This chapter explores connections between problem posing and problem solving by examining a particular type of problem posing in which the solver’s goals are reexamined and reformulated as needed to solve the given problem. We present examples of this type of problem posing in two different contexts. First, we present an analysis of the problem posing and solving of a high school mathematics teacher as he solves a combinatorics problem based on an array diagram from Alice in Wonderland. We examine his problem posing and solving, documenting how his solution develops from his noticing of the array’s properties and his own problem posing. Second, drawing from our experiences preparing elementary education majors for the Praxis Core Mathematics exam, we document and analyze the challenges our students face solving common proportional reasoning problems and offer some ways teachers can motivate and support their students’ problem posing and solving. We compare and contrast these two different contexts with respect to the ways in which the solvers’ problem posing aids their problem solving.