That's really cool. The borrowing thing is the part of common core that they teach in elementary, and it is the part that enrages conservatives. The point of the homework and practice questions is to repeatedly do the borrowing thing until it becomes automatic and something that they do in their heads all of the time. So, it absolutely enrages the right when kids get the correct answer, but lose points for doing the problem the wrong way.
I was taught to do it the hard way and had to figure out the other tricks for myself much later in life, so now, even after decades of doing it your way, it's more of a struggle than it should be and I just reach for my calculator instead. So I envy you quite a bit.

Keep up the good work with your subversive teaching of common core principles as tips, tricks, cheats and shortcuts. That's actually how they should have branded it, instead of common core, it should have been cheating core, then they would have been all for it.