I personally do not throw anything away. I resew the small under 1.5 inches into squares. Anything not usable as a scrap(the trimmings from blocks, cut threads, batting that cant be used for anything.) I stuff in to a bag until I get enough to make a pillow. Here is a bolster that is completely stuffed with the unusable bits.
Here is a few of the blocks I've made using fabric smaller that 1.5 inches. Yes I did throw in a few bigger pieces, but that was only when I didnt have enough to finish the block. These are all 6.5 inches. Most bits used in these are from trimming things down or trimming the end of a yard of fabric, etc.
These are my small bits yet to be sewn into blocks.
There are many, many followers of Bonnie Hunter that are using her Scrap Users System. I am a huge fan of Bonnie and am trying to make my own usable scrap system based on hers. Here is what I have done. I collect used Ice Cream Buckets from Freecycle. I store all my different size squares and tiny scraps in these buckets.
They are easily stacked and stored out of the way in a closet.
I do keep my 1.5 inch squares in a square container purchased at the dollar store. This box is constantly emptying because I participate in many trades to build the variety I have to make my Postage Stamp quilt someday. Still need alot of these.
Here are all the sizes of blocks I have cut so far. I just cut the biggest size I can get from a scrap. Then I keep cutting squares until I cant do anymore out of the scrap.
These are some of my strings. Still working on organizing them. These are all sizes that would work for string blocks.
I have all of the 1.5, 2.5, and 4.5 inch strings folded up and put into tissue boxes that I have taken off the top. When they are neatly folded I can fit about 40 in then and be able to see the colors available to me.
How do you store your scraps?