ABOUT ZERO

Far, far away, beyond the seas and mountains, there was the country of Tsifiria. Very honest numbers lived in it. Only Zero was distinguished by laziness and dishonesty.

One day everyone learned that Queen Arithmetic had appeared far beyond the desert, calling the inhabitants of Tsifiria to her service. Everyone wanted to serve the queen.

Between Cyphyria and the kingdom of Arithmetic lay a desert crossed by four rivers: Addition, Subtraction, Multiplication and Division. How to get to Arithmetic? The numbers decided to unite (after all, it is easier to overcome difficulties with comrades) and try to cross the desert.

Early in the morning, as soon as the sun's slanting rays touched the ground, the numbers set off. They walked for a long time under the scorching sun and finally reached the Slozhenie River. The numbers rushed to the river to drink, but the river said: “Stand in pairs and join forces, then I will give you a drink.” Everyone followed the river's orders. The lazy Zero also fulfilled his wish, but the number with which he formed was not satisfied: after all, the river gave as much water as there were units in the sum, and the sum did not differ from the number.

The sun is getting hotter. We reached the Subtraction River. She also demanded payment for the water: stand in pairs and subtract the smaller number from the larger one; Whoever answers less will receive more water. Once again, the number paired with Zero was the loser and was upset.

And at the River Division, none of the numbers wanted to be paired with Zero. Since then, none of the numbers are divisible by zero.

True, Queen Arithmetic reconciled all numbers with this lazy person: she began to simply assign Zero next to the number, which from this increased tenfold.

And the numbers began to live and live and make good things.

VICTORY OF KNOWLEDGE

It was a long time ago...

In a certain kingdom, in a certain state, an illiterate king ascended the throne: as a child he did not like mathematics and native language, drawing and singing, reading and work... This king grew up ignorant. I'm ashamed in front of the people. And the king decided: let everyone in this state be illiterate. He closed schools, but allowed only military studies in order to conquer more lands and become rich.

Soon the army of this state became large and strong. It worried all nearby countries, especially the small ones.

The ignorant king's name was Pud. He became the leader of his robber army.

Next door to the state of the ignorant was the country of Length. Her king was smart and educated person: knew arithmetic, various languages; in addition, he had an excellent command of military science.

The army in this country was small but well trained. It was famous for its reconnaissance and long-distance runners.

King Pud approached the state of Length with his troops and set up camp near the border. How to save the state? His king, knowing that Pud and his subordinates did not know how to count and did not know what the words kilo (thousand), centi (hundred), deci (ten) meant, decided to carry out a military operation.

Two days later, a large plywood doll appeared on a cart in front of the Puda army camp. The sentries did not want to let her through, but the doll said that she was a gift from the state of Length to King Pudu. The sentries were forced to let the doll pass.

The carriage with the doll entered the camp. Pud and his entourage looked at the doll and were surprised at its size and ability to speak in a human voice.

The doll said that her name was Kilo and that she had younger brothers, Meter and Decimeter.

The sun is getting lower and lower. Night fell on the earth. When the entire Puda camp fell asleep, the doll opened, and 1000 dolls named Meter came out of it, and from each of them - 10 dolls, called Decimeter, from each Decimeter - 10 Centimeter warriors. They surrounded the sleeping enemy army and destroyed it. Only King Pud escaped (he would later be found in another kingdom).

So the smart king, who loved science, defeated the ignoramus - King Pud. And all neighboring states began to live in peace and friendship.

HERO OF THE PLANET "VIOLET"

Today there was a celebration all over the Earth. For the first time in history, a person went to the planet "Violet", where intelligent beings lived.

Half an hour of flight passed. And suddenly, from behind the engine room, a noise was heard that was not specified in the instructions. Fortunately, there was no accident. There was a boy Kolya on the ship. What to do? The astronauts decided to report the incident to the mission control center and continue the expedition.

Finally the crew reached an unknown planet. A few kilometers from the landing site there was an amazing city: all the houses in it were spherical in shape. The inhabitants of Violet did not know how to calculate the area of ​​a rectangle. The earthlings decided to help them, and at the same time check what their stowaway was capable of.

Kolya was scared: he didn’t like mathematics, he always copied homework from his comrades. But there was no way out. With difficulty he remembered that a square with a side of 1 cm has an area of ​​1 square. cm, 1m - 1 sq. m, etc. How to find the area of ​​a rectangle? Kolya drew a rectangle that contained 12 small squares. There are 4 squares along the larger side, and 3 along the smaller side. Then Kolya drew 1 more rectangle. It fit 30 squares, the length of the rectangle was 10 squares, and the width was 3.

What to do? - thought Kolya. - The sides of the rectangle are equal to 4 and 3 squares, and the area is 12, the sides of the rectangle are equal to 10 and 3 squares, and the area is 30. I know! - the boy shouted. “To find out the area of ​​a rectangle, you need to multiply the length by the width.”

Kolya reported to the ship's commander that the mission had been completed.

NIGHT ARGUMENT

One day, when the evening had long ended and the morning had not yet begun, the following story happened on the school board. Since the attendants forgot to erase the board, the examples that the children solved in class remained on it.

“But no,” said the minus sign. “Everything in the world decreases: in spring snow, melt water, and money.”

“Who’s that performing there like that?” - asked the multiplication sign. “Everything in the world is multiplying: spring shoots, spring warmth, and summer berries.”

“But no,” said the division sign. “Everything in the world is shared: joy, candy, and the harvest of each year.”

“I’ve been listening to you all for a long time and I have to say that you’re all wrong here,” said the equals sign. “Everything in the world is equal, both gain and loss. The world is based on the law of equality: if it leaves somewhere, it will definitely arrive somewhere else.”

BIG NUMBERS AND WORKING ZERO

Somehow Big Numbers decided to rest, relax and went to the tavern. There were Russian Big Numbers there: Raven, Deck, Darkness and noble foreigners: the twin brothers Billion and Billion, as well as Trillion, Quadrillion, Quintillion and Sextillion.

They dine, as expected, on pancakes with caviar, they break wine glasses, gypsies dance in front of them, the bathhouse is heated, in a word, everything is as it should be during a big party. And Nolik serves them. The poor guy runs back and forth like a clockwork. First give one thing, then another, then collect glass, then throw some wood in the stove... And he receives more kicks and pokes. Slow, they say.

- Why are you hanging around under my feet? – Raven barked.

“He has no place among us, the high nobility,” said Quadrillon, “let him go out.”

And the Deck just slapped him on the head.

Nolik endured and endured, could not stand it, why on earth would he suffer? And he left to work in another tavern.

And our noble revelers, without the hard-working Nolik, became ordinary Ones, and their arrogance immediately disappeared. They are looking for him now, but where can you find him, hard worker Nolik?

ALMOST BY ANDERSEN

Once upon a time there lived a Unity and her friend - an imaginary Unity. The imaginary One, of course, always followed the One. Wherever she steps, there she goes. She so wanted to take the place of a real One!

And in the country of Tsifiria, where the matter took place, the old King decided to marry his son, Prince Nolik.

“I’m already old,” said the King, “it’s time for you to get down to business and sit on the throne.” What kind of king will you be without a queen?

Meanwhile, all the figures - the brides of the kingdom - became worried.

- I am always in the retinue of the most smart people, said Five. – I am the most worthy bride of Prince Nolik, I should be the Queen!

“No to me,” Seven objected to her. “It’s about me that people make up wonderful proverbs: “Try on seven times, cut once,” “Seven nannies have a child without an eye,” “In one fell swoop, beat seven”...

“First of all, the Queen must be graceful, and intelligence is a gain,” said Deuce, and her swan neck became even longer. Look how beautifully the royal crown will sit on me!

The Six invited their friends to help them - a witch, a secret councilor and a fortune teller, but the magic spells did not help her. Eight, with its rounded shapes, drove the entire male part of Tsifiria crazy, but not Nolik and not the old king.

And Nolik, let it be known, chose his bride a long time ago - he secretly sighed for the graceful One. “What a wonderful ten we will be!” - he dreamed...

Meanwhile, the imaginary Unit realized that her time had come.

“Don’t you see what kind of friends surround you,” she whispered to her friend Unity. - Eight is a fidgety girl, Five is a pushover, Two is frivolous, and Six imagines that she can do anything, but in fact it’s difficult for her to bewitch even Nolik... If you agree to Nolik’s proposal, they will eat you before the wedding.

And while the simple-minded One was sobbing, the imaginary One ran to Nolik.

“Look at me,” she said to the Prince. – I am beautiful, mysterious, no worse than Unity, and I have many special abilities. Marry me!

Nolik thought and decided to marry One’s treacherous girlfriend.

But no matter how he attached himself to his bride, they didn’t get any beautiful ten. How to walk down the aisle here?

“This is all because he can’t forget One,” the Imaginary One shouted angrily. - Cut off her head immediately!

Her order was immediately carried out, but the Imaginary Unit immediately fell unconscious.

- Save her, save her! - Nolik shouted.

The magical Six and her company had to intervene in what was happening: they quickly got living water both Unity and the imaginary Unity came to life.

And Nolik realized that he had always loved only One. He apologized, Unity forgave him, and they got married.

This was a feast for the whole world! The numbers sang, danced, played various puzzles...

But they decided not to expel the imaginary Unit from the country. In the country of Tsifiria, all numbers are needed, even imaginary ones. Only they should know their place.

MAJESTIC FRACTION

Once upon a time there was a Fraction, and she had two servants - the Numerator and the Denominator. Fraction pushed them around as best she could. “I am the most important,” she told them. “What would you do without me?” She especially loved to humiliate Denominator. And the more she insulted him, the smaller the denominator became, the more the Fraction swelled in its own greatness.

And Drobya, I must admit, was not the only one. For some reason, some people also think that the more they humiliate others, the more magnificent they themselves become. At first the Fraction became as big as a table, then as a house, then as a globe... And when the Denominator became completely invisible, the Fraction began to take on the Numerator. And he, too, soon turned into a speck of dust, into a zero...

Have you guessed what happened to Drobya? Zero in the numerator, zero in the denominator. God knows what happened!

ADVENTURE POINT

The little dot was very lonely. Lost in the vast Space, she had neither relatives nor friends. No attempts to entertain herself helped, after them it became even more sad... One day, moving carefully, she saw something long, so long that neither the beginning nor the end was visible.

- Hello! Who are you? – Tochka was happy.

“Don’t interfere,” the stranger waved him off, “I can’t be distracted from my direction.” You don't fall for him, so I don't need you.

The point was not offended. Indeed, everyone has their own affairs, and the fact that there was someone else in Space was already good. It turns out you just have to not stand still.

Suddenly, Dot felt dizzy: some line was moving around her. She was continuous, closed, and you didn’t know which way to look in order to talk to her.

“Good afternoon...” Tochka said timidly, “I won’t bother you?”

- You're already interfering! I almost lost my center because of you,” she heard in response, “the most important thing for me is to maintain a distance from my center.” That's my whole point. So, go outside so as not to fool me...

After saying goodbye, Tochka began to think. She just didn't know where to move next.

- And yet I’m shorter! When will you learn precision?! – the little girl suddenly heard behind her.

Turning quickly, she hurried towards the voices. Three desperate debaters did not immediately notice her. When she said hello, the first question from them was: “What is your length?”

-What is the length? – Point was confused.

- No, look at her! She doesn't know what length is! Do you know how to measure and compare?

- Not yet...

“Then go your way and don’t get in the way, we’re very busy.”

This was too much. Now Tochka didn’t know what to do at all. But, as often happens in the most hopeless situations, she was unexpectedly lucky.

- Hurry up! I can't get distracted from my direction.

This has already happened. Looking incredulously, Dot approached the one who called her and saw almost the same picture as at the first meeting. A bright line, going into the distance and getting lost there, began next to her.

“Well, we’re together, now you won’t be lonely.” Let me show you infinity. Do you know what this is?

– I don’t know and I’m even a little afraid. I was looking for a friend, but I kept hearing that I was in the way, and I probably didn’t want anything anymore...

- That's funny! You know what? I need to hurry, and so that you don’t get bored anymore, I’ll cut off a piece for you near my starting point.

- But...

– Don’t be afraid, I am infinite. Let's just move my starting point. Neither my length nor direction will be affected by this. And you and my previous starting point will become the ends a small piece lines and you will be inseparable. Between you you will find many of your girlfriends... In general, you will not be bored anymore. See you!

ABOUT HOW THE Dwarfs LEARNED ABOUT PROPORTIONS

Once upon a time there lived four dwarfs. Their names were Pif, Paf, Poof and Pef. Once upon a time under New Year they found a very large Christmas tree. And since they usually found small Christmas trees, they also had few toys (only 62 balls, 1 icicle, 1 star).

The gnomes decided to buy more toys. But they didn’t know how many more toys were needed for such a large Christmas tree. Then they began to think, count, and figure things out. After a while Pif exclaimed:

"I have an idea. Our small Christmas trees were 1 meter high, and this tree is 6 meters high. In order for us to buy toys, we need to create a proportion: , and then 384 – 64 = 320 (toys).”

The gnomes bought 320 toys and had a wonderful New Year. With a decorated Christmas tree.

COUNTRY OVERVIEW GEOMETRY

The country of Geometry is huge and beautiful. She never knew slavery and wars. Because everything in it is subject to one law - harmony. This country has existed for many centuries, and for many centuries its inhabitants have religiously observed this law.

How do they do it? Here, for example: Three sisters (sides of one triangle). They always live in harmony with each other, but sometimes they have quarrels. And then each of the sisters remembers that she is less than the sum of the other two sisters, but greater than their difference. This means that she will be stronger if the other two sisters quarrel with each other. But then the triangle ends. The family will fall apart and harmony will disappear. Therefore, the sisters do not quarrel and resolve all disputes peacefully.

Points in Geometry are held in special esteem. Each figure monitors and cares for its points. Just like every body takes care of its own figure.

For example, straight line l looks after point M (x0; y0), y = kx.

Thanks to this, point M (x0; y0) feels great, to the delight of the line and its neighbors.

We can give many examples of how the inhabitants of Geometry serve Harmony. But let's leave it at that for now. And we will wait for news from this magical land - Geometry.

ABOUT HOW ORDER CAME INTO THE KINGDOM OF MATHEMATICS

Once upon a time there lived in the same village two little Ones - twin girls. Their parents died unexpectedly and left the One sisters alone. It was hard for them to live without their parents, and then in the house that stood next to their hut, the harmful, harmful old woman Devoyka settled. She didn’t like Unity and constantly found fault with them. As soon as the Ones get excited, the hunchbacked old woman is right there, knocking with her stick, swearing: “Why are you making noise, aren’t you giving me peace?” The sisters sit down to sing songs - again the grandmother hobbles, bent over, to their house: “Why did they shout, I won’t save you from you!” The Unity sisters were afraid to stick their pointy little noses out of the hut once again.

But one evening there was a knock on their door. Two young men stood on the threshold. They asked the sisters for permission to spend the night in their house, as they were very tired after long journey. The sisters warmly greeted the guests, warmed them up, fed them, and had a polite conversation with them. The guests said that they were pages of the great Queen Mathematics. She sent them on an assignment - to resolve a lawsuit in one of the cities of the kingdom. And their names are Plus and Equal. Before the guests had time to finish their story, there was a knock on the door... Again the old woman Deuce was on the threshold: “What are you talking about here, looking out at night?” The skinny Ones clung to each other with fear. “Eh! - said the guests. “Yes, you have a mess here too, but the matter can be fixed, go into the hut.” Before the old woman had time to come to her senses, Plus had already grabbed one One with one hand, and the other with the other, and Equally stood between them and the old woman. And suddenly...

The grandmother’s face smoothed out and broke into a smile: “My granddaughters, orphans, I didn’t just drop in on you, I came to take you from the dilapidated hut to my home. Enough of you alone, come and join me. The three of us are more satisfying and more fun.”

Since then, Unity has a grandmother - loving and caring. They still live together amicably and happily. And in the kingdom of Mathematics, complete order reigns.

ABOUT TWO ANGLES AND BISSECTRISE, OR FORMATION OF AN ADJACENT ANGLE

Whether it was or not, I don’t know. However, I will tell you a story that every Geometry kid knows and which every Church Geometry employee copies when they come to work.

And it was all like that. One day, two Angles met on the same plane. The eldest, who was 130° (here the year is replaced by 1?), and the youngest, who was only 50?. They met and immediately argued which of them was more important, better, and braver. The younger one claimed that he was stronger because he was younger, and, according to him, he had more strength. The eldest considered himself the very best, because he is the eldest and has seen a lot in his 130°. The argument could no longer continue, and they decided to hold a tournament.

Bisector knew about the tournament, and she decided to defeat her two enemies, and thereby become the head of Geometry.

The tournament began at the appointed time. There were two Angles present. In the midst of the battle, Bisector suddenly appeared, leaving the fighters at a loss. The elder Angle entered the battle with Bisector, then the younger one, but this did not lead to success. Victory seemed to be on Bisector's side. She was triumphant and already imagined herself in the role of ruler. Suddenly an idea came to the Angles. They decided to join forces and drive the villain out of the country.

The triumphant Bisector did not notice that instead of two Angles, two ardent opponents, an Adjacent Angle appeared, which instantly defeated her. The bisector begged for forgiveness. Since then, the Bisector has been in the service of the king, and two Angles, two ardent opponents, have become one whole Adjacent Angle and are in the service of the king, protecting Geometry from enemies.

ABOUT GEOMETRIOLANDIA

DIVIDED INTO TWO PARTS

A long time ago there was a country called Geometriolandia, it was ruled by two brothers, Cube and Square. Everything was peaceful with them, the kings ruled the country together and there were no disagreements between them. All residents were equal to each other until a quarrel occurred between the rulers. And it all started like this... The brothers had a sister, Pyramid, everyone loved her very much and listened to her opinion. But the Pyramid wanted to establish who was more important in the country, because the inhabitants were different. Some people's house was Space, while others' house was Plane.

And then one fine sunny morning, when no one suspected that anything could happen, the Pyramid came to his brother Cube. Cube listened carefully to his sister's request to establish inequality between residents. And as usually happens, their beloved sister is believed more than all the residents. The morning became unpleasant, because the rulers began to argue which of them was more important.

“I live in Space, so I am more important than you!” said Cube. “But another body cannot live without me!” - Kvadrat asserted. And they would have argued for a long time if the Pyramid had not proposed to split into two different countries.

Since then, there have been two countries: Planimetry and Stereometry, and they live, although close, but separately.

THE SMALLEST, BUT AT THE SAME TIME THE BIGGEST FIGURE

Once upon a time there was a number Zero and all the other numbers laughed at him, even Unit often laughed at him.

What can you do? You're just empty space! - Eight joked.

You'll see! If I exist, then I am needed for something! - Null answered offended.

Zero ran away, and all the other numbers laughed for a very long time. Zero was terribly upset that with all the other numbers you could calculate something, but with zero nothing... Zero's mood worsened.

But then at one fine moment Null approached all the numbers and, as always, he was greeted with grins. But then he smiled and said:

But before you laugh, let me stand behind one of you. - suggested Null.

Come on! - Five agreed.

Zero stood behind Five and all the numbers were amazed to see that Five had turned into Fifty. And now the numbers have realized that without Zero, the smallest number, they remain just numbers, but with Zero they become ten times larger.

ABOUT DIVIDING DECIMAL FRACTIONS.

"MYSTERIOUS DREAM"

One day I had the following dream: it was as if I was in a country called Delandia. I dreamed that I was near a palace. I saw that a sad couple sat down on a bench located in a park near the palace, I went up to them and asked:

Why are you sad? It's such a beautiful day! They answered me:

We are sad because the queen of this country issued a decree.

And they showed me to the wall of the palace, on the wall hung a decree that read:

“I, the queen, command that marriages between people of unequal importance be prohibited; those who violate this decree face expulsion from the country.”

Well, I still don’t understand the reason for your tears,” I said.

The fact is that we wanted to get married, they said, but the royal decree crossed out all our plans.

What prompted this decree? - I asked.

According to the laws of our kingdom, it is a serious crime if, when dividing one number by another, the result is a number less than one.

At this time, the palace clock rang out. I opened my eyes and realized that it was a dream.

Guys, how do you think the fairy tale ends?

You will find the answer in this picture.

SPEED, TIME AND DISTANCE

Once upon a time there were very close relatives, three quantities: Speed, Time and Distance.

One day, their dear aunt Proportionality came to visit them. From her father - Equations, these three quantities knew that she was an extraordinary magician and inventor, able to transform into direct and reverse.

The next day, my aunt woke up late, just before lunch, and immediately invited the children to play the game “Relationships.” But Sister Speed’s mood had already deteriorated from the long wait for her aunt. She sat down on a bench and announced that she would not jump, change or reincarnate. To which her aunt replied:

Not yet! Sit and relax with the number 15, for example, and at this time I will turn into Direct Proportionality.

She touched her with a magic wand to Speed's palm, and the number 15 appeared on it.

Meanwhile, Distance and Time were jumping and frolicking. If the Distance increased by 3 times, then the Time increased by 3 times; and if the Distance decreased by 2 times, then the Time decreased by 2 times. But their ratio remained a constant number all the time, and was equal to 15.

30:2=15

45:3=15

He was shown by Sister Speed, sitting on a bench. Then brother Distance decided to become a constant value and also sit on the bench and rest. But he doubted whether he would succeed or not.

Aunt Proportionality explained that to do this she needed to become Inverse Proportionality. She turned her hat back to front and began to run backwards. And so that brother Path remained constant, she suggested that Speed ​​and Time multiply. Therefore, as soon as Time began to decrease several times, Speed ​​increased by the same amount and vice versa.

They jumped, frolicked, changed, however, their product was always a constant number and equaled 60. Brother Distance, sitting on the bench, showed it.

15*4=60

10*4=60

Aunt noticed that this game can be played with other quantities, making up proportions.

In the evening, Aunt Proportionality left for her county of Attitude. The great children said goodbye to her and invited her to visit her the following weekend.

ABOUT THE ISOSceles TRIANGLE

In a certain kingdom, in a certain state, there lived a family: mother-side, father-side and son-Foundation. They lived without grieving, but their son Foundation did not have to marry. The father says:

Well, that's enough, son. The time has come to get a wife.

And their son was so helpless that he was so frightened that his knees shook from morning to evening. He thought, thought, and decided to go to the neighboring kingdom - to try his luck. They equipped him as if he were traveling to distant lands. And in that kingdom lived: father -d, mother -p and beautiful daughter Mediana. She had a nanny, Geometry. Then in the fairy tale everything goes as usual, but no! That nanny was harmful, and that’s why they loved her in this kingdom. She gave the Foundation three tests:

Before you marry Median, please answer:

1) Which triangle is called isosceles?

2) Which triangle is called equilateral?

3) What is the median of a triangle?

For our Foundation, these questions turned out to be too complex.

Maybe you guys can answer?

Today, the issue of developing students’ creative abilities in the theory and practice of teaching is especially relevant, since recent research has revealed that schoolchildren have significantly more opportunities than previously thought to learn material, both in familiar and non-standard situations.
In modern psychology there is a point of view on creativity: all thinking is creative (there is no non-creative thinking).
Human thinking and the ability to create are the greatest gift of nature. The upbringing environment either suppresses a genetically determined gift or helps it to reveal itself. Favorable environment and qualified pedagogical leadership can transform a “gift” into an outstanding talent.
The teacher’s task is not only to teach the child mathematics and other subjects, but also to develop cognitive abilities guys using this item.
Indeed, if you ask schoolchildren which subject they like more than others, most of them are unlikely to name mathematics, although they take it seriously. And how often do we hear unflattering comments about our subject – “boring” science. And we mathematicians are often called “crackers” and “bores.” It's a shame to the core. But this is not the fault of the subject, but, probably, the fault of those who teach it.
And among teachers of literature and history there are no less “nerds”. But ours educational material much less entertaining than literary and historical. What excites the soul more: “The square of the hypotenuse is equal to the sum of the squares of the legs” or “I loved you. Love, perhaps, has not completely died out in my soul”?

“A mathematician who is not partly a poet will never achieve perfection in mathematics”, said K. Weierstrass.
Some questions school mathematics seem insufficiently interesting, sometimes boring, hence one of the reasons for poor mastery of the subject is lack of interest. I think that by increasing interest in the subject, it would be possible to significantly speed up and improve its study.
Although we do not have such an arsenal of influence on the soul as literature, history, etc., we also have something.
There are no easy paths to science. And mastering mathematics “easily and happily” is not so simple. It is necessary to use all opportunities to ensure that children study with interest, so that most teenagers experience and realize the attractive aspects of mathematics, its capabilities in improving mental abilities and overcoming difficulties.
In my lessons I pay great attention to gaming technologies as a type of transformative creative activity, in close connection with other types of educational work.

“Making school work as interesting as possible for a child and not turning this work into fun is one of the most difficult and most important tasks didactics,” wrote K.D. Ushinsky.

The increase in mental load in mathematics lessons forces every teacher to think about how to maintain interest in the material being studied and intensify the activities of students throughout the lesson. The emergence of interest in mathematics among most students depends on how skillfully the teacher organizes his work. It is necessary to ensure that every child works actively and enthusiastically, strives for continuous knowledge and development of his childhood imagination. This is especially important in adolescence, when permanent interests and inclinations towards a particular subject are still being formed and determined. It is during this period that one should strive to reveal the attractive sides of mathematics.

One way to solve this problem is to use game situations in mathematics lessons. Every teacher needs to remember that teenage students, and even more so those with poor academic performance, especially quickly get tired of prolonged monotonous mental work. Fatigue is one of the reasons for the loss of interest and attention to learning. It is possible to reduce the fatigue of students from performing monotonous computational exercises with the help of game situations.
It would seem that a fairy tale and mathematics are incompatible concepts. A bright fairy-tale image and a dry abstract thought! But fairytale problems increase interest in mathematics. This is very important for students in grades 5-6.

Lesson-fairy tale.

Material party this lesson are game actions that are regulated by the rules of the game, contribute to the cognitive activity of students, give them the opportunity to demonstrate their abilities, apply existing knowledge and skills to achieve the goals of the game. The teacher, as the leader of the game, directs it in the right didactic direction, maintains interest, and encourages those lagging behind.

Fairy tales are needed in grades 5-6. In lessons where there is a fairy tale, it always reigns good mood, and this is the key to productive work. A fairy tale banishes boredom: Thanks to a fairy tale, humor, fantasy, invention, and creativity are present in the lesson. And most importantly, students learn mathematics.

Game plots and situations most often arise during game lessons: fairy tale lessons, travel lessons, etc. But also different stages lessons.

1. The more students complete tasks and exercises, the better and deeper they assimilate the mathematics program. And they help very well in achieving this goal oral tasks, oral counting. Such activities develop active thinking and intelligence, and increase the speed of calculations.

The benefits of mental calculations are enormous. By applying the laws of arithmetic operations to mental calculations, students not only repeat them, consolidate them, but, most importantly, learn them not mechanically, but consciously. With oral calculations, such valuable human qualities as attention, concentration, endurance, ingenuity, and independence develop. Oral arithmetic promotes memory training and opens up wide opportunities for the development of students' creative initiative.

Math "Percentage, it's not boring"

Also, when studying this topic, I often use problems with “half-joking” content and problems with fairy-tale characters.

1. Little Red Riding Hood was bringing pies to her grandmother. On the way, she ate 20% of the pies, gave 10% of all the pies to the hare, 50% of the remaining pies to the wolf, and brought the last 7 to her grandmother. How many pies did Little Red Riding Hood have at the beginning?

2. Carlson first ate 50% of the jam in the jar, then ate 80% of the remaining jam, then the last 5 spoons. How much jam was in the jar if the spoon holds 25 g.

3. King Pea decided to marry off his daughter, Princess Nesmeyana. Nesmeyana set the condition: “I will marry the prince who will solve all my riddles.” 40% of the grooms immediately stopped wanting to get married, 20% solved only half of the riddles, 16% only one riddle, 22% did not solve any. How many suitors wooed Nesmeyana if she did get married?

Upon completion of the topic (almost any), you can give the task: “Come up with a fairy tale, a story, a task based on the material you have studied.” Children are great inventors and happily complete these tasks, while the teacher accumulates a wealth of material.
Children often confuse the numerator and denominator, so you can offer them such a fairy tale.
Once upon a time there lived two brothers in a two-story house. The one who lived on the second floor loved to be clean and washed often, so he was called the Numerator. And the one who lived on the first floor did not like to wash, and even the Numerator poured water out of the window and splashed his brother. That's why he was splashed and smeared, and they called him the Denominator. And so it went, clean is on top, the numerator, Spattered is on the bottom, the denominator.
Activation of knowledge on the topic “PERCENT”

The Tale of a Cunning and Greedy King

One cunning and greedy king once summoned his guards and solemnly declared: Guardsmen! You serve me well! I decided to reward you and increase everyone’s monthly salary by 20%!” "Hooray!" - the guards shouted. “But,” said the king, “only for one month. And then I will reduce it by the same 20%. Do you agree?” “Why not agree? – the guards were surprised. “Let it be for at least one month!” So it was decided. A month passed and everyone was happy. “Bot great! - the old guard said to his friends over a glass of beer. – I used to get 10 dollars a month, but this month I got 12 dollars! Let's drink to the king's health!

Another month has passed. And the old guard received a salary of only 9 dollars 60 cents. "How so? - he became worried. “After all, if you first increase your salary by 20%, and then reduce it by the same 20%, then it should remain the same!” “Not at all,” explained the wise astrologer. “The increase in your salary was 20% of 10 dollars, i.e. 2 dollars, and the decrease was 20% of 12 dollars, i.e. 2.4 dollars.”

The guards were sad, but there was nothing to do - after all, they themselves agreed. And so they decided to outwit the king. They went to the king and said: “Your Majesty! You, of course, were right when you said that raising your salary by 20% and then lowering it by the same 20% is the same thing. And if this is the same thing, then let's do it again, but only in reverse. Let’s do this: first you lower our salary by 20%, and then increase it by the same 20%.” “Well,” replied the king, “your request is logical; let it be your way!”
Exercise. Calculate how much the old guard now received at the end of the first month and at the end of the second. Who outsmarted whom?
Here are some more fairy tales that can be used in math lessons.

Tale of Zero

Once upon a time there lived Null. At first he was very small, like a poppy seed. Zero never refused semolina porridge and grew up big and big. Thin, angular numbers 1, 4, 7 were jealous of Zero. After all, he was round and impressive.
“Be in charge of him,” everyone around prophesied.
And Null put on airs and puffed himself up like a turkey.
They somehow put Zero in front of Two, and even separated it with a comma to emphasize its exclusivity. So what? The size of the number suddenly decreased tenfold! They put Zero in front of other numbers - the same thing.
Everyone is surprised. And some even began to say that Zero has only appearance, but no substance.
Null heard this and became sad... But sadness is no help to trouble, something must be done. Zero stretched out, stood on tiptoes, squatted, lay on his side, but the result was still the same.
Now Null looked with envy at the other numbers: although they were inconspicuous in appearance, each one meant something. Some even managed to grow into a square or a cube, and then they became important numbers. Zero also tried to rise into a square, and then into a cube, but nothing worked - he remained himself. Null wandered around the world, unhappy and destitute. One day he saw how the numbers lined up in a row, and reached out to them: he was tired of loneliness. Null approached unnoticed and stood modestly behind everyone. And oh, miracle!!! He immediately felt the strength in himself, and all the numbers looked at him friendly: after all, he increased their strength tenfold.”

Tale of Zero

Far, far away, beyond the seas and mountains, there was the country of Tsifiria. Very honest numbers lived in it. Only Zero was distinguished by laziness and dishonesty. One day everyone learned that Queen Arithmetic had appeared far beyond the desert, calling the inhabitants of Tsifiria to her service. Everyone wanted to serve the queen. Between Cyphyria and the kingdom of Arithmetic lay a desert crossed by four rivers: Addition, Subtraction, Multiplication and Division. How to get to Arithmetic? The numbers decided to unite (after all, it is easier to overcome difficulties with comrades) and try to cross the desert. Early in the morning, as soon as the sun's slanting rays touched the ground, the numbers set off. They walked for a long time under the scorching sun and finally reached the Slozhenie River. The numbers rushed to the river to drink, but the river said: “Stand in pairs and join forces, then I will give you a drink.” Everyone followed the river's orders. The lazy Zero also fulfilled his wish, but the number with which he formed was not satisfied: after all, the river gave as much water as there were units in the sum, and the sum did not differ from the number. The sun is getting hotter. We reached the Subtraction River. She also demanded payment for the water: stand in pairs and subtract the smaller number from the larger one; Whoever answers less will receive more water. Once again, the number paired with Zero was the loser and was upset. The numbers wandered further through the sultry desert. The Multiplication River required the numbers to multiply. The number paired with Zero received no water at all. It barely made it to the Divide River. And at the River Division, none of the numbers wanted to be paired with Zero. Since then, none of the numbers are divisible by zero. True, Queen Arithmetic reconciled all numbers with this lazy person: she began to simply assign Zero next to the number, which from this increased tenfold. And the numbers began to live and live and make good things.

Stupid King

In a certain kingdom of Mathematics there lived numbers. They lived amicably, were very hardworking, counted a lot and increased the wealth of their country. The numbers worked a lot, added, multiplied, divided everything equally and were very happy.

But one day the number zero decided to proclaim himself king. This king became very cruel and evil, humiliating all other figures. They endured the numbers, endured it, and decided to teach King Zero a lesson. When did it come dark night, they packed up all their things and went into the nearest forest. There they hid their cruel king.

And King Zero was left to live alone. His kingdom began to decline. No one multiplied, no one added, all the hardworking numbers disappeared. The king became sad and realized that he couldn’t do anything without all the numbers. I decided to go into the forest and ask all the numbers for forgiveness. That’s what I did and returned all the numbers to the state. And everyone began to live happily and cheerfully. After all, zero only means something with other numbers.

Majestic fraction

Once upon a time there was a Fraction, and she had two servants - the Numerator and the Denominator. Fraction pushed them around as best she could. “I am the most important,” she told them. “What would you do without me?” She especially loved to humiliate Denominator. And the more she insulted him, the smaller the denominator became, the more the Fraction swelled in its own greatness.
And Drobya, I must admit, was not the only one. For some reason, some people also think that the more they humiliate others, the more magnificent they themselves become. At first the Fraction became as big as a table, then as a house, then as a globe... And when the Denominator became completely invisible, the Fraction began to take on the Numerator. And he, too, soon turned into a speck of dust, into a zero...
Have you guessed what happened to Drobya? Zero in the numerator, zero in the denominator. God knows what happened!

Mathematical fairy tale “THE TALE ABOUT HOW THEY WERE DIVIDED BY ZERO, BUT THEY DID NOT DIVIDE.”

Two squared

They lived and lived, but did not bother with the indicator and the basis of the degree. Everything went smoothly with them, they didn’t quarrel, didn’t fight, and if they did, they immediately made up. The base was doing household chores, and the indicator was building new home for them. And then one day, on a cloudy, but at the same time warm day, the Foundation and the Indicator quarreled. And they had a big fight...
The base threw buckets of water on the ground and began shouting at the indicator that it wanted them to disperse. The indicator did the same for the Foundation. They swore, swore, swore, and eventually their construction site fell into disrepair, the well was overgrown with grass, old house leaned sideways and began to collapse, the whole earth dried up. But even despite this, the parts of the degree did not make peace with each other... During another quarrel, a once frequent guest, number 4, dropped in on them. “What are you doing?! Why are you fighting?!” she exclaimed.
“I don’t want to live with this reason!” replied the Indicator.
“But I don’t want to live with this Indicator!” answered the Foundation.
After thinking about it a little, the Four came to a brilliant, important decision:
“If you had not quarreled, then your house would have been built, the plot would have been cleared and green, the well would have been in good condition! Your quarrel led to the destruction of your life! And what’s even more unpleasant - to the destruction of mine. You are part of me! You- Two is in the Square, and I am Four! You and I are not just friends, we are very close relatives, and as soon as you started quarreling, I began to get sick... Now I still have a runny nose..."
The Base and the Indicator looked at each other...And hugged. They forgot all past grievances, quarrels and adversities, and soon they built a house and invited the Four to live with them, who reunited and reconciled them.
And they began to live and live and make money on decimal fractions.

In the country of Mathematics, in the city of Chetnoye, the number 13 appeared.
But no one communicated with him just because it was an odd number.
=And so number 1 decided to meet him. They became best friends.
So they became friends that they united, and the number 14 came out. After all, 13+1=14!
By developing interest in mathematics through such activity methods, I am convinced of their effectiveness. There is a positive trend in students’ academic performance and quality of knowledge. In addition, the above methods have a health-saving orientation: they relieve fatigue, mental stress, and increase students’ performance in the classroom.
It should be assumed that all children are talented from birth, and the goal of all adults, these children around them: teachers, parents is not to extinguish the spark of talent. In my work, I feel the support of parents who are constantly interested in the success of their children and stimulate their interest in the subject. Working with strong students also affects the growth of the teacher himself. This encourages me to engage in self-education, and I will be happy to share my creative findings with colleagues when speaking at a methodological association.
What needs to be done so that talented children grow into talented adults, i.e. could they realize themselves, achieve recognition and success?
We cannot change genetics, what is given is given. Attempts to change the social environment also do not lead to success. This means that we only have the opportunity to create an intellectual environment in the classroom, at school, in the city.
Children are naturally inquisitive and eager to learn. In order for them to demonstrate their talents, it is necessary correct guidance development of creative abilities in class and outside of class time.
“Stimuli of mathematicians of all times: curiosity and the desire for beauty”, wrote Dieudonne J., and we try to use them in our work.
All this will happen if the teacher’s attitude towards children and the subject, and the children’s attitude towards the subject and the teacher, are of the nature of positive creative cooperation.
Thus, teaching mathematics gives the teacher a unique opportunity to develop a child at any stage of the development of his intellect.
New searches await me ahead, new concerns in teaching and educating the younger generation. Summary of a mathematics lesson in 5th grade “Journey to the Land of Mathematics”

“The subject of mathematics is so serious,
that it is useful not to miss opportunities
make it a little entertaining."

B. Pascal

Fairy tales and old stories

The Peasant and the Devil

A peasant walks and cries: “Ehma! My life is bitter! The need is completely gone!
There are only a few copper pennies dangling in my pocket, and even those need to be given back now. And how does it happen to others that for all their money they get more money! Really, at least someone would want to help me.”

Just as I had time to say this, lo and behold, the devil was standing in front. Well,” he says, “if you want, I’ll help you.” And it's not difficult at all. Do you see this bridge across the river? I see! - says the peasant, and he himself became afraid. Well, once you cross the bridge, you will have twice as much money as you already have. If you go back, it will again be twice as large as it was. And every time you cross the bridge, you will have exactly twice as much money as you had before this crossing.
Oh? - says the peasant. True word! - the devil assures. - Only, mind you, an agreement! For the fact that I double your money, every time you cross the bridge, give me 24 kopecks. Otherwise I don't agree. Well, that's no problem! - says the peasant. - Since the money will always double, why not give you 24 kopecks every time? Come on, let's try!
He walked across the bridge once and counted the money. Indeed, it has doubled. He threw 24 kopecks into the line and crossed the bridge a second time, again
there was twice as much money as before. He counted out 24 kopecks, gave it to the devil and crossed the bridge for the third time. The money doubled again.
But it turned out to be exactly 24 kopecks, which according to the agreement... he had to give to the devil. He gave them away and was left without a penny. How many
did the peasant have money at first?

Peasants and potatoes

Three peasants were walking and went to an inn to rest and have lunch. They ordered the hostess to cook potatoes and fell asleep. The hostess cooked potatoes, but did not wake up the guests, but put the bowl of food on the table and left.
— One peasant woke up, saw potatoes and, so as not to wake up his comrades, counted the potatoes, ate his share and fell asleep again.
-Soon the other one woke up; He didn’t realize that one of his comrades had already eaten his share, so he counted all the remaining potatoes, ate the third part and fell asleep again.
-Then the third one woke up; Believing that he was the first to wake up, he counted the remaining potatoes in the cup and ate a third of them.
Then his comrades woke up and saw that there were 8 potatoes left in the cup. Only then did the matter become clear. Count how many potatoes the hostess served on the table, how many you have already eaten and how many more everyone should eat so that everyone gets it equally.

Two shepherds

Two shepherds, Ivan and Peter, met. Ivan says to Peter: “Give me one sheep, then I will have exactly twice as many sheep as you!” And Peter
He answers: “No, it’s better, give me one sheep, then we will have an equal number of sheep!” How many sheep did each person have?

Peasant women's bewilderment

Two peasant women were selling apples at the market. One sold 2 apples for 1 kopeck, and the other sold 3 apples for 2 kopecks. Each basket had 30
apples, so the first one expected to get 15 kopecks for her apples, and the second 20 kopecks. Both together they had to earn 35 kopecks, realizing
These peasant women, in order not to quarrel and not to interrupt each other's buyers, decided to put their apples together and sell them together, and they reasoned like this:

“If I sell a couple of apples for a penny, and you sell three apples for 2 kopecks, then in order to get our money, we need to sell five apples for 3 kopecks!” No sooner said than done. The traders put their apples together (there were only 60 apples) and began selling them at 3 kopecks for 5 apples.

They sold out and were surprised: it turned out that they got 36 kopecks for their apples, that is, a kopeck more than they thought they would get!

The peasant women wondered: where did the “extra” penny come from and which of them should receive it? And how, in general, should they divide all the proceeds now? And really, how did this happen?

While these two peasant women were sorting out their unexpected profits, the other two, having heard about it, also decided to earn an extra penny. Each of them also had 30 apples, but they sold it like this: the first gave a pair of apples for one penny, and the second gave 3 apples for a penny. The first, after the sale, was supposed to gain 15 kopecks, and the second - 10 kopecks; both together would therefore earn 25 kopecks.

They decided to sell their apples together, reasoning in exactly the same way as those first two traders: if I sell a couple of apples for one penny, and you sell 3 apples for a penny, then in order to get our money, we need every 5 apples sell for 2 kopecks.

They put the apples together, sold them for 2 kopecks for every five pieces, and suddenly... it turned out that they only earned 24 kopecks, and missed out on a whole kopeck. These peasant women also wondered: how could this happen and which of them would have to pay with this penny?

Camel division

An old man who had three sons ordered that after his death they should divide the herd of camels that belonged to him in the following way:

so that the eldest takes half of all the camels,

middle - third and

the youngest - the ninth part of all camels.

The old man died and left 17 camels. The sons began dividing, but it turned out that the number 17 is not divisible by 2, 3, or 9. At a loss as to what to do, the brothers turned to the sage. He came to them on his own camel and divided everything according to the will. How did he do it?

Answers

Peasant and devil:

Before stepping onto the bridge for the first time, the peasant had 21 kopecks.

Peasant and potatoes:

The hostess served 27 potatoes on the table, and each peasant had 9 potatoes.

Two shepherds:

Ivan had 7 and Peter had 5 sheep.

Peasant women's bewilderment:

Having piled up their apples and started selling them together, they, without noticing it themselves, were selling them at a different price than before.

Camel division:

The eldest brother received 9 camels, the middle one 6 camels, the youngest 2.

A TALE ABOUT NUMBERS

Far, far beyond the seas, beyond the forests, there was the kingdom of Mathematics and numbers lived in it. They all lived very far from each other and rarely met...

"UNIT"

Once upon a time there lived in the kingdom of Mathematics Unit. She lived alone - all alone in such a blue palace - a corner

And she had one corner there where there was one table

and one chair, one cabinet in which there was one cup

and one saucer. And I bought one in the store

everything one at a time: one candy, one book, one boot...

Unity was bored by herself and she decided to make friends with someone and Unity went for a walk around the kingdom. Suddenly, a wolf jumped out from behind a tree towards Unity. He was also alone and no one wanted to be friends with him, they thought he was evil. And Unity felt sorry for the wolf, and she invited him to play together. So the one and the wolf became friends and together they recited a poem:

Guys, I'm one!

Very thin, like a knitting needle!

I look a little like a hook

Or maybe on a broken twig.

The account is kept from me

And for this I am honored!

"TWO"

E Back in the kingdom of mathematics there lived the number Two. She also lived in her own house, like this:

Her house had two rooms.

Two had a friend, a wise owl, and they loved to play different games. They especially loved games with the number two:

How many ears are there on the top of your head?

How many eyes?

Well, how many arms and legs?

Near Deuce’s house there was a beautiful lake, and swans swam in it. When the couple came to the lake, the swans asked her to tell them a poem: Two looks like swans:

There is a neck and a tail too.

The swan can tell

How do we find out the number two?

"TROIKA"

IN Troika also lived in the Kingdom of Mathematics. She lived in this red palace

Everyone loved her because she was kind and obedient. Her house had three large rooms. Troika's neighbors were three bears. They all lived in love and harmony. Every day Troika treated the little bear with three candies. One day the bears went into the forest to pick mushrooms and invited Troika with them, but she got so carried away that she got lost. Troika looked around and saw a clearing nearby; in the clearing she saw three hedgehogs. The trio treated each hedgehog to a mushroom, and they showed her the way home. At home, the three bears were very happy about Troika and told her a poem:

Oh! Hurry up and take a look!

The number three has appeared!

Three third of icons

Consists of two hooks.

"FOUR"

D Another resident of the Kingdom of Mathematics was Four, she lived in such a palace

There were four rooms in the palace. The Hedgehog lived in one room, the Cat lived in another, the Turtle lived in the third, and the owner of the Four herself lived in the fourth. They had fun, sang and danced.

One day, Four told their friends that there are four directions to the world: north, south, east and west, and they wanted to go on a journey. They took four apples, four cookies, four juices with them, boarded a plane and flew north. There was a lot - a lot of snow and polar bears lived there. The four and their friends were very cold and decided to go south. It was hot in the south, unusual birds sang and interesting animals were found there. When our travelers got to the east, they were met by an eastern prince who proudly rode an elephant. And in the west, the Four introduced their friends to cowboys - brave heroes. The travelers were very tired and flew home to the kingdom of Mathematics. At home, Hedgehog, Cat and Turtle composed a poem for the Four:

I have a flag in my hand!

Look quickly, my friend,

How good is he?

Looks like a four!

"FIVE"

Five lived in a beautiful green palace.

She had five rooms. In the biggest

There was a table in the room, there were five chairs around it, and on the table there were five cups and five saucers.

Around the palace where Five lived there was a large orchard. Apple and pear trees grew there. Five's neighbors were Bunny, Hedgehog and Squirrel. Once they asked Five to treat them to fruit, and Five said: “If you count how many apple trees and how many pears grow in the garden, then I will treat you.”

Then Five treated everyone to apples and pears. And Bunny, Hedgehog and Squirrel told her a poem:

The wind inflates the sail,

And the flag plays on the mast.

The wind wants to show

Number five to all the guys!

"SIX"

The Kingdom of Mathematics was the Blue Sea. And so near the Blue Sea lived the Six. Here in this blue palace, which had six rooms.

Six had six kittens: the first was white, the second was brave, the third was smart, the fourth was noisy, the fifth had a red tail, and the sixth loved to sleep. The kittens had six bowls from which they drank milk and six baskets in which they slept. Every evening, Six gave the kittens milk and then put them to bed. Let's help the six feed and tuck the naughty kittens.

And when the kittens lay down in their baskets, Six told them a poem: On the fence at the gate

Number six perched:

Like a little snail

There is a curl and horns.

"SEVEN"

In the Kingdom of Mathematics, on the street of Yellow Dandelions, lived seven. She lived in this colorful palace

Seven has been friends with the rainbow for a long time,

and therefore her palace was decorated in seven

colors of the rainbow. There were seven rooms in the palace.

Seven and Rainbow often had fun, black paint was jealous of them and, on her orders, the robbers grabbed Seven and threw him into the dungeon.

To free the Seven you need to answer the following questions:

How many colors are there in a rainbow?

How many days are there in a week?

How many dwarves does Snow White have?

How many kids did the goat have?

Well done! Now Black Paint has freed the number Seven, and for her liberation she will tell you a poem:

The sun is hot,

The heron spreads its wings,

And he will straighten them out completely,

Turns into number seven!

"EIGHT"

This is where the Eight lived in such an unusually beautiful palace.

She was round-faced, ruddy, maybe a little plump,

but she was never upset about it and was always cheerful.

Eight loved cleanliness and often tidied up the eight rooms.

Eight lived on the very edge of the kingdom, where it often snowed, and one day Eight and his friend Spider decided to build a snowman. But for some reason they didn’t succeed except large clods snow. Let's tell Eight and Spider how to make a snowman.

When eight saw the snowman, she thought for a long time what number he reminded her of. The snowman told her a poem:

Eight has two rings

Without beginning and end.

We'll ask Vanka to stand up

Show us the number eight

One circle and two circles

It's just my friend.

« NINE"

Back in the kingdom of Mathematics there lived the number Nine.

She lived in such an unusual palace, in which

there were nine rooms.

One fine sunny day Nine had

birthday, she invited Chanterelle, Magpie, Mouse, Bunny, Hedgehog, Bear, Kitten and Wolf. But Nine did not know how to count and could not accommodate all the guests at the table:

How many chairs should be placed at the table?

How many cups should I put in?

How many pieces should a birthday cake be cut into?

The hostess also prepared a surprise for the guests; she asked them the riddle “What number will nine turn into if it turns over?”

The guests prepared a poem for the birthday girl:

The cat lay down on the ledge,

The fluffy tail hung down.

Kitty, cat, what's up

You look like a nine!

"ZERO and TEN"

IN in the very center of the kingdom lived Zero. He had a very interesting palace

There was not a single corner in this palace; there was nowhere to put a table or chair. In general it was empty. And therefore Zero

became a slacker.

Once the sad Zero was sitting and crying, and at that time

Number One decided to visit the other numbers. And then she came to visit zero, brought a delicious pie and chocolate. One saw that Zero had nothing and invited him to his home. They spent the whole day together, liked each other and decided to get married. But how can it be, they are different numbers, how can they live together? They thought and thought and came up with a common name for themselves, Ten, so that no one could separate them.

Ten invited all the numbers to the wedding. There was a lot of food, all friends came with gifts. This is the poem they gave to the Ten:

Zero had a girlfriend

The one is a laugher.

She joked about zero

And turned it into a top ten!

All the numbers liked being together so much that no one wanted to go home, and they decided to build a big city and call it Tsifland. So they did, and began to live amicably and happily.

Ten smart sisters

Everything has been considered for a long time.

Look, they're standing next to each other

WITH you are already familiar with them.

For a preschool child, a fairy tale is especially dear. And a mathematical fairy tale can also become an excellent teaching tool. In such fairy tales, heroes meet magic numbers and incredible geometric shapes. Thanks to good deeds and sorcery, the child develops an idea of ​​time, quantity, shape and other mathematical concepts. Mathematical tales are not a means of memorizing information, but a way to successfully comprehend the basics of science.

What is a mathematical fairy tale

Mathematical fairy tale - literary text, based on the adventure genre. In the plot, the main characters are associated with certain mathematical concepts, which have an unusual, “live” appearance that attracts the attention of readers. Fictional characters perform logical operations during feats, and the child carries out the process in his head, which is the primary task game-based learning. It is amazing that in fairy tales there is often no logic, but in mathematical fairy tales it imperceptibly settles in the memory of listeners with valuable knowledge.

Comprehension in kindergarten mathematical foundations starts with the younger group. The teacher must prepare the children for the gradual development of the initial laws of logic and other important processes training. If we are talking about fairy tales, then younger group Children should read them more often before quiet time, since at home most parents prefer TV and games on tablets and smartphones. This fact is confirmed by statistics compiled in Russia by Online Market Intelligence (OMI) in 2012.

The percentage of parents who are ready to pass on their gadgets to their children (indicating the child’s age). About 4,000 people took part in the survey

If parents are ready to work with their child on their own, books of fairy tales for little ones will come to their aid. For example, “The Adventures of Kubarik and Tomatik, or Fun Mathematics” by G.V. Sapgir and Yu.P. Lugovskoy. This book invites children to go on adventures with their friends - Tomatik and Kubarik - and find out what one, many, higher, lower, longer, shorter, etc. mean.

Goals and objectives of texts for preschoolers of the junior, middle and senior groups

In the younger group, the teacher, with the help of mathematical fairy tales, introduces children to the simplest quantitative concepts, such as “many”, “one”, “none”. In ordinary fairy tales, he points to the shapes of objects associated with geometric figures. IN middle group mathematical tales are synthesized with folk tales which children already know well. Let's take Kolobok, for example. The teacher, while reading, will highlight the serial number of each “step” of Kolobok, thereby demonstrating how Kolobok moves step by step main character. And the fairy tale “Teremok” will help you count the number of heroes in the house. Between fairy tales the teacher uses finger gymnastics, with the help of which numbers are studied.

Using fairy tales, we teach the meanings of geometric shapes and their names

The middle group has the following tasks:

1. Learn to count to five.
2. Master knowledge of quantitative and ordinal numbers, fractions and whole parts.
3. Strengthen the ability to navigate in time.
4. Strengthen the skill of recognizing geometric shapes.
5. Train spatial orientation (the child’s awareness of directions: between, under, behind, in front, etc.).

IN senior group(children 5–6 years old) become heroes of fairy tales mathematical concepts, be it zero or square. When introducing preschoolers to a fairy tale, the teacher should not forget to ensure that the children understand the plot and meaning of the story. Auxiliary tools Fascinating games related to logic, such as:

• selection of identical pairs;
• making a rectangle equal to the provided sample;
• determining which items are more numerous.

Games will help the child establish the idea of ​​equality and integrity of numbers and things. The operations performed by children contribute to mental development, the development of skills to synthesize, analyze and compare data.

In the senior group, mathematical fairy tales are used to achieve the following goals:

1. Learn to count to twenty, recognize the missing number and count backwards.
2. Relate the number of things to a number.
3. Understand the meaning of the following quantities: width, length, height, volume (capacity) and mass (weight).
4. Be able to distinguish and understand complex geometric shapes: line segment, angle, polygon, three-dimensional shapes.
5. Develop the ability to navigate by the clock, quickly determine the hour and pronounce it out loud.
6. Be able to perform simple arithmetic operations.
7. Develop the ability to replace the hero of a fairy tale with a certain object (“Rubik’s Cube” - pick up a cube).
8. Remember the names of the days of the week and months and their order.

The kindergarten approves the curriculum for the year. It must comply with the documents:

• Constitution of the Russian Federation, art. 43, 72;
• Convention on the Rights of the Child (1989);
• Preschool education concept;
• SanPin 2.4.1.2660–10;
• Law of the Russian Federation “On Education” (as amended by the Federal Law of January 13, 1996 No. 12 - Federal Law);
• Model regulations on preschool educational institution, approved by decree of the Government of the Russian Federation dated September 12, 2008. No. 666.

There is no clear indication of the skills that a child should have, but the Federal State Educational Standard for Preschool Education states:

The child... ... ...has basic understanding of living nature, natural science, mathematics, history, etc.; the child is capable of making his own decisions, relying on his knowledge and skills in various types activities.

Ministry of Education and Science of the Russian Federation

Order 1155

At the request of parents, they can be provided with a curriculum kindergarten, where all the skills that are taught to children are spelled out. Teachers will tell you how and in what form the training will take place and provide additional information.

IN preparatory group Fairy tales include tasks on simple mathematical operations (in two actions), logical operations and methods for solving them. It is important to introduce children to the standards of length measures: meters and centimeters, to tell them in a fairy tale form about money, their correct use. Before school, classes will begin that cover the basics of mathematics and a fairy tale will help you understand and master more complex information.

We use texts correctly depending on the age of the child

Fairy tales are classified by genre: tales about animals, social stories and fairy tales. Each variety has its own rules for plotting and creating characters.

Older children preschool age attracted by fairy tales. Key Specific Features fairy tales mathematical nature consist in a significantly developed plot action. This is expressed not only in special techniques and methods of composition, narration and style, but also in the need for the hero to overcome a number of obstacles, performing mathematical actions in order to achieve the goal.

N.I. Kravtsov; S.G. Lazutin

Russian folk art

Types of mathematical fairy tales:

• digital;
• oriented-temporal;
• geometric;
• complex;
• conceptual.

Each fairy tale has a structure consisting of three main parts: an imaginary country, a conflict between the characters, a resolution of the conflict, and a happy ending. A mathematical fairy tale certainly has a bias towards one particular area of ​​mathematics: arithmetic or simple geometry. If the plot presents figures, then the child will remember the names of the forms and their appearance, and if there are numbers, then he will sooner learn to count.

A fairy tale for preschoolers should have pictures: it is difficult for them to reproduce unusual characters in their heads, especially if their understanding of mathematics is reduced to zero. Only images accompanied by text (in that order!) are able to fully reveal the content of the tale. Theatrical fairy tales are also good, but often in carefree fun, that part of the meaning that should remain remains is lost on the memory. The child will need time to work out the logical turns in the actions of the characters, because mathematical fairy tales carry a certain intellectual load. If you make a performance, then the child’s perseverance will evaporate.

When reading a fairy tale, it is important not to forget to point out the description of the characters and their actions. In the older group, in addition to images, it would be good to pick up real objects that look like characters - this way the child will compare figures or numbers with rational actions taking place in adventures. Taking the book in your hands, you begin to slowly read. If the fairy tale has no images, then print them out and provide them separately, or draw them. Strive to ensure that your child, when difficulties arise in understanding, asks questions rather than just listens. The increasing complexity of the material being presented was discussed earlier.

Popular math tales

Let's look at a few examples of popular fairy tales that will help us teach a child to count.

0 and 1

Once upon a time in the city of Mathematics there lived numbers and numbers. They always argued about who was more important and older, they even came up with unusual signs for themselves “<», «>», «+», «=», «-».
Among them lived a one and a zero.
They really wanted to go to school, but they were not accepted because they were small.
The friends thought and thought and came up with the idea that they needed to stick together.
And the number 10 came out of them.
They grew in number and were taken to school.
Everyone in the city began to respect them. This is how the numbers 1 and 0, or the number 10, began to live together. And the other numbers looked at their friendship and also began to live more friendly.
This is how numbers greater than 10 appeared.

Fairy tales instill a love of mathematics

G. N. Obivalina

Cinderella

In one fairy-tale kingdom, there lived a girl named Cinderella. She was an orphan, raised by her stepmother, who had two daughters of her own. The daughters were very lazy, and Cinderella had to do all the housework. One fine day the King invited everyone to a ball. But Cinderella’s stepmother did not allow her to go to the ball. She ordered Cinderella to solve all the problems that her daughters had not solved before she returned:
There are 4 corners in the room. There was a cat in every corner. Opposite each cat are 3 cats. How many cats are there in the room?
How to bring water in a sieve?
What kind of dishes can you not eat anything from?
And also Cinderella had to wash the dishes: 5 spoons, 5 cups and 5 plates. How many dishes did you wash? Cinderella quickly completed her stepmother’s task and sat down to do her needlework.

G. N. Obivalina

Blog of Galina Nikolaevna Obivalina

Three princesses

In a distant kingdom there lived a king with three daughters. They loved to solve problems and solve riddles in the evenings. For each correct answer, the princesses received a gift. The eldest princess loved to receive gifts of gold, the middle princess of diamonds, and the youngest loved flowers and animals.
One evening the king said: “I brought many different gifts from distant countries. Which of my daughters solves the problems correctly will receive gifts.
Task No. 1 - For the eldest princess: pick 5 yellow apples from one apple tree, and 5 red apples from the other. How many apples did you pick?
Task No. 2 - For the average princess: in your box there are 6 rings with diamonds. I brought you 2 more rings. How many rings will you have in total?
Task No. 3 - For the youngest princess: you had 9 kittens, and 2 ran away. How many kittens are left?
All the princesses solved their problems correctly, and the king gave the eldest princess a golden chest, the middle princess 2 rings with diamonds, and the youngest princess a cheerful puppy.
Here's a fairy tale for you, and a glass of butter for me.

G. N. Obivalina

Blog of Galina Nikolaevna Obivalina

Video: plasticine mathematical tale about zero

Video: cartoon story based on the animated series “38 Parrots”

Card index of useful literature

1. “Journey to Digital City: a mathematical fairy tale” Shorygina Tatyana Andreevna (3 books).
2. "Mathematical tales. A manual for children 6–7 years old” Erofeeva Tamara Ivanovna.
3. "Mathematical tales. Benefit for children 5 - 6 years old. In 2 issues” Erofeeva Tamara Ivanovna, Stozharova Marina Yurievna.
4. “The Adventures of Treugoshi: A mathematical fairy tale for children from 2 to 4 years old” Shevelev Konstantin Valerievich.
5. “About King Rabbit and the cunning Fox: A mathematical fairy tale for preschoolers 5–7 years old” Lukyanova Antonina Vladimirovna (art. Dushin M.V.).
6. “The Adventures of Kubarik and Tomatik, or Fun Mathematics” Sapgir Genrikh Veniaminovich, Lugovskaya Yulia Pavlovna.
7. “Adventures in the Land of Geometry” Erofeeva Tamara Ivanovna.
8. “Mathematics for kids in fairy tales, poems and riddles. For children 3–6 years old” Deryagina Lyudmila Borisovna.
9. “Learning to count. A fun journey, or How to find new friends and learn to count to ten” Gorbushin Oleg Yuryevich.
10. “Numbers, counting and Kolya’s pencil” Rick Tatyana Gennadievna.