Is a rectangular table consisting of rows and columns. The use of tables is so familiar that it usually does not require further explanation to understand them.
As an example, consider Table 2.1.
Table 2.1. home library
When compiling a table, only the one that interests the user is included in it. For example, in addition to those information about books that are included in table 2.1, there are others: publisher, number of pages, cost. However, for the compiler of Table 2.1, there was enough information to distinguish one book from another (columns "Author", "Title", "Year") and to find a book on the shelves of bookshelves (column "Shelf"). It is assumed that all shelves are numbered and, in addition, each book is assigned its own inventory number (column "Number").
Table 2.1 is an information model of the book stock of the home library.
Table may reflect some process occurring in time (Table 2.2).
Table 2.2. Weather
| Day | Precipitation | Temperature (degrees C) | Pressure (mmHg) | Humidity (percentage) |
| 15.03.04 | Snow | -3,5 | 746 | 67 |
| 16.03.04 | No precipitation | 0 | 750 | 62 |
| 17.03.04 | Fog | 1,0 | 740 | 100 |
| 18.03.04 | Rain | 3,4 | 745 | 96 |
| 19.03.04 | No precipitation | 5,2 | 760 | 87 |
The readings were taken over five days at the same time of day. Looking at the table, it is easy to compare different days in terms of temperature, humidity, etc. This table can be considered as an information model of the process of changing the state of the weather.
Tables 2.1 and 2.2 are the most commonly used table type. We will call them tables of the "object-property" type. One line of such a table contains information about one object (a book in the library or the weather at 12-00 on a given day). Columns - separate characteristics (properties) of objects.
Of course, rows and columns in tables 2.1 and 2.2 can be swapped, rotated by 90 0 . Sometimes they do. Then the rows will correspond to the properties, and the columns to the objects. But most often tables are built in such a way that there are more rows in them than columns. As a rule, there are more objects than properties.
Tables of the "object - object" type
Another common type of table is a table showing relationships between different objects. Let's call them object-to-object tables. Here is an example of a progress table that is understandable to every student (Table 2.3).
Table 2.3. academic performance
Rows refer to students - this is the first kind of objects; columns - to school subjects - the second kind of objects. In each cell at the intersection of a row and a column - the grade received by this student in this subject.
Table 2.4 is also of the object-to-object type. However, unlike the previous table, the rows and columns in it refer to the same kind of objects. This table contains information about the availability of roads between settlements from the map from § 2.
Table 2.4. Roads
Binary matrices
In mathematics, a rectangular table made up of numbers is called a matrix. If the matrix contains only zeros and ones, then it is called a binary matrix. The numerical part of table 2.4 is a binary matrix.
Table 2.5 also contains a binary matrix.
Table 2.5. Electives
It provides information about the visit of four students to three electives. It should be clear to you by now that one means visit, zero means non-visit. From this table it follows, for example, that Rusanov visits geology and dancing, Semenov - geology and floriculture, etc.
The tables, which are binary matrices, reflect the qualitative nature of the relationship between objects (there is a road - there is no road; visits - does not visit, etc.). Table 2.3 contains quantitative characteristics student achievement in subjects, expressed by marks of a five-point system.
We have considered only two types of tables: "object-property" and "object-object". In practice, other, much more complex tables are also used.
Briefly about the main
Rectangular tables are widely used to represent information models.
In an object-property table, one row contains information about one object. Columns - separate characteristics (properties) of objects.
An object-to-object table reflects the relationship between different objects.
A numerical rectangular table is called a matrix. A matrix composed of zeros and ones is called a binary matrix.
Questions and tasks
1. What is the convenience of tabular presentation of information?
2. Give examples of tables that you have to deal with at school and at home. Determine the type to which they refer: "object-property" or "object-object".
3. What is a matrix? What is a binary matrix?
4. Present in tabular form information about the hobbies of your classmates. What type of table are you using for this purpose?
Timetable of classes
| lesson number | 9a | 9b | 10a | 10b | 11a | 11b |
| 1 | ♦ | | | ♦ | | |
| 2 | ♦ | | ♦ | ♦ | | |
| 3 | | ♦ | ♦ | | | |
| 4 | | ♦ | | | ♦ | |
| 5 | | | | | ♦ | ♦ |
| 6 | | | | | | ♦ |
Complete the following tasks:
determine the minimum number of physical education teachers required for such a schedule;
find one of the options for the schedule, in which you can get by with two physical education teachers;
there are three physical education teachers at the school: Ivanov, Petrov, Sidorov; distribute the lessons between them in the table so that no one has “windows” (empty lessons);
Distribute the lessons among the three teachers so that everyone has the same workload.
6. In a computer network, a node is a server with which all other servers are directly connected. Given the following binary matrix. In it, C1, C2, C3, C4, C5 are the designations of the network servers.
| C1 | C2 | C3 | C4 | C5 | |
| C1 | 1 | 0 | 0 | 1 | 0 |
| C2 | 0 | 1 | 0 | 1 | 0 |
| C3 | 0 | 0 | 1 | 1 | 0 |
| C4 | 1 | 1 | 1 | 1 | 1 |
| C5 | 0 | 0 | 0 | 1 | 1 |
Determine which server is the host.
I. Semakin, L. Zalogova, S. Rusakov, L. Shestakova, Informatics, Grade 9
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"Tabular Models. Tables of the "object-property", "object-object" type.
Lesson type: lesson-lecture.
Target: give a clear concept of tabular information models.
Lesson objectives
Tutorials:
give an idea about tables, matrices, binary matrix;
introduce students to the types of tables;
to teach to distinguish tables of different types;
explore: table as a way of presenting information.
Developing:
development of cognitive interests;
develop students' creative thinking, logical thinking;
to form the ability of schoolchildren to apply modern software in solving problems, to develop cognitive interest.
development of attention, memory, thinking;
development of creative abilities;
development of self-control, ability to take notes.
Educational:
instill interest in the subject;
education of attentiveness, accuracy, discipline, education of information culture of students;
to form the skills of independence and discipline;
educate the information culture of schoolchildren;
contribute to the education of purposefulness, perseverance.
Solved educational tasks:
expand understanding of models and modeling;
form / systematize the idea of tabular models as a variety of information models;
form / update the skills of creating and modifying tables.
Knowledge and skills:
know the concept of a table;
understand that the table is a display of various processes;
know and distinguish types of tables;
know the concept of matrix, binary matrix.
Equipment: board, computer, projector, presentation on the topic.
LESSON PLAN
Organizational moment - 2 min.
Checking d / s - 5 min.
Updating knowledge - 4 min.
Explanation of a new topic - 13-15 min.
Consolidation of new material - 16-18 minutes.
Summing up the lesson - 1 min
Homework - 1 min
DURING THE CLASSES
Organizational moment (2 min.)
Subject, number on the board;
Greetings(Hello guys, sit down);
Checking the readiness for the lesson (pens, pencil, ruler, notebook, textbook, diary and safety);
Orally pronounce the lesson plan.
Checking d / s - (5 min)
Checking orally, then the children hand over the forms.
Knowledge update.
One common form of information model isrectangular table , consisting of rows and columns(slide 2). The use of tables is so familiar that it usually does not require further explanation to understand them. Already in school life you have to meet with a lot of tables(slide): class schedule, gradebook, duty schedule, periodic table, tables of physical properties of substances, tables of historical dates and much more. The information in the tables is necessarily ordered according to some principle. For example, in the class magazine - in alphabetical order of the names of students; in the class schedule - by day of the week and number of lessons, etc. This ordering allows you to quickly find the information you need in the table.
Explanation of the new topic
There are several types of rectangular tables(slide).
The most commonly used table type istables of type "object-property" .
Oneline such a table containsinformation about one object (a book in the library or the state of the weather at 12-00 on a given day).columns (graphs) - separatecharacteristics (properties) of objects .
The headings of the columns are usually located in the top row of the table. Here is an example of a rectangular table(slide). This table is an example of a table like"object-property". Each row of such a table refers to a specific object. The first column usually identifies this object, the subsequent columns reflect the properties (characteristics) of the object.
When compiling a table, it includes only the information that the user is interested in.(sweet).
Of course, rows and columns in tables can be swapped by rotating them 90°. Sometimes they do. Then the rows will correspond to the properties, and the columns to the objects. But most often tables are built so that they have more rows than columns. As a rule, there are more objects than properties.
Table example(slide).
Tables are another common type of tables.reflecting relationships between different objects . They are called object-to-object tables.
Here is an example of a progress table that is understandable to every student(slide).
Rows refer to students - this is the first kind of objects; columns - to school subjects - the second kind of objects. In each cell of the table, at the intersection of a row and a column, there is an estimate obtained by a given student in a given subject. In such a table, rows and columns can change places: in the rows - subjects, in the columns - students.
(slide)In mathematics, a rectangular table made up of numbers is calledmatrix. If the matrix contains only zeros and ones, then it is called a binary matrix.An important variety of object-to-object tables arebinary matrices. Binary matrices displayquality connection between objects whether there is a connection or not.
For example, if students could choose the subjects they study at their discretion, then information about who studies what could be presented in the form of the following table (in it, one indicates the subject being studied, and zero indicates not being studied)(slide).
(slide)The following table also hasobject-to-object type and binary matrix type.
However, unlike the previous table, the rows and columns in it refer to the same kind of objects. This table contains information about the availability of direct roads between settlements, according to the map.
The tabular way of presenting data is universal. Any data structure, including those presented in the form of a graph, can be reduced to a tabular form. Bringing information into a tabular form is calleddata normalization (slide).
The following must be observedtable formatting rules (slide).
The title of the table should give an idea of the information it contains.
Headings of columns and rows should be concise, without unnecessary words and, if possible, abbreviations.
For numerical values in the table, units of measurement must be indicated. 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, they are indicated in the headings of the corresponding rows or columns.
It is desirable that all cells of the table be filled. If necessary, they enter the following symbols:
?
- data unknown;X
- data is not possible;
↓ - data must be taken from the overlying (or underlying) cell.
Example(slide, slide)
In order to compile a tabular model based on the information presented in text form, it is necessary(slide):
highlight in the text the names of objects, the names of the properties of objects and the values of the properties of objects;
clarify the structure of the table;
fill in the table, transferring information from the text into it.
When highlighting object names, property names and their values in the text, it is convenient to underline them with different lines. Let's agree to underline object names with a straight line, property names with a double line, and property values with a dotted line.
Consolidation of new material.
Questions and tasks (slide)
1. What is the convenience of tabular presentation of information?
2. Give examples of tables that you have to deal with at school and at home. Determine the type to which they refer: "object-property" or "object-object".
3. What is a matrix? What is a binary matrix?
4. Present in tabular form information about the hobbies of your classmates. What type of table are you using for this purpose?
5. Four football teams: the Italian team "Milan", the Spanish team "Real", the Russian team "Zenith", the English team "Chelsea" met in the group stage of the Football Champions League. They were trained by coaches from the same four countries: Italian Antonio, Spaniard Rodrigo, Russian Nikolay, Englishman John. It is known that the nationality of all four coaches did not match the nationality of the teams. It is required to determine the coach of each team, if it is known:
a) Zenit does not train with John and Antonio.
b) Milan promised never to take John as head coach.
Answer:
6. (slide)Looking at the table, determine which of the five servers is the host.
The solution is the following: Since, according to this definition, the node 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 is line C4. This means that the C4 server is a node server.7. (slide)The next task associated with the same table could be as follows: draw a diagram of a computer network, depicting servers as circles, and connections as lines.
Answer:
This example once again demonstrates that the graphical form is more convenient for visual perception of the system structure, and the tabular form is more convenient for computer processing.
Summing up the lesson
Briefly about the main (sweet)
Rectangular tables are widely used to represent information models.
In an object-property table, one row contains information about one object. Columns - separate characteristics (properties) of objects.
An object-to-object table reflects the relationship between different objects.
A numerical rectangular table is called a matrix. A matrix composed of zeros and ones is called binary.
The binary matrix reflects the qualitative nature of the links between objects.
Homework: (slide)
Review all the material learned in the lesson. Find additional material on the Internet on this topic and study.
Five classmates - Irena, Timur, Camilla, Eldar and Zalim became winners of Olympiads for schoolchildren in physics, mathematics, computer science, literature and geography. It is known that: the winner of the Olympiad in Informatics teaches Irena and Timur how to work on a computer; Camilla and Eldar also became interested in computer science; Timur was always afraid of physics; Camilla, Timur and the winner of the Literature Olympiad go swimming; Timur and Kamilla congratulated the winner of the Mathematics Olympiad; Irena regrets that she has little time left for literature. Which Olympiad did each of these guys win?
Table structure and design rules
To describe a number of objects that have the same set of properties, tables consisting of columns and rows are most often used.
You are well aware of the tabular presentation of the lesson schedule, the schedules of buses, planes, trains and much more are presented in tabular form.
The information presented in the table is clear, compact and easily visible.
The table may contain information about various properties of objects, about objects of the same class and different classes, about individual objects and groups of objects.
A properly formatted table has the following structure:
The following table rules must be observed.
- The title of the table should give an idea of the information it contains.
- Headings of columns and lines should be concise, without unnecessary words and, if possible, abbreviations.
- 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.
- It is desirable that all cells of the table be filled. If necessary, they enter the following symbols:
- \(?\) - data unknown;
- × - data is not possible;
- ↓ - data must be taken from the overlying cell.
In order to compile a tabular model based on the information presented in text form, it is necessary:
- Select in the text the names of objects, the names of the properties of objects and the values of the properties of objects;
- Refine the structure of the table;
- “Populate” the table by transferring information from the text into it.
When highlighting object names, property names and their values in the text, it is convenient to underline them with different lines. Let's agree to underline object names with a straight line, property names with a double line, and property values with dashed lines.
Conventionally, the whole set of tables can be divided into simple and complex.
Simple tables
Table of type "object-properties" (OS)
Table type "objects-properties" is a table containing information about the properties of individual objects belonging to the same class.
General view of OS type tables:
The number of rows in the table depends on the number of available objects, and the number of columns on the number of properties under consideration.
This table contains information about some of the ancient Russian cities that store unique monuments of our culture and history and form the world-famous Golden Ring of Russia. This information is reflected in the header of the table.
The following objects are presented in the table: "Vladimir", "Kostroma", Pereslavl-Zalessky" and "Gus-Khrustalny", belonging to the "city" class. For each object, the values of the properties "year of foundation", "founder" and "attraction", expressed in numbers and words, are given.
In small tables (of \(3 - 4\) rows), objects can be listed in any order. If there are many objects in the table, then they must be arranged in some meaningful order, according to some rule. For example, in the table \(2.2\), cities can be listed alphabetically, in ascending or descending order by the year they were founded.
If there are more properties in the OS type table than objects, then it can be “turned on its side”: the rows are turned into graphs, and the graphs into rows.
Table type "objects - objects - one" is a table containing information about a single property of pairs of objects, most often belonging to different classes.
In this table, the head (top header) has a complex (two-tier) structure.
An OOO table can be "turned on its side", rows turned into columns, and columns into rows.
In the LLC type table, one property of a pair of objects is fixed, therefore its cells always contain values of the same type: either numbers, or words, or graphic images.
Complex tables
Table type "objects - objects - several" (UN)
Table type "objects - objects - several" is a table containing information about several properties of pairs of objects belonging to different classes.
General view of UN type tables:
In this table, the head (top header) has a three-tiered structure.
Material and Information Models
All models can be divided into two large classes: material models and information models.
material models.
Object models allow you to represent in material visual form objects and processes that are inaccessible for direct research (very large or very small objects, very fast or very slow processes, etc.).
Models of buildings and structures allow architects to choose the best urban planning solutions, aircraft and ship models allow engineers to choose their optimal shape.
Subject models are often used in the learning process. In the course of geography, we get the first ideas about our planet Earth by studying its model - a globe (Fig. 4.3), in the course of physics we study the operation of an internal combustion engine according to its model, in chemistry, when studying the structure of matter, we use models of molecules and crystal lattices, in biology we study the structure of a person by anatomical dummies.
information models.
Information models represent objects and processes in figurative or symbolic form, as well as in the form of tables, flowcharts, graphs, etc.
figurative models
Figurative models (drawings, photographs, etc.) are visual images of objects fixed on any information carrier (paper, photographic and film, etc.). Figurative information models are widely used in education, where it is required to classify objects according to their external features (remember educational posters in botany, biology and physics).
Graphic Information Models
Map as an information model. Is it possible to call a map of the area (Fig. 4.4) an information model? Of course you can! Firstly, map describes the specific area that is the object of modeling for it. Secondly, it is graphic information. The map is created for a specific purpose: with its help, you can get to the desired settlement. In addition, using a ruler and taking into account the scale of the map, you can determine the distance between different points. However, this map does not provide any more detailed information about settlements, except for their position.
The electrical circuit diagram has no external resemblance to a real electrical circuit (Fig. 4.6). Electrical appliances (light bulb, current source, capacitor, resistance) are depicted with symbolic icons, and the lines are the conductors of electric current connecting them. An electrical circuit is needed in order to understand the principle of operation of the circuit, so that it is possible to calculate currents and voltages in it, in order to correctly connect its elements when assembling the circuit.
On fig. 4.7 is a diagram.
Scheme is a graphical representation of the composition and structure of a complex system.
Structure- this is a certain order of combining the elements of the system into a single whole.
The structure of the Moscow metro is called radial-ring.
Graph - process model.
Graphs are often used to display various processes. On fig. 4.8 shows a graph of temperature changes over a certain period.
 |
| Rice. 4.8. temperature chart |
You have dealt with maps, drawings, diagrams, graphs before. It's just that you didn't connect them with the concept of an information model before.
Iconic information models.
Sign information models are built using different languages (sign systems). A sign information model can be presented in the form of a text (for example, a program in a programming language) or a formula (for example, Newton's second law F = ma).
Tabular Models
Information models in the form of tables are widespread. In the table of chemical elements of D. I. Mendeleev, the chemical elements are arranged in the cells of the table according to the increase in atomic weights, and in the columns - according to the number of valence electrons. It is important that by the position in the table it is possible to determine some of the physical and chemical properties of the elements (Fig. 4.9).
Tables of type "object-property"
Another common form of information model is rectangular table, consisting of rows and columns. The use of tables is so familiar that it usually does not require further explanation to understand them.
As an example, consider Table 4.1.
| Table 4.1. home library | |||||||||||||||||||||||||||||||||||||||||||||
|
When compiling a table, it includes only the information that interests the user. For example, in addition to those information about books that are included in table 4.1, there are others: publisher, number of pages, cost. However, for the compiler of Table 4.1, there was enough information to distinguish one book from another (columns "Author", "Title", "Year") and to find a book on the shelves of bookshelves (column "Shelf"). It is assumed that all shelves are numbered and, in addition, each book is assigned its own inventory number (column "Number").
Table 4.1 is information model book fund of the home library.
The table may reflect some process occurring in time (Table 4.2).
| Table 4.2. Weather | ||||||||||||||||||||||||||||||
|
The readings were taken over five days at the same time of day. Looking at the table, it is easy to compare different days in terms of temperature, humidity, etc. This table can be considered as information model of the weather state change process.
Tables 4.1 and 4.2 are the most commonly used type of tables. We will call them tables of type "object-property" . One line of such a table contains information about one object (a book in the library or the weather at 12-00 on a given day). Columns - separate characteristics (properties) of objects.
Of course, the rows and columns in tables 4.1 and 4.2 can be swapped, rotated by 90°. Sometimes they do. Then the rows will correspond to the properties, and the columns to the objects. But most often tables are built in such a way that there are more rows in them than columns. As a rule, there are more objects than properties.
Object-to-object tables
Another common type of tables are tables that reflect relationships between different objects. Let's call them object-to-object tables . Here is an example of a progress table that is understandable to every student (Table 4.3).
| Table 4.3. academic performance |
Rows refer to students - this is the first kind of objects; columns - to school subjects - the second kind of objects. In each cell at the intersection of a row and a column - the grade received by this student in this subject.
Table 4.4 is also of type object-object. However, unlike the previous table, the rows and columns in it refer to the same kind of objects. This table contains information about the availability of roads between settlements.
| Table 4.4. Roads | ||||||||||||||||||||||||||||||||||||
|
Binary matrices
In mathematics, a rectangular table made up of numbers is called matrix . If the matrix contains only zeros and ones, then it is called binary matrix . The numerical part of table 4.4 is a binary matrix.
Table 4.5 also contains a binary matrix.
It provides information about the visit of four students to three electives. It should be clear to you by now that one means visit, zero means non-visit. From this table it follows, for example, that Rusanov visits geology and dancing, Semenov - geology and floriculture, etc.
In tables that are binary matrices, reflects the qualitative nature of the relationship between objects(there is a road - there is no road; visits - does not visit, etc.). Table 4.3 contains quantitative characteristics of pupils' progress in subjects, expressed in grades of a five-point system.
We have considered only two types of tables: "object-property" and "object-object". In practice, other, much more complex tables are also used.
When building some types of information models, a system of graphic elements and a sign system are simultaneously used. Yes, in block diagrams algorithms, various geometric shapes are used to designate elements of the algorithm and a formal algorithmic language is used to write program instructions (Fig. 4.10).
An important role is played by information models that display hierarchical systems. In biology, the entire animal world is considered as a hierarchical system (type, class, order, family, genus, species), in computer science a hierarchical file system is used, etc.
In a hierarchical information model, objects are distributed by levels, from the first (upper) level to the lower (last) level. Only one element can be placed at the first level. The basic relationship between levels is that a higher-level element can consist of several lower-level elements, while each lower-level element can be part of only one top-level element.
A convenient way to visualize hierarchical information models are graphs. The elements of the hierarchical model are displayed in the graph as ovals ( graph vertices).
Elements of each level, except the last one, are in a "consist of" relation to elements of a lower level. Such a relationship between elements is displayed in the form graph arcs(directed line in the form of an arrow).
Graphs that have one top-level vertex resemble trees that grow from top to bottom, therefore they are called trees. Tree arcs can only connect objects of neighboring hierarchical levels, and each lower-level object can be connected by an arc to only one top-level object.
To describe the historical process of family generational change, information models are used in the form family tree. As an example, consider a fragment (X-XI centuries) of the family tree of the Rurik dynasty (Fig. 4.11).
test questions
1. What examples of material models can you name?
2. What are some examples of different forms of information models that you can think of?
3. Give various examples of graphic information models.
4. Build a graphic model of your apartment. What is it: map, diagram, drawing?
5. What form of graphic model (map, diagram, drawing, graph)
6. What is the convenience of tabular presentation of information?
7. Give examples of tables that you have to deal with at school and at home. Determine the type to which they refer: "object-property" or "object-object".
8. What is a matrix? What is a binary matrix?
Tasks for self-fulfillment
4.1. Question with a detailed answer. Build a fragment of the hierarchical file system model of your computer.
4.2. Question with a detailed answer. Construct a fragment of a hierarchical model of the animal world.
4.3. Question with a detailed answer. Build a fragment of the family tree model of your family.
4.4. Build a graphical model of your own performance in two different disciplines of the school curriculum (the most favorite and the most "unloved"). Use this model to predict your future learning process in these subjects.
4.5. Present in tabular form information about the hobbies of your classmates. What type of table are you using for this purpose?
4.6. The use of a tabular model often facilitates the solution of an information problem. In the following table, the filled cells in the class schedule correspond to physical education lessons in grades 9-11 of the school.
| Timetable of classes | |||||||||||||||||||||||||||||||||||||||||||||||||
|
Complete the following tasks:
- determine the minimum number of physical education teachers required for such a schedule;
- find one of the options for the schedule, in which you can get by with two physical education teachers;
- there are three physical education teachers at the school: Ivanov, Petrov, Sidorov; distribute the lessons between them in the table so that no one has "windows" (empty lessons);
- Distribute the lessons among the three teachers so that the workload is the same for everyone.
6. In a computer network, a node is a server with which all other servers are directly connected. Given the following binary matrix. In it, C1, C2, C3, C4, C5 are the designations of the network servers.
| C1 | C2 | C3 | C4 | C5 | |
| C1 | 1 | 0 | 0 | 1 | 0 |
| C2 | 0 | 1 | 0 | 1 | 0 |
| C3 | 0 | 0 | 1 | 1 | 0 |
| C4 | 1 | 1 | 1 | 1 | 1 |
| C5 | 0 | 0 | 0 | 1 | 1 |
Determine which server is the host.
