I'm using my mat upside down because too many lines is too confusing and I use the ruler. Do you have 24 x 6 ruler? Folded fabric is 22 inches, so there is room to spare. Fold, straighten, cut.
You slide the amount of fabric you want to cut off under the ruler until the long edge reaches the correct line. Line it up with the folded edge and the bottom edge of the ruler perfectly even. Keep the long edge even with the inch marker on the ruler and cut. The piece under the ruler is your strip and the remainder that's loose is for the next cut.