Gather pictures of railroads together and have students discuss railroad tracks. They travel for miles and miles, and the lines never touch. Talk about why the railroad tracks must remain parallel and what would happen if they were no longer parallel. Then, discuss what makes the railroad tracks interesting from a design standpoint. Have students incorporate railroad tracks into a painting, drawing, or computer design. Talk about how railroad tracks or parallel lines appear close up and how they appear as they get close to the horizon.
Take out a globe and have students use tracing paper to trace the lines of longitude and latitude as they travel around the world. See whether the lines of longitude ever touch each other. Talk about the way that the lines are parallel, even though they are going around a globe and discuss how this can be used in design. Have students do an art project where they draw lines similar to longitude or latitude on a globe or sphere and create designs between the lines. Or use a computer program to explore parallel lines on a sphere.
Incorporate design elements into a study of parallel lines. Focus on the way that you can look at several elements, like clothing design, to see where parallel lines can come into play. Design a striped shirt on which the lines do not touch each other. Are they still parallel or not?