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Abstract: In the article the idea of engineering thinking formation of the 5th grade pupils in the process of mathematics teaching is revealed. The skills of taking decisions are determined as the method of its formation. The necessity of using inventive activity in teaching mathematics is proved. The top-priority constituent of inventive activity is interaction of pupils’ personal experience and the information, which allows to create the situation of taking decisions and to form the skills to make decisions on its basis. The inventive activity components are revealed and the components of self-regulation are added. The theory of solving inventive tasks as one of the ways of inventive activity is described. The specific characteristic of this theory is pupils’ realization of the objective information. The stages of inventive activity formation of engineering thinking and developing the skills of taking decisions are elaborated. It’s proved that the effectiveness of engineering thinking formation of the 5th grade pupils depends on the necessity of creation in the teaching mathematic process of individual educational trajectory. Its efficiency is determined by the choice of optimal teaching techniques and speed of educational process. It is necessary to use such teaching methods which correspond to the individual pupils’ possibilities and abilities. By the way of such instrument the problematic tasks are chosen. The presence of the goal and non-systematic and non-actualized situations determine its structure. The conclusion is made that such organization of teaching process is closely connected with the engineer’s professional activity and allows forming engineering thinking.