Fold three or four of the pieces of construction paper into fourths. Start like you are folding a letter, but make four sections instead of three. Then, glue the papers end to end, until you've made a "C" shape when you stand them on their sides.
Lay the shape out on your cardboard base. Mark the ends of the "C" and then mark every three inches around the curve. Glue a popsicle stick so that it stands up on each mark. A hot glue gun will work more effectively than squeezing school glue onto the ends of the sticks and holding them in place.
Glue two popsicle sticks to each fold on your paper, one on each side of the fold. Then, pour a hot glue line along the curve of the "C" and set your paper into place. Also, glue the inside of the support popsicle sticks standing up from the cardboard and secure them to the paper.
Take another piece of construction paper. Fold it in half, and then bring the edges of each side toward the middle, creasing at one inch, to create the stage. Hot glue two popsicle sticks to the cardboard, and then glue the one-inch folded edges to the popsicle sticks. Cut a piece of cardboard to the height of the stage. Glue an edge to the cardboard base so that it will hold the stage up.
Paint your detailing on the inside and outside of the paper. Most scholars agree that there were probably three different levels of gallery seating, so paint the railings and seats. Scatter some straw on the cardboard near the stage to mirror the look of the original theater. For the outside, paint some archways near the bottom, running around the outside, and then windows along the galleries.