Blow up a large balloon to medium size. Tie off the end of the balloon as far up as possible so the narrowing near the tie is minimal.
Prepare the paper mache. Follow the directions if you bought a pre-mix, or skip this step if you bought pre-coated strips. To make paper mache from scratch, boil five cups of water while mixing in a cup of flour. Boil mixture and stir for 3 minutes.
Cut or rip 2 inch thick strips of newspaper and dip individually into the mix. Apply the strips to the balloon until it is covered in a thin layer. Leave a small hole around the tie of the balloon.
Wait one hour to let the first layer dry, unless the pre-mixed mache offers a different drying time. Apply several more layers to the balloon, waiting an hour between each layer until the cast is the thickness you desire.
Pop the balloon inside of the cast. Divide the brain into the different sections and paint each section a unique color.