Okkay, you've only got half a yard/meter of fleece and you either don't have a sewing machine or feel intimidated by having to cut up your fabric. Even worse, the idea of seams breaking up the terrific pattern horrifies you! Time for geometry to save the day!
Lay out your fabric and start in the center. Draw a big spiral and you'll be amazed at how far your fabric will seem to grow.
As a bonus, because there are no straight lines, the resulting scarf will ruffle very gently as it drapes in a very attractive manner.