Here’s a neat video showing a visual approach to multiplying muli-digit numbers. The algorithm is just a visual representation of the standard mechanical procedure that we all know, but somehow computing the product from these criss-crossed lines makes it look easier.
One problem I see is that the algorithm may lead to confusion if there zeroes as digits. One solution would be to develop a placeholder to represent each zero—a squiggly line or dashed line, perhaps? Also, the diagram could get messy if the numbers have a lot of 7’s, 8’s, and 9’s.
How about this as a trivial modification? It seems to be a lot cleaner and doesn’t suffer from the two problems I mentioned.
[via y of x]
David Richeson: Division by Zero 
What you propose is essentially the same as lattice multiplication, laid out in a slightly different way. Nice!
Very nice, very good!
Your method clearly corrects and identifies weakness with the earlier method.
However your method is much closer to non-visual multiplication; whereas it would appear to me that her method is more visual.
The key questions remain: which is faster, easier and can handle anything? Answer: ordinary multiplication without any visually drawn lines “at best”, and your method secondly [which ultimately mirrors ordinary multiplication].
How to prove the answer? Standardized tests with time limits: who gets more correct answers and is able to answer a greater quantity of questions?
One more thought: it is very interesting to observe different ways – particularly visual ways of tackling multiplication.
Have you ever come across the Jap. abacus method -they train very hard , compete and over time, some people can even do math in their heads without an abacus in front of them!
This is called “expert memory” and there is no short cut per se apart from massive practice resulting in probably 10,000 hours, or 4 hours a day for 10 years.