I recently bought a 3-pack of the Enviroboard Microwavable Sterilization Antibacterial Cutting Board ($(removed)).
They are made from BPA-free plastic and as you can see in this photo, they are very flexible, but not flimsy. You are supposed to roll them up and stick them in a microwave for 60 seconds, to sterilize them. I don't always sterilize them after I use them unless I'm cutting meat. After using them for a while, the surface of the mats will show cut marks, but they hold up well.
The back of the mats are textured to prevent slipping. They don't slip on the wood table I use to prepare food. I'm not sure how they'd work on tile or granite.
These mats are about 15 inches long and 10 inches wide. I'm getting ready to cut a sweet potato.
After chopping two potatoes into slices, I curl the board and pour the pieces into a bowl, where I mix them with a little olive oil and salt. I like being able to curl the board to prevent spillage.
Here they are laid out on the silicone baking mat I reviewed a while back. I could have done a better job of Apollonian circle packing to ensure that no pieces overlapped, but I was hungry.
20 minutes later, and I had freshly baked sweet potato chips. My daughter and I ate them all in a few minutes. When my wife got home she smelled them and asked where they were, and was sad that there weren't any left. I will make more now.