13

16

15

16

4

16

6

16

8

16

10

16

12

16

14

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.

0

12

3

4

56

7

8

910

11

12

13

1415

16

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.

Reading A Ruler

0

1/162/16

3/16

4/16

5/16

6/16

7/16

8/16

9/16

10/1611/16

12/16

13/16

14/1615/16

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.

0

1/161/8

3/16

1/4

5/16

3/8

7/16

1/2

9/165/8

11/16

3/4

13/167/8

15/16

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

0

1/161/8

3/16

1/4

5/16

3/8

7/16

1/2

9/165/8

11/16

3/4

13/167/8

15/16

1

Did you notice a trend?

The longest lines were of course whole numbers.

Reading A Ruler

0 1

The second longest line is 1/2.

Reading A Ruler

The third longest line has a denominator of 4.

1/4

1/2

3/4

The fourth longest lines always have a denominator of 8.

Reading A Ruler

The shortest lines always have a denominator of 16.

1/161/8

3/16 5/16

3/8

7/16 9/16

5/811/16 13/16

7/815/16

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.

5

A

6

Reading A RulerReading A Ruler What is the correct

measurement for the letter A.

The answer is 10-3/16.

What is the correct measurement for the letter B.

The answer is 10-3/8.

What is the correct measurement for the letter C.

The answer is 10-3/4. 10

A

11

B C

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 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.

15/16

Reading A Ruler

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.

5.

Measurement Quiz

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”