Start by sorting out your fabric scraps, matching them by length and color to get the look you want. Trim the edges to get rid of any fraying, and then iron the strips to prep the surface.
Stitch the strips together along the longer sides, using a 1/4" allowance.
When you have panels large enough for 4-6 coasters, stop sewing and press the seams open.
Use the larger bowl to trace circles onto the fabric panels and backing fabric.
For the batting and interfacing, trace circles using the smaller bowl.
Insert interfacing between one piece of the batting and one backing piece, centered, then press to fuse.
Place the backing fabric right side up, then add the patchwork panel right side down (so the right sides match).
Pin through the center to keep the layers together.
Sew around with a 1/2" allowance, just outside the batting, backstitching both ends and leaving a 2-inch gap for turning.
Turn the coaster right side out through the gap, smooth the seams out with a point turner, push the gap inside and press.
Close the gap by edge stitching around the coaster.
Quilt by sewing along the seams between strips, adding decorative stitching along the edges if desired.