What tasks are to be solved at mathematics lessons in terms of Federal state educational standard?

The paper presents the authors, approach to the selection of material for mathematics lessons in terms of the implementation of new standards. The paper defines the requirements for the tasks which are recommended for solving in class to achieve new learning outcomes. It also characterizes the tasks that satisfy the selected criteria: applied tasks, design tasks, tasks of the regional content, metasubject tasks. Besides, the paper describes their capabilities in achieving new results in mathematics education and gives the examples of the described tasks.