I was wondering myself, so I went to see the performance (which closed today). In the play, large blocks and four sets of stairs are used to transform the architecture of the stage. As I watched, the performers easily lifted, slid and pivoted the set pieces to change the architecture of the stage and to build various set properties from beds, to tables, to ships, to palaces. In the side of each set piece were oval holes used as handholds. The pieces seemed so sturdy and so solid that it was curious how they could be so light.
I talked with the designer Denys Karn about what kind of material she used for building it and she told me that they used a material called "Plycorr." They started with a standard wooden frame and then instead of using 3/4" plywood (which one normally would use), they used 1" thick Plycorr on the tops where actors stood and 1/2" Plycorr for the sides. They taped the edges and then glued fabric to it.
She did warn that the material is about $75/sheet, when plywood is usually only $50/sheet, and that it does not last as long. She also warned that if the area is large enough, cross-braces might be needed to add support. If using for your school play, careful planning and use of the material only on certain set pieces could make still be a worthwhile expense.
As a thank you for her answer, I promised to post a link to Nightwood Theatre's current fundraising campaign, 10,000 Women. Click the link to find out more about how Nightwood Theatre supports women artists in a male-dominated industry.