Here are a few uses for those old mats:
They make great bottoms for purses or bags you are making
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I've cut up several (that got worped) into smaller pieces. Cut a piece of thin plywood the same size as the mat. On one side of the plywood layer a piece of the stuff you put into pot holders to keep the heat from burning you (can't remember the name of the stuff) and a piece of cotton batting (optional - if you leave the batting out you can iron seams flatter), then cut a piece of Duck fabric or some other heavy duty cotton fabric, big enough to cover the board and over lap to the other side by 3/4". Glue the fabric to the other side of board as smoothly as possible. Be sure to miter the corners so that you don't have a blob of fabric on the corners. Next, and finally, Glue the mat board to the side of the board you just glued the fabric to (make sure the other glue is dry before starting this step). Now you have a small ironing board on one side and a cutting board on the other side. Put the board something heavy and big enough to weight the whole board down until the glue is dried completely. I made mine about 9 X 11" and it fits perfectly in my sewing bag. It sits right along side of my sewing machine and keeps me from getting up and down all of the time to walk to the ironing board. I know it is more healthy to do the walking, however, I have arthritis and very little cartiledge in my knees, so walking is painful for me.
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Use one of the old mats for just cutting paper and the like with an old cutter and old blade. This saves the extra wear and tear on the mat you use for fabric.
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I know I had a few more things to do with old mats, but they seemed to have escaped my mind. The moment I hit "post" they'll pop back in, I'm sure.