Draw a triangle on the construction paper with a pencil. This will serve as the front part of your weather vane's arrow. Cut out the shape with scissors.
Draw a rocket shape on the construction paper to be the tail fin of the arrow. Make it slightly larger than the triangle. Cut it out with scissors.
Tape the triangle to one end of the straw and the tail fin to the other end. Hold the straw on the tip of your finger and find the point at which it will balance. This is the arrow's center of gravity.
Stick the pushpin down through the center point of the straw and into the top of an eraser on a pencil. Take your wind vane outside and test it in the wind.