This is the PARCC page where you can click on links that take you to the actual online "live" samples of PARCC questions. You can click on math only questions for grade bands (3-5, 6-8, high school), or ELA only questions.
A mathematics consultant created a series of open-ended math questions for elementary through high school. This document has the questions as well as answers and rubrics.
Ohio's Online Resource Center has a very good collection of inquiry-oriented, open-ended math questions that you can choose based upon grade level and topic! The range is from third grade to high school, so finding a quality question that meets your students' needs is easy!