My question is this - While you are working a piece what do you with partial
strands.

I use the floss away bags or you can just buy snack size baggies in the store.
Or if you aren't using the bags you can take those extra strands and loop them
thru one end of your skein of floss. That way they are there for you to use
later when you need that color and they are on the correct color skein so you
know what color it really is.