As for the qualitative definition of the theoretical structure of the concept of algorithm, obtained by building a system of its study on the basis of component analysis in the article, it should be completed by studying the types of algorithmic processes. Three common types of such processes (linear, branching and recursive) play a slightly different role here. The first two types are somewhat simple, as we tried to show in Example 1, it would be natural to use them in the study of the components of the algorithm. Recursive processes can be applied to the play of already separated concepts. There are plenty of examples in various sections of Algebra, such as the "sequences" section, in particular. Finding the approximate value of an expression using the Heron formula can be a good example of recursive processes. The purpose of the research is to develop a methodological system that identifies opportunities to improve the quality of integrated mathematics teaching in V-IX grades and connect it with computer technology as well as identifies ways to apply it in the learning process. Textbooks often show the performance of a particular action on a few specific examples. We come across different situations here. Sometimes the rule is stated after the solution of the work, and sometimes the work is considered after the expression of the rule. The third case is possible, there is no definition of the rule in the textbook, but specific examples of the application of the formed algorithm are considered. This is quite common in school textbooks, especially when considering complex algorithms. In such cases, it is accepted to call the solutions of the studies as examples. The sample solution must meet certain requirements. Let's separate some of them from the point of view of the formed algorithm: the most characteristic cases of the considered type of problem should be considered; numerical data should be selected in such a way that the necessary calculations can be performed orally in order to draw students' attention to the sequence of elementary operations that make up the steps of the formed algorithm. If the problem-solving example meets these requirements, then the type of problem assigned to it can be considered as an algorithm for solving the problem. If, depending on the initial data, there are several fundamentally different cases of problem solving, it is necessary to consider examples of problem solving for each such case.