This course, in conjunction with Math 112, is intended to give pre-service elementary school teachers a deep understanding of the mathematical systems that they will be expected to teach. The content of Math 111 includes the arithmetic systems of the whole numbers, the integers, and the rationals (at least in fraction form). For each system, students are expected to understand not only how to perform the four arithmetic operations, but also what those operations accomplish in real life, why the operations work the way they do, and how to model or represent those operations in concrete or semi-concrete ways. The study of the integers includes some basic number theory. Underlying all topics in Math 111 are the notions of estimation, mental arithmetic, problem solving, mathematical communication, and viewing mathematics as a logical and sensible system rather than a set of memorized procedures. Intended for elementary education majors.