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What is the advantage of using the partialsums algorythm? 

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The advantage of this method, for students who have difficulty with the traditional algorithm, is that mental regrouping is not required; all the partial sums are recorded separately before being combined.
Also, the method yields a correct sum whether the partial sums begin with the ones or the leftmost column. Lefttoright addition (see figs. 1b and 


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What is an advantage of the scratch method for addition? 

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Students saw an advantage in recording the partial sums, which does not require them to carry numbers mentally. Also, this algorithm appeals to students’ desire to work quickly because, as the examples show, they do not have to record all the complete partial sums. 


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Equal Additions Method of Subtraction 

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[image]
In figure 4, instead of a ten being taken from the 6 tens, as would be done in the traditional algorithm, a ten is added to the 5 ones to give 15 ones. To compensate, 1 ten is added to the subtrahend, resulting in 8 tens. The 9 ones are then subtracted from the 15 ones. The next step is to add 10 tens to the 6 tens in the minuend so that 8 tens can be subtracted. To compensate, 1 hundred is added to the 8 hundreds, yielding 9 hundreds. The amount of 8 tens is then subtracted from 16 tens. Next, 10 hundredsadded to the 4 hundreds results in 14 hundreds; to compensate, 1 thousand is added to the subtrahend. Then 9 hundreds can be subtracted from 14 hundreds, and 2 thousand is subtracted from 5 thousand. 


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What is an advantage of using the Equal Additions Method of Subtraction? 

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The main advantage of this procedure is that it does not rely on one’s skill in regrouping but on a knowledge of individual addition and subtraction facts. Equal additions is an interesting optional method for relating subtraction to addition. 


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[image]
Lowstress subtraction involves renaming the minuend and writing it between the original minuend and the subtrahend before subtracting individual digits (Hutchings 1975). In figure 5, 6 tens are renamed as 5 tens and 10 ones; the 10 ones are regrouped with the 5 ones to make 15 ones. Next, because 7 tens cannot be subtracted from 5 tens, 4 hundreds is renamed as 3 hundreds and 10 tens; the 10 tens are regrouped with the 5 tens to make 15 tens. This process continues until the minuend is rewritten so that no impasses to subtraction remain and the problem is ready to be completed. 


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Partial products algorythm 

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What is an advantage of using the partial products algorythm? 

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The partialproducts method does not require simultaneous regrouping of addition with multiplication. Teachers can easily assess multiplication facts that students consistently miss by examining partial products before they are renamed and added. 


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Stacking Algorythm for division 

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BREAK APART NUMBERS STRATEGY 

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EXAMPLE: 456 + 20 = (400 + 50 +20 +6) 470 + 6
476
455 + 10 + 10
455 + 10 = 465
465 + 10 = 475
475 + 1 = 476
237 + 43
237 + 10 + 10 + 10 + 10 + 1 + 1 +1
247, 257, 267, 277, 278, 279, 280 

