The article examines methodological approaches to achieving the objectives of a mathematics lesson within the framework of the competency-based approach in modern education. It analyses of the role of problem-based learning and active teaching methods in enhancing students’ functional literacy in accordance with the requirements of the State Educational Standard (SES). As practical examples, real-life cases and problem situations are presented for the topics “Percentages”, “The Pythagorean theorem”, and “Properties of the quadratic function”. The effectiveness of using digital technologies, such as GeoGebra, as well as the development of students’ independent learning culture in the educational process, is also considered. The article is proposed as a methodological guideline who mathematics teachers.