[metmom]

Some math methods work best when you have paper and pencil ("the old way"), and others work best when you're trying to do math in your head (what I suspect is the point of the given exercise).

The common core way is no benefit to doing mental math.

The best mental math is the old way. Knowing your addition and multiplication facts down cold, by memorizing them.

[Monitor]

The common core way is no benefit to doing mental math.

This is a way of doing mental math, and remarkably similar to how I have been doing mental math for decades (I'm a 50 year old engineer), so this method is not unique to common core.

The best mental math is the old way.

For you, maybe. I can only hold so many digits in my head at once. Beyond that, I resort to tricks, like the lesson shown above. It's a valuable skill to teach, even if you don't think you have any use for it.

Knowing your addition and multiplication facts down cold, by memorizing them.

You are assuming basic addition and multiplication tables aren't also being taught, and memorization drills given. And again, only so much can be memorized. Beyond that, I rely mental math tricks.