This study, based on observation of 90 fifth-grade mathematics classes in Chinese elementary schools, examined how the task features, high cognitive demand, multiple representations, and multiple solution methods may relate to classroom discourse. Results indicate that high cognitive demand tasks were associated with teachers' use higher order questioning. Higher order questioning but not the high cognitive demand tasks themselves generated participatory responses among students. However, when teachers pursued multiple solution methods, they were more inclined to ask memorization and procedural lower order questions than explanatory and analytical higher order questions. Contrary to our hypothesis, high cognitive demand tasks and higher order questions related to teacher authority in evaluating students' answers whereas neither cognitive demand, multiple representations, nor teachers' pursuit of multiple solution methods were directly related to teacher-student joint authority in discourse. Implications regarding the relationship between tasks and discourse and instructional practice in a cultural context are discussed.