I don't throw away any scraps. One of the things I do with the 1-1/2" strips is shown here. Normally, the dark green larger corner is done scrappy but I had all these greens and decided to do a green quilt top. So I did need some yardage - and this is a green I had had for a while
I cut a base from something I know I'll never use -- if you make 48 squares and then sew in row 6 wide by 8 long and add a border, it will make a nice child's quilt, or make larger for lap quilts.
This beige base is cut at 7" to allow for some distortion when adding strips and also so that you don't need to be exactly perfect in placing your strips. I sew strips on one half to fill, starting with the longest piece right sides together, the edge of the strip about 1/2" from the corner, and do assembly line sewing -- sew the first strip on all the bases, press toward the corner, then sew another, press, etc. to cover to the corner. Then put a ruler on the press line of the first strip at the 2" mark and mark with a pencil. If you want a smaller corner, make a longer line, perhaps 2-1/2 or 2-1/4". Cut your corner pieces, put then right sides together with the edge on the pencil line, sew 1/4" seam, press. Lay a 6-1/2" ruler on the block with the diagonal line of the 6-1/2" square along the sewing line of the first strip and trim. A second square appears when all the blocks are put together like I have shown,
I also save 2-1/2" strips in another box. For these strips I use an 9" base and trim with an 8-1/2" ruler. I use these two sizes becasuse these are two small rulers I have for cutting squares.