In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the well-known "S-Pattern" task and vignettes to take an in-depth look into how a teacher can foster these connections. They share sample tasks for grade bands -- PK-Grade 2; Grades 3-5; Grades 6-8; and Grades 9-12 -- with various solutions and ideas for how a teacher might use the task with a focus on the connections they discuss. Using connections helps students see relationships between their representations and strategies on mathematical tasks in ways that deepen and advance understanding and helps them become better problem solvers.