Lesson topic:
The simplest mathematical models.
Practical work 6We create graphic and verbal models.
Goals:
systematize and summarize the information received by students in the previous lesson;
expand students' understanding of iconic information models;
supplement and generalize students' ideas about mathematical models.
Tasks:
Educational:
to consolidate students' ideas about models and modeling, types of information models, mathematical models;
systematization of the acquired knowledge.
Developing:
the development of analytical and synthesizing thinking, the formation of the ability to observe, draw conclusions, the development of resourcefulness, the ability to overcome difficulties in order to achieve the intended goal.
Educational:
fostering a positive attitude towards knowledge, instilling interest in Informatics, developing skills of self-organization and self-control.
Lesson type: a lesson in consolidating the studied material and developing practical skills and abilities.
Lesson type: combined.
Forms of work in the lesson: independent, individual work.
Methods: verbal (story), illustrative, practical.
During the classes
1. Organizational moment
2. Repetition of the passed material
1) What is a model?
2) Why do you need a model?
3) When is the model applied?
3. Learning new material. Formation of the concept of a mathematical model, modeling
The main language of information modeling in science is the language of mathematics.
Models built using mathematical concepts and formulas are called mathematical models.
Consider the text of a small note from the school wall newspaper:
After a major overhaul, the Dolphin pool has literally changed: spacious changing rooms and showers sparkle with brand new tiles, breathtaking views of an intricate slide and a five-meter tower, attracts the blue smooth surface of water paths.
But most importantly, the builders redesigned the pool's water supply system. Previously, the pool was filled with water from one pipe. It took 30hours. Now the builders have brought another pipe that fills the pool for 20hours. How little time it will now take to fill the pool if both pipes are turned on!
This text can be seen as a verbal model of the pool. Let's try to solve the problem contained in the note: find out how many hours the pool will fill through both pipes.
If we discard information that is insignificant from the point of view of the task at hand, then the condition of the task can be formulated as follows:
The pool is filled through the first pipe in 30 hours, through the second pipe - in 20 hours. How many hours will it take for the pool to fill up through both pipes?
Let's try to solve the problem in general terms, indicating the time of filling the pool through the first and second pipes A and B, respectively. We take the entire volume of the pool as 1, and denote the required time by t.
Since the pool is filled through the first pipe in A hours, 1A is the part of the pool that is filled with the first pipe in 1 hour; 1B - the part of the pool filled with the second pipe in 1 hour.
Therefore, the rate of filling the pool with the first and second pipes together will be: 1A + 1B.
We can write: (1A + 1B) ⋅t = 1.
We have obtained a mathematical model describing the process of filling a pool from two pipes.
Let's transform the expression in brackets: 1A + 1B = A + BA⋅B.
We get A + BA⋅B⋅t = 1.
Now the required time can be calculated by the formula: t = A⋅BA + B.
There are points on the highway A and B separated from each other by 20km. The motorcyclist drove out of the point B in the opposite direction A , with speed 50km / h.
Let's compose a mathematical model describing the position of the motorcyclist relative to point A in t hours.
In t hours, the motorcyclist will travel 50t km and will be at a distance of 50t + 20 km from A. If we denote the distance (in kilometers) of the motorcyclist to point A with the letter s, then the dependence of this distance on the time of movement can be expressed by the formula: s = 50t + 20, t≥0.
Graphic information models are the simplest type of models that convey the external features of an object - size, shape, color.
Their dignity is high information content.
4. Practical work.
A sheet of practical work is given to the table for each student. When working with more complex software, tasks of varying degrees of complexity are provided
Task 1. Create the presented geometric compositions from the ready-made mosaic shapes.
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5. Lesson summary.
6. Homework.
Notes in a notebook. Create a geometric furniture arrangement using cubes.
Lesson topic:
Tabular information models. The structure and rules for the design of the table. Simple tables.
Target: Form students' knowledge about geometric patterns in human life. To acquaint with the varieties of mosaic compositions. To develop skills in building geometric models in a graphical editor, using the example of creating mosaic compositions.
Tasks:Educational
developing skills in working with software;
selection of a specific software tool for the implementation of the task;
development of skills and abilities for solving practical problems in the relevant programs.
Developing
development of attention, ability to analyze;
development of logical thinking;
development of abilities for certain types of activities (design, engineering graphics, programming, etc.)
Educational
the formation of independence of thought, clarity and organization in work, the ability to control their activities;
work efficiently in accordance with the available time.
Lesson type: combined.
Lesson type: Consolidation of the studied material using modern computer technologies.
Handout: Tasks for practical work.
During the classes
1. Org. moment
Greetings. Checking those present.
Lesson goal setting:
Let's try ourselves as a parquet designer.
Let's try ourselves as a constructor.
Familiarity with the lesson plan.
2. Updating.
What is a Model?
What is the purpose of creating models?
What process is called modeling, formalization and visualization?
What are the stages of modeling.
Name the types of models by the way they are presented?
3. Learning new material.
Table structure and design rules
To describe a number of objects with 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 timetable, in the tabular form the timetables of buses, airplanes, trains and much more are presented.
The information presented in the table is clear, compact and easy to see.
The table can 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:
Table number
General table header
The following rules for the design of tables must be observed.
1. The title of the table should give an idea of the information it contains.
2. Headings of columns and lines should be short, not contain unnecessary words and, if possible, abbreviations.
3. Units of measurement must be indicated in the table. If they are common for the entire table, then they are indicated in the table heading (either in brackets or separated by a comma after the name). If the units of measurement differ, then they are indicated in the headings of the lines or columns.
4. Practical work
It is desirable that all table cells are filled. If necessary, the following symbols are entered into them:
? - data unknown;
x - data is not possible;
↓ - data should be taken from the cell above.
In order to draw up a tabular model based on the information presented in text form, you must:
1) select in the text the names of objects, names of properties of objects and values of properties of objects;
2) clarify the structure of the table;
3) "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. We agree to underline the names of objects with a straight line, the names of properties - double, and the values of properties - with dashed lines.
For instance:
The capital of France is Paris.
The depth of the lake is 3 m.
The girl's name is Masha.
Each of the properties considered in these examples ("capital", "depth", "name") characterizes only one object. We will call such properties single.
5. Lesson summary.
Evaluation of work results. Pay special attention to the quality of the executed graphic models.
Table structure and design rules
To describe a number of objects with 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 timetable, the timetables of buses, airplanes, trains and much more are presented in tabular form.
The information presented in the table is clear, compact and easy to see.
The table can 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 rules for the design of tables must be observed.
- The heading of the table should give an idea of the information it contains.
- Headings of columns and lines should be short, not contain unnecessary words and, if possible, abbreviations.
- Units of measurement must be indicated in the table. If they are common for the entire table, then they are indicated in the table heading (either in brackets or separated by a comma after the name). If the units of measurement differ, then they are indicated in the headings of the lines or columns.
- It is desirable that all table cells are filled. If necessary, the following symbols are entered into them:
- \ (? \) - data unknown;
- × - data is not possible;
- ↓ - data should be taken from the cell above.
In order to draw up a tabular model based on the information presented in text form, you must:
- Select in the text the names of objects, names of properties of objects and values of properties of objects;
- Clarify the structure of the table;
- "Populate" the table by transferring information from the text to it.
When highlighting object names, property names and their values in the text, it is convenient to underline them with different lines. We agree to underline the names of objects with a straight line, the names of properties - double, and the values of properties - with dashed lines.
The whole set of tables can be conventionally divided into simple and complex.
Simple tables
Table of type "object-properties" (OS)
Property-objects table 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 depends on the number of properties in question.
This table provides information about some of the ancient Russian cities that preserve the unique monuments of our culture and history and form the world famous Golden Ring of Russia. This information is reflected in the heading of the table.
The table shows the objects: "Vladimir", "Kostroma", Pereslavl-Zalessky and "Gus - Khrustalny", belonging to the class "city". For each object, the property values "year of foundation", "founder" and "point of interest" are given, expressed in numbers and words.
In small tables (of \ (3 - 4 \) rows), objects can be listed in any order. If there are a lot of objects in the table, then they must be arranged in some meaningful order, according to a certain rule. For example, in the table \ (2.2 \) cities can be listed in alphabetical order, in ascending or descending order of their foundation years.
If the table of the OS type contains more properties than objects, then it can be “turned on its side”: the lines can be turned into graphs, and the columns into rows.
Table of type "objects - objects - one" is a table containing information about one property of pairs of objects, most often belonging to different classes.
In this table, the head (top heading) has a complex (two-tiered) structure.
An LLC-type table can be “turned on its side”; rows can be turned into graphs, and columns into rows.
In a table of LLC type, 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 of type "objects - objects - several" (UN)
Table of type "objects - objects - several" is a table containing information about several properties of pairs of objects belonging to different classes.
General view of UN tables:
In this table, the head (top heading) has a three-tiered structure.
The work includes 9 tasks, after which the students should be able to: add rows and columns to the table; remove rows and columns from a table; merge table cells; split table cells; create simple and complex tables; build tabular models.
Task 1. Giants
1. Create a 4 × 4 table (tab Insert group Tables). Set the font size to 11 pt for the entire table. Enter the following information about the tallest people in the table:
2. Center the rows of the table, highlight the first row of the heading in bold.
3. Modify the table to add additional rows to it. For this:
1) call the context menu by right-clicking in any cell of the row, above or below which you need to add a row;
2) select the command from the context menu Insert, and then - Insert Rows Above or Insert Rows Bottom.
4. Modify the table by adding a column (column) to it.
5. Sort the table in descending order of values in the "Age" column. For this:
1) place the cursor in an arbitrary cell of the table;
2) using the button Sorting (Home - Paragraph - Sorting) call the dialog box Sorting;
3) set the desired sorting options:
6. Remove the line "Jacob Loll" from the table (they say his height was exaggerated). For this:
1) select the line you want to delete;
2) right click and select from the context menu ( table) command Delete lines.
7. Delete the column (column) "Age".
8. Sort the information in the table in ascending order of values in the "Growth" column.
9. Format the table like this:
Working with tables - Design - Table styles - (Choose any style you like).
10. Save the document in your own folder under the name Giants1.
Task 2. The nature of Russia
1. Make a colorful inscription:
2. Create a table based on the sample. For this:
1) create a 10 x 3 table;
2) merge cells 2-6 of the first column (select these cells, call the context menu (Table menu) and give the Merge Cells command);
3) concatenate cells 7-9 of the first column. 
3. Fill in the table based on the information contained in the file Nature of Russia.doc.
4. Save the table in your own folder under the name Mammals2.
Task 3. The Golden Ring of Russia
1. Based on the information contained in tables 1 and 2 § 2.5 (§ 11 textbook of the 6th grade of the Federal State Educational Standard) of your computer science textbook, make a table that looks like:
2. Enter in the table information about 3-4 ancient Russian cities.
3. Change the page orientation to landscape. For this:
1) open the tab Page layout;
2) in a group Page settings click on the button Orientation;
3) choose an option Landscape.
4. Modify the table to add the Coat of Arms column to the right of the Founder column.
5. Insert into the corresponding cells of the table the images of the coats of arms of the cities of the Golden Ring from the Herba.rar archive.
6. Modify the table by adding a column “Distance from Moscow” to the right of the column “Point of interest”.
7. Save the table in your own folder under the name Ring.
Task 4. Prediction of academic performance
1. Create a table with the following structure: 
2. Fill in the first box with the names of all subjects taught in grade 7.
3. Fill in the table with your existing quarter scores.
4. Think about academic performance in what subjects you can improve. Fill in the table with your estimated quarterly and yearly grades.
5. Save the table in your own folder under the name Forecast.
Task 5. Climate
1. Present the following text in the form of a table (information is for 2004):
In Mari El, the amount of precipitation in July was 79 mm. In the Perm region, the average temperature in July was +18 degrees. In the Krasnoyarsk Territory, the average temperature in January was -18 degrees. In the Moscow region, the amount of precipitation in January was 45 mm. In the Orenburg region, the average temperature in January was -11 degrees. In Udmurtia, the amount of precipitation in July was 61 mm. In Mari El, the amount of precipitation in January was 26 mm. In the Orenburg region, the average temperature in July was +21 degrees. In the Krasnoyarsk Territory, the amount of precipitation in July was 55 mm. In the Orenburg region, the amount of precipitation in January was 35 mm. In the Perm region, the amount of precipitation in January was 52 mm. In Mari El, the average temperature in January was -10 degrees. In the Orenburg region, the amount of precipitation in July was 89 mm. In the Moscow region, the average temperature in July was +20 degrees. In Udmurtia, the average temperature in January was -13 degrees. In the Krasnoyarsk Territory, the amount of precipitation in January was 36 mm. In Udmurtia, the average temperature in July was +19 degrees. In the Moscow region, the amount of precipitation in July was 66 mm. In Udmurtia, the amount of precipitation in January was 41 mm. In the Perm region, the amount of precipitation in July was 45 mm. In Mari El, the average temperature in July was +20 degrees. In the Krasnoyarsk Territory, the average temperature in July was +17 degrees. In the Perm region, the average temperature in January was -14 degrees. In the Moscow region, the average temperature in January was -8 degrees.
The table can have the following structure:
2. Save the table in your own folder under the name Climate.
Task 6. Paper production
1. Using the given text, build a table with the same structure as in the previous task.
In 1970, the USSR produced a total of 4.2 million tons of paper. In 1970, the USSR produced 17 kg of paper per capita. In 1980, 81 kg of paper was produced in Belgium per capita. In 1970, Bulgaria produced a total of 0.2 million tons of paper. In 1980, Bulgaria produced a total of 0.3 million tons of paper. In 1980, the USSR produced a total of 5.3 million tons of paper. In 1970 In Belgium, 68 kg of paper was produced per capita. In 1980, 36 kg of paper was produced in Bulgaria per capita. In 1970, the UK produced a total of 3.6 million tons of paper. In 1970, the UK produced 65 kg of paper per capita. In 1980, a total of 0.8 million tons of paper were produced in Belgium. In 1970, 24 kg of paper was produced in Bulgaria per capita. In 1980, the UK produced a total of 3.0 million tons of paper. In 1980, the USSR produced 20 kg of paper per capita. In 1970, a total of 0.7 million tons of paper were produced in Belgium. In 1980, per capita in Great Britain
population was produced paper 54 kg. In 1980, a total of 0.8 million tons of paper were produced in Belgium.
2. Try to modify the table to provide additional information:
In 1989, Bulgaria produced a total of 0.4 million tons of paper. In 1989, Belgium produced 112 kg of paper per capita. In 1989, the USSR produced a total of 6.3 million tons of paper. In 1989, Belgium produced 1.1 million tons of paper. In 1989, the UK produced a total of 3.6 million tons of paper. In 1989 In the USSR, 22 kg of paper was produced per capita. In 1989, the UK produced 63 kg of paper per capita. In 1989, 42 kg of paper was produced in Bulgaria per capita.
3. Save the table in your own folder under the name Paper.
Task 7. Logic problem
1. Think over the structure and create a table to solve the following logical problem.
Vanya, Petya, Sasha and Kolya have surnames starting with the letters B, P, C and K. It is known that:
1) Vanya and S are excellent students;
2) Petya and V are C grade students;
3) In growth above P;
4) Kolya with a height below P;
5) Sasha and Petya have the same height.
What letter does each boy's last name begin with?
2. Record the solution to the problem in the table.
3. Write the answer to the problem under the table.
4. Save the created document in a file named Logics.
Task 8. Most-most
In reference books and encyclopedias, find information to fill out one of the following tables.
a) Largest lakes
b) The longest rivers
2. Create a table in a word processor.
3. Save the document in your own folder under the name The most.
