I use jigsaw piece holders. I prefer the large flat one which has two flaps that open up. The only problem it is too large to transport pieces to class.
One plus ? Of the ladies in the class I go followed the First Lady who had a brainwave. She numbers all the rows and pins one row together in a neat little pile. She tha wraps them carefully , pressed and starched in kitchen foil. Keeps them flat . Does this to all her rows. A few of us have followed her example.it stops creases keeps in order and stops any form of fraying.her blocks always look perfect as if she had just ironed etc.