Modeling and formalization. Lecture: Models of objects and their purpose Models are used to represent a material object

4. Modeling and formalization(9 cells).

4.1 Models and simulations

A person seeks to know the objects of the surrounding world, he interacts with existing objects and creates new objects.

One of the methods of cognition of objects of the surrounding world is modeling, consisting in the creation and study of "deputies" of real objects. "Substitute object" is called model, and the original object is prototype or original.

Model is an object that has some properties of another object ( original) and used instead.

For example, in conversation we replace real objects with their names, window dressers use a mannequin - a model of a human figure, designers build models of airplanes and cars, and architects - models of buildings, bridges and parks. A model is any visual aid used in school lessons: a globe, a model, a map, a diagram, a table, etc.

What can be modelled?

You can build models of objects. For example ,

Reduced copies of buildings, ships, planes, ...

Models of the nucleus of an atom, crystal lattices

Blueprints

You can build process models. For example ,

Changing environmental conditions

Economic Models

Historical patterns

You can build models of phenomena. For example ,

Earthquake

Solar eclipse

Models are used by humans to:

Representations of material objects (a layout of a residential area development in an architect's workshop);

Explanations of known facts (model of the human skeleton in the biology classroom);

Testing hypotheses and obtaining new knowledge about the objects under study (flight model of an aircraft of a new design in a wind tunnel);

Forecasting (photos taken from space of the movement of air masses);

management (train schedule), etc.

The model is important not in itself, but as a tool that facilitates the knowledge or visual representation of the object. Modeling is the process of creating and using models to study originals.

When to use simulation:

original does not exist

Ancient Egypt

Consequences of a nuclear war

examination of the original is life-threatening or expensive:

Testing a new spacesuit for astronauts

Development of a new aircraft or ship

the original is difficult to examine directly:

Solar system, galaxy (large sizes)

Atom, neutron (small sizes)

Processes in an internal combustion engine (very fast)

Geological phenomena (very slow)

only some properties of the original are of interest

Aircraft fuselage paint test

The more attributes of an object the model reflects, the more complete it is. It is impossible to reflect in the model all the features of the object - the original, and it is not necessary. Features of the object - the original, which must be reproduced in the model, are determined modeling purpose- the purpose of the future model. These features are essential for this model in terms of the purpose of modeling.

Modeling Goals

study of the original study of the essence of an object or phenomenon

analysis (“what happens if …”) learn to predict the consequences of various influences on the original

synthesis ("how to make ...") learn to manage the original by influencing it

optimization (“how to do better”) choosing the best solution under given conditions

What do all models have in common? What properties do they have?

First, the model is not an exact copy of the original object: it reflects only a part of its properties, relationships and behavior. For example, you can put on a suit on a mannequin, but you cannot talk to him. A car model may be without a motor, while a house model may be without electrical wiring and plumbing.

Secondly, since any model always reflects only a part of the features of the original, it is possible to create and use different models of the same object. For example: the ball can reproduce only one property of the Earth - its shape; an ordinary globe reflects, in addition, the location of the continents; and the globe, which is part of the current model of the solar system, is also the trajectory of the Earth around the Sun. The original may correspond to several different models and vice versa!

The more attributes of an object the model reflects, the more complete it is. However, it is impossible to reflect in the model all the properties of the original object, and most often it is not necessary. After all, when creating a model, a person, as a rule, pursues a very specific goal and seeks to most fully reflect only those features of objects that seem important to him, significant to realize this goal. If, for example, an aircraft model is created for a collection, then it reproduces the appearance of the aircraft, and not its flight characteristics.

The requirements for the model depend on the purpose of modeling: what features of the original object it should reflect. The type of model is determined by the goals of modeling.

You can reflect the features of the original in the model in one of two ways. The nature of the models can be of two types. Firstly, material (natural, physical, object) models. They copy, reproduce the features of the original. Examples of full-scale models are dummies and models - reduced or enlarged copies that reproduce the appearance of the modeling object (globe), its structure (solar system model) or behavior (radio-controlled car model).

Secondly, information models - description of the features of the original in one of the information coding languages (in the form of a verbal description, formulas, diagrams or drawings).

Computer science considers the construction of information models with the help of computer technology. An information cultured person should be able to build various information models, both with the help of a computer and without it.

4.2 Classification of models

There are many options for classifying information models. Let's consider some of them.

If we take the classification subject area, then physical, ecological, economic, sociological and other models can be distinguished.

Depending on account time factor distinguish between dynamic (changing over time) and static (not changing over time) models.

Models by area of application there are training (including simulators), experimental - when creating new technical means, scientific and technical.

Depending on the presentation forms information about the modeling object, there are sign, figurative and mixed (figurative-sign) types of information models.

Models by structure there are

Tabular models (match pairs)

Exist special types of models. These include:

- imitation- it is impossible to calculate or predict the behavior of the system in advance, but it is possible to simulate its response to external influences. The challenge is to find the best solution method
trial and error(multiple experiments)

Examples : drug trials in mice, monkeys, … models of the learning process

- gaming- taking into account the actions of the enemy. The task is to find the best course of action in
the worst case.

Examples : models of economic situations; models of military operations; sport games; staff training

4.3 Information models

The original object can be replaced by a set of its properties: names (values) and values. A set of properties containing all the necessary information about the objects and processes under study is called information model.

For example, the information model of a country house is a card from the catalog, according to which the customer of a construction company can choose a suitable project. Each card in the catalog contains a table with the names (values) of the properties of the house and the values of these properties.

All property names in information models are always symbolic elements, because the name can only be expressed in symbols. But the values of quantities can carry both sign and figurative information. For example, the value of the quantity "appearance" can be expressed by a figurative element (drawing), and the values of the remaining quantities are expressed using signs (numbers, words, commas). A figurative element of an information model can be not only a drawing or a photograph, but also a three-dimensional layout or video recording. However, it must be possible to associate this element with the characteristics of a particular object. For example, in the line "Appearance" in the catalog of houses, a layout code may be indicated. And in order for the layouts themselves to be elements of the information model, and not decoration, they need to be provided with labels with ciphers.

Information models represent objects and processes in figurative or symbolic form. According to the method of presentation, the following types of information models are distinguished:

Figurative models (drawings, photographs, etc.) are visual images of objects fixed on any information carrier (paper, photo and film, etc.). A lot of information is given to specialists by satellite photographs of the Earth's surface.

Sign information models are built using various natural and formal languages (sign systems). A sign information model can be represented in the form of text in a natural language or a program in a programming language, a formula (for example, the area of a rectangle S = butb) etc.

Mixed information models combine figurative and symbolic elements. Examples of mixed information models are geographical maps, graphs, diagrams, etc. All these models use both graphic elements and signs at the same time.

4.4 Stages of building an information model

Any model is built to solve some problem. The construction of an information model begins with an analysis of the conditions of this task, expressed in natural language (Fig. 2.2).

As a result of the analysis of the condition of the problem, the object of modeling and the purpose of modeling are determined.

After determining the purpose of modeling in the object of modeling, properties, main parts and relationships between them that are essential from the point of view of this particular goal are distinguished. In this case, it should be clearly defined what is given (what initial data is known, what data is acceptable) and what needs to be found in the problem being solved. Relationships between input data and results should also be indicated.

The next step in building an information model is formalization - the presentation of the identified relationships and identified essential features of the modeling object in some form (verbal description, table, figure, diagram, drawing, formula, algorithm, computer program, etc.).

Formalization- this is the replacement of a real object by its formal description, i.e. its information model.

Information models exist separately from modeling objects and can be processed independently of them. Having built an information model, a person uses it instead of the original object to study this object, to solve the task.

4.5 Verbal models.

One of the types of information sign models is verbal models. Word patterns- these are descriptions of objects, phenomena, events, processes in natural languages. They are also called text models. For example, the heliocentric model of the world proposed by Copernicus was verbally described as follows:

The earth rotates on its axis and around the sun:

All planets orbit around the sun.

The verbal model consists of separate elements - words, interconnected in meaning. In turn, words consist of elements - letters, interconnected by spelling rules. Words are subsystems for text and supersystems for letters. The text as a whole is a model - a description of the original. It can reflect various properties of the described object. The quality of a verbal information model depends on the correct spelling of words, the accuracy of their selection, the correct combination of words into sentences, and the order of words and sentences in the text.

Verbal models can describe situations, events, processes. Many verbal models are contained in school textbooks, encyclopedias. We use verbal descriptions in communication (in letters, when talking ...) To build these models, we use the usual spoken language we are used to.

There are some features of spoken languages:

Polysemy, synonymy, homonymy - the same word can have several meanings, several words can have the same meaning, the same meaning.

Words can be used both literally and figuratively.

These features make human speech expressive, colorful, emotional. But their presence makes it impossible to use the spoken language in many sciences, when creating verbal (sign) information models for the exact sciences. Mathematics, chemistry, computer science, and other sciences, on the basis of the spoken language, create their own formalized scientific language containing many terms (words that are unique to this science). Formalized means not having polysemy, synonyms, homonyms. In a formalized language, each word has exactly one meaning and meaning.

Verbal descriptions are very diverse, they can be performed in different styles. First of all, there are conversational and book styles. The book style has the following varieties: scientific, official business, journalistic, artistic.

Scientific style is used to convey accurate scientific information. The most important qualities of scientific style are consistency and clarity of presentation. In the texts of the scientific style there are a large number of words-professionalisms, terms.

Artistic style is the style of artwork. Its main purpose is to influence the reader or listener with the help of figurative means of language (comparisons, metaphors, epithets, etc.)

Official business style is used in the preparation of documents.

Journalistic style is used when writing articles, notes in magazines and newspapers.

Working with verbal information models (historical, biological, geographical, artistic and other descriptive texts) requires a thoughtful attitude to what is read. The better the text is designed, the better it is formatted, the easier it is to read and analyze.

Works of fiction are also models, as they fix the reader's attention on certain aspects of human life. Analyzing a literary work, you single out objects and their properties in it, relationships between characters, connections between events, draw parallels with other works, etc. The most directly related to the concept of a model is such a literary genre as a fable. The meaning of this genre is to transfer relationships between people to relationships between fictional characters, such as animals.

4.6 Mathematical models

The main language of information modeling in science is the language of mathematics. Information models built using mathematical concepts and formulas are called mathematical models.

Example 1. In fig. 2.3 shows the geometric model of the proof of the Pythagorean theorem. It is so simple that the proof of the equality c2 = a2 + b2 becomes obvious.

International competitions about their results:

1) The first place will be taken by an athlete from China, and an athlete from Ukraine will be third.

2) Ukraine will be in last place, and Germany - in the penultimate one.

3) Germany will definitely be fourth, and China will take the first place.

4) Russia will be the first, and Italy - in the second place.

5) No, Italy will be fifth and Germany will win.

At the end of the competition, it turned out that each expert was right in only one statement. What places did the participants take in the competition?

A person seeks to know the objects of the surrounding world, he interacts with existing objects and creates new objects.

One of the methods of cognition of objects of the surrounding world is modeling, consisting in the creation and study of "deputies" of real objects. The “substitute object” is usually called the model, and the original object is called prototype or original.

The model is important not in itself, but as a tool that facilitates the knowledge or visual representation of the object.

The creation of models is resorted to when the object under study is too large (model of the solar system) or too small (model of the atom), when the process proceeds very quickly (model of an internal combustion engine) or very slowly (geological model), when the study of the object may be dangerous to others (a model of an atomic explosion), lead to the destruction of itself (a model of an airplane) or the creation of a real object is very expensive (an architectural model of a city), etc.

What do all models have in common? What properties do they have?

First, the model is not an exact copy of the original object: it reflects only a part of its properties, relationships and behavior. For example, you can put on a suit on a mannequin, but you cannot talk to him. A car model can be without a motor, and a house model can be without electrical wiring and plumbing.

The more attributes of an object the model reflects, the more complete it is. However, it is impossible to reflect in the model all the properties of the original object, and most often it is not necessary. After all, when creating a model, a person, as a rule, pursues a very specific goal and seeks to most fully reflect only those features of objects that seem important to him, essential for the realization of this goal. If, for example, an aircraft model is created for a collection, then it reproduces the appearance of the aircraft, and not its flight characteristics.

The requirements for the model depend on the purpose of modeling: what features of the original object it should reflect.

You can reflect the features of the original in the model in one of two ways.

First, signs can be copied, reproduced. Such a model is called natural (material). Examples of full-scale models are dummies and models - reduced or enlarged copies that reproduce the appearance of the modeling object (globe), its structure (solar system model) or behavior (radio-controlled car model).

Secondly, the features of the original can be described in one of the information coding languages - give a verbal description, give a formula, diagram or drawing. Such a model is called informational.

Models are used by humans to:

Representation of material objects (a layout of a residential area development in an architect's workshop);

Explanations of known facts (model of the human skeleton in the biology classroom);

testing hypotheses and obtaining new knowledge about the objects under study (flight model of an aircraft of a new design in a wind tunnel);

Forecasting (photos taken from space of the movement of air masses);

management (train schedule), etc.

i Briefly about the main

A model is an object that is used as a "substitute", a representative of another object (original) for a specific purpose. The model is not an exact copy of the original object: it reflects only a part of its properties, relationships and behavior. You can create and use different models of the same object. The process of creating and using a model is called modeling.

Distinguish natural and information models. Full-scale models - real objects, in a reduced or enlarged form, reproducing the appearance, structure or behavior of the object of modeling. Information models are descriptions of the original object in information encoding languages. Models are used by man for: representing material objects, explaining known facts, obtaining new knowledge about the objects under study, forecasting and managing, etc.

Questions and tasks

1. What is the model?

2. Name the main properties of models.

3. What is simulation?

4. How can you call the relationship between the original object and its model?

5. What models are called full-scale? Give 2-3 examples of full-scale models.

6. What models are called informational? Give 2-3 examples of information models.

7. For each of the listed models, name the actions that a person can perform both with it and with the original object:

radio-controlled aircraft model;

a verbal description of the jacket;

plan of the apartment

life-size plasticine teapot;

a mental picture of a future trip.

What actions can be performed only with the original?

8. In what situation can artificial flowers and fake fruits be used as “substitute” models for real flowers and fruits? What properties and relations of objects do these models reflect, and which do not?

9. Give examples of using models for:

a) presentation of material objects;

b) explanations of known facts;

c) testing hypotheses and obtaining new knowledge about the objects under study;

d) forecasting;

e) management.

§ 2.2. Information Models

In table. 2.1 shows an example of an information model of a country house - a card from the catalog, according to which the customer of a construction company can choose a suitable project. Each card in the catalog contains the names (values) of the properties of the house (on the left) and the values of these properties (on the right).

Table 2.1

A figurative element of an information model can be not only a drawing or a photograph, but also a three-dimensional layout or a video recording. However, it must be possible to associate this element with the characteristics of a particular object. For example, in the line "Appearance" in the catalog of houses, a layout code may be indicated. And in order for the layouts themselves to be elements of the information model, and not decoration, they need to be provided with labels with ciphers.

Information models represent objects and processes in figurative or symbolic form. According to the method of presentation, the following types of information models are distinguished - fig. 2.1.

What examples of information models can be given for educational institutions? How can educators use them in their work? Let's try together to find answers to the questions posed.

What is a model

What are iconic information models? Examples of them are used in their work by all teachers who own modern information technologies. In general, a model is a different way of representing the analyzed reality.

Varieties

It is possible to give examples of information models of a material and ideal type.

Full-scale variants are based on an objective example, they exist independently of a person, his consciousness. Currently, they are divided into physical and analog versions, which are based on the phenomena associated with the subject under study.

Ideal models are associated with human thinking, his perception, imagination. Among them, one can note intuitive ones that do not fit into any classification option.

Giving examples of a figurative information model, one of such models can be mentioned. Let's take a closer look at their classification.

Text Ideal Models

Verbal models are used by teachers of the humanities cycle. They help to describe a certain area, phenomenon, object, event in successive sentences. How would such an information model of the lesson look like? Let's take an example from a literature course. When studying the novel by L. N. Tolstoy "War and Peace", the teacher describes the image of Natasha Rostova. To do this, he uses the text model. The children, listening to the teacher, create, on the basis of his perception of the image of this heroine, their own image of the heroine of Tolstoy.

If a history teacher asks his pupils: “Give examples of a figurative information model of the events that occurred during the Battle of Kulikovo, based on the viewed fragments,” the guys create their own image of that battle. They convey it in the form of sentences linked into a story.

You can give examples of information models of verbal form and from the course of physics. When studying the topic "Pressure of Solids" in the seventh grade, the teacher tells the children how difficult it is to move on loose snow without skis. Then the students are asked to explain the reason for such a phenomenon, to identify the parameters on which the studied physical quantity depends. The image that arises in the minds of the children after the teacher's story helps them answer the question posed.

As examples of such a model, one can note the textbook, the rules of the road.

Mathematical models

They are considered a broad class of iconic models. Mathematical models are based on the use of ratios, comparisons, and other methods used in this science. Giving examples of information models based on mathematical methods, we can mention the solution of quadratic equations, drawing up proportions. All sections of geometry, involving the derivation and proof of theorems, are also associated with the construction of a mathematical model. Not without them, and such a school subject as economics.

Information Models

They are considered a class of iconic models that describe any information processes: the emergence, transfer, change, application of information in different systems. Examples of tabular information models at school can be found in the 10th grade geography course. When studying economic geography, the tabular model helps to visually see the main characteristics of the country, to use the material to compile a complete story.

In addition, examples of tabular information models can be found in any school course. In chemistry, this is a table of the solubility of compounds, as well as the periodic system of Mendeleev. In physics without tables, it is difficult for a teacher to explain the basic terms studied in the topic "Electricity". In history, with their help, knowledge is systematized, the guys enter important historical dates in one column, and in the other they describe the events that correspond to them.

Relationship of models

There is a conditional line between informational, mathematical, verbal models. All 3 examples of information models are found in school disciplines. So, for mathematics, physics, computer science, mathematical and informational options are considered the most popular. But without a verbal model, the guys will not be able to explain phenomena, algorithms, equations and inequalities.

Simulation features

Before considering examples of graphical information models, let's find out the features of modeling. The model is an artificially created object. This is necessary to simplify the idea of a real object or phenomenon. The model fully reflects all the features of the original process itself. If the task is given: “Give an example of an information model”, you need to understand the essence of the process.

We are talking about building a model that is designed to study information phenomena and processes. In computer science, programming can be considered as such a subject. Using a certain mathematical programming language, it is possible to present textual material in a graphical form.

Modeling involves the construction of a model that is designed to study and study the original object, phenomenon, process. The created copy is only endowed with those qualities and properties that are characteristic of the original object, but allows some deviations from the ideal.

Activity approach

Full-fledged models can be obtained using a systematic approach. This is especially true within educational institutions. The transformations that have affected schools in recent years have made it possible to establish a logical connection between individual disciplines.

Such an activity-based learning option contributes to the formation of a harmoniously developed personality who understands the unity of the living world, the interconnection of individual processes and phenomena.

If teachers ask: "Give an example of an information model," he can safely choose any academic subject. There is no such discipline in which tables, graphs, diagrams, presentations would not be used.

Features of the modern school

The new standards that have been introduced into Russian schools involve considering the same phenomenon from different points of view. For example, from a physics course, children will learn that electrons are necessary for the flow of electric current in metals. They receive information about the charge of this negative particle, determining their number in different metals. In chemistry lessons, schoolchildren are told about the probability of placing electrons at energy levels.

When studying the topic "Oxidation-reduction reactions", schoolchildren get information about what happens to these negative particles during chemical interaction. Despite the fact that information is provided from different positions, we are talking about one object - electrons. Such a systematic approach makes it possible to form in the minds of schoolchildren a complete picture of the structure of matter, its transformations.

In the above example, the object under study is considered as a complete system, an integral part of a single whole (substance). Depending on the academic discipline, certain characteristics and additions are used. In the case of a systematic approach, it is not causal explanations for the existence of an object that come to the fore, but the need to include other components from it.

The formation of universal models acquires special significance during experimental activities. Using a personal computer, you can calculate the parameters that will be associated with the analyzed object.

Such modeling is important for the scientific knowledge of natural phenomena. In a school informatics course, such actions are called a computational experiment, which is based on three important concepts: a model, an algorithm, and a program.

The use of a personal computer within the school is possible in three main options:

carrying out direct calculations using a PC;
creating a database, turning it into a program or a specific algorithm;
maintaining an interface between the computer and the student.

Model features

Among the most common features by which it is possible to classify all models, we single out: the purpose of application, the scope of knowledge, the time factor, and the presentation option.

Depending on the goal set for the model, experimental, educational, game, simulation, scientific and technical versions of the models are distinguished. So, for example, at the primary stage of school education, the most applicable and significant game technologies that allow children to feel like a teacher, doctor, policeman. Game models in children of seven to eight years old are well formed, since in preschool educational institutions they are used as an indispensable element in the formation of the child's personal qualities.

Varieties of models

Depending on the field of knowledge for which the model is being compiled, economic, biological, sociological, and chemical types are currently distinguished. For example, for the natural science cycle, it is important to form a model that would allow one to explain the phenomena occurring in animate and inanimate nature. In sociology, the emphasis is on the processes taking place in society.

According to the time factor, static and dynamic variants of models are distinguished. The static option characterizes the parameters and structure of the object, allows you to describe the selected phenomenon (object) in a specific period of time, helps to obtain reliable and timely information about it.

Any model has a specific form, type, presentation option, description. The school is supposed to consider material and non-material models to a greater extent, depending on the specifics of the academic discipline.

Material models assume a real embodiment, they fully repeat the internal or external structure of the object itself. For example, in geography, such a reduced model is a model of the globe (globe), on which all the seas and oceans, continents and islands are plotted. These models are directly related to the research approach to teaching modern schoolchildren. They are necessary when teaching chemistry, physics, biology, astronomy, geography.

Non-material modeling involves the use of a theoretical method of cognition.

Conclusion

Any information model is a collection of information about a phenomenon, object, process. With its help, you can characterize any process that occurs in animate and inanimate nature. A variety of graphs, maps, tables, diagrams, which are actively used by teachers at all levels of education, give a positive result.

Intuitive (mental) modeling contributes to the creation of a first impression of the process occurring in chemistry or biology. Thanks to the combination of all options for information models, the younger generation of our country forms an adequate assessment of the unity of the living and non-living world. School graduates can independently build any models, use them to study, analyze, evaluate events and phenomena.

1. Insert missing words.

2. Continue the phrases.

a) Model- an object that is used as a "substitute", a representative of another object (original) for a specific purpose.
b) Natural (material) model
c) Information model

3. Mark true statements.

4. Why is it advisable to resort to modeling in the presented situations?

5. Determine which of the following models are informational and which are natural (connect with arrows).

6. For each of the given models, write down an action that can be performed both with it and with the original object, as well as an action that cannot be performed with the model.

7. Describe examples of using models for:

8. Carefully read the text of clause 2.1 "Models of objects and their purpose". What method of understanding the world around you met? Describe it.

9. Specify information models.

10. Specify the pairs of objects that can be said to be in the "Object - Model" relationship.

11. Fill in the scheme of varieties of information models.

12. Give examples:
a) figurative information model - drawings, drawings
b) sign information model - verbal description, formulas
c) mixed information model - tables, graphs, charts, diagrams (maps, graphs, flowcharts)

13. Have you met with information models in everyday life. Give an example.
Tables with formulas, with physical characteristics.
Schedule of lessons.
Various charts.
Formulas in mathematics, physics.
Drawings of various mechanisms.
Photos, illustrations in textbooks and on posters.

14. Carefully read the text of paragraph 2.2 "Information Models". Make a plan for retelling this paragraph

15. Use a history textbook and give an example of a verbal model of a historical event.
Consequences of the events of the 13th century:
the events of this century marked the beginning of the defense of Russian lands from the countries of Western Europe;
The Golden Horde yoke caused enormous damage to the economic, political and cultural development of Russia.

16. Use a geography textbook and give an example of a verbal model of a geographical feature or natural process.
The ocean is the main custodian of water, which has long amazed researchers with its unusual properties.
Water permeates the entire geographical envelope and performs a variety of work in it.

17. Use a biology textbook and give an example of a verbal model of an object of flora or fauna.
Symbiosis is a mutually beneficial relationship between two organisms.

18. Give examples:

a) polysemantic words: key (from the lock) - key (spring), pen (for writing) - handle (door), leaf
iron - leaf (of a tree)
b) the use of words in the direct and figurative meaning:
spring weather - spring mood, gold items - golden hands, a toy for children - to be a toy in someone's hands
c) synonymous words: storage - warehouse, sickness - illness, hippopotamus - hippopotamus, key - spring, relaxation - relaxation, joy - fun
d) words - homonyms: key (from the lock) - key (spring), scythe (hair) - scythe (tool), bow (weapon) - bow (plant)
e) words - professionalism: industrialization, individualization, affected area, differential, integral, relaxation, motivation, economic development.

19. a) The model of what kind of relations between people is built in I. A. Krylov's fable "The Wolf and the Lamb"? Give lines of fable that support your idea.
Before us is an example of an authoritarian style of relationship. On the one hand, the wolf, as the personification of strength, and, on the other hand, the lamb, as a weakness. The lines: “He sees the lamb, strives for prey” and “the strong one is always to blame for the strong” confirm our reflections.

b) Models of what characters of people are built in I. A. Krylov’s fable “The Dragonfly and the Ant”? Give lines of fable that support your idea.
The model of a careless type of character (dragonfly) and a hardworking one (ant) is contrasted. The lines: “who wants to be full in winter” and “did you sing all the time? This is the case: so go dance!”

20. Proverbs, sayings, popular expressions are original models that we use in speech to give it figurativeness and emotionality. Read the stories of the origin of sayings and describe the modern situations they serve as models for.

21. Think of and write down sequences.

22. Carefully read the text of paragraph 2.3 "Verbal Information Models". Answer in writing the question “Why is natural language not always suitable for creating information models”?

23. Build a mathematical model for solving the problem.
One package contains n ceramic tiles measuring 33 cm x 33 cm.
Let X be the desired number of packages, then:
X \u003d (axb) / (33x33) / n

24. Build a graphical model for solving the problem.
From point A to point F there is a straight road 35 km long. Bus stops are located at points B, C, D, E. It is known that AC=12 km, BD=11 km, CE=12 km, DF=16 km. Find the distance: AB, BC, CD, DE and EF.

25. Why the figure below can be considered a geometric model of the formula

26. The gardener has 22 meters of wire with which he wants to mark the border of the future flower bed on the ground. He needs to choose the shape of the flower bed from the following options:

The size of one cell is 1 m x 1 m. Will the gardener have enough wire to mark the border of each of the presented flower beds?
The 1st requires 20 m, the 2nd -22 m, the 3rd - 22 m, the 4th - 24 m.
→ not enough only for the 4th flower bed.

27. Carefully read the text of paragraph 2.4 "Mathematical models". Answer in writing the question: “Why is the main language of information modeling in science the language of mathematics, and not natural language?”

28. Give an example of the tables you met at school.

29. Give an example of a table that you have come across in everyday life.

30. Indicate the main elements of the structure of a well-formed table, indicating the places of the general, top and side headings, as well as the row, column and cell of the table.

31. Write down the basic rules for the design of tables.
1. The title of the tables should give an idea of the information contained in it.
2. The headings of the graphs should be short, not contain unnecessary words and, if possible, abbreviations.
3. The table must indicate the units of measurement. If they are common to the entire table, then they are indicated in the table header (either in brackets or separated by a comma after the title). If the units of measurement differ, then they are indicated in the headings of rows or columns.
4. It is desirable that all cells of the table be filled. If necessary, they enter the following symbols:
? - data unknown,
8-data not possible,
↓-data must be taken from the overlying cell.

32. Make the necessary additions to the diagram.

33. Give an example of a table like "objects - properties".

34. Give an example of a table of the type "objects - objects - one."

35. Give an example of a table like "objects - objects - several."

36. Give an example of a table like "objects - properties - objects".

37. Carefully read the text of clause 2.5 "Tabular Information Models". Answer in writing the question: “What are the advantages and disadvantages of tabular information models?”

38. Five friends live in a small town: Ivanov, Petrov, Sidorov, Grishin and Alekseev. Their professions are different: one is a painter, the other is a miller, the third is a carpenter, the fourth is a postman, the fifth is a hairdresser. Petrov and Grishin never held a paint brush in their hands. Ivanov and Grishin are all going to visit the mill where their friend works. Petrov and Ivanov live in the same house as the postman. Ivanov and Sidorov play towns every Sunday with a carpenter and a house painter. Petrov took football tickets for himself and the miller. Determine the profession of each of the friends.

39. Students of the Pedagogical Institute organized a pop quartet. Michael plays the saxophone. The pianist studies at the Faculty of Geography. The drummer's name is not Valery, and the student of the Faculty of Geography is not called Leonid. Mikhail does not study at the Faculty of History. Andrey is not a pianist and not a biologist. Valery does not study at the Faculty of Physics, and the drummer does not study at the Faculty of History. Leonid does not play the double bass. What instrument does Valery play and what faculty does he study at?

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40. Carefully read the text of paragraph 2.6 "Tabular solution of logical problems." Describe a class of logical problems that can be conveniently solved using tables.

41. Mini-study. During the week, record in a spreadsheet the time you spend on school, doing homework, helping around the house, being active, sleeping, and more.
On one's own
Write a short text about how your week is going. Rate how your week is going. What would you like to change so that time is used more efficiently?
On one's own

42. Carefully read the text of paragraph 2.7 "Computing tables". Formulate the main feature of calculation tables.

43. Consider the general view of the Microsoft Excel application. Connect the labels with arrows to the corresponding window elements familiar to you from working with the Microsoft Word application.

44. Carefully read the text of paragraph 2.8. "Spreadsheets". Formulate the main advantages that information processing with the help of spreadsheets provides in comparison with manual processing.

45. Observe the weather in your locality for a full month. Record the results of observations in the table.

46. During the week, record in a table how you manage your free time: how much time you devote to reading books, how much to watching TV, how much to chatting with friends, etc.
On one's own

Analyze how you use your personal time. Write a short text about it.
On one's own

47. Every schoolchild has a rest every year during vacations, weekends and holidays. In all the remaining days, the student is supposed to study. In accordance with the regulatory legal acts in force on the territory of the Russian Federation, non-working holidays are considered: January 1-5, January 7, February 23, March 8, May 1, May 9, June 12, November 4. If a non-working holiday falls on a weekend, an additional non-working day is provided.
On the 2007 calendar, mark all non-working days (weekends and holidays) with a red marker, vacation days with a green marker.

On one's own

48. Conduct a short survey among relatives, friends, acquaintances or neighbors on the following questions:
1) What do you read (educational or scientific, popular science, fiction, glossy magazines and newspapers)?
2) How much time per day do you spend reading (up to 30 minutes, from 30 minutes to 1 hour, more than 1 hour)?
Interview at least 10 people. Present information in tables.
On one's own

49. The result of a sudden impact on the human body of any environmental factor is called trauma.

Based on the diagram representing the structure of childhood injuries, make an appropriate verbal description. Support it with real life examples.
According to the statistics of child injuries for 2002, it was recorded:
45% - cases of domestic,
36% - street,
11% - school,
4% - road,
4% - sports injuries

Give examples yourself.

50. Data on world population growth are presented using a table, bar chart and graph.

Which of the presented information models gives the most visual representation of population growth and why?
Of the models presented, the chart gives the most visual representation of population growth.
This diagram provides accuracy and clarity of information. Using this chart, it is convenient to compare the population of different periods.

51. Match.

52. Workers of three specialties work in the workshop - turners (T), locksmiths (C) and millers (F). Each worker has a rank not less than the second and not more than the fifth. Diagram a) shows the number of workers with different categories, and diagram b) shows the distribution of workers by specialty. Each worker has only one specialty and one category.

53. The following initial data and calculation formulas are included in the spreadsheet:

54. Carefully read the text of clause 2.9 "Graphs and charts". Formulate the main advantages and disadvantages that diagrams have.

55. Briefly describe a real life situation in which you or your family members have used the chart.
When repairing radios, electrical engineers use electrical circuits.
It is convenient to use route maps when traveling.
Subway maps help a person navigate when moving.
There are visual schemes of actions in various situations.
Apartment schemes help in creating design solutions.

56. Continue the phrases:
a) A scheme is a representation of some object in general, main terms with the help of symbols.
b) A geographical map gives us a reduced generalized image of the Earth's surface on a plane in one or another system of symbols.
c) A drawing is a conditional graphic representation of objects with an exact ratio of their sizes, obtained by the projection method.
d) The block diagram is one of the most visual ways of writing algorithms; in this case, conventions are used.

57. What values will the variables a and b have after the execution of the algorithm?

61. The relation between elements of sets X and Y is given by the equation y=x+1. Draw this relationship using a graph if X=(3,6,9,12), Y=(7,10,13).

62. Build a directory tree with the following full filenames.

63. According to the multi-level list "Devices of a personal computer" (work 5 of the computer workshop), build a tree diagram of relationships.

64. The table shows the cost of transportation between neighboring railway stations. The numbers at the intersections of the rows and columns of the table indicate the cost of travel between the corresponding neighboring stations. If the intersection of a row and a column is empty, then the stations are not adjacent.

65. The table shows the cost of transportation between neighboring railway stations.

66. The table shows the cost of transportation between neighboring railway stations.
The cost of travel along the route is the sum of the fares between the corresponding neighboring stations. Determine the least cost to travel from A to B.

67. Sergey is a big fan of skateboarding. He often goes to the Sport store to find out the prices of some goods. In this store you can buy a fully assembled skateboard. But you can buy a platform, one set of 4 wheels, one set of 2 wheel holders, and a set of metal and rubber parts (bearings, rubber spacers, bolts and nuts), and build your own skateboard.
The prices for these products are presented in the table:

68. To make chains, it is allowed to use five types of beads, denoted by the letters A, D, G, O, U. Each chain must consist of three beads, while the following rules must be observed:
1) in the first place is one of the letters: A, O, U;
2) after a vowel in a chain, a vowel cannot again go, and after a consonant - a consonant;
3) the last letter cannot be A.
Write down all the chains that can be built according to these rules.

69. Write out the basic concepts of Chapter 2 "Information Modeling" and give their definitions.
Model - an object that is used as a "substitute", a representative of another object (original) for a specific purpose.
information model– descriptions of original objects in coding languages.
Natural (material) model- real objects, in a reduced or enlarged form, reproducing the appearance, structure and behavior of the object.
Mathematical model- a model built using mathematical concepts and formulas.
Model verbal- description of the situation, event, process in natural language.
table- a list of information, numerical data, given in a certain system and separated by columns; variety of information models. Used to describe a number of objects that have the same set of properties.
Table type "objects - objects - several" (UN) is a table containing information about several properties of pairs of objects belonging to different classes.
Table type "objects - objects - one" (OOO) is a table containing information about a single property of pairs of objects, most often belonging to different classes.
Table type "objects - properties" (OS) is a table containing information about the properties of individual objects belonging to the same class.
Table type "objects - properties - objects" (OCO) is a table containing information about the properties of pairs of objects belonging to different classes, as well as about single properties of objects of one of the classes.
Table computing– a table in which the values of some properties are calculated using the values of other properties from the same table.
Scheme- representation of some object in general, main terms with the help of symbols.