This paper investigates the 17 types of symmetry that can be employed to create wallpaper patterns. Such patterns cover the entire floor or wall (a two-dimensional plane) using the repetition of a geometric shape or small tiles with various shapes fitted together without gaps or overlaps. The resulting pattern or tiling is called a tessellation of the plane and occurs frequently in architecture and decorative art. In this paper, the author develops her procedure for tessellating a plane using different transformations such as translations, rotations, reflections, glide reflections, or any combination. With these, students can be taught a technique necessary to make their designs and drawings and thereby develop or renew their appreciation of art and mathematics, especially in algebra and geometry.