ALGORITHMS
AN
ALGORITHM FOR
CALCULATION
IS A STEP‑BY‑STEP
PROCEDURE
THAT BREAKS BIG
PROBLEMS
INTO SMALL STEPS
AND,
IF FOLLOWED PROPERLY,
ALWAYS
WORKS.
A
GOOD ALGORITHM IS CLEAR,
COMPLETE,
EFFICIENT,
UNAMBIGUOUS,
AND RELIABLE.
This method starts from left to right, in the same manner as we teach children to read. As we move from left to right, each place value is acknowledged by its real value ‑ the 4 in the first number is 400, not 4, etc.. Students should be encouraged to use mental math skills to compute the final answer.
In an addition problem, if you add a
number to one addend and subtract the same number from the other addend, the sum
in the new problem is the same as the sum in the problem you started with. The
goal is to make one of the addends end in zero, because it is easy to add
numbers that end in zero to other numbers.
Like
Partial Sums, this method starts from left to right, acknowledging each place
value along the way. When students have written the answers for each part, they
should be encouraged to use mental math skills to compute the final
answer.
In
a subtraction problem, if you add the same number to both numbers in the
problem, the answer to the new problem is the same as the answer to the problem
you started with. This will also work if you subtract the same number from both
numbers in the problem. The goal is to change the second number so that it ends
in a zero, which differs from the Opposite‑Change Method in addition where
either number could be changed so that it ended in a zero.
In
the Add‑Up Method, start with the subtrahend (bottom number) and add up until
you reach the minuend (top number).
In
Lattice Multiplication, students first will design a lattice box. The boxes will
either be square or rectangle, depending on the numbers being multiplied. A
two‑digit times two‑digit problem will look like a square box and a three‑digit
by two‑digit problem will need a rectangular box. Students then "weave" by
multiplying each number on the side by each number on the top. Then, each number
Inside the diagonals Is added and recorded at the bottom of the
diagonal.
The
Lattice Method can be used to multiply decimals. Simply find the intersection of
the decimal points along the horizontal and vertical lines; then slide it down
Its diagonal.
Like
Partial Sums and Partial Differences, Partial Products has students dealing with
place value of numbers as they multiply. The problem is broken up into a series
of smaller multiplication problems that students can easily do using mental
math. Every number at the top gets multiplied by every number on the bottom, and
then the results from each are added to find the product.
The
Area Model looks similar to Lattice and Partial products in that a box is used
(Lattice) and each number is broken into the place value representation (Partial
Products). After each of the numbers is multiplied, the results are added
together to get the product.
This
algorithm for multiplication developed by the Egyptians over 4000 years ago
eliminates the need for all multiplication facts except for the "2s°. The idea
of doubling, which students find easy and fun, is used repeatedly. This
algorithm was used well into the Middle Ages.
LOW STRESS DIVISION
In
this division model, we begin by thinking In terms of multiples
of
10, which Is easy for kids to think about. Students am seeking the answer to how
many 12s are In 158, by first thinking are there ten 12s In 158? After
subtracting, they continue to ask am there ten 12s In 38? Since the answer Is
no, they move on to a number which Is less than 10. Some students who know some
extended basic facts will be able to determine that there am three 12s In 38,
while others can comfortably take out one 12 at a time. Either way, the same
result Is obtained.