Dot arrays provide opportunities for students to notice structures like commutativity and distributivity, giving these properties an image that can be manipulated and explored. These images also connect to ways that we organize discrete objects in everyday life. This article describes how the authors developed an array of dot tasks that have been found beneficial to students. These tasks allow students to reconnect and redevelop a sense for multiplicative efficiency and understanding, particularly with large numbers. They quickly come to realize that expectations go beyond a memorized procedure and involve reasoning and justifiation.