Reading Dimensions Using a Standard Ruler
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Transcript of Reading Dimensions Using a Standard Ruler
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
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38
4 14
A. _______
B. _______
C. _______
Practice
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E. _______
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38
4 14
2 14
A. _______
B. _______
C. _______
Practice
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38
4 14
2 14
1 916
A. _______
B. _______
C. _______
Practice
D. _______
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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