My husband made me a set out of plywood that I then covered in fabric. He simply cut three pieces from the sheet 2 feet by 6 feet, sanded them down and added hinges. I used some cute quilting fabric and a simple staple gun to add some attitude. It was very simple took about forty minutes. My only concern with your approach is that I'm not sure how long foam board would last. It would be a good deal lighter and a lot flimsier then plywood which could be a good or bad thing depending on what you want from them. I just don't want you to spend your time and money on something that may break within a few weeks.

I would think foam board would fall over pretty easily because it's so light. And I don't think it will last very long.

Were you thinking of a fabric hinge? Or duct tape, perhaps. You can't really attach anything similar to traditional hardware to foam board.

, I guess you could just use white glue to glue the fabric cover on. And to glue a wide fabric strip between the two panels to be a hinge.

If you can get to a big art store, you might see if you can find really thick foam board--I've seen 1/2-inch. But it's expensive.

There is also rigid insulation at places like Home Depot. $16 or even less per sheet; 1" thick, which might be more stable. Lightweight enough to carry (so, lighter than plywood), but heavier than foam board, so perhaps less likely to tip easily. Something to think about.

You could also attac a band of weights on the bottom to keep the foam board from tipping, but it's kinda hard.

If it's not too expensive, I'd suggest you use duct tape to hinge a smaller pair of foamboards and see how well they stand there.