The focus of this workshop is to study two different approaches for creating mosaic designs and to compare them. A traditional and well-known method in this regard is using a compass and straightedge. The other method that will be introduced and discussed during this workshop is the use of the modularity method. Modularity is a special cutting and pasting process of tiles to create tile designs. During this workshop the participants will create a series of designs using a compass and straightedge, and then through some hands-on activities, they will discover that the same designs could be constructed using modularity. The cuts in the modularity method are elementary in that they cut the tiles (mainly squares) along line segments, such as the diagonals, to divide the tile into two or three pieces. For certain designs, there are more detailed methods of cutting that the participants should execute to construct more complex geometric shapes.