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Alternative Algorithms
EXAM 2
15
Mathematics
12/08/2010

Additional Mathematics Flashcards

 


 

Cards

Term
ARTICLE
Definition
Term
Partial Sums Algorithm
Definition

 

[image]

Term
What is the advantage of using the partial-sums algorythm?
Definition

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 left-most column.
Left-to-right addition (see figs. 1b and

Term
Scratch Method
Definition
[image]
Term
What is an advantage of the scratch method for addition?
Definition
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.
Term
Equal Additions Method of Subtraction
Definition

[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.

Term
What is an advantage of using the Equal Additions Method of Subtraction?
Definition
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.
Term
Low stress Subtraction
Definition

[image]

 

Low-stress 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.

Term
Partial products algorythm
Definition
[image]
Term
What is an advantage of using the partial products algorythm?
Definition
The partial-products 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.
Term
Lattice Multiplication
Definition
[image]
Term
Stacking Algorythm for division
Definition
[image]
Term
NOTES
Definition
Term
BREAK APART NUMBERS STRATEGY
Definition
  • Based on place value

EXAMPLE: 456 + 20 =
(400 + 50 +20 +6)
470 + 6

476

 

  • Count bys

455 + 10 + 10

455 + 10 = 465

465 + 10 = 475

475 + 1 = 476

 

  • Count on

237 + 43

237 + 10 + 10 + 10 + 10 + 1 + 1 +1

247, 257, 267, 277, 278, 279, 280

Term
Definition