This article reflects on the author's experience in teaching courses in mathematics content and methods in teacher preparation programs. It shows how technology-enhanced inquiry into a seemingly mundane task on situated addition found in a popular textbook for prospective elementary teachers, can reveal hidden properties of integers associated with their representations as a sum of consecutive counting numbers. The paper shows how a pedagogical framework based on the notion of "hidden mathematics curriculum" enhanced by the use of a spreadsheet can be put to work in designing unified mathematical activities for elementary and secondary pre-teachers. The paper also shows how computing can motivate transition from conjecturing to formal proof. (Contains 6 figures.)