Presentation on mathematics "logic problem solving". If Denis is older than Yegor What is an urban-type settlement

Task 18, basic level.

Logic tasks.

Objective 1.The school acquired a table, a blackboard, a tape recorder and a printer. It is known that a printer is more expensive than a tape recorder, and a board is cheaper than a tape recorder and cheaper than a table. Select the statements that are true under the specified conditions.

1. A tape recorder is cheaper than a blackboard.
2. A printer is more expensive than a board.
3. The board is the cheapest purchase.
4. The printer and the board cost the same.

Solution.The solution can be as follows. We compare the cost of items using inequalities.

P> M, M> D,

C> D.

These inequalities clearly show that the board is the cheapest, the printer is more expensive than the board. Statements 1 and 4 are false.

Answer 23.

Objective 2.Twenty graduates of one of the eleventh grades took the Unified State Exam in Russian. The lowest score obtained in this class was 28 and the highest was 83. Select the statements that are true under the specified conditions.

1. Among these graduates there is a person who received 83 points for the Unified State Exam in Russian.
2. Among these graduates there are twenty people with equal USE scores in the Russian language.
3. Among these graduates there is a person who received 100 points for the Unified State Exam in the Russian language.
4. The points for the Unified State Exam in the Russian language of any of these twenty people are at least 27.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Solution.The first statement is correct, since the highest score in this class is 83, which means someone else got it.

The second statement is not true, since at least one student received 28 points and at least one student received 83.

The third statement is not true, as the highest score received by the students is 83.

The fourth statement is correct, since the smallest score is 28.

Answer 14.

Tasks for an independent solution.

Objective 1.Victor is older than Denis, but younger than Yegor. Andrey is not older than Victor. Select the statements that are true under the specified conditions.

1. Egor is the oldest of the four people.

2. Andrey and Egor are the same age.

3. Victor and Denis are the same age.

4. Denis is younger than Yegor.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Objective 2.The hostess bought a cake, pineapple, juice and cold cuts for the holiday. The cake was more expensive than pineapple, but cheaper than sliced ​​meat, juice was cheaper than cake. Select the statements that are true under the specified conditions.

1. Pineapple was cheaper than sliced ​​meats.

2. They paid more for the juice than for the cold cuts.

3. Cold cuts are the most expensive purchase.

4. Cake is the cheapest purchase.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Objective 3.The hostess bought fruit drinks, ice cream, crab sticks and fish for the holiday. Ice cream was more expensive than crab sticks, but cheaper than fish, fruit drink was cheaper than ice cream. Select the statements that are true under the specified conditions.

1. Fruit drink was cheaper than fish.

2. They paid more for the fruit drink than for the ice cream.

3. Fish is the most expensive purchase.

4. Among these four purchases, there are three, the cost of which is the same.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Task 4.The firm purchased a rack, a table, a projector and a copier. It is known that a rack is more expensive than a table, and a copier is cheaper than a table and cheaper than a projector. Select the statements that are true under the specified conditions.

1. The table is cheaper than a copier.

2. A rack is more expensive than a copier.

3. Copier is the cheapest purchase.

4. Rack and copier cost the same.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Task 5.When a cat walks along the fence, the dog Sharik, who lives in a booth near the house, barks. Select the statements that are true under the given condition.

1. If the ball does not bark, then a cat is walking along the fence.

2. If Sharik is silent, then the cat is not walking along the fence.

3. If a black cat is walking along the fence, the Ball does not bark.

4. If a white cat walks along the fence, the Ball will bark.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Task 6.Residential buildings with more than 5 floors have an elevator. Select the statements that are true under the given condition.

If the building does not have an elevator, then this building has more than 6 floors.

If the building does not have an elevator, then this building has less than 6 floors.

If the building has more than 8 floors, then there is no lift.

If the house has more than 7 floors, then it has an elevator.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Task 7.There are 30 students in the group, 20 of them passed the test in economics and 20 passed the test in English language... Select the statements that are true under the specified conditions.

1. There are 11 students in this group who did not pass either of these two tests.

2. At least 10 students from this group passed the tests in both economics and English.

3. No more than 20 students from this group passed tests in both economics and English.

4. There are 20 students in this group who did not pass the test
in English, but passed the economics test.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Task 8.There are only 12 residential buildings in the urban-type settlement. The height of each house is less than 30 meters, but not less than 9 meters. Select the statements that are true under the specified conditions.

1. There is a residential building 30 meters high in the village.

2. The difference in height between any two residential buildings in the village is more than 3 meters.

3. There is no residential building 8 meters high in the village.

4. The height of any residential building in the village is not less than 7 meters.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Problem 9.In a pet store, 30 fish were launched into one of the aquariums. Each fish is more than 2 cm in length but does not exceed 8 cm. Select statements that are true under the conditions indicated.

1. The seven fish in this aquarium are shorter than 2 cm.

2. There is no fish in this aquarium with a length of 9 cm.

3. The difference in the length of any two fish is no more than 6 cm.

4. The length of each fish is more than 8 cm.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Problem 10.In residential buildings with more than 12 floors, electric stoves are installed instead of gas ones. Select the statements that are true under the given condition.

1. If the house has gas stoves, then this house has more than 13 floors.

2. If the house has gas stoves, then this house has less than 13 floors.

3. If the house has more than 17 floors, then gas stoves are installed in it.

4. If the house has gas stoves, then it has no more than 12 floors.

In your response, write down the numbers of the statements you selected, without spaces, commas, or other additional characters.

Problem 11.Olya is younger than Alice, but older than Ira. Lena is not younger than Ira. Select the statements that are true under the specified conditions.

1. Alice and Ira are the same age.

2. Among these four people, there is no one younger than Ira.

3. Alice is older than Ira.

4. Alice and Olya are the same age.

Topic: "Solving logical problems".

Lesson objectives:

Cognitive:

1. Formation and development of various types of memory, attention, imagination.

2. Formation and development of general educational skills and abilities.

3. Formation overall ability seek and find new solutions, unusual ways achieving the required result, new approaches to considering the proposed situation.

4. Formation of interdisciplinary communication.

Developing:

1. Develop speech, thinking in the course of mastering such techniques mental activity, as the ability to analyze, compare, synthesize, generalize, highlight the main thing, prove and disprove.

2. Develop the motor sphere.

3. Develop cognitive ability child.

4. Development of control and self-control skills.

Educating:

1. To foster in children a sense of friendship, camaraderie.

2. Foster a love of the subject.

3. To foster a system of moral interpersonal relations.

Adaptive

1. Adaptation to the topic of the lesson; adaptation teacher - student; student-student adaptation.

2. To form the main groups of students' competencies in different stages lesson.

Lesson equipment:

Ø interactive whiteboard, multimedia projector;

Ø presentation prepared in MS Power Point;

Ø Handout.

Lesson type:

Lesson in explaining and consolidating knowledge

Methods:

Visual;

Analytical;

Independent work;

Forms of organizing educational activities:

frontal, individual.

Requirements for the knowledge and skills of students:

students should know:

basic methods for solving logical problems.

students should be able to:

solve logic problems in various ways.

During the classes

1. Organization of the class.

So, friends, attention!
The bell rang again
Sit down comfortably
Let's start the lesson now.

The topic of our lesson is "Solving logical problems".

Without logic, it is almost impossible to make

into our world of ingenious finds of intuition.

Kirill Fandeev (musician, composer)

2. Actualization of knowledge, abilities, skills.

1. Train your mind! (intellectual warm-up)

1) A ruler, pencil, compasses and elastic band are on the table. You need to draw a circle on a piece of paper. Where to begin?
Answer: You need to get a sheet of paper.

2) One train goes from Moscow to St. Petersburg with a delay of 10 minutes, and the other - from St. Petersburg to Moscow with a delay of 20 minutes. Which of these trains will be closer to Moscow when they meet?
Answer: At the time of the meeting, they will be at the same distance from Moscow

3) The boy fell from 4 steps and broke his leg. How many legs will a boy break if he falls off 40 steps?
Answer: Just one, because the second one is already broken, or not one more, if you're lucky

4) How to correctly say: "9 and 7 will be 15" or "9 plus 7 is 15"?
The answer is 9 + 7 = 16.

3.Exploring a new topic

What does it mean to solve logic problems?

In the classroom, we will compare, analyze, generalize, draw conclusions.

Logical problem solving methods:

Reasoning method

Table Method

Graph method

Euler circles method

By means of the algebra of logic

Reasoning method.

Table method:

Solving problems in a tabular way: The tabular method for solving logical problems is simple and intuitive. But it can only be used when you want to establish a correspondence between two sets. It is more convenient when the sets have five to six elements.

To solve the problem in a tabular way, you need to know the following rules:
1. Each row and each column of the table can contain only one "+" sign.
2. If in a row (or column) all “places”, except one, are occupied by “-”, then in the free space you need to put a “+” sign; if the row (or column) already has a "+" sign, then all other places must be occupied by a "-" sign.

Thus, the solution will be completed when we are able to place one plus in each row and column.

Let's get down to the tasks

1. Lesson summary: In mathematics, there are varioustypes of logical tasks.

2. The methods are in logical analysisconditions, the choice of the corresponding laws of mathematics and ways of optimal solutions.

3. ... Tricky tasks help to learn to think independently, develop logic, interest in mathematics. With their help, you can feel the connection between mathematics and real-life problems.

And in conclusion…

. “If two people have one apple and they exchange them, each of them will have only one apple. But if two people have one idea and they exchange them, each will have two ideas. " B. Shaw

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Where do you live? In the town? In a village or a village? Have you ever thought about the differences between one settlement and another? Most likely not. Few people pay attention to such trifles in Everyday life... Therefore, we decided to reveal a little the nuances of territorial division in Russia. Today we will consider urban-type settlements.

Types of settlements in Russia

Administrative divisions in our country can be represented as follows:

• village;
• village;
• village;
• settlement;
• town.

If we talk about the types of settlements in more detail, then it should be noted that a village is considered to be a settlement in which even less than ten people can live. There are no infrastructure and leisure facilities.

The expanded village in which the school is built, Kindergarten and a polyclinic becomes a village. Most often, the villages are located in close proximity to the city and have constant transport links with it.

All the listed infrastructure facilities and a church are located in the village. Its presence is required to obtain the status of this settlement. In addition, villages can be formed at a distance from cities and regional centers.

There is another type of settlement - ZATO. These settlements are closed and, according to their characteristics, belong to urban-type settlements. Its residents are employees of secret enterprises of strategic importance for our country. Usually the population of ZATO is small, it rarely exceeds two thousand people. Until the nineties of the last century, these settlements were strictly secret and did not even have their own names.

What is an urban-type settlement?

Urban-type settlements (abbreviated as urban-type settlements) are settlements with a population of at least three thousand people. Moreover, more than 80% of the population should be employed outside the agricultural sector. We can say that the urban settlement is an intermediate link between the village and the city.

Urban-type settlement: the history of its appearance in Russia

V pre-revolutionary Russia there was no such thing as "urban-type settlements". The administrative-territorial division did not provide for such a unit, but in the early twenties of the last century, the government of the young country decided to make serious changes to the definitions and names of some territorial units. For the first time, the definition of a settlement was introduced, from which after that an urban-type settlement was formed.

Urban settlement: classification

Urban-type settlements do not represent Russia unified structure... This name is generic. In fact, PGT can be divided into several subspecies:

• resort villages;
• summer cottages;
• workers' settlements.

Each of these types can be safely attributed to PGTs, but they have their own characteristics and features. For example, a workers' settlement is located very close to a city or a large city-forming enterprise. All its residents can work in one place, and the population often does not exceed two thousand people.

Resort and summer cottage settlements are located in places where sanatoriums and health resorts have been built. The population of these UGTs serves various institutions and is subject to seasonality. This is especially true of dacha settlements, they retained their status only if there were at least one and a half thousand people in it throughout the year.

Urban settlement: description

PGT in general outline practically does not differ from the city. In central Russia, where many ancient cities are located, the population of urban-type settlements often exceeds the number of urban residents by several times. However, they are still referred to as PGTs.

An urban-type settlement is usually quite large. The average urban settlement has a population of 15,000. On its territory there are polyclinics, schools, preschool institutions and numerous shopping centers. Quite often, several roads pass through an urban-type settlement, including those of federal significance. Often, such a settlement has several parks or is crossed by a river. In this case, it occupies just a huge territory.

We can say that the urban settlement is the same city, but it lacks social infrastructure facilities. Children have nowhere to engage in creative work, adults do not have the opportunity to get into a theater or museum. This is what prevents this settlement from obtaining the status of a city. On average, the population of urban-type settlements ranges from one to two thousand people to two hundred thousand people.

City and urban-type settlement: differences

These two types of settlement are very similar to each other and, at first glance, do not have significant differences. But in fact, there are some differences.

First of all, the differences are noticeable in the management of the settlement. The PGT has a head who has a staff of administrative staff. But according to the tariff scale, his position is called “head of an urban-type settlement”. In the city, the mayor is the head, and in his absence deputies deal with important issues. Next come lower-level officials.

It is unlikely that you will find an urban-type settlement, whose residential buildings have thirty floors, although this is not prohibited by law. But in reality, the urban settlement is built up with houses no higher than nine floors.

A private house in an urban-type settlement is not uncommon. Quite often, residents prefer to build on their own land plot, thus expanding the boundaries of the settlement. This is impossible in the city. A person can purchase land for individual construction only outside the village. Within the city limits, free land is always given away for high-rise construction.

The most important and noticeable difference between the urban settlement and the city is the infrastructure facilities. Usually urban-type settlements do not have a swimming pool, circus and theater. All other entertainment and leisure facilities of the urban settlement are identical to the city ones.

How are zip codes formed?

Urban-type settlements have the same index formation system as other settlements in the country. After the forties of the last century, an innovative postal identification system was introduced, which is still in effect.

Six-digit indices are adopted in our country. In this case, the first three digits indicate the settlement code, and the second three - the number of the post office. Big cities may have several codes that facilitate the delivery of correspondence to the addressee. But PGTs usually have one code and several post offices.

The largest and sparsely populated urban settlements in Russia

At the moment, federal law does not regulate the receipt locality the status of an urban-type settlement. This is done by the local authorities. But the spread in the population of urban settlements within the country is quite large. For example, the largest settlement is considered to be the Sunzha settlement; more than sixty thousand people live in it. More than a hundred urban-type settlements have a population of less than one thousand people. But the smallest is considered the PGT Kozhim. It is located in the Komi Republic, and only four people live on its territory.

Moscow region

The urban-type settlements of the Moscow region are quite numerous, at the moment there are twenty-four territorial units:

• Nakhabino.
• Tomilino.
• Malakhovka.
• Vlasikha.
• Kraskovo.
• Kalininets.
• Monino.
• Beloozersky.
• Tuchkovo.
• October.
• Specific.
• Sofrino.
• Selyatino.
• Zaprudnya.
• Big Vyazemy.
• Mikhnevo.
• Fryanovo.
• Ilyinsky.
• Andreevka.
• Bykovo.
• Nekrasovsky.
• Shakhovskaya.
• Pravdinsky.
• Obukhovo.

The most densely populated is the village of Nakhabino, with a little more than forty thousand inhabitants. And the smallest was the urban-type settlement Obukhovo, its population is ten thousand people.

We can say that urban settlements in the Moscow region are characterized by rapid population growth and transformation into a different status. Sociologists attribute this to the proximity of Moscow. The huge metropolis is gradually expanding and is approaching urban-type settlements. As a result, they merge into a single territorial unit and become part of the city. This practice is actively used all over the world, because million-plus cities tend to develop and grow not only in height, but also in width.

In conclusion, I would like to say that urban-type settlements are an intermediate administrative-territorial unit. During the period of urbanization decline, they lose their importance and number, but at the time of the rapid growth of cities, it is urban settlements that become a kind of recharge for numerous urban enterprises in need of working hands.