the odd and even numbers (interactive slide presentation)

For e-classroom, students love to do some manipulation with the mouse clicks, select their choices creating independent decisions, discovery and sometimes for fun while learning some ideas and basic concepts especially in math that strengthen the foundations in math.
please check my sample interactive presentation

http://www.slideshare.net/PepitoDalupe/the-odd-and-even-numbers-interactive-slide-project?qid=cc73d819-22dd-4e9a-9a09-570ddbed8bc4&v=&b=&from_search=1

the presentation provides the characteristics of odd and even numbers to click with the mouse. upon knowing the terms the learners may do the start game. it has the automated response to the numbers clicked if it is correct or wrong. its for fun and learning.

how to draw a regular polygon decagon using the 360 degrees protractor

Materials: one coupon bond, eraser, pencil, crayons, ruler and 360 degrees protractor
1. Place the 360 degrees protractor on the piece of paper 0 degree parallel to x- axis.

2. Mark the following degree measures: 0 degree, 36 degrees, 72 degrees, 108 degrees, 

    144 degrees, 180 degrees,  216 degrees, 252 degrees, 288 degrees,  and 324 degrees.

 



3. Remove the 360 degrees protractor.

 





4. Connect the points.

 

  

5. Color and label the polygon. Now you have a regular polygon decagon!



 

 

how to draw a regular polygon nonagon using 360 degrees protractor

Materials: one coupon bond, pencil, eraser, crayons, ruler, and 360 degrees protractor
 1. Place the 360 degrees protractor on the piece of paper where 0 degree is parallel to x- axis.

2. Mark the following degree measures: 0 degree, 40 degrees, 80 degrees, 120 degrees,

     160 degrees,  200 degrees, 240 degrees, 280 degrees, 320 degrees.

 



 

3. Remove the 360 degrees protractor.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4. Connect the points and color the polygon. Now you have a nonagon!

 

 

 

 

 





 

how to draw a regular polygon octagon using 360 degrees protractor

Materials: one piece of coupon, ruler, pencil, crayons, 360 degrees protractor
1. Place the 360 degrees protractor on the paper, 0 degree parallel  to the x- axis.

2.  Mark the following degree measures 0 degree, 45 degrees, 90 degrees, 135 degrees, 

     180 degrees, 225 degrees, 270 degrees,  315 degrees

 

 





 

 

 

3. Remove the 360 degrees protractor and connect the points. Color the regular

    polygon you made. Now! you have just made a regular polygon octagon.

 

 





 

 

how to draw a regular polygon heptagon using 360 degrees protractor

Materials: 1 ruler, crayons, pencil, eraser, one piece of coupon, 360 degrees protractor
1. Place the 360 degrees protractor on the piece of paper. The 0 degree parallel to x- axis.

2. Mark the following degree measures  0 degree, 51.43 degrees, 102.86 degrees, 154. 29

    degrees, 205.72 degrees, 257.15 degrees and 308.58 degrees. Remove the 360 degrees

    protractor and connect the points. Color and label the regular polygon. Now you have a

    regular polygon heptagon. 

 

 

 

 

 

 

 



how to draw a regular polygon hexagon using 360 degrees protractor

Materials: 1 piece of coupon, ruler, eraser, pencil, crayons, 360 degrees protractor
1. Place the 360 degrees protractor on the paper , the 0 degrees must be parallel to
     the x- axis.
 

 



 

2. Mark the degree measure 0 degree, 60 degrees, 120 degrees, 180 degrees, 240 degrees,

   and 300 degrees

3. Remove the 360 degrees protractor and connect the points. Color the polygon.
    Now you have the regular polygon hexagon.

 

how to make a regular polygon pentagon using 360 degrees protractor

Materials: one coupon, eraser, pencil, ruler, crayons, 360 degrees protractor
1. Place the 360 degrees protractor on the piece of coupon, Set the protractor 0 degrees parallel
    y axis

2.   Mark the following degree measures 0 degree, 72 degrees, 144 degrees, 216 degrees,
      and 288 degrees.

3. Remove the 360 degrees protractor and connect the points. Color with crayons and
    label the polygon. Now you have the regular polygon  pentagon.

 

how to draw a regular polygon quadrilateral using 360 degrees protractor

Materials: piece of coupon, ruler, eraser, 360 degrees protractor, crayons, pencil
1. Position the 360 degrees protractor 0 degree parallel to x- axis.

2. Mark the following degree measures 45degrees, 135 degrees, 225 degrees, and
   315 degrees. see the figure below:

3. Remove the protractor and connect the points. Color the polygon and the background.
     Now it's a quadrilateral





 
 



how to draw a regular polygon triangle using 360 degrees protractor

Materials:   paper, ruler, pencil, 360 degrees protractor, eraser and crayons.

1. place the 360 degrees protractor on the paper. the 0 degrees above the y- axis.

2. Mark the following degree measure 0 degree, 120 degrees and 240 degrees
    as shown in the figure below.

 

3. Remove the protractor and connect the points and color  . Now,  it's a triangle

 

how to divide fractions

Observe the fractions from division mathematical operation and changed to multiplication process.

 

 

 

 

 It can also be factored as seen in the second column then easily eliminating common factors from numerator and denominator.  

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how to find the common ratio of geometric sequence

A sequence is geometric sequence if the sequence reveals a common ratio.  To get the common ratio divide the 2nd term with the first term or  the 3rd term with the 2nd term,  ....:
Examples of sequences
1. 1, 5, 25, 125....
    5  =   5            the common the ratio is 5    indicated as     r= 5    the ratios were all checked
    1                     ( don't  jump to conclusion if  only one ratio is tested..)    

     25 = 5 
      5

      125 =5
       25

  2. 100, 50, 25, 5......
        50  =   1                r= 1
       100      2                     2

        25   =   1
        50        2

        5      =   1
       25          2  

  

In # 3 the common ratio of the geometric sequence  , r= 1/2
        
Practice Test
Find the common ratio of the following geometric sequences
1.   1, 4, 16, 64 ...
2.   1/2, 1, 2, 4,....
3.   500, 250, 125, ....
4    1/9, 1, 9, 81,...
5.  -5, 25, - 125,....
6.   1/3, 1/9, 1/27, . . .

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how to multiply fraction and fraction, improper fraction, whole number, mixed numbers etc.

To multiply fraction and fraction


To multiply fraction and fraction

To multiply fraction and whole number

To multiply fraction and improper fraction

To multiply fraction and mixed number

To multiply 2 mixed numbers

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how to add fraction and whole number, improper fraction, mixed numbers

Addition of fraction and whole numbers
Examples:
1. 1/3 + 5 = 5 1/3
2. 4/6 + 12 = 12 4/6   or 12 2/3

Addition of fraction and improper fraction
Pre requisite : how to add fractions with different denominators
Examples:
1. 2/5 + 9/4 =

    2(4)  + 9 (5)   =
    5(4)      4(5)

      8   + 45       = 
      20    20     

        53    or 2 13/20
        20

2.    5/7 + 6/5 =

       5(5) + 6(7)  =
       7(5)    5(7)

         25   +  42    =
         35       35 

         67     or  1 32/35
         35



Addition of fraction and mixed numbers
Examples:
1. 4/9 + 3 1/4 =

     4/9 +  13/4                      3  1/4 = (4)(3)+1 =13/4   changed to improper fraction

      4(4)  + 13 (9) =
     9(4)        4(9)

      16     +   117  =
      36           36

      133    or  3 25/36
       36
Addition of mixed numbers and mixed numbers

2.  2 2/3  + 4 1/5  =       both mixed numbers

     8/3   +  21/5   =           changed to improper fractions

     8(5)   + 21(3)  =
     3(5)       5(3)

      40    +   63  =
      15         15

      103  or   6  13/15
       15  

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how to divide integers

To divide integers with like signs, divide the integers and quotient is always positive.

Examples:
1. (-20)/(-5) = 4      positive quotient
2. (100)/(10) = 10   positive quotient

To divide integers with unlike signs, the quotient is always negative

Examples:
1. (-36)/ (6) = -6   negative quotient
2. (81)/ (-9) = -9  negative quotient

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how to find the common difference in arithmetic sequence

Pre requisite : how to add of integers, how to subtract  integers
To get the common difference in arithmetic sequence, subtract  the 2nd term to the first term, or  3rd term to 2nd term.....
Examples
1. 2, 4, 6, 8,....
    4 - 2 = 2      so the common difference is 2.. upon evaluating 6-(4), 8-(6), ....    will reveal
                        a common difference of 2 
6-(4)=
(6) +(-4) = 2

8-(6)=
8+(-6) =   2
                       knowing the common difference will give the discovery of succeeding pattern are
                        arithmetic sequence.
                       common difference is used in generating the next pattern as
                       2 + 2 = 4,  4+2 = 6,   6 + 2 = 8       so the arithmetic sequence is 2, 4, 6, 8 ......
                   

        

2. 12, 6, 0, -6, -12....
    (6)-(12) =
     (6) + (-12) = -6    so the common difference  is -6 upon evaluating 0 -(6), (-6)-(0), (-12)-(-6)...
                          will reveal a common difference of -6.
                          exposing....
     0 - (6)=
     0 +(-6)= -6    difference

     (-6)-(0) =
     (-6) + 0  = -6  difference

     (-12) - (-6)=
     (-12) + (6) = -6   difference     therefore the common difference is -6




Exercises:  Find the difference of the following arithmetic sequence.
1. 5, 10, 15, 20, .......
2. 3, 6 , 9, 12, .......
3. 100, 75, 50, 25, ....
4. 1/2, 1, 3/2, 4/2,.....
5. -4, -1, 2, .....
6. 3, 0, -3, -6, .....     







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how to multiply integers

To multiply integers with like signs, the multiply the factors and the product is always positive
 Examples
1. (-5) (-4) = 20
2. (9 ) (2)  = 18    
To multiply integers with unlike signs, the multiply the factors and the product is always negative.
Examples:
1. (-12) (2) = -24
2. (15) (-3) = -45

To multiply multiple products
Examples
1. (2) (-2) (1) = (-4) (1) = -4
2. ( -1) (1) (1) (-2) = (-1) (-2) = 2
3. (1) (2) (-3) (1) (-1) = (2)(-3) (-1) = (-6) (-1) = 6
                                   or
                                   =(2) (3) = 6

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The Odd and Even Numbers

     A  Math IQ test  was given to a 67  applicants of  AZ Security Agency . From the numbers 1, 2, 3, 4, 5, 6, up 100    identify the numbers that are  even and the odd numbers.
      
Name:________________                  Position Applied:_______________
                         
Part I                               Odd                                    Even
                          _______________                 ______________
                          _______________                 ______________
                         ________________                ______________

                        (100 pts.)

Part II   Why are  odd and even  words  appropriate  for its names?(Hint: count the
              letters )   (20 pts.)  

Part III   The total applicants are 67 , find sum of the given two digits? And  identify the sum if
               odd or even.  (20 pts.)
-------------------------------------------------------------------------------------------------------
The questions may become difficult if odd and even numbers could not be identified.


So odd numbers are whole numbers that are not divisible by 2 or can not  be divided exactly by 2
examples
1. 1, 3, 5, 7, 9, 11, ......
While even numbers are whole numbers that are divisible by 2 or can be divided by 2 exactly without remainder.
examples
2, 4, 6, 8, 10, 12,........ it is  multiple of 2

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how to subtract integers

to subtract the two integers , change the sign of the subtrahend and proceed to the law of addition of integers.
Examples
1. (-9) - (5)
    (-9) + (-5)  = -14    change the sign of the subtrahend integer and proceed to the law of
                                   addition of integers   ( see addition of integers with like signs)

2. (20) - (-45)
    (20) + (45)  =  65    change the sign of the subtrahend integer and proceed to the law of
                                   addition of integers   ( see addition of integers with like signs)     

3. (20) - (45)
    (20) +(-45)  =  -25 change the sign of the subtrahend integer and proceed to the law of
                                   addition of integers   ( see addition of integers with unlike signs)
4. (-55)- (-40)
    (-55) + (40)  = -15 change the sign of the subtrahend integer and proceed to the law of
                                   addition of integers   ( see addition of integers with like signs)
to be continued.....
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how to add of integers

Integers are  signed numbers which consists of positive numbers, negative numbers and zero.
To add integers it is grouped into two 1) addition of integers with the same signs  2)  addition of integers with unlike signs.

Addition integers with like signs
get the sum of the integers and affix the common sign
examples
1.   (-2) + (-12)  =   -14             the common of both integers is negative since -2 and -12 , upon
                                                  getting the sum or total affix the common which is negative before
                                                  the number.
2.     15  +  25    =  40                both numbers are positive so the common sign is positive.
                                                   if no sign is indicated in the answer it's positive.
3.     (-5)  + (-4)  + (-7) =   -16   getting the sum of integers the affix the common sign which is
                                                   negative before the number.

Addition of integers with unlike signs
Subtract from highest integer absolute value to the smaller integer absolute value and affix the sign
of integer with greatest absolute value to the answer.

Examples:
1. (-12) +  9    =    -3              the absolute value  /-12/ = 12   while /9/= 9   so 12- 9 = 3 then affix
                                               the sign of higher integer absolute value to the answer


2.  20 +  (-15) =   5                 the absolute value of /20/ = 20 while /-15/ = 15 so 20-15 = 5  then
                                                affix sign of  higher integer absolute value to the answer.

Visual examples:





1. (-4) + (-6 )    two groups of negative hexagons
                          combined together indicated by plus sign

 

                                                                      
  the negative pentagon                                                 arranging for easy counting,

   into one group                                                           the sum of negative pentagon is -10

 



2.  5 + 3                  the two groups of positive stars

                                to be combined together 


        

     grouping together                                                        arranging and counting, 8 positive stars

                                                                            






        3.    4 + (-5)     4 green positive chips combined with 5 yellow
                                 negative chips

                                       

arranging and eliminating pairs of positive and negative chips
so the remaining chips is only one  negative yellow.

in real life situation it may be a group of singles, then married
so eliminated to singleness. the only remaining single is one
female  if + is male .

                                                      if yellow chips are amount to be paid with + signs. the remaining
                                                      one negative. so still in debt for one chip.
to be continued....
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