Unlike the stand algorithm, which begins with a person multiplying the digit in the one’s place of the multiplier with the digit in the one’s place of the multiplicand, the efficient algorithm begins with students multiplying the digit in the farthest left place value of the multiplier with the digit in the farthest left in the multiplicand. It
continues to multiply the left most digit of the multiplier by each additional place value of the multiplicand – working left to right. To prevent confusion, we have created a dot method that helps students establish and keep accurate place values for all their answers / partial products.
While students using the standard algorithm have no concept of the size of the answer until they have nearly completed the problem, the opposite is true of the efficient (left to right) algorithm. Because students are multiplying left to right, they can estimate or guess with a fair degree of accuracy as to the size of the problem’s answer.
Standard Right to Left Multiplication
The final multiplication problem and the extra problems (including addition of the partial products) written to the side will look like the ones below.
Another difference between the two algorithms is where the addition takes place. I see this multiplication problem as being comprised of three zones. The first zone is called the multiplication zone; this is the area above the line holding the multiplier and multiplicand and this is where students do all their multiplying.
The second zone is the addition zone; this is the area in between the two lines holding all the partial products. Students know they must add all the partial products to get a final product, which goes in the third zone; also called the answer zone.
Students using the efficient Multiplication algorithm use the efficient Addition algorithm to add the partial product rows. Because they are only adding single digits, they can move through the problem quickly.
Overall, having a strong multiplication algorithm like this simplifies the process and makes the work smooth and seamless.