I am one who saves everything. If it's 1/2 inch wide, I make 1/8 inch seams. Of course, it depends on the color and the type of fabric. I have made several confetti quilts. If the piece is missing a little bit on one corner, add a little piece there. You would be surprised at how much it takes to put on a little corner. Those seams eat up a lot.
I have made several freedom quilts. Start with a small piece of a very bright color, any shape and start sewing another small piece to it. Just be sure your seam is a straight line. Trim with ruler and cutter, not "by eye". Add pieces log cabin style, on each side as you go around and around and around. They can be any width that is 2 12 inches or less. I get 4 or more blocks going at once so I can chain stitch. When the square gets near your target size (8 or 9 or 12 inches etc.) add what will make it come out near that measurement. Around the outside I sometimes add a strip made up of lots of small pieces. Then square to the size you want. When you have all your squares made, put it together with sashing: white or black work wonderfully, or use your favorite color. Just keep this sashing as plain as possible; if it is big print or too busy, it will make the whole quilt look way too busy. Corner stones would be very nice. On the last one I made, the cornerstones were 2 1/2 inches square, and one of them had eleven pieces in it. I always tried to make them at least 4 or 5 pieces, so you can see I use really small pieces. Another thing: the smaller my pieces, the smaller I make my seam allowance. Those small squares all have 1/8 in. seam allowances.
Anything left from this goes in an old pillow case to give to the animal shelter or sprinkled outside for the birds. LOL