As promised, here are the directions for how to make fleece burp rags with the whole "rag quilt" idea in mind...
1. Cut your fabric. I used fleece on the back and a white cotton fabric for the front. After washing the fabric, I cut them into 8 x 20 inch pieces (you will only need one cut of each fabric to make one burp rag).
4. ... then, with the wrong side of the fabric up, fold down the corner and iron flat. Continue doing this until all sides of your fabric are pressed down.
5. Pin the wrong sides of both fabrics together and stitch.
I like the double stitch look, but I don't have the option of dual needles with my sewing machine. So I used a straight stitch about 1/2 inch in from the edge of the folded fabric (white cotton in this case) and then did another straight stitch right along the edge of the white fabric. Sure made a nice finish!
6. Trim off excess fleece (I kept a half-inch border of fleece around the edges).
7. Snip the fleece around the edges to give it that rag or fringe look.
TADA!!! You're done!
Now you have cute little fleece burp rags to match your easy little fleece baby blanket. Fun stuff eh?