Download Reading Dimensions Using a Standard Ruler

Reading Dimensions Using a
Standard Ruler
Todd Andrus
Landon Ashcroft
Zac Hirschi
Brad Parker
Jared Thomas
Joseph Woodard
TEE 4400
Dr. Gary Stewardson
Fall 2011
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
3
4
Denominator
Types of
Numbers & Fractions
Whole Numbers:
Types of
Numbers & Fractions
Whole Numbers:
0 1 2 3 4 5…
Types of
Numbers & Fractions
Whole Numbers:
Mixed Fractions:
0 1 2 3 4 5…
Types of
Numbers & Fractions
Whole Numbers:
Mixed Fractions:
0 1 2 3 4 5…
3 1 1
3
1 9 ...
16 8 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:
5
8
Improper Fractions:
18
16
1
4
9
8
9
...
16
6
...
4
Reducing Fractions
8
?
16
Reducing Fractions
What is the largest
whole number that will
divide into both the
numerator and
denominator?
8
?
16
Reducing Fractions
8 1


16 2
8
8
16
8
Reducing Fractions
8 1

16 2
Reducing Fractions
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.
8
?
16
This only works with fractions that have an even denominator.
Reducing Fractions
8
?
16
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
8 4

16 8
Reducing Fractions
8 4
 ?
16 8
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
8 4 2
 
16 8 4
Reducing Fractions
8 4 2
  ?
16 8 4
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
8 4 2 1
  
16 8 4 2
Reducing Fractions
8 4 2 1
  
16 8 4 2
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
8 1

16 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  3


16 4
12
4
16
4
Reducing Fractions
12 3

16 4
Reducing Fractions
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.
12
?
16
Remember, this only works with fractions that have an even
denominator.
Reducing Fractions
12
?
16
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
12 6

16 8
Reducing Fractions
12 6
 ?
16 8
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
12 6 3
 
16 8 4
Reducing Fractions
12 6 3
  ?
16 8 4
Can both numerator
and denominator be
divided evenly by 2?
Reducing Fractions
12 3

16 4
Practice
Fraction
10
16
Lowest Terms

?
Practice
Fraction
10
16
Lowest Terms

5
8
Practice
Fraction
36
64
Lowest Terms

?
Practice
Fraction
36
64
Lowest Terms

9
16
Reducing Fractions
Improper Fractions
11
4
Mixed Fractions

?
Reducing Fractions
Improper Fractions
11
4
Mixed Fractions

How many times
will 4 go into 11,
and what is the
remainder?
?
Reducing Fractions
Improper Fractions
11
4
Mixed Fractions

2
4 goes into 11 two times.
Reducing Fractions
Improper Fractions
11
4
Mixed Fractions

3 is the remainder
and goes in the
numerator
2
3
Reducing Fractions
Improper Fractions
11
4
Mixed Fractions

3
2
4
4 stays in the
denominator
Reducing Fractions
Improper Fractions
19
16
Mixed Fractions

?
Reducing Fractions
Improper Fractions
19
16
Mixed Fractions

How many times
will 16 go into 19,
and what is the
remainder?
?
Reducing Fractions
Improper Fractions
19
16
Mixed Fractions

1
16 goes into 19 one time.
Reducing Fractions
Improper Fractions
19
16
Mixed Fractions

3 is the remainder
and goes in the
numerator
1
3
Reducing Fractions
Improper Fractions
19
16
Mixed Fractions

3
1
16
16 stays in the
denominator
Practice
Improper Fractions
9
2
Mixed Fractions

?
Practice
Improper Fractions
9
2
Mixed Fractions

1
4
2
Practice
Improper Fractions
11
4
Mixed Fractions

?
Practice
Improper Fractions
11
4
Mixed Fractions

3
2
4
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 Drawings
Measurements are specified on the drawing by
utilizing:
•
•
•
•
extension lines
dimension lines
arrowheads
dimensions
Extension Lines
Extension 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.
Dimensions
Dimensions are numerical measurements of a part;
written in conjunction with dimension lines.
1 43
3 12
5 18
9 15
16
Practice
1 43
3 12
5 18
9 15
16
What type of dimension element is
identified with the red oval?
a) extension line
b) object line
c) dimension line
d) arrowhead
Practice
1 43
3 12
5 18
9 15
16
What type of dimension element is
identified with the red oval?
a) extension line
Practice
1 43
3 12
5 18
9 15
16
What type of dimension element is
identified with the red oval?
a) extension line
b) object line
c) dimension line
d) arrowhead
Practice
1 43
3 12
5 18
9 15
16
What type of dimension element is
identified with the red oval?
d)
arrowhead
Practice
1 43
3 12
5 18
9 15
16
What type of dimension element is
identified with the red oval?
a) extension line
b) object line
c) dimension line
d) arrowhead
Practice
1 43
3 12
5 18
9 15
16
What type of dimension element is
identified with the red oval?
c) dimension line
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
The 8 at the beginning of the ruler indicates it is
divided into
1
8
inch increments.
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.
Reading a ruler
On the other edge of the ruler the inches are divided
into
1
16
inch increments.
The 16 at the beginning of the ruler indicates the smallest
units represented.
Reading a ruler
When reading a ruler divided in
1
8
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
1
16
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.
1
2
inch lines
Red lines represent 12 inch increments.
They are the second longest lines.
1
4
inch lines
Red lines represent
1
4
inch increments.
They are slightly shorter than the
1
2
inch lines
1
8
inch lines
Red lines represent 18 inch increments.
Notice how the lines get shorter as the fractions get smaller.
1
16
inch lines
Red lines represent
1
16
inch increments.
Reading a ruler
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
2
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?
2
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?
Dimension X is 1
increment past the
whole number 2
1
2
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?
1
2
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.
1
2
8
Reading a ruler
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 1
inch mark but before the
2 inch mark
1
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 1 inch mark?
1
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 1 inch mark?
Dimension X is 4
increments past the
whole number 1
4
1
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 1 inch mark?
4. Is dimension X in lowest terms?
4
1
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 1 inch mark?
4. Is dimension X in lowest terms?
No,
4
8
reduces to
1
2
1
1
2
Reading a ruler
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
16 side of the ruler,
therefore 16 is in the
denominator
16
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?
16
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
2
16
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?
2
16
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 13
increments past the
whole number 2
13
2
16
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?
13
2
16
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
13
2
16
Reading a ruler
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
16 side of the ruler,
therefore 16 is in the
denominator
16
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?
16
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 3
inch mark, but before the 4
inch mark
3
16
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 3 inch mark?
3
16
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 3 inch mark?
Dimension X is 12
increments past the
whole number 2
12
3
16
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 3 inch mark?
4. Is dimension X in lowest terms?
12
3
16
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 3 inch mark?
4. Is dimension X in lowest terms?
No,
12
16
reduces to
3
4
3
3
4
Practice
A. _______
D. _______
B. _______
E. _______
C. _______
F. _______
Practice
3
8
A. _______
D. _______
B. _______
E. _______
C. _______
F. _______
Practice
3
8
A. _______
D. _______
1
4
B. _______
4
E. _______
C. _______
F. _______
Practice
3
8
A. _______
D. _______
1
4
4
B. _______
E. _______
1
2
4
C. _______
F. _______
Practice
3
8
A. _______
9
1
16
D. _______
1
4
4
B. _______
E. _______
1
2
4
C. _______
F. _______
Practice
1
3
8
A. _______
9
16
D. _______
1
4
4
B. _______
1
2
E. _______
1
2
4
C. _______
F. _______
2
Practice
1
3
8
A. _______
9
16
D. _______
1
4
4
B. _______
1
2
2
E. _______
1
2
4
C. _______
15
16
F. _______