It's funny, I do those "cluster problems" in my head to solve most multiplication and division problems...I presume that I invented the method myself at some point during basic education, as these books are encouraging kids to do.  The standard algorithms are great on paper but suck to do in your head for anything very complex (at least for me...)<p>I can see the point though about disadvantaged kids having trouble with this.  If someone is struggling and does not have good parental support, it would be hard to learn basic math skills reliably this way. Rote memorization of methods and figures is useful at pretty much all levels of math, and if you just want kids to be able to multiply two numbers, drilling them on one method makes a lot more sense than trying to create young mathematicians.