Determine the size you want your planetarium to be. This can depend on a number of factors, including available space in your classroom and the number of children your planetarium is being made for. Don't make it too large, or the cardboard won't be able to support its weight.
Sketch out your planetarium's design so that you will have a better sense of how many triangles you will need to create your planetarium.
Use a knife to cut out a large number of identical cardboard triangles, all about 2-feet high, with matching tabs along the edge that can be folded back. Spray-paint the insides of the triangles white, and let them dry.
Use the binders to connect some of your triangles into a tube that will be the circumference of the planetarium. This tube will be the wall holding up the dome of your planetarium.
Assemble the dome itself by constructing a geodesic shape from the triangles, connecting the cardboard tabs together with the binders. Start with the sides of the tube wall and work your way inward to form a dome. When complete, lift the planetarium so it can rest on four chairs or tables so that students can sit under it.
Place your projector under the dome and point it straight up. Use a laptop computer with images of the sky along with the projector to display all the components of the sky onto inside surface of the dome.