Yes, you can sew them to the cardboard. Pin them in place on the cardboard, bristol board or foam core with all the corners touching in the middle. This allows you to use a needle and thread to tack all 4 of the inner corners in one go. Sew one stitch across each corner going through the seam allowance so you don't spoil your blocks. Leave the thread tail hanging when you start o you can tie the 2 tails together once you are done tacking the corner. Once the center is tacked down and tied off, move around the board tacking the rest of the corners.