Models and modelling

Before engineers build a new bridge, they make a small scale model of it and test it. In a geography lesson we use a globe instead of the Earth, and in a city we find our way with the map on a phone. Weather forecasters compute tomorrow’s weather with a computer program. In all these cases people work not with the real object itself but with its model.

This lesson opens the “Modelling” module. Here you will learn what a model is, the kinds of models and the stages of computer modelling. In the next lessons we work in detail with three information models: tables, trees and graphs. In the 2025–2026 university entrance exams (group I, informatics) every paper had 2 tasks from this section: one on a table model and one on a graph model.

Object and model

A model is always a model of something. The real object being studied — a thing, a process or an event — is called the original. A model does not keep all the properties of the original, only those that matter for the goal. That is exactly why a model is simpler, cheaper and safer than the original: breaking a model of a bridge is far easier than breaking a real one.

One object can have several models, depending on the goal. For a doctor, a student’s height, weight and blood group matter; for the school register, the name, surname and marks; for an artist, a portrait. The other way round, one model can describe several objects: the formula s = v · t models the uniform motion of a car, a cyclist and a train alike.

Kinds of models

Models are grouped by different features. The most important split is by the way a model is represented: a model is either a physical thing or information.

Information models are divided into several kinds by their form:

• Verbal model — a spoken or written description in a natural language: a recipe, a lost-and-found notice, a device manual.
• Table model — information in rows and columns: a school timetable, a class register, a train timetable, the periodic table of the elements.
• Graphic model — information as a picture: a technical drawing, a map, a scheme (a circuit diagram, a metro map), a chart, a flowchart, a graph and a tree.
• Mathematical model — a formula, an equation or an inequality: P = 2(a + b), s = v · t.
• Computer model — a model built as a program or a spreadsheet; you can experiment with it on a computer.

By time, models are static or dynamic. A static model describes an object at one moment: the plan of a house, the structure of a molecule, a class list. A dynamic model shows how an object changes over time: the height of a falling stone second by second, a weekly weather forecast, a city’s population year by year.

Formalisation: from words to formulas and tables

A verbal description is often long and vague: “the fence goes round the garden on all four sides”. To calculate with it, compare it or hand it to a computer, the description is turned into a form written by strict rules: a formula, a table, a scheme or an algorithm.

1. 1
   Goal

   Decide what you study and what you want to find.

2. 2
   Quantities

   Choose the important quantities and give them letters (a, b, P …); drop the rest.

3. 3
   Relation

   Write the relation between the quantities as a formula, a table or a scheme.

4. 4
   Check

   Test the model on a simple case whose answer you know.

The stages of computer modelling

A computer model is an information model written as a program or a spreadsheet. Its great advantage: where a real experiment is dangerous, expensive or impossible — a building in an earthquake, the motion of planets, the effect of a new medicine — you can run hundreds of “experiments” on a computer.

1. 1
   1. Stating the problem

   What is given, what must be found and what is the goal of the modelling?

2. 2
   2. Building the information model

   Choose the important properties, write down the assumptions (for example, “air resistance is ignored”) and formalise: formula, table, scheme.

3. 3
   3. Creating the computer model

   Design an algorithm, write a program or build a spreadsheet.

4. 4
   4. The computer experiment

   Run the model with different starting values and record the results.

5. 5
   5. Analysing the results

   Compare the results with reality. If they do not match, go back to stage 2 and refine the model.

h0 = 45      # initial height, m
g = 9.8      # m/s²
t = 0
while True:
    h = h0 - g * t ** 2 / 2
    if h <= 0:
        break
    print(t, round(h, 1))
    t = t + 0.5
print("falls between", t - 0.5, "and", t, "s")

0 45.0
0.5 43.8
1.0 40.1
1.5 34.0
2.0 25.4
2.5 14.4
3.0 0.9
falls between 3.0 and 3.5 s