Reading Dimensions Using a Standard Ruler

Todd Andrus TEE 4400Landon Ashcroft Dr. Gary StewardsonZac Hirschi Fall 2011Brad ParkerJared ThomasJoseph Woodard

Objectives

• Terminal Objective– read dimensions using a standard ruler

• Performance Objective– given a diagram of a standard ruler with extension

and dimension lines, read dimensions to a 16th of an inch, using proper or mixed fractions in their lowest terms, with a minimum score of 90% correct.

Objectives

• Enabling Objectives– define the following terms: whole numbers, proper

fractions, improper fractions, mixed fractions, numerator, and denominator

– identify extension lines, dimension lines, arrowheads, and dimensions

– explain how to identify units on a standard ruler– reduce fractions to their lowest terms– change improper fractions to proper fractions

Fractions

3

4

Fractions

Numerator 

3

4

Fractions

Numerator 

Denominator

3

4

Types of Numbers & Fractions

Whole Numbers:

Types of Numbers & Fractions

Whole Numbers: 0 1 2 3 4 5…

Types of Numbers & Fractions

Whole Numbers: 0 1 2 3 4 5…

Mixed Fractions:

Types of Numbers & Fractions

Whole Numbers: 0 1 2 3 4 5…

Mixed Fractions: 33

16 1

1

8 9

1

4...

Types of Fractions

Proper Fractions:

Types of Fractions

Proper Fractions:5

8

1

4

9

16...

Types of Fractions

Proper Fractions:

Improper Fractions:

5

8

1

4

9

16...

Types of Fractions

Proper Fractions:

Improper Fractions:

5

8

1

4

9

16...

18

16

9

8

6

4...

Reducing Fractions

8

16?

8

16?

Reducing Fractions

What is the largest whole number that will divide into both the numerator and denominator?

8

16

1

2

Reducing Fractions

88

168

Reducing Fractions

8

16

1

2

If you are unable to identify the largest whole number that will divide into both the numerator and denominator, dividing both numbers by 2 will reduce the fraction using multiple steps.

This only works with fractions that have an even denominator.

Reducing Fractions

8

16?

Reducing Fractions

8

16?

Can both numerator and denominator be divided evenly by 2?

Reducing Fractions

8

16

4

8

Reducing Fractions

8

16

4

8?

Can both numerator and denominator be divided evenly by 2?

Reducing Fractions

8

16

4

8

2

4

Reducing Fractions

8

16

4

8

2

4?

Can both numerator and denominator be divided evenly by 2?

Reducing Fractions

8

16

4

8

2

4

1

2

Reducing Fractions

Can both numerator and denominator be divided evenly by 2?

8

16

4

8

2

4

1

2

Reducing Fractions

8

16

1

2

Reducing Fractions

12

16?

Reducing Fractions

12

16?

What is the largest whole number that will divide into both the numerator and denominator?

Reducing Fractions

12

16

3

4

124

164

Reducing Fractions

12

16

3

4

If you are unable to identify the largest whole number that will divide into both the numerator and denominator, dividing both numbers by 2 will reduce the fraction using multiple steps.

Remember, this only works with fractions that have an even denominator.

Reducing Fractions

12

16?

Reducing Fractions

12

16?

Can both numerator and denominator be divided evenly by 2?

Reducing Fractions

12

16

6

8

Reducing Fractions

12

16

6

8?

Can both numerator and denominator be divided evenly by 2?

Reducing Fractions

12

16

6

8

3

4

Reducing Fractions

12

16

6

8

3

4?

Can both numerator and denominator be divided evenly by 2?

Reducing Fractions

12

16

3

4

PracticeFraction Lowest Terms

10

16 ?

Fraction Lowest Terms

10

16

5

8

Practice

36

64 ?

PracticeFraction Lowest Terms

36

64

9

16

PracticeFraction Lowest Terms

Reducing FractionsImproper Fractions Mixed Fractions

11

4 ?

11

4 ?

How many times will 4 go into 11, and what is the remainder?

Reducing FractionsImproper Fractions Mixed Fractions

11

4 2

4 goes into 11 two times.

Reducing FractionsImproper Fractions Mixed Fractions

11

4 2

33 is the remainder and goes in the numerator

Reducing FractionsImproper Fractions Mixed Fractions

4 stays in the denominator

11

4 2

3

4

Reducing FractionsImproper Fractions Mixed Fractions

19

16 ?

Reducing FractionsImproper Fractions Mixed Fractions

19

16 ?

How many times will 16 go into 19, and what is the remainder?

Reducing FractionsImproper Fractions Mixed Fractions

19

16 1

16 goes into 19 one time.

Reducing FractionsImproper Fractions Mixed Fractions

19

16 1

33 is the remainder and goes in the numerator

Reducing FractionsImproper Fractions Mixed Fractions

16 stays in the denominator

19

16 1

3

16

Reducing FractionsImproper Fractions Mixed Fractions

PracticeImproper Fractions Mixed Fractions

9

2 ?

9

2 4

1

2

PracticeImproper Fractions Mixed Fractions

11

4 ?

PracticeImproper Fractions Mixed Fractions

11

4 2

3

4

PracticeImproper Fractions Mixed Fractions

Lines on Drawings

The physical shape of an object is shown

• object lines

• hidden lines • center lines

Measurements are not specified with these lines.

Lines on DrawingsMeasurements are specified on the drawing by utilizing:

• extension lines• dimension lines • arrowheads• dimensions

Extension LinesExtension lines are fine, solid, straight lines that align with the features on the object to be specified.

Dimension Lines and Arrowheads

Dimension lines are fine, solid, straight lines with arrowheads. They point to extension lines, and indicate the feature on the object that is being measured.

Arrowheads are placed at the end of dimension lines to identify the referenced extension line.

DimensionsDimensions are numerical measurements of a part; written in conjunction with dimension lines.

3 12

9 1516

1 34

5 18

Practice

What type of dimension element is identified with the red oval?a)    extension lineb)    object linec)    dimension lined)    arrowhead

1 34

3 12

5 18

9 1516

Practice

What type of dimension element is identified with the red oval?a)    extension line

1 34

3 12

5 18

9 1516

Practice

What type of dimension element is identified with the red oval?a)    extension lineb)    object linec)    dimension lined)    arrowhead

1 34

3 12

5 18

9 1516

Practice

What type of dimension element is identified with the red oval?

d)    arrowhead

1 34

3 12

5 18

9 1516

Practice

What type of dimension element is identified with the red oval?a)    extension lineb)    object linec)    dimension lined)    arrowhead

1 34

3 12

5 18

9 1516

Practice

What type of dimension element is identified with the red oval?

c)    dimension line

1 34

3 12

5 18

9 1516

Reading a ruler

Rulers are typically divided by 8ths, 16ths, 32nds, and

64ths of an inch.

For this lesson we will use rulers with 8th and 16th

increments.

Reading a ruler

If the ruler does not indicate units, you will have to count

the number of lines in one inch to determine the increments.

of the ruler.

The 8 at the beginning of the ruler indicates it is

divided into 18 inch increments.

On the other edge of the ruler the inches are divided

into 116 inch increments.

Reading a ruler

The 16 at the beginning of the ruler indicates the smallest

units represented.

Reading a ruler

When reading a ruler divided in 18 inch increments, the

8 represents the denominator and the number of

units counted represents the numerator.

Reading a ruler

When reading a ruler divided in 116 inch increments, the

16 represents the denominator and the number of

units counted represents the numerator.

1 inch lines

Red lines represent whole inch increments.

They are the longest lines on the ruler.

12 inch lines

Red lines represent 12 inch increments.

They are the second longest lines.

14 inch lines

Red lines represent 14 inch increments.

They are slightly shorter than the 12 inch lines

18 inch lines

Red lines represent 18 inch increments.

Notice how the lines get shorter as the fractions get smaller.

116 inch lines

Red lines represent 116 inch increments.

X

What is the dimension represented by X above?

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

Dimension X is on the 8 side of the ruler, therefore 8 is in the denominator 8

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

8

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

Dimension X is past the 2 inch mark, but before the 3 inch mark

28

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

28

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

Dimension X is 1 increment past the whole number 2

21

8

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

4. Is dimension X in lowest terms? 21

8

Reading a ruler

X

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

4. Is dimension X in lowest terms?

Dimension X is in lowest terms.

21

8

Reading a ruler

X

What is the dimension represented by X above?

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

X

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

Dimension X is on the 8 side of the ruler, therefore 8 is in the denominator

X

8

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

X

8

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

Dimension X is past the 1 inch mark but before the 2 inch mark

X

18

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 1 inch mark?

X

18

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 1 inch mark?

Dimension X is 4 increments past the whole number 1

X

14

8

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 1 inch mark?

4. Is dimension X in lowest terms?

X

14

8

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 1 inch mark?

4. Is dimension X in lowest terms?

X

11

2No, 48 reduces to 1

2

Reading a ruler

What is the dimension represented by X above?

X

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

X

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

X

Dimension X is on the 16 side of the ruler, therefore 16 is in the denominator 16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

X

16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

X

Dimension X is past the 2 inch mark, but before the 3 inch mark

216

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

X

216

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

X

Dimension X is 13 increments past the whole number 2

213

16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

4. Is dimension X in lowest terms?

X

213

16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 2 inch mark?

4. Is dimension X in lowest terms?

X

Dimension X is in lowest terms

213

16

Reading a ruler

What is the dimension represented by X above?

X

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

X

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

X

Dimension X is on the 16 side of the ruler, therefore 16 is in the denominator 16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

X

16

Reading a ruler

316

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

X

Dimension X is past the 3 inch mark, but before the 4 inch mark

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 3 inch mark?

X

316

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 3 inch mark?

X

Dimension X is 12 increments past the whole number 2

312

16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 3 inch mark?

4. Is dimension X in lowest terms?

X

312

16

Reading a ruler

What is the dimension represented by X above?

1. What is the smallest ruler increment represented for dimension X?

2. How many whole numbers are represented in dimension X?

3. How many increments are past the 3 inch mark?

4. Is dimension X in lowest terms?

X

33

4No, 1216 reduces to 3

4

Reading a ruler

A. _______

B. _______

C. _______

Practice

D. _______

E. _______

F. _______

D. _______

E. _______

F. _______

Practice

38A. _______

B. _______

C. _______

A. _______

B. _______

C. _______

Practice

D. _______

E. _______

F. _______

38

4 14

A. _______

B. _______

C. _______

Practice

D. _______

E. _______

F. _______

38

4 14

2 14

A. _______

B. _______

C. _______

Practice

D. _______

E. _______

F. _______

38

4 14

2 14

1 916

A. _______

B. _______

C. _______

Practice

D. _______

E. _______

F. _______

38

4 14

2 14

1 916

2 12

D. _______

E. _______

F. _______

A. _______

B. _______

C. _______

Practice

38

4 14

2 14

1 916

2 12

1516