The necessity to perform diagnostic procedures within the contemporary process of teaching mathematics is caused by the importance of timely obtaining of the information on the current maturity level of the subject, meta-subject, and personal learning outcomes of students. The task is to choose an assessment technique adequate in educational trends and scientifically grounded. The authors propose to solve the issue of estimation of cognitive universal activities of the 7-9 grades’ students at the mathematics lessons in the conditions of two-subject monitoring. The paper shows that cognitive universal learning activities are a dynamic and important newly formed structure of a person depending on the age peculiarities in the formation process and should be considered in the maturity level assessment. The authors propose and substantiate the structure and step-by-step composition of the cognitive universal learning activities, which allow demonstrating them in a diagnosable view. It made it possible to identify and characterize the maturity level and criteria of the considered learning activities, assessment stages and procedures, and diagnostic tools. The paper presents the author’s conceptual model to assess cognitive universal learning activities when teaching mathematics, which demonstrates the important characteristic of the assessment process – a nonlinear nature. The research resulted in the identification of a specific principle of the assessment of cognitive universal learning activities – a two-subject principle. The implementation of this principle makes it possible to use the subject material to determine the maturity level of both the subject and meta-subject learning results. The authors describe the diagnostic tools, present the diagnostics process chart, the system of assessing certain tasks and give an example of typical assignments on the Equations topic of Algebra course for 7th grade.