The main goal of this work is to teach pupils the rational use of the knowledge they have gained in the lessons on  algebra for squaring numbers. In the paper, a method of squaring some three- and four-digit numbers are considered. In addition, one inverse problem to squaring is solved, given the square of a number to find the number itself. The research methodology used in the research work is based on the "reduced multiplication formulas" from the 7^th-grade of a comprehensive school. It is known that lessons organized in a playful way are in demand among students. Based on the results of the study, 7^th-grade students are offered a project of a mathematical game organized in extracurricular activities. It is shown that by organizing mathematical games in extracurricular activities, it is possible to develop the student's qualities for conducting scientific research and increase interest in mathematics.