The very nature of algebra concerns the generalization of patterns (Lee 1996). Patterning activities that are geometric in nature can serve as powerful contexts that engage students in algebraic thinking and visually support them in constructing a variety of generalizations and justifications (e.g., Healy and Hoyles 1999; Lannin 2005). In this article, we discuss geometric patterning tasks that engage students with wide-ranging levels of ability, interest, and motivation. This succession of tasks is likely to elicit recursive reasoning strategies to build mathematical sequences on previous terms' values or explicit formulas to determine any value in the sequence. The tasks are increasingly complex in terms of mathematical patterns, numeric computations, and visualization demands.