Types of information models. Integrated lesson "Formalization and visualization of models. Types of information models" Information model of organizing classes in the school is

Grade 11

Theme lesson: Statistics. Statistical data. Construction of regressive models using a tabular processor.

Objectives: Teach students to create and explore information models using spreadsheets.

Requirements for knowledge and skills:

Students should know:

Stages of modeling;

stages of obtaining regressive models.

Students should be able to:

Simulate in compliance with all stages;

Work in the MS Exsel application.

Software-methodical support: PC, MS Excel spreadsheets.

During the classes:

Org. moment(greeting, preparation of the workplace, landing students).

Objectives lesson:today at the lesson, we must learn how to create models describing the relationship between the quantitative characteristics of statistical data.

Task lesson:according to proposed statistics, build the most appropriate model.

Theme lesson: Statistical data. Building regressive models.

Repetition of the material studied.

Purpose: Knowledge control.

Method: testing.

Option 1

1. The model is the replacement of the object being studied by another object, which reflects:

A) all directions of this object;

B) some parties of this object;

B) the essential sides of this object;

D) insignificant aspects of this object.

2. The result of the formalization process is:

A) descriptive model;

C) graphic model;

B) mathematical model;

D) subject model.

3. The information model of organizing classes at school is:
A) the arrangement of the rules of the behavior of students

C) the schedule of lessons;

B) list of class;

D) List of textbooks.

4. The material model is:

A) airplane layout;

C) drawing;

B) card;

D) diagram.

5. Family family tree is:

B) network information model;

A) anatomical lion;

C) ship model;

B) the layout of the building;

D) diagram.

7. Indicate in the modeling process of the temperature mode of the room

simulation object:

A) air convection in the room;

C) room;

B) the study of temperature

D) temperature, room mode;

8. The correct order of the specified stages of mathematical modeling of the process:

analysis analysis;

determination of modeling purposes;

conducting research;

search for mathematical description.

Corresponds to the sequence:

A) 3-4-2-1;

C) 2 - 1 - 3 - 4;

B) 1 - 2 - 3 - 4;

D) 3-1-4-2.

nine . From how many objects, as a rule, is the system?

A) of several;

C) from an infinite number;

B) from one;

D) She is not divisible.

10. What is the name of the graph designed to display nesting, subordination,

inheritance, etc. Between objects?

A) scheme;

C) table.

B) network;

D) a tree;

11. The oral presentation of the information model is called:
A) graphic model;

C) tabular model;
B) the verbal model;

D) a logical model.

12. Streamlining information on a specific feature is called:
A) sorting;

C) systematization;

B) formalization;

D) modeling.

(Answers: 1-B, 2-b, 3-B, 4-A, 5-b, 6-g, 7-g, 8-A, 9-A, 10-B, 11-B, 12-A )

Option 2.

1 . What is the simplified presentation of the real object?

A) original;

C) model;

B) prototype;

D) system.

2. The process of building models is called:

A) modeling;

C) experimentation;

B) design;

D) Design.

3. The information model consisting of rows and columns is called:
A) table;

C) scheme;

B) schedule;

D) drawing.

4. What is the general name of models that are a totality of useful and

the desired information about the object?

A) material;

C) subject;

B) informational;

D) verbal.

5. The circuit of the electrical circuit is:

A) tabular information model;

B) the hierarchical information model;

B) the graphics information model;

D) the verbal information model.

6. The icon model is:

A) map;

C) globe;

B) children's toys;

D) Building layout.

7. Indicate in the modeling of the process of study of the temperature mode of the room

simulation:

A) air convection in the room;

B) study of the temperature mode of the room;

B) room;

D) Temperature.

8. The correct definitions of concepts are given in paragraphs.

simulated parameter - features and properties of the original object that should

be sure to possess the model;

simulated object - subject or group of objects, structure or behavior

which are investigated by modeling;

the law is the behavior of the simulated object.
A) 1 - 2 - 3;

C) 1 - 3;
B) 2-3;

D) 1- 2.

9. A tool for computer simulation is:
A) scanner;

C) printer;

B) computer;

D) monitor.

10. What is the name of the means for a visual representation of the composition and structure of the system?

A) table;

C) text;

B) graph;

D) drawing.

11.Cax are called models in which based on the analysis of various conditions

is the decision?

A) verbal;

C) tabular;

B) graphic;

D) logical.

12. The solution to the task of automating ticket sales requires us to use:

A) graphic editor;

C) operating system;

B) text editor;

D) programming language

(Answers: 1-B, 2-A, 3-A, 4-B, 5-B, 6-A, 7-g, 8-g, 9-b, 10-b, 11-g, 12-g)

4. Study of the new material

Statistics and statistics

Statistics - Science of collective, measuring and analyzing mass quantitative data.

Consider an example from medical statistics. Specialists collected information from different cities on the average carbon monoxide concentration in the atmosphere C and the incidence of asthma (the number of chronic patients per 1000 inhabitants P.

Consider a tabular and graphical representation of statistical data.

With mg / cubic meters

R Bol. / Thousand

2,5

2,9

3,2

3,6

3,9

4,2

4,6

108

171

How to build a mathematical model of this phenomenon now? It is necessary to obtain the formula for dependence P from C. The schedule of the desired function should be close to the points of the experimental data chart.

Basic requirements for the desired function:

It should be easy to use it in further computing;

The graph of this function should pass near the experimental points so that the deviations of these points about the schedule are minimal and uniform.

The function obtained in this way is called in statistics regression model.

2) Obtaining a regression model occurs in two stages:

Selection of type of function;

Calculate function parameters.

Most often, the choice is made among the following functions:

Linear function;

Quadratic function;

Logarithmic function;

Exponential function;

Power function.

In all these formulas X - argument, y - the value of the function, A, B, C - the parameters of the functions.

If one of the functions is selected, you need to select the parameters so that the function is located as close as possible to the experimental points.

Exists least square method (MNC). The essence is the desired function should be constructed so that the sum of the squares of the deviations of the Y-coordinate of all experimental points from the Y-coordinate of the function graphics would be minimal.

Charts regression model are called trend. (English word Trend is translated as a general direction or trend).

We describe the obtaining algorithm using MS Excel regression models on MNA with a trend construction.

Enter tabular data.

Build a point chart, where as a signature to the OX axis, select the text "Linear Trend" (the remaining inscriptions and the legend can be ignored).

Click the mouse over the field of the diagram; Run the team diagram - add a trend line;

In the window that opens on the Type tab, select "Linear Trend";

Go to the "Parameters" tab and set the checkboxes on the checkboxes "Show equations on the chart" and "Place the value of the value of amplosication in the diagramR ^ 2 "and click OK.

Similarly, we also receive other trends.

We obtained a regressive mathematical model and can predict the process by calculations. Now it is possible to estimate the incidence of asthma not only for those values \u200b\u200bof the concentration of carbon monoxide, which were obtained by measurements, but also for other values. This is very important from a practical point of view. For example, if the city is planned to build a plant that will throw into the atmosphere of carbon monoxide, then, having calculated the possible concentration of gas, one can predict how this will affect the incidence of asthma city residents.

Two ways to predict the regressive model:

Restoration of values \u200b\u200b- forecast within the experimental values \u200b\u200bof an independent variable.

Extrapolation - forecasting outside experimental data

Build the following this:

21,845 * A2 * A2-106.97 * A2 + 150,21

Substituting the values, we get:

Condition of carbon monoxide (mg / cubic meters)

The number of patients with asthma per 1 thousand inhabitants

(The number is fractionable, but we remove the fractional part - because this is the number of people)

2 Method: We continue the trend beyond the experimental data:

During extrapolation, it is impossible to leave the experimental area. Abroad the character of addiction may change

5.Computer workshop

Practical tasks

Exercise 1 The present table is given a forecast of the average daily temperature for the last week of May in various cities of the European part of Russia. Cities are ordered alphabetically. The geographical latitude of these cities is also indicated. Build several options for regression models (at least three), reflecting the temperature dependence on the latitude of the city. Select the most suitable feature.

Latitude, gr.s.sh.

Temperature

Krasnodar

Novorossiysk

Rostov-on-Don

Severodvinsk

Cherepovets

Yaroslavl

Task 2. According to the average daytime temperature in our city for the last week (10 days) by graphic extrapolation, try predicting the temperature after 2 to 5 days. Evaluate whether a description of a linear trend is suitable for describing the nature of temperature change over time.

Temperature about S.

Note:

The table in MS Excel is more convenient to build as follows:

Temperature

Homework Come up with your examples of practical tasks for which it would make sense to fulfill the recovery of values \u200b\u200band extrapolation calculations. (Data can be taken from statistical tables shown as examples)

6.Instation of the results of the lesson

What new we studied in the lesson? What did you learn?

So today in the lesson we learned how to build regressive models based on statistical data and predict in two ways to further develop events. Estimates will be exhibited for the test + active work in the lesson.

We estimate the work of the class and call students who distinguished themselves in the lesson.

Homework:According to the following table, build with MS Excel linear, quadratic, exponential and logarithmic regression models. Define the parameters, select Model.

Literature:

Theoretical and practical material is based on the material set forth in the following print editions:

Semaakin I.G. Informatics 11 class

Chapter 2. Mathematical modeling in planning and management.

§.6. Representation of dependencies between values.

p.2.7. About statistics and statistical data.

p.2.8. Least square method.

§.9. Construction of regression models using a tabular processor.

2) Semaakin I.G. Information systems and models. Elective course: Tutorial

Chapter 2 Computer Mathematical Modeling

3) Semaakin I.G. Information systems and models. Elective course: workshop

Section 2 Computer Mathematical Modeling

4) Ugrinovich N.D. Study of information models. Tutorial

Test on the topic "Models and modeling"

Option 1

1. The model is the replacement of the object being studied by another object, which reflects:

a) all sides of this object;

b) some parties of this object;

c) the essential sides of this object;

d) insignificant aspects of this object.

2. The result of the formalization process is:

a) descriptive model; c) graphic model;

b) mathematical model; d) subject model.

3. The information model of the organization at school is:

a) the set of rules of the behavior of students; c) the schedule of lessons;

b) list of class; d) List of textbooks.

4. The material model is:

a) airplanes layout; c) drawing;

b) card; d) diagram.

5. Family family tree is:

b) the hierarchical information model;

c) network information model;

d) the verbal information model.

a) anatomical lion; c) ship model;

b) the layout of the building; d) diagram.

b) study of the temperature mode of the room;

c) room;

d) Temperature.

8. The correct order of the specified stages of mathematical modeling of the process:

1) analysis of the result; 3) determination of modeling purposes;

2) conducting research; 4) Search for a mathematical description.

Corresponds to the sequence:

a) 3 - 4 - 2 - 1; c) 2 - 1 - 3 - 4;

b) 1 - 2 - 3 - 4; d) 3 - 1 - 4 - 2;

9. From how many objects, as a rule, is the system?

a) of several; c) from an infinite number;

b) from one; d) She is not divisible.

10. What is the name of the graph designed to display nesting, subordination, inheritance, etc. Between objects?

a) scheme; c) table;

b) network; d) a tree.

11. The oral presentation of the information model is called:

a) graphic model; c) tabular model;

b) the verbal model; d) a logical model.

12. Streamlining information on a specific feature is called:

a) sorting; c) systematization;

b) formalization; d) modeling.

Option 2.

1. What is the simplified representation of the real object?

a) original; c) model;

b) prototype; d) system.

2. The process of building models is called:

a) modeling; c) experimentation;

b) design; D) Design

3. The information model consisting of rows and columns is called:

a) table; c) scheme;

b) schedule; D) drawing.

4. What is the general name of the models that are a totality of useful and necessary information about the object?

a) material; c) subject;

b) informational; d) verbal.

5. The circuit of the electrical circuit is:

a) tabular information model;

b) the hierarchical information model;

c) the graphics information model;

d) verbal information model

6. The icon model is:

a) card; c) globe;

b) children's toys; d) Building layout.

7. Indicate in the modeling of the process of study of the temperature mode of the room, the purpose of modeling:

a) air convection in the room;

b) study of the temperature mode of the room;

c) room;

d) Temperature.

8. The correct definitions of concepts are given in paragraphs.

1) Simulated parameter - features and properties of the object - the original that the model must necessarily have;

2) the simulated object is an object or group of objects, the structure or behavior of which is investigated by modeling;

3) The law is the behavior of the simulated object.

a) 1 - 2 - 3; c) 1 - 3;

b) 2 - 3; d) 1 - 2.

9. The computer simulation tool is:

a) scanner; c) printer;

b) computer; d) monitor.

10. What is the name of the means for a visual representation of the composition and structure of the system?

a) table; c) text;

b) graph; d) drawing.

11. What are the models in which the solution is based on the analysis of various conditions?

a) verbal; c) tabular;

b) graphic; d) logical.

12. The solution to the task of automating ticket sales requires us to use:

a) graphic editor; c) operating system;

b) text editor; d) programming language.

Crossword on the topic "Models and modeling"

Horizontally:

1. Some subject.

2. Description of the model using a formal language.

3. Count, designed to display nesting, subordination, inheritance, etc. Between objects.

4. The common name of the models that can be born.

5. Tool for computer simulation.

6. The common name of the models that represent the totality of the useful and necessary information about the object.

Vertically:

7. Information model consisting of rows and columns.

8. A means for a visual representation of the composition and structure of the system.

9. The process of building models.

10. Count displaying a sequence of action.

11. Simplified representation of a real object, process or phenomenon.

Answers:

Horizontally:

1. Object; 2. Formalization; 3.Derevo; 4. Material; 5. Computer; 6. Information.

Vertically:

7. Table; 8. Graph; 9. Modeling; 10. Scheme; 11. Model.

Test on the topic "Models and modeling"

Option 1

1. The model is the replacement of the object being studied by another object, which reflects:

a) all sides of this object;

b) some parties of this object;

c) the essential sides of this object;

d) insignificant aspects of this object.

2. The result of the formalization process is:

a) descriptive model; c) graphic model;

b) mathematical model; d) subject model.

3. The information model of the organization at school is:

a) the set of rules of the behavior of students; c) the schedule of lessons;

b) list of class; d) List of textbooks.

4. The material model is:

a) airplanes layout; c) drawing;

b) card; d) diagram.

5. Family family tree is:

b) the hierarchical information model;

c) network information model;

d) the verbal information model.

a) anatomical lion; c) ship model;

b) the layout of the building; d) diagram.

7. Specify in modeling the process of studying the temperature mode of the room modeling object:

b) study of the temperature mode of the room;

c) room;

d) Temperature.

8. The correct order of the specified stages of mathematical modeling of the process:

1) analysis of the result; 3) determination of modeling purposes;

2) conducting research; 4) Search for a mathematical description.

Corresponds to the sequence:

a) 3 - 4 - 2 - 1; c) 2 - 1 - 3 - 4;

b) 1 - 2 - 3 - 4; d) 3 - 1 - 4 - 2;

9. From how many objects, as a rule, is the system?

a) of several; c) from an infinite number;

b) from one; d) She is not divisible.

10. What is the name of the graph, designed to display nesting, subordination, inheritance, etc. Between objects?

a) scheme; c) table;

b) network; d) a tree.

11. The oral presentation of the information model is called:

a) graphic model; c) tabular model;

b) the verbal model; d) a logical model.

12. Streamlining information on a specific feature is called:

a) sorting; c) systematization;

b) formalization; d) modeling.

Option 2.

1. What is the simplified representation of the real object?

a) original; c) model;

b) prototype; d) system.

2. The process of building models is called:

a) modeling; c) experimentation;

b) design; D) Design

3. The information model consisting of rows and columns is called:

a) table; c) scheme;

b) schedule; D) drawing.

4. What is the general name of the models that are a totality of useful and necessary information about the object?

a) material; c) subject;

b) informational; d) verbal.

5. The circuit of the electrical circuit is:

a) tabular information model;

b) the hierarchical information model;

c) the graphics information model;

d) verbal information model

6. The icon model is:

a) card; c) globe;

b) children's toys; d) Building layout.

7. Indicate in the modeling of the process of study of the temperature mode of the room, the purpose of modeling:

a) air convection in the room;

b) study of the temperature mode of the room;

c) room;

d) Temperature.

8. The correct definitions of concepts are given in paragraphs.

1) Simulated parameter - features and properties of the object - the original that the model must necessarily have;

2) the simulated object is the object or group of objects, the structure or behavior of which is investigated by modeling;

3) The law is the behavior of the simulated object.

a) 1 - 2 - 3; c) 1 - 3;

b) 2 - 3; d) 1 - 2.

9. The computer simulation tool is:

a) scanner; c) printer;

b) computer; d) monitor.

10. What is the name of the means for a visual representation of the composition and structure of the system?

a) table; c) text;

b) graph; d) drawing.

11. What are the models in which the solution is based on the analysis of various conditions?

a) verbal; c) tabular;

b) graphic; d) logical.

12. The solution to the task of automating ticket sales requires us to use:

a) graphic editor; c) operating system;

b) text editor; d) programming language.

The organization model is a special systematized complex of teacher's patterns during the student's training, which is divided into two types: adragological and pedagogical.

In general, the model is various ways of presenting reality. Each model has a specific appearance, form, description and presentation option. In school institutions, for example, the consideration of material and intangible information models is mostly expected. Any information model is a set of information about the object, process, phenomenon, with which you can characterize the process originating in nature. Thus, the information model of organizing classes at school is the schedule of lessons, because organizational information is borne for teachers and students. The information model in the field of education is various sciences - biology, botany, zoology and others, as they represent information on external features and characteristics in educational posters, illustrations on subjects taught. Due to the combination of information models in all possible options, an adequate assessment of a living or non-living world is formed in the younger generation.

Abstract lesson on the topic
"Types of information models"

educational: to master the table and hierarchical form of the presentation of the information model;
educational: the formation of independence and responsibility when studying a new material;
developing: Develop the ability to describe information models, highlighting essential modeling objectives.

Software - Didactic Safety lesson: PC, projector, screen, cards with dough and tasks.
Type of lesson: Studying a new material.

During the classes:

Org. Moment: 2 min.

greeting;
check present.

Actualization of previous knowledge: 10 min

Test (2 options)

Option 1

1. The model is the replacement of the object being studied by another object, which reflects:

all directions of this object;
some sides of this object;
the essential sides of this object;
in-interests of this object.

2. The result of the formalization process is:

descriptive model;
mathematical model;
graphic model;
subject model.

3. The information model of the organization at school is:

arrangement of the rules of the behavior of students;
class list;
timetable;
list of textbooks.

4. The material model is:

airplane layout;
map;
drawing;
diagram.

5. The icon model is:

anatomical lion;
building layout;
ship model;
diagram.

6. Specify in modeling the process of studying the temperature mode of the room modeling object:

air convection in the room;
room;
temperature.

7. The correct order of the specified stages of mathematical modeling of the process:
1) analysis of the result;
2) conducting research;
3) determination of modeling purposes;
4) Search for a mathematical description.
Corresponds to the sequence:
3-4-2-1;
1-2-3-4;
2-1-3-4;
3-1-4-2.

8. From how many objects, as a rule, is the system?

from several;
from one;
from an infinite number;
she is indivisible.

9. What is the name of the graph, designed to display nesting, subordination, inheritance, etc. Between objects?

scheme;
network;
table.
tree;

10. The oral presentation of the information model is called:

graphic model;
verbal model;
mathematical model;
logical model.

11. Streamlining information on a specific feature is called:

sorting;
formalization;
systematization;
modeling.

Option 2.

1. What is the simplified representation of the real object?

original;
prototype;
model;
system.

2. The process of building models is called:

modeling;
constructing;
experimentation;
design.

3. The information model consisting of rows and columns is called:

table;
schedule
scheme;
drawing.

4. What is the general name of the models that are a totality of useful and necessary information about the object?

material;
subject;
information;
wonderful.

5. The icon model is:

map;
kids toys;
the globe;
building layout.

6. Indicate in the modeling of the process of study of the temperature mode of the room, the purpose of modeling:

air convection in the room;
study of the temperature mode of the room;
room;
temperature.

7. The correct definitions of concepts are given in paragraphs.
1) the simulated parameter - features and properties of an object of the original that the model must necessarily have;
2) the simulated object is an object or group of objects, the structure or behavior of which is investigated by modeling;
3) The law is the behavior of the simulated object.

1-2-3;

8. The computer simulation tool is:

scanner;
a computer;
printer;
monitor.

9. What is the name of the means for a visual representation of the composition and structure of the system?

table;
graph;
text;
picture.

10. What are the models in which the solution is based on the analysis of different conditions?

verbal;
graphic;
mathematical;
brain teaser.

11. Construction of the model in the formal language is called:

sorting;
formalization;
systematization;
modeling.

III. Studying a new material: 20 min
Message Topics lesson.
Let's analyze such a life situation: you need to purchase a mobile phone. When buying what do you pay attention to first (appearance)? What information do you mean?

Is this complete information about the object? What is the best form of information about the appearance of the phone?
What else do you pay attention when buying a phone (phone function? What information do you mean?
The information is submitted in the form of a table.

Parameter	The value of the parameter
Cost
Infrared port
Talking
Vibrating alert

This table is the best form of the presentation of the functionality of the phone?
In this example, two table models of one real object are built - mobile phone. The first model is convenient in graphical representation, and the second is in the table. When building a tabular information model, the goal of creating a model is of particular importance.
With the help of tables, information models are built in various objects of Nr, in mathematics - multiplication table, chemistry Table Mendeleev, schedule of lessons, trains. For example, a tabular model of the cost of individual computer devices. The first column of the table contains a list of objects (devices included in the computer, and in the second - their price. Give an example of a tabular information model?
In the tabular information model, the list of similar objects or properties is placed in the first column (or row) of the table, and the value of their properties in the following columns (or rows of the table).
The class of objects is a set of objects combined by some common properties.
Properties - characteristics, signs of an object.
Each property has a name and value.
From the following tables below, find the object class, properties of objects.

Annual estimates

Build a tabular model by positional viewing systems.