Several years ago I cut all my misc piles of fabrics into 2", 3-1/2" and 5" squares using Joan Ford's "Scrap Therapy" They are sorted into size/color plastic shoe boxes. These sizes all "Play Good" together, like 2 2" squares make a 3-1/2" square . Check out her books, I think she has 3 or so that have patterns to use these size squares. I saw recently that Moda's new precut size is 3-1/2" "Treats". We will probably see some new patterns coming out for that precut.

This has worked well for me since I cut these sizes..

I like the way Tartan does hers.

If you ask me...it all depends on the type of quilts you tend to/like to make. If you enjoy scrap quilt making and you tend to stick to the same sizes, say 2.5 inch squares or strips then it makes sense to do as much pre cutting as you can. The theory is if you have the right sizes already to go then you won't have to spend time sorting, pressing and cutting.
On the other hand if you tend to do quilts that are of coordinated fabrics or make all different types one time it might be a mini log cabin and the next time a feathered star and the next time applique kitties then it just doesn't make sense to do all the precutting and storing cause you never know what sizes colors or shapes you will want.
Good luck with finding what works best for you and your scraps.

Like you, I'm not a fan of chopping up my scraps for the very same reason. That being said, I do save all my scraps 1.5" square & larger. They have come in very handy at times to mend things & extend pieces not quite large enough. Thankfully I make mostly scrappy quilts, so it works for me. I am just trying to come up with a better way to store them all in as small a unit as possible. I even save all my scraps of batting & sew them together for quilts.

I do all different sizes, start 6 1/2 down to 1 1/2.

I couldn't see cutting all my scraps down, so anything, say 1/8 yard or so, get pressed, folded and sorted by color. However, all those smaller scraps get cut down into 1.5" squares, 2.5" squares, 2" strips, 2.5" strips and 1.5" strips of 2.5" to 12.5" in length for scrappy log cabins. I've made several Bonnie Hunter patterns and log cabins. I'm also making string blocks out of anything narrower than 1.5". It's working well for me.

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Nice quilts, loisf...

Loisf -those are beautiful!

I save every tiny little piece to make "fabric" that I then use in quilts. It's fun when I need to do some mindless sewing to pull out the crumb box and just start putting pieces together. I save these pieces of "fabric" in a drawer and when I get enough I pull them out and start playing on the design wall to see what I can come up with.

Rob

Once in a while. I mostly take what's left after a project and put in a scrap box, even if there are strips. I figure I may want to cut them to a certain size later. I have found little boxes with 3 inch squares that I do not remember what they were for.

I store my scraps in containers separated by colors. No, I don't pre-cut them into scrap sizes. I prefer to keep them as they are until I am ready to make something. As I need them, I cut them. I applique so I would never cut them down to a certain size so I can call it my "Scrap stash". I just like having my different colored containers of scraps