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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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