Mathematical modelling in solving text problems in mathematics

A practical task is
 
a task arising in production activities, in different fields of knowledge, in the 
surrounding reality. These tasks are not mathematical, but many of them can be solved by means of 
mathematics. To do this, students must translate the problem into mathematical language and apply 
mathematical methods to solve it. Solving practical problems by means of mathematics consists of three 
stages. 
At the 
first stage
 
- the 
formalisation stage 
- the 
transition is made from the practical problem to be solved 
to the construction of its mathematical model; at the 
second stage, the 
mathematical problem formulated 
at the first stage is solved; at the 
third stage, the 
interpretation stage, 
the 
solution to the mathematical 
problem is translated into the language of the original practical problem. Mathematical modelling is so 
widely used to study the real world that creating students' understanding of its essence, leading them to 
mastery of each of the stages should be the subject of constant concern of a mathematics teacher. 
Mathematical modelling is carried out according to the given three-stage scheme. 

---

https://papers.online-conferences.com/index.php/titfl/issue/archive 
151 
The most responsible and complex is the first stage 
- the 
construction of the mathematical model itself. It 
is carried out logically on the basis of a deep analysis of the phenomenon (process) under study and 
requires the ability to describe the phenomenon (process) in the language of mathematics. Realisation of 
the first stage requires many skills, including the ability to identify the essential factors determining the 
phenomenon (process) under study, the ability to choose a mathematical apparatus for compiling the 
model. 
Essential at the second stage is the skilful planning of the process of solving the formulated mathematical 
problem, the allocation of the components of the problem, the ability to analyse and refine the compiled 
model, At the third stage, the main thing 
is the 
ability to competently translate the result of solving a 
mathematical problem into the language of the original problem. 
Of great importance at this stage is the mastery of methods of verifying the solution of a practical 
problem, the ability to extend the solution found to other practical problems. 
Consider the application of mathematical modelling of practical problems in the study of progressions and 
in solving text problems to make equations. 
Task1. 
For the manufacture and installation of the lowest reinforced concrete ring of the well they paid 26 sum, 
and for each subsequent ring 2 sum less, 
than for the previous one. In addition, another 40 sum were paid upon completion of the work. The average 
cost of manufacturing and installing one ring was 
sum. how many rings were installed?