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Lesson objectives:
- To form in students the concept of formalization, information model. Learn to build a tabular information model using spreadsheets and visualize the model.
- To develop students' research competence when formalizing a model through structuring educational material using spreadsheets.
- For weak students: Arouse interest in the modeling process through the use of feasible tasks, educational software allowing the student to work in accordance with his individual abilities.
- For intermediate students: Develop a sustainable interest in the subject through the construction of tabular models.
- For strong students: Develop a sustainable interest in the modeling process through solving various problems in Excel.
- Contribute to enriching the inner world of students, increasing interest in studying the subject, fostering a culture of behavior and computer literacy.
Software and teaching software: PC, software: Excel, PowerPoint, MS Word, Internet, task cards, interactive whiteboard, presentation.
Requirements for knowledge and skills:
Students should know:
- What is a model, modeling, formalization;
- The main stages of constructing a tabular model.
Students should be able to:
- Structure information using spreadsheets;
- Visualize the model using diagrams.
Lesson progress
I. Org. moment.
II. Updating previous knowledge:
1. Students take an electronic test in two versions and saved in their own folders.
Option 1
1) A model is the replacement of the object under study with another object that reflects:
- all sides of a given object;
- some aspects of this object;
- essential aspects of this object;
- insignificant aspects of a given object.
2) The information model for organizing classes at school is:
- set of rules for student conduct;
- class list;
- lesson schedule;
- list of textbooks.
3) The material model is:
- aircraft model;
- map;
- drawing;
- diagram.
4) Indicate the modeling object in the modeling of the process of studying the temperature regime of the room
- air convection in the room;
- room;
- temperature;
5) The oral presentation of the information model is called:
- graphic model;
- verbal model;
- mathematical model;
- logical model.
Option 2
1) What is a simplified representation of a real object called?
- original;
- prototype;
- model;
- system.
2) The process of building models is called:
- modeling;
- design;
- experimentation;
- design.
3) Information model, consisting of rows and columns, is called:
- table;
- schedule
- scheme;
- drawing.
4) What is the general name of models that represent a set of useful and necessary information about the object?
- material;
- subject;
- informational;
- verbal.
5) Indicate the purpose of modeling in modeling the process of studying the temperature regime of the room:
- air convection in the room;
- study of the room temperature;
- room;
- temperature.
2. Explain what a model, modeling is. Give examples of educational models. What is a material model? What is an information model?
3. Complete the task on the interactive whiteboard:
Fill out the table:
III. New topic:
Using multimedia support. Problematic question: “How can you display information models using a computer?” Let's try to find out today.
Man has long used modeling to study objects, processes, phenomena (in the future we will call all of this objects of modeling) in various fields. Throughout history, humanity has used various ways and tools for creating information models. These methods have been constantly improved. Thus, the first information models were created in the form of rock paintings. Currently, information models are usually built and studied using modern computer technologies.
The first stage of any research is the formulation of a problem, which is determined by a given goal. The problem is formulated in ordinary language. Based on the nature of the formulation, all problems can be divided into two main groups. The first group includes tasks in which it is necessary to study how the characteristics of an object will change under some influence on it, “what will happen if?...”. The second group of tasks: what impact must be made on the object so that its parameters satisfy some given condition, “how to do it so that...”.
The second stage is object analysis. The result of analyzing an object is the identification of its components (elementary objects) and the determination of connections between them.
The third stage is the development of an information model of the object. The construction of the model must be related to the purpose of the modeling. Each object has large number various properties. In the process of building a model, the main, most essential properties that correspond to the goal are identified.
Everything that was mentioned above is formalization, i.e. replacing a real object or process with its formal description, i.e. its information model. How does this happen?
Examples from mathematics, physics, chemistry, geography, music, etc.
Information model of a water molecule
Verbal model:“A water molecule consists of an oxygen atom and two hydrogen atoms.”
Geometric model:
Chemical model: H2O
Right Triangle Information Model
Verbal model:“A right triangle is a triangle in which one of the angles is right”
Geometric model:
Mathematical model: <А+<В+<С=180° , АВ 2 =АС 2 +ВС 2
I draw your attention to the mathematical model. It is written in mathematical language or formal language. You and I know that languages can be natural and formal. Natural languages are used to create descriptive information models. With the help of formal languages, formal information models (mathematical, logical, etc.) are built. One of the most widely used formal languages is mathematics. Models built using mathematical concepts and formulas are called mathematical models. However, in some cases specialized formal languages are used (in chemistry - the language of chemical formulas, in music - musical notation, etc.)
The process of building information models using formal languages is called formalization.
Modeling of any system is impossible without preliminary formalization. In fact, formalization is the first and very important stage of the modeling process.
In the process of studying formal models, their visualization is often used. To visualize algorithms, block diagrams, spatial relationships between objects - drawings, models of electrical circuits - electrical diagrams are used. When visualizing formal models using animation, the dynamics of the process can be displayed, graphs of changes in quantities can be constructed, etc. Example on slide .
To reflect systems with different structures, the following types of information models are used: tabular, hierarchical, network.
One of the most common forms of representing information models is tables. Very often, information in various documents, reference books, and textbooks is presented in tabular form. With the help of tables, information models are built in various subject areas, for example, in mathematics - the multiplication table, chemistry - the periodic table, lesson schedules, train schedules.
Tabular – objects and their properties are presented in the form of a list, and their values are placed in rectangular cells. The list of objects of the same type is placed in the first column (or row), and the values of their properties are placed in the following columns (or rows).
Let's look at this life situation: you need to buy a mobile phone. When buying, what do you pay attention to first (appearance)? What information matters?
The information is presented in the form of a table.
Is this complete information about the object? What is the best way to present information about the appearance of a phone? What else do you pay attention to when buying a phone (phone features)? What information matters? The information is presented in the form of a table.
|
Parameter |
Parameter value |
Price |
|
Infrared port |
|
Talk mode |
|
Vibration alert |
|
Is this table the best way to present the phone's functionality? In this example, two tabular models of one real object are built - a mobile phone. The first model is convenient in graphical representation, and the second in tabular representation. When building a tabular information model, the purpose of creating the model is of particular importance.
Thus, the tabular form gives conciseness and clarity to the data, structures the data, and allows you to see patterns in the nature of the data.
An important role is played by information models that reflect hierarchical systems . In biology, the entire animal world is considered as a hierarchical system (phylum, class, order, family, genus, species); in computer science, a hierarchical file system and classification of computers are used. To describe the historical process of changing generations of a family, dynamic information models in the form of a family tree are used. As an example, we can consider a fragment (X – XI) centuries of the family tree of the Rurik dynasty. In a hierarchical model, objects are arranged in levels. Each higher-level element can contain several lower-level elements, and each lower-level element can be part of only one upper-level element.
A convenient way to visually represent hierarchical information models are graphs. Elements of the hierarchical model are displayed in the graph as ovals (vertices of the graph). Graphs that have one top-level vertex resemble trees that grow from top to bottom, which is why they are called trees. As an example, we can consider a fragment of the family tree of the Rurik dynasty.
Let us schematically present the following description:“Natural resources are divided into exhaustible and inexhaustible by reserve. Exhaustible resources are either non-renewable or renewable. In addition, according to their purpose, natural resources are divided into multi-purpose, industrial, and agricultural.” (Slide)
Now let's present this information in the form of a hierarchy.
Network information models – used to reflect systems in which the connections between elements have a complex structure. An example of network models is, for example, various regional parts of the global computer network Internet (American, European, Russian, Australian, and so on) are interconnected by high-speed communication lines. At the same time, some parts (for example, the American one) have direct connections with all regional parts of the Internet, while others can exchange information with each other only through the American part (for example, the Russian and Australian ones). The vertices of the graph are regional networks. Connections between vertices are two-way in nature and therefore are depicted by non-directional lines ( ribs), and the graph itself is therefore called unoriented.
IV. Fastening:
Task 1.
Build a tabular model using positional number systems.
What is a number system? What two classes are number systems divided into?
How does a positional number system differ from a non-positional number system?
Notation |
Base |
Alphabet of numbers |
Binary |
||
Decimal |
0,1,2,3,4,5,6,7,8,9 |
|
Octal |
||
Hexadecimal |
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F |
Based on knowledge about the graph, let's build a hierarchical model for the above example. What is a graph, graph vertices, arcs?
What is the top?
Task 2.
A verbal description of such a phenomenon as the growth of the Earth's population is given. Build models that would help to more clearly imagine this phenomenon.
As shown by research, humanity as a single system has existed for more than a million years. The development of this system can be judged by changes in its key parameters. One of these parameters is the number of people on Earth.
In 1000 there were 305 million people in the world, in 1500 - 440 million, in 1800 - 950 million, in 1900 1 billion 660 million, in 1950 - 2 billion 530 million, in 1980 - 4 billion 430 million, in 1990 - 5 billion 290 million, in 2000 - 6 billion 250 million.
Task 3.
The following graph shows a possible blood transfusion system. Indicate what kind of blood a person with the first, second, third, or fourth blood group can receive.
Problem 4.
Determine which of the five servers is the hub? (Students' answers)
The solution is very simple: since, according to this definition, the hub server is the one with which all other servers are directly connected, then in the matrix you need to look for a row consisting only of ones. This line is C4. This means that the C4 server is a hub server. As an additional task, I propose to draw this computer network, depicting the servers as circles and the connections between them as lines. Now we are convinced that the tabular information model allows you to analyze information faster.
“Forms of information models” - Types. Network information models. Properties. Communication of regional units. List of similar objects. Table of the “object - properties” type. Classifications of objects. Types of information models. Hierarchical models. Information models. Objects. Static hierarchical models. Student. Dynamic hierarchical models.
“Models on graphs” - Graph. Composition of the graph. Course of reasoning. Road map. Hierarchy. Task. Chain. Roads. Information models on graphs. Semantic Web. Root. Relationship between graph and table. File structure. Tree. Weighted graph. Undirected graph. Roads between five settlements. Directed graph.
“Tabular model” - “Home Library” table. Tabular logical information models. Teenager. Types of tables. Concepts for the “Progress” table. Analysis of initial conditions. Tables of the “objects-properties” type. Concepts for the “Books” table. Tables of the object-object type. Table "Progress". Tabular information models.
“Types of information models” - Tabular models. Verbal models. An example of an object-property table. Diagram. An example of a binary matrix table. An example of an object-object table. Drawing. Examples of graphical information models: Map. Graph. Graphic models. ToC. Time. Types of information models. Schedule. Temperature change graph.
“Graphical information models” - Part drawing. Network and tree. Graphs. Graph of the crossing problem. Variety of graphic information models. Graphic information models. Schemes in physics. Movement description graph. The most important. Diagram. Geographic map of Eurasia. Questions and assignments. Key words. Weighted graph. Using graphs to solve problems.
“Information models on graphs” - Information models on graphs. Draw the system as a graph. System analysis. A tree is a graph that has no loops. Basic concepts. What is a "graph"? Plan. Solving the problem. Present your plan as a graph. Assignments. The information model of an object is its description. Structure is a certain order of combining elements.
There are a total of 16 presentations in the topic
11th grade
Lesson topic: Statistics. Statistics. Building regression models using a spreadsheet processor.
Goals: Teach students to create and explore information models using spreadsheets.
Requirements for knowledge and skills:
Students should know:
Modeling stages;
stages of obtaining regression models.
Students should be able to:
Model in compliance with all stages;
Work in MS Excel application.
Software and methodological support: PC, MS Excel spreadsheets.
Lesson progress:
Org. moment(greeting, preparing the workplace, seating students).
Lesson objectives: Today in the lesson we must learn how to create models that describe the relationship between the quantitative characteristics of statistical data.
Lesson objective: based on the proposed statistical data, build the most suitable model.
Lesson topic: Statistics. Construction of regression models.
Repetition of learned material.
Target: Knowledge control.
Method: testing.
Option 1
1. A model is the replacement of the object under study with another object that reflects:
A) all sides of this object;
B) some sides of this object;
B) essential aspects of this object;
D) insignificant aspects of this object.
2. The result of the formalization process is:
A) descriptive model;
B) graphical model;
B) mathematical model;
D) subject model.
3.
The information model for organizing classes at school is:
A) a set of rules for student behavior
B) lesson schedule;
B) class list;
D) list of textbooks.
4. The material model is:
A) aircraft model;
B) drawing;
B) map;
D) diagram.
5. The family tree is:
B) network information model;
A) anatomical model;
B) model of the ship;
B) building layout;
D) diagram.
7. Indicate in the simulation the process of studying the temperature regime of the room
modeling object:
A) air convection in the room;
B) room;
B) temperature study
D) temperature, room conditions;
8. The correct order of the indicated stages of mathematical modeling of the process:
result analysis;
defining modeling goals;
conducting research;
search for a mathematical description.
Matches the sequence:
A)3-4-2-1;
B) 2 - 1 - 3 - 4;
B) 1 - 2 - 3 - 4;
D)3-1-4-2.
9 . How many objects does a system typically consist of?
A) from several;
B) from an infinite number;
B) from one;
D) it is not divisible.
10. What is the name of a graph designed to display nesting, subordination,
inheritance, etc. between objects?
A) scheme;
B) a table.
B) network;
D) tree;
11.
The oral presentation of an information model is called:
A) graphical model;
B) tabular model;
B) verbal model;
D) logical model.
12.
Organizing information according to a certain criterion is called:
A) sorting;
B) systematization;
B) formalization;
D) modeling.
(Answers: 1-c, 2-b, 3-c, 4-a, 5-b, 6-d, 7-d, 8-a, 9-a, 10-b, 11-b, 12-a )
Option 2
1 . What is a simplified representation of a real object called?
A) original;
B) model;
B) prototype;
D) system.
2. The process of building models is called:
A) modeling;
B) experimentation;
B) design;
D) design.
3.
An information model consisting of rows and columns is called:
A) table;
B) diagram;
B) schedule;
D) drawing.
4. What is the general name of models that represent a combination of useful and
necessary information about the object?
A) material;
B) subject;
B) informational;
D) verbal.
5. The electrical circuit diagram is:
A) tabular information model;
B) hierarchical information model;
B) graphical information model;
D) verbal information model.
6. The iconic model is:
A) map;
B) globe;
B) children's toys;
D) building layout.
7. Specify the goal in modeling the process of studying the temperature regime of the room
modeling:
A) air convection in the room;
B) study of the temperature regime of the room;
B) room;
D) temperature.
8. Correct definitions of concepts are given in paragraphs
modeled parameter - signs and properties of the original object, which should
must have a model;
modeled object - an object or group of objects, structure or behavior
which are studied using modeling;
law - the behavior of the modeled object.
A) 1 - 2 - 3;
B)1 - 3;
B)2-3;
D)1-2.
9.
The computer modeling tool is:
A) scanner;
B) printer;
B) computer;
D) monitor.
10. What is the name of the tool for visually representing the composition and structure of the system?
A) table;
B) text;
B) graph;
D) drawing.
11.What are the names of the models in which, based on the analysis of various conditions
is a decision being made?
A) verbal;
B) tabular;
B) graphic;
D) logical.
12. Solving the problem of automating ticket sales requires the use of:
A) graphic editor;
B) operating system;
B) text editor;
D) programming language
(Answers: 1-c, 2-a, 3-a, 4-b, 5-c, 6-a, 7-d, 8-d, 9-b, 10-b, 11-d, 12-d)
4. Learning new material
Statistics and statistical data
Statistics – the science of collecting, measuring, and analyzing mass quantitative data.
Let's consider an example from medical statistics. Experts have collected information from different cities on the average concentration of carbon monoxide in the atmosphere C and on the incidence of asthma (the number of chronic patients per 1000 inhabitants of P.
Let's consider a tabular and graphical presentation of statistical data.
With mg/cub.m.
R Bol./thousand
2,5
2,9
3,2
3,6
3,9
4,2
4,6
108
171
How can we now build a mathematical model of this phenomenon? It is necessary to obtain a formula for the dependence of P on C. The graph of the desired function should pass close to the points of the experimental data diagram.
Basic requirements for the required function:
It should be simple enough to be used in further calculations;
The graph of this function should pass near the experimental points so that the deviations of these points from the graph 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:
Selecting the type of function;
Calculation of 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 is the argument, y is the value of the function, a, b, c are the parameters of the functions.
When choosing one of the functions, you need to select the parameters so that the function is located as close as possible to the experimental points.
Exists least squares method(MNC). The bottom line is that the desired function must be constructed so that the sum of the squared deviations of the y-coordinates of all experimental points from the y-coordinates of the function graph is minimal.
Regression model graphs are called trends. (The English word trend is translated as general direction or tendency).
Let us describe the algorithm for obtaining regression models using OLS with the construction of a trend using MS Excel.
Enter tabular data.
We build a scatter diagram, where we select the text “Linear trend” as the label for the OX axis (the rest of the labels and the legend can be ignored).
Click on the diagram field; execute the command Chart – Add trend line;
In the window that opens, on the “Type” tab, select “Linear trend”;
Go to the “Parameters” tab and check the boxes “show equations on the diagram” and “place the amplification confidence value on the diagram” R^2" and click OK.
We get other trends similarly.
We have obtained a regression mathematical model and can predict the process through calculations. Now it is possible to estimate the incidence of asthma not only for those values of carbon monoxide concentrations that were obtained by measurements, but also for other values. This is very important from a practical point of view. For example, if a city plans to build a plant that will emit carbon monoxide into the atmosphere, then by calculating the possible concentration of the gas, you can predict how this will affect the incidence of asthma in city residents.
Two methods of forecasting using a regression model:
Restoring values is a forecast within the experimental values of the independent variable.
Extrapolation—prediction beyond experimental data
We build the following ET:
21.845*A2*A2-106.97*A2+150.21
Substituting the values, we get:
Carbon monoxide concentration (mg/cu.m.)
Number of asthma patients per 1 thousand inhabitants
(The number turns out to be a fraction, but we remove the fractional part - because this is the number of people)
Method 2: We continue the trend beyond the experimental data:
When extrapolating, one should not go far from the experimental area. Beyond its boundaries, the nature of dependence may change
5. Computer workshop
Practical tasks
Task 1 The table below provides 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 geographic latitude of these cities is also indicated. Construct several variants of regression models (at least three), reflecting the dependence of temperature on the latitude of the city. Select the most suitable function.
Latitude, deg.N.
Temperature
Krasnodar
Novorossiysk
Rostov-on-Don
Severodvinsk
Cherepovets
Yaroslavl
Task 2. Based on the average daily temperature in our city for the last week (10 days), by graphical extrapolation, try to predict the temperature in 2 - 5 days. Assess whether the description of a linear trend is suitable for describing the pattern of temperature change over time.
Temperature about C
Note:
It is more convenient to build a table in MS Excel as follows:
Temperature
Homework Come up with your own examples of practical problems for which it would make sense to perform value recovery and extrapolation calculations. (Data can be taken from the statistical tables shown as examples)
6.Summing up the lesson
What new did we learn in class? What have you learned?
So, today in class we learned how to build regression models based on statistical data and predict further developments of events in two ways. Grades will be given for the test + active work in class.
We evaluate the work of the class and name the students who excelled in the lesson.
Homework: Based on the data in the following table, use MS Excel to construct linear, quadratic, exponential and logarithmic regression models. Define parameters, select model.
Literature:
Theoretical and practical material is based on the material presented in the following printed publications:
Semakin I.G. Computer Science 11th grade
Chapter 2. Mathematical modeling in planning and management.
clause 2.6. Representation of dependencies between quantities.
clause 2.7. About statistics and statistical data.
clause 2.8. Least squares method.
clause 2.9. Building regression models using a spreadsheet processor.
2) Semakin I.G. Information systems and models. Elective course: Study guide
Chapter 2 Computer mathematical modeling
3) Semakin I.G. Information systems and models. Elective course: Workshop
Section 2 Computer mathematical modeling
4) Ugrinovich N.D. Research of information models. Tutorial
Option 1
1. A model is the replacement of the object under study with another object that reflects:
A) all sides of this object; C) essential aspects of this object;
B) some sides of this object; D) insignificant aspects of this object.
2. The result of the formalization process is:
A) descriptive model; B) graphical model;
B) mathematical model; D) subject model.
3. The information model for organizing classes at school is:
A) a set of rules for student behavior B) a lesson schedule;
B) class list; D) list of textbooks.
4. The material model is:
A) aircraft model; B) drawing;
B) map; D) diagram.
5. The family tree is:
A) tabular information model; B) network information model;
B) hierarchical information model; D) verbal information model.
A) anatomical model; B) model of the ship;
B) building layout; D) diagram.
7. In the modeling of the process of studying the temperature regime of the room, indicate the modeling object:
A) air convection in the room; B) room;
B) study of temperature D) temperature, room conditions;
8. The correct order of the indicated stages of mathematical modeling of the process:
1) analysis of the result; 3) determination of modeling goals
2) conducting research; 4) search for a mathematical description.
Matches the sequence:
A) 3-4-2-1; B)2-1-3-4;
B)1-2-3-4; D)3-1-4-2.
9. How many objects does a system typically consist of?
A) from several; B) from an infinite number;
B) from one; D) it is not divisible.
10. What is the name of a graph designed to display nesting, subordination, inheritance, etc. between objects?
A) diagram; B) a table.
B) network; D) tree;
11. The oral presentation of an information model is called:
A) graphical model;
B) tabular model;
B) verbal model; D) logical model.
12. Ordering information according to a certain criterion is called:
A) sorting; B) systematization;
B) formalization; D) modeling.
Test on the topic: “Models and Simulation”
Option 2
1. What is a simplified representation of a real object called?
A) original; B) model;
B) prototype; D) system.
2. The process of building models is called:
A) modeling; B) experimentation;
B) design; D) design.
3. An information model consisting of rows and columns is called:
A) table; B) diagram;
B) schedule; D) drawing.
4. What is the general name of models, which represent a set of useful and necessary information about an object?
A) material; B) subject;
B) informational; D) verbal.
5. The electrical circuit diagram is:
A) tabular information model;
B) hierarchical information model;
B) graphical information model;
D) verbal information model.
6. The iconic model is:
A) map; B) globe;
B) children's toys; D) building layout.
7. In the modeling of the process of studying the temperature regime of the room, indicate the purpose of the modeling:
A) air convection in the room;
B) study of the temperature regime of the room;
B) room;
D) temperature.
8. Correct definitions of concepts are given in paragraphs
1) modeled parameter - characteristics and properties of the original object that the model must necessarily possess;
2) modeled object - an object or group of objects, the structure or behavior of which is studied using modeling;
3) law - the behavior of the modeled object.
A) 1 - 2 - 3; B) 1 - 3;
B) 2-3; D) 1-2.
9.
The computer modeling tool is:
A) scanner; B) printer;
B) computer; D) monitor.
10. What is the name of the tool for visually representing the composition and structure of the system?
A) table; B) text;
B) graph; D) drawing.
11. What are the names of models in which, based on an analysis of various conditions, it is accepted solution ?
A) verbal B) tabular;
B) graphic; D) logical.
12. Solving the problem of automating ticket sales requires the use of:
A) graphic editor; B) operating system;
B) text editor; d) programming language