A Random Walk: Stumbling across Connections

Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three solutions to the task that draw on statistical, probabilistic (and stochastic), and algebraic methods are described. This task has been used with both secondary school students, mainly juniors and seniors, and in-service mathematics teachers during extended 90- to 120-minute blocks. Although serving slightly different purposes with different groups of students, the task supports introducing, developing, and reviewing some important mathematical ideas, with connections between at least some of the methods presented here being discussed.