Likelihood designing pedagogical taking into account a principle of uncertainty and difficult interaction with Wednesday of humanitarian systems has allowed to create and successfully to realize in practice scientifically-methodical system of formation of the cores natural-science competentions studying youth in the conditions of the integrated natural-science formation, consisting of two interconnected generalized methodical components realized at level of general and vocational training. Dynamism and now additivity properties of our system have allowed to deduce on higher qualitative level сформированность skills trained - on level of the cores natural-science competentions.