I don't throw away anything either. I store all my scraps by width. I use shoe boxes for my scraps. Don't know if this helps but here is what works for me.
1. Under 2 inch
2. 2 to 21/2 inch
3. Under 4 inch.
4. Assorted squares
5, Assorted pieces of batiks
For my larger pieces I went to the dollar store and bought some plastic shoe boxes for anything fat quarter size to 1 yard, I have about 8 of these. Anything bigger than a yard is folded in a large plastic totes. I have 4 of these. I like all my fabric folded and organized to look like book bindings. It just makes looking for fabric much easier. Hope this makes sense?