Basic Rocket
A basic paper towel rocket will begin with the tube, some construction paper, scissors, tape and glue. The tube becomes the fuselage. Cut a circle out of the construction paper, between 3 and 5 inches across. Cut a straight slit from the edge of the circle to the center of the circle, then fold the slit edges over each other, forming a cone out of the circle. When the cone is the size you want it for the nose of the rocket, put a bead of plain white glue on the outer slit edge, press it down, and hold it until the glue adheres. Run a bead of glue along the edge of one end of the tube, then press the cone onto the end to make a nose cone. Let it dry. Cut three to four triangles out of the construction paper for fins. Cut slits at the open end of the rocket, from the bottom toward the top, long enough for the fins to slide into them and be flush with the bottom of the tube. Fold the edge of the fins on the inside of the tube and tape them in place.
Building Stages
To add stages to the rocket, so you can simulate them breaking away after launch, you can add a couple of toilet paper tubes. Toilet paper tubes are 1 1/2 inches in diameter, like paper towel tubes, but shorter. By snipping four equally spaced, short cuts into one end of the toilet paper tube, you can allow that end to contract enough to slide it into the main fuselage of the rocket until it is snugly attached. If this is a bottom-side, breakaway stage, attach your fins to the lower end of the toilet paper tube, opposite where it fits into the paper towel tube, instead of into the bottom of the paper towel tube.
Decorating a Tube Rocket
Rockets can be painted, colored with markers, wrapped in foil, covered in stickers or even enameled and painted. To enamel and paint your rocket, first brush on a layer of white school glue diluted half and half with water. Let that coat dry, then add another coat and let it dry. The surface will be hard and smooth, and you can paint it using acrylic paint. A combination of paint and stickers can make for a very interesting rocket, too.
Blast Off
If you really want some excitement from your paper towel tube rocket, make a blast-off mechanism. NASA recommends finding a plastic photographic film container and taping or gluing a solid cardboard bottom over the bottom end of your rocket. Then glue the film container lid onto the bottom, with the lip of the lid facing down. Fill the film canister half full of water. Hold your rocket by the edge of the film canister lid, then drop a fizzing antacid tablet in the canister and snap the lid on quickly, with the rocket pointed up. Step back, because when that tablet makes enough carbon dioxide, the cap will pop and the rocket will take off.
Inventing Fire
You can also add flames coming out of the bottom of your rocket. A bundle of red and yellow yarn or ribbon makes a good launch-flame. Bundle the yarn or ribbon until it is a little thicker than the 1 1/2-inch hole in the bottom of the rocket. Tie a piece of twine around the end to hold the bundle together. Dip the tied end into white glue. Push the tied end into the hole on the bottom of the rocket. Let it dry, then trim the extended tips of the "flame" however you like.