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This paper aims to present concepts of authentic assessment (AA) and AA tasks, one of the remarkable points compared with other assessment forms. Through some authors' researches, the article presents characteristics of AA tasks to distinguish other learning tasks, such as AA tasks must have problems posed in the contexts associated with real-life; AA tasks require students to use high-order thinking; AA tasks require students to respond by creating real products or quality performances; AA tasks orient the criteria to assess the students' performance results. In addition, several AA tasks in teaching Mathematics towards developing competencies for primary school students are designed and analyzed to clarify typical features of AA tasks.