Making plastic from corn, soy, and other products has been going on for some time. However, you can make your own from potatoes as shown on The Green Parent. I'm not sure how you could use the end product would be but as a learning exercise it would be useful.
These types of products raise the big question of food versus fuel and now plastic. It is a difficult thing to balance but if we can change the way we use plastic it won't be so ubiquitous. Plastic has been around for so long and used in so many ways we take it for granted and forget about the resources used to make it. Think of how many potatoes you would need to grow to make all the plastic you use around the house.