Promotion of mathematical competencies: problem-solving, modeling, representation. Problem-solving, modeling, and representation are general competencies that can be developed through working on problem-based text tasks in elementary school mathematics classes. To foster these skills, the text tasks should not only be appropriate for the respective age group but also have a suitable level of difficulty to trigger thinking activities and address the zone of proximal development. The practical volume contains about 70 text tasks that have been tested in grades 1 to 4 and evaluated for their potential in developing problem-solving and modeling competencies. Children in elementary school were observed while solving problem-based text tasks, and interview protocols were created. The analyses of these documents provide a practical insight.