Stack seven craft sticks on top of each other. Secure them tightly by twisting a rubber band around each end of the stack or hot-gluing them together. This stack will act as the fulcrum.
Stack the two remaining craft sticks on top of one another. Secure them by twisting a rubber band around one end of the stack several times. You should be able to spread the craft sticks apart at the end opposite the rubber band. The upper craft stick of this small stack will act as the lever arm.
Slide stack of seven craft sticks between stack of two craft sticks from open end all the way to the rubber band holding the opposite end. The stack of seven craft sticks should be perpendicular to the stack of two sticks. The lower of the two sticks should lie flat, while the upper stick will extend up at an angle.
Secure the fulcrum and lever craft sticks with a rubber band. Place one end of the rubber band around the fulcrum stack and slide it all the way to the lever stack. Twist the rubber band over and slide it around the shorter end of the lever stack, then twist it again over the opposite end of the fulcrum stack. Twist the rubber band back over the whole assembly again several times, in the same way.
Hot glue the plastic spoon's handle to the lever arm craft stick, so that the spoon faces up and can hold a projectile.
Hold the edges of the fulcrum with one hand. Use your other hand to place the ping pong ball in the spoon, then push the spoon down and release it.