I was taught to use the lines on the ruler because they are straight. Where on a cutting mat they can be distorted and cause you to cut your fabric wrong. And I know that for a fact that the mats are squiggly sometimes. I have one of those Ironing board/cutting board ones and the lines on the cutting board side is all squiggly. But then again I only use if for ironing. I never cut on that cutting board side.