Boris Orehov

The paper presents the author’s experiences in formation ideas about the possibilities of the axiomatic method in the process of construction and investigation of mathematical models in an integrated course of mathematics for 10th grade students. Starting from the consideration of vector sets on the plane jointly with linear operations, a method to introduce a system of linear space axioms is presented. The development of models for the internal laws of mathematics is illustrated by investigation the system of natural numbers extensions to the system of integers and rational numbers.