Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the fundamental theorem of calculus. The lessons were designed on the basis of observed student difficulties and the existing scholarly literature. We show how a combination of dynamic tools and guide questions allows students to construct their understanding of these calculus ideas.