Introduction. The article is devoted to the assertion of the need to develop and include in the educational process of growing personalities competence-oriented tasks provided by the technology of geometric origami modeling. Relevance. In modern mathematical education, there is an active search for improving the quality of education using competence- based approach.Purpose setting. In the scientific literature, as it turned out, no studies have been found indicating effective means of asserting a competence-based approach to the study of the topic «Area», which led to the need to develop and include in the educational process competence-oriented tasks designed within the framework of technology associated with the recognition, modification and evaluation of the area ratios of geometric shapes.Methodology and methods of the study. In theoretical studies, competence-based, environmental and synergetic, cognitive-visual approaches are considered. The method of conducting experimental work using visual and graphic means aimed at revealing the category of area as an additive scalar quantity is recreated from the analysis of geometric shapes arising during the geometric modeling of origami, which the child explores and sets their boundaries.Results. The effectiveness of the considered approach to the topic «Area» is proved.Conclusions. The scope of implementation of the research results is presented.