Draw a pentagon with six-inch sides on light blue construction paper. Cut out the pentagon.
Cut a 6.5-inch by 1.5-inch rectangle out of dark blue construction paper. Glue the rectangle to the front of the pentagon, making sure the bottom of the rectangle lines up with the bottom of one of the pentagon's sides. The rectangle is the hat's band.
Draw an ellipse on dark blue paper to form the hats visor, using the hat's band as a guide for size. Cut out the ellipse. Glue the ellipse to the back of the hat's band so that about three-quarters of the ellipse is visible from the front. (Reference 1)
Cut a 3-inch-by-2-inch square out of red paper. Write "U.S. Mail" on the square using black marker. Glue the red square to the pentagon, just above the center of the hat's band.
Punch holes at both ends of the hat's band. Tie pieces of yarn to the holes. Secure the hat to the child's head by tying the pieces of yarn together.