Wk 5 Algorithms

8/6/2019 Wk 5 Algorithms

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` THE ROLE OF ALGORITHMS` CHILDRENS USE AND UNDERSTANDING OF ALGORITHM IN WHOLE NUMBER

OPERATIONS` CALCULATORS AND ABACUS


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` Algorithm originates from the name of an Arab Mathematician name Al Khorizmi

` Pupils can be introduced to algorithmafter they have understand wholenumber, place value and basic facts


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` A rule for solving a problem in a certainnumber of steps.

` Every step is clearly described` They are use to solve a problem efficiently` The most familiar algorithms are the

elementary school procedures for adding,subtracting, multiplying, and dividing


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` When we teach mathematics, should we make

decisions about how students learn best?` Do we think students learn best when they areactively constructing knowledge or when theyare following routines and procedures?

` How active, or passive, do we want our studentsto be in their learning of mathematics?


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(I) LONG METHOD (WORDS)

25 = 2 TENS 5 ONES

+ 56 = 5 TENS 6 ONES7 TENS 11 ONES

= 8 TENS 1 ONES


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(II) LONG METHOD (NUMBERS)25 = 20 + 5

+ 56 = 50 + 6

70 + 11= (7 0 + ( 1 0 + 1)= (7 0 + 1 0 ) + 1= 8 0 + 1

= 81


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(III) PARTIAL SUMTENS ONES

2 5 2 5

+ 5 6 OR 5 61 1 1 17 0 7 0 8 1 8 1


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(IV) CONVENTIONAL ALGORITHM

2 5

+ 5 68 1


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I EXPANDED NOTATION METHOD (words)` The concept of subtraction can be shown using

words to identify the values in the arithmetic

problem. This method directly relates to the visualmethod and can be used as a transition to amethod using numbers


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I EXPANDED NOTATION METHOD (words)3 TENS and 5 ONES 3 5

- 1 TENS and 7 ONES -17

2 TENS and 15 ONES 18- 1 TENS and 7 ONES

1 TENS and 8 ONES


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II EQUAL ADDITION METHOD (alternate method)` A subtraction problem that requires trading can be

worked by "adding" the same value to both the

minuend and the subtrahend to avoid trading".This method only works under subtraction.


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II EQUAL ADDITION METHOD (alternate method)3 5 + 3 = 3 8 3 5

- 17 + 3 = -20 - 1718 18


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III WRITING TWO-DIGIT NUMBER ASSOMETHING PLUS A "TEEN" NUMBER

Subtract 29 from 57.57 = 50 + 7 = 4 0 + 1729 = ( -)20 + 957 - 29 = 20 + 8 = 28Notice that only 57 was put into something and

"teen" form.


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IV USING BIGGER NUMBERS.You simply have one or more extra zeroes at the

end

Subtract 1 29 from 3 213 21 = 3 00 + 20 + 1 = 3 00 + 1 0 + 11

= 200 + 11 0 + 113 21 = 200 + 11 0 + 11129 = ( -) 1 00 + 20 + 9

3 21 - 129 = 1 00 + 90 + 2 = 1 92


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I LONG MULTIPLICATION

23 95 8233

583 0 00000000 (= 2 3 ,95 8, 233 0 )

71874 699 (= 2 3 ,95 8, 233 3 0 )191665 864 (= 2 3 ,95 8, 233 8 00 )

+11 97911 65 (= 2 3 ,95 8, 233 5 ,000 )13 96 764983 90 (= 1 3 9 ,676 ,4 98, 3 90 )


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II LATTICE OR SIEVE MULTIPLICATION3 45 X 12

34 5 x0 0 0 1

3 4 5 0 0 1 2

6 8 04 1 4 0

3 45 X 12 = 414 0


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III PEASANT OR BINAR Y MULTIPLICATION Eg: 3 x 1111 3

5 6 2 121 24

---33

Describing the steps explicitly:11 and 3 are written at the top11 is halved ( 5 .5 ) and 3 is doubled ( 6 ). The fractional portion is

discarded ( 5 .5 becomes 5 ).5 is halved ( 2 .5 ) and 6 is doubled (1 2 ). The fractional portion is

discarded ( 2 .5 becomes 2 ). The figure in the left column ( 2 ) is even ,so the figure in the right column (1 2 ) is discarded.

2 is halved (1) and 1 2 is doubled ( 24). All not -scratched -out values are summed: 3 + 6 + 24 = 33 .


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I SUBTRACTION PROCEDURE15 3 = 5 3 15

-3 112-3 .. 2

9-3 .. 3

6-3 4

3

-3 . 50


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` An abacus , also called a counting frame , is a calculatingtool used primarily in parts of Asia for performing arithmeticprocesses.

` Today, abacuses are often constructed as a bamboo framewith beads sliding on wires

` Originally they were beans or stones moved in grooves insand or on tablets of wood, stone, or metal.

` The abacus was in use centuries before the adoption of thewritten modern numeral system and is still widely used bymerchants, traders and clerks in Asia , Africa , andelsewhere.

` The user of an abacus is called an abacist; he or she slidesthe beads of the abacus by hand. [2]


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Wk 5 Algorithms