My handwriting used to be terrible. One time in third grade, my teacher handed me back an essay I wrote saying she wanted me to submit an essay, not a Chinese jigsaw puzzle. Now my handwriting is pretty good because I haven't used cursive since fifth or sixth grade, and I write in all capital letters to make it simple. At work I handle a lot of registration forms and participant waivers, and probably at least half of these forms have some part that is completely indecipherable, so annoying.
As for math, I don't know much about Common Core, but I know that at least the math portion of it would help people count change and do mental math better than trying to regroup and carry the one in your head. Think of the example at the top of this page where someone paid $1.01 for a 76 cent coffee refill. We know the change is 25 cents because we pretend the .76 is .75 and the 1.01 is just 1. The cashier was probably trying to do it the old fashioned way, which is to cross out the last 1, make it an 11 by taking from the next column, oh wait it's a zero so now we need to make it a nine and then cancel out the 1 in the left column, now we subtract the 6 from the 11, etc. That is so much more complicated than just realizing the .76 can be made into .75 and the 1.01 can be 1, but for some reason we have people outraged about trying to teach kids to do math this way, probably just because whatever news source they watch/facebook pages they follow told them to be.