I don't know if I invented something new, or if everyone already knows this, but when working with the small scraps from my butterfly quilt, I figured out a way to make scrappy half-square triangles without having to cut triangles.
Start with a square of your background fabric (I used 6.5 inch squares) and press a crease across the diagonal. Then with right sides facing, line up your first scrap, overlapping the crease by about 1/4 inch. It doesn't matter if you overlap on the right or left of the crease, because these blocks are reversible. Stitch in the crease through both layers.
Turn your block to the right side and flip and press the strip so that you're looking at the right side of both fabrics.
Add new strips by sewing them right sides together to the previous strip with a 1/4 inch seam allowance.
Sew, press and flip until you fill up one side of the triangle square.
When your block is half filled, turn it to the wrong side, and trim the overhanging bits of the strips to the same size as your foundation block.
These blocks can be set in a number of ways.
This setting is one of my favorites.
I made a crib quilt from my blocks by adding an inner border that matches the background fabric, and a flashy outer border.