Reading-a-Ruler by xiaopangnv

VIEWS: 14 PAGES: 122

									Reading Dimensions Using a
      Standard Ruler
 Todd Andrus                 TEE 4400
 Landon Ashcroft   Dr. Gary Stewardson
 Zac Hirschi                  Fall 2011
 Brad Parker
 Jared Thomas
 Joseph 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      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:     0 1 2 3 4 5…



Mixed Fractions:
            Types of
        Numbers & Fractions

Whole Numbers:     0 1 2 3 4 5…


                       3 1 1
Mixed Fractions:    3    1 9 ...
                      16 8 4
           Types of Fractions

Proper Fractions:
           Types of Fractions

                    5   1    9
Proper Fractions:              ...
                    8   4   16
           Types of Fractions

                      5   1    9
Proper Fractions:                ...
                      8   4   16

Improper Fractions:
           Types of Fractions

                      5    1    9
Proper Fractions:                 ...
                      8    4   16

                      18   9    6
Improper Fractions:               ...
                      16   8    4
Reducing Fractions



    8
      ?
   16
                  Reducing Fractions



                          8
                            ?
What is the largest
                         16
whole number that will
divide into both the
numerator and
denominator?
Reducing Fractions



    8 1 8


      
         8




   16   2
        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  312


      
          4




   16   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              Lowest Terms



  10
                          ?
  16
           Practice
Fraction              Lowest Terms



  10                        5
              
  16                        8
           Practice
Fraction              Lowest Terms



   36
                           ?
   64
           Practice
Fraction              Lowest Terms



   36                         9
              
   64                        16
        Reducing Fractions
Improper Fractions       Mixed Fractions


11
                             ?
4
        Reducing Fractions
Improper Fractions                Mixed Fractions


11
                                      ?
4            How many times
             will 4 go into 11,
             and what is the
             remainder?
        Reducing Fractions
Improper Fractions       Mixed Fractions


11
                                 2
4                        4 goes into 11 two times.
        Reducing Fractions
Improper Fractions        Mixed Fractions


11                                            3
                         3 is the remainder
                         and goes in the




                     
                         numerator



                                     2
4
        Reducing Fractions
Improper Fractions       Mixed Fractions

11                                   3
                                  2
 4                                   4
                         4 stays in the
                         denominator
        Reducing Fractions
Improper Fractions       Mixed Fractions


19
                              ?
16
        Reducing Fractions
Improper Fractions                 Mixed Fractions


19
                                        ?
16           How many times
             will 16 go into 19,
             and what is the
             remainder?
        Reducing Fractions
Improper Fractions       Mixed Fractions


19
                                   1
16                       16 goes into 19 one time.
        Reducing Fractions
Improper Fractions        Mixed Fractions


19                                            3
                         3 is the remainder
                         and goes in the




                     
                         numerator



                                      1
16
        Reducing Fractions
Improper Fractions       Mixed Fractions


19                                    3
                                  1
16                                   16
                         16 stays in the
                         denominator
                Practice
Improper Fractions         Mixed Fractions


  9
                              ?
  2
                Practice
Improper Fractions         Mixed Fractions


  9                              1
                              4
  2                              2
                Practice
Improper Fractions         Mixed Fractions


11
                               ?
4
                Practice
Improper Fractions         Mixed Fractions


11                                3
                               2
 4                                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.




                     14
                      3

                          31
                           2
                               51
                                8
                                    9 15
                                      16
          Practice



14
 3

     31
      2
          51
           8
               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



14
 3

     31
      2
          51
           8
               9 15
                 16

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



14
 3

     31
      2
          51
           8
               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



14
 3

     31
      2
          51
           8
               9 15
                 16

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



d) arrowhead
          Practice



14
 3

     31
      2
          51
           8
               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



14
 3

     31
      2
          51
           8
               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 inch increments, the
                                8

8 represents the denominator and the number of
units counted represents the numerator.
               Reading a ruler
When reading a ruler divided in 16 inch increments, the
                                 1


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   1
                      2   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   1
                      8   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



                                                                            8
                                                  side of the ruler,
                                                  therefore 8 is in the
                                                  denominator
                      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    2
                                                                           8
                                          3 inch mark
                      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?



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




                                                                           8
                      Reading a ruler
             X




What is the dimension represented by X above?



                                                                         1
1. What is the smallest ruler increment represented for dimension X?
2. How many whole numbers are represented in dimension X?



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

                                                 Dimension X is 1



                                                                         8
                                                 increment past the
                                                 whole number 2
                      Reading a ruler
             X




What is the dimension represented by X above?



                                                                         1
1. What is the smallest ruler increment represented for dimension X?
2. How many whole numbers are represented in dimension X?



                                                                       2
3. How many increments are past the 2 inch mark?
4. Is dimension X in lowest terms?



                                                                         8
                      Reading a ruler
             X




What is the dimension represented by X above?



                                                                         1
1. What is the smallest ruler increment represented for dimension X?
2. How many whole numbers are represented in dimension X?



                                                                       2
3. How many increments are past the 2 inch mark?
4. Is dimension X in lowest terms?



                                                                         8
                                            Dimension X is in
                                            lowest terms.
                     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?




                                                                            8
                                                  Dimension X is on the 8
                                                  side of the ruler,
                                                  therefore 8 is in the
                                                  denominator
                      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
                                                                         1
                                                                             8
                                             2 inch mark
                      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?



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




                                                                           8
                      Reading a ruler
         X




What is the dimension represented by X above?



                                                                           4
1. What is the smallest ruler increment represented for dimension X?
2. How many whole numbers are represented in dimension X?



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

                                                   Dimension X is 4



                                                                           8
                                                   increments past the
                                                   whole number 1
                      Reading a ruler
         X




What is the dimension represented by X above?



                                                                         4
1. What is the smallest ruler increment represented for dimension X?
2. How many whole numbers are represented in dimension X?



                                                                       1
3. How many increments are past the 1 inch mark?
4. Is dimension X in lowest terms?



                                                                         8
                      Reading a ruler
         X




What is the dimension represented by X above?



                                                                              1
1. What is the smallest ruler increment represented for dimension X?
2. How many whole numbers are represented in dimension X?



                                                                            1
3. How many increments are past the 1 inch mark?
4. Is dimension X in lowest terms?

                                                 No,   4
                                                       8   reduces to   1
                                                                        2

                                                                              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?




                                                                           16
                                                  Dimension X is on the
                                                  16 side of the ruler,
                                                  therefore 16 is in the
                                                  denominator
                      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
                                                                       2
                                                                           16
                                        inch mark, but before the
                                        3 inch mark
                      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?



                                                                         13
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          2
                                                                         16
                                            increments past the
                                            whole number 2
                      Reading a ruler



                  X
What is the dimension represented by X above?



                                                                         13
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?
                                                                       2
                                                                         16
                      Reading a ruler



                  X
What is the dimension represented by X above?



                                                                         13
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?
                                                                       2
                                                                         16
                                            Dimension X is in
                                            lowest terms
                     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?




                                                                           16
                                                  Dimension X is on the
                                                  16 side of the ruler,
                                                  therefore 16 is in the
                                                  denominator
                      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
                                                                       3
                                                                           16
                                     inch mark, but before the 4
                                     inch mark
                      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?



                                                                         12
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
                                         Dimension X is 12
                                         increments past the
                                         whole number 2
                      Reading a ruler



                        X
What is the dimension represented by X above?



                                                                         12
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?
                                                                       3
                                                                         16
                      Reading a ruler



                        X
What is the dimension represented by X above?



                                                                          3
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?
                                                                        3
                                            No,   12
                                                  16   reduces to   3
                                                                    4
                                                                          4
                Practice




A. _______   D. _______

B. _______   E. _______

C. _______   F. _______
                Practice




      3
      8
A. _______   D. _______

B. _______   E. _______

C. _______   F. _______
                  Practice




        3
A.      8
     _______   D. _______
     414
B. _______     E. _______

C. _______     F. _______
                Practice




      3
      8
A. _______   D. _______
     414
B. _______   E. _______
    214
C. _______   F. _______
                Practice




      3
      8
A. _______       1  9
                   16
             D. _______
     414
B. _______   E. _______
    214
C. _______   F. _______
                Practice




      3
      8
A. _______        1 16
                     9
             D. _______
     414
B. _______
                  212
             E. _______
    214
C. _______   F. _______
                Practice




      3
      8
A. _______       1  9
                   16
             D. _______
     414
B. _______
                  212
             E. _______
    214
C. _______
                  15
                  16
             F. _______

								
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