Master class "Solution of Logic Tasks"
Actualization

To determine the subject of the lesson and what will be speaking, read the statements. What are they connected, and what word is missing?

"Mathematics then learning it is necessary that she is in order by order" (Lomonosov)

............ - This, apparently, the ability to prove some truth. (J. Lamryuer)

Of course that logics. There are many different logical tasks and today at the lesson we will look at some of them.

The subject of the decision of the logical task.

One of the active working methods in the lesson is the creation method problem situationswhich makes a lot of improves the master's assimilation with students and develops attentiveness in them, the flexibility of the mind, the consequence of which is the high activity of students in the lessons.

For me, in the process of learning, the main thing is to have a small problem in lessons and together with them to find the answer to the question.

First of all, you must interest students, create intrigue

1) a long time ago one oriental lord, enlightened and wise, wished to learn everything about mathematics of all times and peoples. He caused the approximate and announced his will.

We command, "he said," write me everything about mathematics. How she arose, what was before, what happened now, what will be in the future.

And gave for this five years.

From all over the kingdom, the wise of the wise men were collected, and they declared the desire of the Lord.

Potted five years, and came close to the palace.

Your desire, about Vladyka, executed! Looking out the window, and you will see what I wanted. A camel came up in front of the palace so long that the end was lost somewhere around the horizon. And on each camel, two huge bale are loaded. And in each bale there were ten fat volumes.

What is it? - the ruler was surprised.

This is a world mathematics.

You are laughing at me! - Vladyka became angry. - Why, before the end of my life, I will not have time to read the tenth more thing that they wrote! No, let me write me short story mathematics.

And gave for this year.

The prescribed time passed, and again it seemed from the walls of the Palace caravan. And there was only ten camels in it, and two bale on each camel and ten books in each bale.

Vladyka was even more angry.

Let me write to me the most important thing. How much time do you need it?

Tomorrow, about the Lord. You will get what you wish!

Tomorrow? - The ruler was surprised. - Good.

As soon as the sun rose on the azure sky, as Vladyka demanded the sage. The sage entered, carrying a small leg of sandalwood in his hands;

You will find in it, about Vladyka, most importantly in mathematics of all times and peoples, "said the sage.
But before we open the casket and read what is written there, I suggest you solve some tasks who knows some of them were in those volumes.

Formulation of the problem:

Task1.

The seminar was trained by teachers who taught different subjects. We need to get acquainted with five of them. It is known that their names of Alena, Berta, Vera, Galina, Daria. One of them is a teacher of mathematics, the other - a teacher of geography, the third - teacher of physics, the fourth - teacher of biology, the fifth - teacher of history. They talked about themselves the following.

Faith and Galina do not use the textbook of mathematics in their work.
Galina and Berta live in the same house with physics teacher.
Alena and Galina presented a beautiful vase history to the history teacher.
Berta and Galina helped the geography teacher to prepare an open lesson.
Berta and Daria on Saturdays are found at the teacher of history, and the physics teacher on Sundays comes to visit Alena.

Which of them teaches what item?

Read the task. Try to solve. Why not work?

"Opening" of a new knowledge

In mathematics there is a reception that significantly accelerates, almost automates the solution of the tasks of this species - these are logical tables.

Between the elements of which sets, we need to establish a match? (name and subject).
Name the names (enter), list items (enter).

name object	mathematics	history	geography	biology	physics
BUT
B.
IN
G.
D.

Is there a key phrase in the condition that will help you push off? Maybe about some of the teachers know more than others (o d). Let's read what is known about g
and, making conclusions, fill in the table using the signs + and -

name object	mathematics	history	geography	biology	physics
BUT				–
B.				–
IN				–
G.	–	–	–	+	–
D.				–

Look carefully on the table and each other. I wonder who you will solve the first, and who of you will be the most attentive?
As a result of an active conversation, the task is solved.
So, we solved all the "incognito", that is, answered the question of the task. Speak that we found out.

name object	mathematics	history	geography	biology	physics
BUT	–	–	+	–	–
B.	+	–	–	–	–
IN	–	+	–	–	–
G.	–	–	–	+	–
D.	–	–	–	–	+

How did we solve the task so quickly? How did the table amounted to? (Slap again).

Primary fixing

Now try to apply your knowledge in practice. Each group gets a task. Discuss approximate time of work.

Task2.

Near our school is a sports complex. There are four sports sections: volleyball, basketball, football and tennis. The guys of our class also recorded in the section of this sports complex. There they met the boys from another school. They were called Anton, Yura, Kostya and Misha. Each of them visited only one of the sections. Somehow on the way to the training session, the guys met and talked. That's what they learned about new acquaintances.

Anton and Kostya do not use the racket in the game.
Volleyball player and football player are engaged in one day with Mikhail
The football player is going to the competition for the costha.
Yuri in the morning makes a jog with a football player.
Mikhail lives in one house with a tennis player.
What kind of sport does each of the new friends do the guys?

Check:
1) Read the task;
2) What did you know about .... All agree? And so on about all 4 guys. You can ask the guys once again to talk about how they reasoned and made a table.

Historical reference

Where did the logic appear?

Logic - science on laws and forms of proper thinking. Originated due to rhetoric in Ancient Greece and ancient India. In India, the competences of speakers were very popular with a large propelusion of viewers. Estimated the arena of the competition, chose the judges, determined what should be the result of the dispute. If two faces argued, then sometimes defeated should have deprived himself to life, or deal with the Winner's slave, go to his faith, or to give the property to the poor in the rags, who managed to challenge him.

The term logic comes from the Greek word Logos, which means "thought", "mind", "pattern"

Task3.

In the camp of 40 children, 30 know how to swim, 27 know how to play chess and five do not know how neither the other. How many guys do you know how to swim and play chess?

Can we solve the task using the table?

We will solve the problem with the help of Euler's circles.

40 - 5 \u003d 35 (man) float and (or)

playing chess.

27 + 30 - 35 \u003d 22 (Human) can swim and play chess.

Where and in which areas of knowledge we need logic?

Solve physical tasks in groups. (5 minutes)

i'm light bulb

Air test

Erudite - aqualant

Answer the question:

Do you know how much it will be 2 to multiply by 2? Do you think 4? I will prove that you are very mistaken.

25-20-5=20-16-4
5(5-4-1)=4(5-4-1)
5=4
5=2*2
So, do you agree that 2 * 2 \u003d 5? Then prove that I am not right.
This is an example of sofism. Sophism is the intentionally false conclusion, which has the visibility of the correct one. Any sophism contains one or more disguised errors. Sembling sophisons primarily develops logical thinking. To detect an error in Sophism, this means to realize it, and the awareness of the error warns its repetition in the future in other mathematical arguments. Sophistication analysis helps conscious assimilation mathematical material, develops observation, thoughtfulness and critical attitude towards what is studied.

But Sofism - Song english students.

The more you study, the more you know.
The more you know, the more you forget.
The more you forget, the less you know.
The less you know, the less you forget.
But the less you forget, the more you know.
So what to learn? Not philosophy, but the dream is lazy!

Today I tried to show that in the course of solving any task you need theoretical knowledge, logical thinking, the ability to justify, prove the loyalty of the statements ..

Let's go back to the parable. What, the most important thing was the wise men in the casket?
The ruler opened the Larz cover. On the velvet pillow lay a small bug of parchment. Only one phrase was written there: "Mathematics is proof and logical thinking."

And now I will imagine the information received in the class in the form of a scheme. (On leaves in each group)

What key word will be in the center? Of course a logical task

Groups represent their schemes.

1. Read the statements of writers and scientists, distinguishing the voice of various persons in the same passage.
2. 3-3 sayings (according to your choice) Make quotes by adding your words and having them or before saying, or at the beginning of it, or in the middle, or at the end so that it was clear where your words, and where words Writer, scientist, to easily read text with a quote. Ploban signs - as with direct speech.
3. Set the content of several statements in the form of an indirect speech with the replacement of pronouns and personal forms of verb (where necessary). For example: Korolenko wrote that he reread "war and peace" three times, and every time this work of Tolstoy seemed to him "all the greatest".

1. I reread "War and Peace". This is the third time, and with each time this work of Tolstoy seems to me more and more great, and the new parties continue to perform everything where the attention was exactly indifferent. Now, in my almost painful mood, the great, truthful, calm epic acts on me deeply in question 2, as the nature itself. Nobody wrote with such an exciting 2 truth ... It is wide, freely, sincerely, truthfully. What amazing abundance of images, what a wave of life, these images are spiritualizing. (V. Korolenko)
2. ... Thanks to its sincerity, Chekhov created new, completely new, in my opinion, for the whole world of the form of Scripture, which I have not met anywhere. His language is amazing. I remember that when I started reading Chekhov for the first time, I first seemed to me some strange, as if awkward. But as soon as I thought, so this language and captured me. (L. Tolstoy)
3. ... I hurry in a few words to state my opinion about the drama "Thunderstorm". Language acting personsAs in this drama, and in all the works of Ostrovsky, long ago, everyone has been appreciated as a tongue of artistic, taken from reality, like the most persons who speakers. (I. Goncharov)
4. Academician D. Likhachev in the book "Letters of Good and Beautiful" writes: "Our language is the most important part of our common behavior in life. And by how a person says, we can immediately and easily judge what we are dealing with ... to learn good intelligent speech for a long time and carefully - listening, remembering, noticing, reading and studying. But although it is difficult - it is necessary. "
5. L. Landau, referring to the youth, once said: "Ground the price of your physics, if she covers everything else for you: the rustling of the forest, sunset paint, ringing rhymes. This is some truncated physics ... I, for example, I do not believe in it. "
6. Anna Akhmatova Lyrics - an integral part of our national Culture, one of the living and not losing 2 freshness of the branches on the tree of great Russian poetry. (A. Teddovsky)
7. Nor say, and the native language always remains relatives. When you want to speak to the soul, not one french word. The head is neudows, and if you want to shine, then another thing. (L. Tolstoy)
8. The flexible, the richer, the more diverse we will assimilate yourself the language in which you chose to think is, the easier, the most distinct and the richer we will express our idea on it. (F. Dostoevsky)
9. Oh, laughter Great business! Nothing is no longer afraid of a man as laughter ... fear of laughter, a person is holding away from what I would have had any power. (N. Gogol)
10. The punctuation marks exist to highlight the thought, bring words to the correct ratio and give the phrase ease and correct sound. They hardly "hold the text and do not give it to crumble." (K. POUST)

Exercise 1.
Below is the statement of K. Poystovsky, consisting of several proposals. All of them are combined with one topic (one main idea).
In relation to each person, it is possible to completely judge by their language not only about its cultural level, but also about his civil value. True love for his country is unthinkable without love for her language. A person indifferent to his native language is a savage ... Indifference to the language is explained by the complete indifference to the past, the present and the future of its people.

• Read the offer that defines the topic of statements. In which sentences this topic reveals?
• Repeating what word is the connectivity of this text fix?
• Try to read the suggestions of this text in this order: the last, second, third, first. Does the consistent presentation of thought persist? Give a detailed answer.
• Based on what type of communication is this text built?

Task 2.
Read the following text.
We have to protect your tongue from clogging, remembering that the words we use now - with the addition of a certain number of new ones, many centuries will serve after us to express ideas still unknown to us, to create new, not visible to our foresee of poetic creations.
And we must be deeply grateful preceding generations that have reported to us this heritage - shaped, capacious, smart language.
It already has all the elements of art and slender syntactic architecture, and the music of words, and verbal painting.
(S. Ya. Marshak).

• What is the main idea s.Ya. Marshak?
• What thoughts are revealed in every paragraph of this text? How is it made on a letter of paragraph? What serves as a signal of its beginning and end when reading out loud?
• Track, with what language means is the connection between paragraphs?

Task 3.
Read the statement of A.M. Gorky. What signs of text does it have?
Native language We must love like a mother, like music, and you need to be able to talk well to convey your thought to another person clear
and just.
You will understand people and their thought - it will be easier to live, and you will become smarter, and everyone will understand you immediately, and this is good!

• Why is this small text dismembered on paragraphs? What two sides of the linguistic communication of people speak each of them?
• How many suggestions in the text? How to determine how to perceive text on rumor? How is it denoted by writing?
• Select the phrase from the first sentence, which could serve as the name of the topic, common to the texts used above. Is the main idea of \u200b\u200beach of them? Prove.

Abstract lesson
Date: 21.02.2017
Subject: Mathematics
Class: 4b.
Teacher: Verekina Svetlana Viktorovna
Practice Manager: Karachevtsva Alla Pavlovna
Topic: Composite statements from two simple statements using logical ligaments "and" or "or their truth.
Type of lesson: ONZ
Objective: to acquaint with complex statements with a logical ligament "and" and consolidate knowledge of composite statements with a logical ligament "or".
Tasks:
Educational: learn to distinguish true statements from false; To determine the truth of statements with a ligament "and" to get acquainted with the rule of determining the truth of the composite statements of the species "A and B".
Developing: develop the techniques of logical thinking: analysis and synthesis, generalization.
Educational: to cultivate respectful attitude to classmates, responsible attitude to the results of their academic work.
Planned objective results:
To be able to distinguish false and true statements, identify the truth of composite statements.

MetaPered Wood:
Regulatory: carry out the formulation of a learning task, its control and correction.
Cognitive: make generalizations, conclusions, extract information from schemes and models.
Communicative: building monologic and dialogic statements, coordination of various positions in collaboration (in pairs).
Personal Wood: educational and cognitive interest in new educational material.

Training Means: Mathematics Tutorial 4th Class, Rudnitskaya V.N., Yudacheva T.V., Computer, Presentation
PC
OK
BY
W.

1.1,1.2,1.3,1.4,1.5,4.1, 4.2
1.2.4.7
1.2.3.6.7.
1-12, 21-26

DURING THE CLASSES:
Pedagogical activity
Teacher
Educational and educational activities of students

Motivation to educational activities.

Hello children. Sit down.
My name is Karina Andreevna, and today I will spend your lesson in mathematics.
- Tell me how you understand the meaning of saying:
To learn hardworking, you need three years to learn laziness - only three days.
Take output.
Greet teachers.

Reflect.
Reason.
Make output
It is difficult to learn hard work. For his appearance, you need a lot and constantly work.

2. Actualization of knowledge.

Verbal counting.
- Look at the screen.
- What is the saying?
- Determine the value of the statements true they or false. If true spellings are cotton with hands, if false show the cross with their hands.
1. 7 increased 6 times, received 42.
2. 64 was divided into 8, received 7.
A.3. Sensitive 10 and 2 is 8.
4. 9 increased by 21, received 30.
5. The manufacture 9 and 7 is 81.
6. Included numbers 48 and 6 are 8.
V.7.Mimena less subtracted.
- How did you define a true statement or false?
- form a composite statement of the type "A or B"

What kind of statement did it work out? Why?
- Try to make a statement of the type "A and B"

Have you guessed what composite statements will we study today?
-Formulate the learning task that we have to solve.
Watch.

The statement is a proposal regarding which it makes sense to the question: it is truly or false.
Determine. Sign.
true
false
true
true
false
true
false
- If the statement is correct, then we can say that it is true, if not true, then false.
The difference is 10 and 2 is 8 or decreasing less subtracted.
True. Repeat the rule.
The product 9 and 7 is 81 and the private numbers 48 and 6 are 8.
- Composite statements from two simple statements using logical ligaments "and" or ".
Formulate a learning task.
- We will work with composite statements with logical ligaments "and" or "or".

3. Problem explanation and fixation of new knowledge.

Organizes the front conversation.
- Look at the slide
- Read each statement and determine truly it or false?
1. Birch - deciduous tree.
2. Birch - coniferous tree.
- Connect these two statements with the union "and".
- What kind of statement did it work?
Read the rule on the slide.

Look at the slide.
Read. Determine the true statement or false.
1 statement truly.
2 Saying false.
Birch - deciduous tree and coniferous tree.
The statement turned out false.
Read.
A composite statement with the Union "and" is true if both are true of its statements. In other cases, it is false.

Phys. Minute

4. Primary consolidation in external speech.

Work on the textbook with. 38 No. 7.
- Make up and pick up the statements so that they match the task.
- Give examples of such statements

Read the task number 9 p.39.
- Read 1 statement.
- From what 2 statements it consists.
- Robin, is this composite statement true or false? Why?
- Read 2 statement.

What is this saying? Why?

Read 3 statements.

What statements it consists of.

Is it true or false? Why?

Read the rule again.

Read. Reason:
Let the first statement - A, second - V.
And February - Winter Month. - True
In February - hot month. - false
The statement is false.
And the week 5 days. - false
At the week of 7 days. - True
The statement is false.
Atcase 15 is divided into 2. - false
The number 15 is divided by 4. - false
The statement is false.
A 47 - 39 \u003d 8. - True
In 55: 5 \u003d 11. - True
Statement is truly.
Read.
1) Bares eat carrots and cabbage.
Hares eat carrots. Hares eating cabbage.
This statement is true, because hares eating carrots - I., hares eating cabbage - I.
2) leaves from trees fall in spring and autumn.
Leaves from trees fall in spring. Leaves from trees fall in autumn.
False, because the leaves from the trees fall only in autumn.
3) in the quadrilateral ABCD 3 vertices and 3 sides.
In the quadrilateral ABCD 3 vertices. In the quadrilateral ABCD 3 sides.
False, because in the quadrilateral ABCD 4 vertices and 4 sides, a - l, div.

5. Independent work With self-test.

Work in pairs.
- Read the statements pairs:
1) Letter w - vowel.
Letter w - consonant.
2) kilogram - a unit of mass.
Kilogram - unit length.
3) in one decimeter 100 cm.
In one decimeter 10 mm.
4) The number 100 is divided into 10.
The number 100 is divided into 5.
- True or false first statement?
second statement and so on.?
- Connect every two union statements "and", set its value of truth, check on the standard.
-What statement turned out: True or false?

Read.
False
True
True
False
False
False
True
True

Letter w - vowel and letter w - consonant. False
Kilogram - a unit of mass and kilogram - a unit of length. False
In one decimeter 100 cm and in one decimeter 10 mm. False
The number 100 is divided into 10 and the number 100 is divided by 5. True

6. Problem explanation and fixation of a new knowledge (continued).

Look at the slide read.
- composite statement "If A.S. Pushkin was born in 1799, he was born in the eighteenth century. " Essential from 2 statements:
1. A.S. Pushkin was born in 1799.
2. He was born in the eighteenth century.
- Determine the true or false first statement? Then second?
- That's right 1 statement is truly, it can be installed using the encyclopedia.
- 2 statement is also true, because in the 18th century the dates from 1701 to 1800 inclusive.
- Since 2 statements are true, which can be said about the composite statement "If A.S. Pushkin was born in 1799, he was born in the eighteenth century "?

Read the rule on page 40, how do you understand it?

Look at №12 p. 40, read the task.
- Connect 2 statements using the words "if, then"
- What did the statement happen?
- Under the number 2, do it yourself, and check all together.

Check, what did the statement happen?
Watch. Read.

The statements turned out true.

Saying "if A.S. Pushkin was born in 1799, he was born in the eighteenth century "- True.
Read the rule.
The composite statement formed by the words "if that" is false, only if the first statement is true, and the second is false.
Read.
If the corona is a bird, then the crow flies.

True.
If the number 4 720 is a four-digit, then after overclocking zero, among 4,720 it turns out a two-digit number.
It turned out a false statement.

7. Inclusion of a new knowledge in the knowledge and repetition system.

Open the notebook, sign the number and cool job.
- Perform №19 p.42
- Spish, find the value of expressions.
(1 doctrine at the board)

Determine which of the numbers 628, 100, 3 639, 5 300 is the value of the expression. Right.
- organizes the execution of the task in the notebook and at the board with the explanation.

-Catch №22 p. 42.

What distance went through a pedestrian?
- How long, he was on the way?
- What is known about his speed on the way back?
- Read the task.

Can we immediately answer the question of the task? Why?
- Can we find out? What action?
- What is still unknown?

Now we can find speed on the way back?
- Look, is the correct expression for solving this task?
- Finish the solution to the problem orally and voice the answer.

Read the task number 23 on with. 43.

What is known about the movement of the cargo and passenger car?
- What speed drove the cargo car?
- What speed drove a light machine?
- What is said about the distance between Moscow and the village?
- What should I find in the task?
- Perform drawing on the board.

Repeat the task.
- We can immediately answer the question of the task?
- Why?
- Knowing speed of cargo and passenger cars, can you find out what the speed of rapprochement?
- What action?
- Knowing the speed of rapprochement and distance from Moscow to the village, can we find the time through which they will meet? What action?
- Record the solution to the notebook with the explanation.
- 1 student works at the board.
- Evaluates the work of the school at the board.
Open. Write.

Calculate.

1)3 639
2)100

Read
The pedestrian was 16 km in 4 hours. On the way back, he reduced the speed of 2 km / h. How much time spent a pedestrian on the way back?
Pedestrian passed 16 km
He passed in 4 hours.
It reduced speed by 2 km / h
How much time spent a pedestrian on the way back?
No, we can not, because we do not know how fast the pedestrian passed 16 km
Yes, the action of division.
Another unknown speed with which a pedestrian walk back.
Yes, the action of subtraction.

Right.
Decide. 16: (16: 4-2) \u003d 8
Answer: 8 h
Read the task.

They simultaneously went to meet each other.
- with a speed of 43 km / h.
- at a speed of 56 km / h.
- Distance between Moscow and the village of 198 km.

After how many hours of cars will meet.
(One student performs drawing on the board)

After how many hours of cars will meet?
- Not.
- We are unknown, the speed of rapprochement of cars.
-Yes we can.

The action of addition. 43 + 56 \u003d 99 (km / h)

Yes. The action of division. 198: 99 \u003d 2 (h)
Record the solution of the problem.
1) 43 + 56 \u003d 99 (km / h) - speed of rapprochement
2) 198: 99 \u003d 2 (h)
Answer: After 2 hours the cars will meet.

8. Reflection of educational activities in the lesson.

Our lesson approached the end, and I ask you to continue the sentences:
1) I learned today
2) I learned today
- Open a diary, write down your homework:
P. 28 RT (in RT) No. 79-82
- The lesson is over.
Perform the reflection of the assimilation of the new content.

Record homework.

Teacher:_______________________________
Practice Manager: ___________________________
Rating: _______________________________