I love our differences! third of a yard is the biggest pieces I ever buy ;) The idea of 1/2 yard being scraps blows my mind.

back on subject, I use a form of Bonnie's scrap saver system too, just not the larger sizes, down to 1 1/2" square.
Lovely to want to sew and already have common sizes precut for me.

It depends how large the scrap is. I try to cut 5 inch squares or 2.5 inch strips as best I can out of a piece that is too small for anything else. Otherwise I keep it whole in my scrap bin. I can use it for applique.

Most of my scraps get cut into strips, mostly 2 1/2 " which I use to make my own jelly roll quilts. Just donated 20 to our Head Start program. Instead of sorting colors, I just do light and dark. I also do a lot of string quilts and they really use of the scraps. Anything else goes for pet beds. But I still think they multiply at night when I'm not watching.