This looks very cool, though it looks inconvenient for multiple problems due to the amount of drawing involved.

A good, practical approach I've liked to use are the techniques in Benjamin and Shermer's "Secrets of Mental Math." One of the examples in the linked article shows a method of drawing for solving 42 * 21. But this is easier to solve mentally by converting this to a simpler problem, as recommended by the book: 42 * 21 = (42 * 20) + (42 * 1) = 840 + 42 = 882.

You can often split up these types of multiplication problems into an easier multiplication problem, plus an addition. You can then solve the entire problem without much or any paper for calculation.