Following is an example of an algorithm which is an alternative to traditional multiplication of numbers 2 digits or greater.

The Lattice Form of Multiplication dates back to the 1200s or before in Europe. It gets its name from the fact that to do the multiplication you fill in a grid which resembles a lattice one might find ivy growing on. Let me see if I can explain it with an example. Let's multiply 469 x 37. First write the 469 across the top, and the 37 down the right side of a 3x2 rectangle. (It's 3x2 because the factors have three and two digits respectively.) Now fill in the lattice by multiplying the two digits found at the head of the column and to the right of the row. When the partial product is two digits, the first (10's) digit goes above the diagonal and the second (1's) digit goes on the lower right of the diagonal. If the partial product is only one digit, a zero is placed in the triangle above the diagonal in the square. At this point, we have the multiplication done. Now we add along the diagonals beginning in the lower right to get the final product. Any "carries" when adding are illustrated outside the rectangle. Multiplication really takes three steps: multiply, carry, add. The method we typically use does the multiply and carry steps together. The lattice method does all three steps separately, so it's really easier!

from Ask Dr. Math