The chalkboard backdrop pictured below was made out of two thin wood boards. They painted the front with chalk paint and once dried wrote on it with chalk. This is the most effective method since it is not reflective. The downside is that these are heavy and require a lot of time and talent to draw.
The background below actually two large plastic boards placed next to each other. These boards were extremely heavy, bendy, and could not lean on a wall without falling. Four of us had to tape the backdrop on pipe and drape to make it work. This couple used a heavy plastic but I believe you can use corrugated plastic as well to keep it lighter.
All in all, these are very difficult and make sure you charge accordingly. It also might be useful to check out Etsy: https://www.etsy.com/search?q=chalkboard%20background