The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into mathematical objects' properties to formulate questions as a way to identify and explore mathematical relationships that eventually are supported through visual and geometric arguments. In this process, the use of a Dynamic Geometry System, such as GeoGebra, becomes important to represent and examine dynamically some attributes (area, lengths and perimeter) and properties of embedded objects. As a result, some of GeoGebra's affordances (dragging or moving objects orderly, finding loci, quantifying parameters, using sliders, etc.) become important in detecting invariants and patterns and ways to validate mathematical relationships.