Then I started noticing that all the other children had soft, snuggly, comfy mats. And Mommy Guilt set in. So I found a yard or so of soft flannel and a roll of ribbon and set to work. I didn't take the time to find a pattern, so there was a lot of unpicking as I had new ideas pop into my head.
The finished version folds up like the original plastic mat. It's basically an envelope with velcro sewn all along one side to make it easy to remove for washing. I sewed ribbon into the top and bottom seams to make it easier to carry.
As I got going, I decided to add a little blanket sewn into the side seam, and a little padded pillow sewn into the top seam.