Computational fluency is vital to one’s success in more advanced math classes, such as Algebra and above. Sadly, many students have, at best, only a procedural understanding of computational algorithms, which often leads to poor retention and misapplication. In this workshop we will explore ways to investigate the validity of several standard non-standard algorithms, drawing on properties of operations. Algorithms for multi-digit addition/subtraction/multiplication/division will be examined, together with related sample student work. Pedagogical aspects will be addressed throughout the session.