Mathematics is not only an exact science, but also quite complex. It is not easy for everyone, and teaching a child to persevere and love numbers is even more difficult. Recently, a method called mathematical fairy tales has become popular among teachers. The results of trial use of them in practice were impressive, and therefore fairy tales have become an effective way to introduce children to science. They are increasingly being used in schools.
Stories about numbers for little ones
Now, before a child enters first grade, he should already be able to write, read and perform the simplest mathematical operations. Parents will benefit from mathematical fairy tales for preschoolers, since with them children will learn the wonderful world of numbers in a playful way.
Such stories are simple stories about good and evil, where the main characters are numbers. They have their own country and their own kingdom, there are kings, teachers and students, and in these lines there is always a moral, which the little listener needs to grasp.
A tale about the proud Number One
One day, Number One was walking down the street and saw a rocket in the sky.
Hello, fast and nimble rocket! My name is Number One. I am very lonely and proud, like you. I like to walk alone and am not afraid of anything. I believe that loneliness is the most important quality, and the one who is alone is always right.
To this the rocket replied:
Why am I alone? Quite the opposite. I take astronauts into the sky, they sit inside me, and around us there are stars and planets.
Having said this, the rocket flew away, and our heroine went further and saw Number Two. She immediately greeted her proud and lonely friend:
Hello Odin, come for a walk with me.
I don't want to, I like being alone. The one who is alone is considered the most important,” said the Unit.
Why do you think that the one who is alone is the most important? - asked Deuce.
A person has one head, and it is the most important, which means one is better than two.
Although a person has one head, he has two arms and two legs. There are even a pair of eyes and ears on the head. And these are the most important organs.
Then One realized that it was very difficult to be alone, and went for a walk with Number Two.
Funny Math Three and Two
In one school state, where all the children loved to study, there lived Number Five. And everyone else was jealous of her, especially Three and Two. And one day two friends decided to expel the A from the state so that the students would love them, and not the coveted grade. We thought and thought about how to do this, but according to the laws of the school state, no one has the right to drive away a figure; it can only leave of its own free will.
Three and Two decided to make a cunning move. They argued with Number Five. If she doesn't win, she has to leave. The subject of the dispute was the answer of a poor student in a mathematics lesson. If he gets a five, then the brave number will win, and if not, then Three and Two will be considered the winners.
Number Five honestly prepared for the lesson. She spent the whole evening studying with the boy, learning numbers and making up equalities. The next day, the student received an “A” at school, our heroine won, and Troika and Deuce had to run away in disgrace.
Mathematical tales for primary school children
Kids enjoy listening to math stories. In mathematics, 3rd grade students learn the material more easily with their help. But children at this age can not only listen, but also write their own stories.
All the stories during this period are chosen to be quite simple. The main characters are numbers and signs. It is very important at this age to show children how to study correctly. Parents and teachers can find a lot of useful information in books for grade 3 (“Mathematics”). We will tell further mathematical fairy tales with different characters.
Parable about big numbers
One day all the big numbers got together and went to a restaurant to relax. Among them were domestic ones - Raven, Deck, Darkness, which are already thousands of years old, and proud foreign guests - Million, Trillion, Quintillion and Sextillion.
And they ordered a sumptuous lunch: pancakes with red and black caviar, expensive champagne, they eat, walk, and indulge in nothing. The waiter working at their table is Nolik. He runs back and forth, serves everything, removes broken wine glasses, takes care of them, sparing no effort. And the distinguished guests keep repeating to themselves: “Bring this, bring that.” Nolik is not respected. And Sextillion also gave me a slap on the head.
Then Nolik got offended and quit the restaurant. And all the tall ones became ordinary Units, worthless. That's it, you can't offend even those who seem unimportant.
Equation with one unknown
And here is another mathematical fairy tale (3rd grade) - about the unknown X.
One day we came across different numbers in one equation. And among them there were integers and fractions, large and single-digit ones. They had never met so closely before, so they began their acquaintance:
Hello. I am a Unit.
Good afternoon. I am Twenty Two.
And I am Two Thirds.
This is how they introduced themselves, got to know each other, but one figure stood to the side and did not identify himself. Everyone asked her, probed her, but to all the questions the figure said:
Can not say!
The numbers were offended by such a statement and went to the most respected Sign of Equality. And he answered:
Don't worry, the time will come and you will definitely find out what this number is. Don’t rush, let this number remain unknown for now. Let's call him X.
Everyone agreed with fair Equality, but still decided to stay away from X and crossed the equal sign. When all the numbers were lined up, they began to multiply, divide, add and subtract. When all the actions were carried out, it turned out that the unknown X became known and was equal to only one number.
This is how the secret of the mysterious X was revealed. Can you solve mathematical fairy tales-riddles?
Stories about numbers for fifth grade
In fifth grade, children become increasingly familiar with arithmetic and methods of calculus. More serious riddles are suitable for them. At this age, it is good to involve children in making up their own stories about the things they have already learned. Let's consider what a mathematical fairy tale should be (grade 5).
Scandal
Different figures lived in the same kingdom of Geometry. And they existed quite peacefully, complementing and supporting each other. Queen Axiom kept order, and her assistants were Theorems. But one day Axiom fell ill, and the figures took advantage of this. They began to find out which of them was more important. Theorems intervened in the dispute, but they could no longer contain the general panic.
As a result of the chaos in the realm of Geometry, people began to get into big trouble. All the railways stopped working because they converged, the houses were skewed because the rectangles were replaced by octahedra and dodecahedrons. The machines stopped working, the machines broke down. It seemed like the whole world had gone awry.
Seeing all this, Axiom grabbed her head. She ordered all the Theorems to line up and follow each other in a logical order. After this, all Theorems had to gather all their subordinate figures and explain to each its great purpose in the human world. Thus, order was restored in the country of Geometry.
The Tale of the Point
There are completely different mathematical fairy tales. Numbers and numbers, fractions and equalities appear in them. But most of all, fifth graders like stories about things they are just beginning to learn about. Many students do not understand the importance of simple, elementary things, without which the entire world of mathematics would collapse. This mathematical fairy tale (5th grade) is intended to explain to them the importance of this or that sign.
Little Dot felt very lonely in the realm of Mathematics. She was so tiny that she was constantly forgotten about, placed anywhere and completely disrespected. Either way it’s straight forward! It is large and long. It is visible, and no one will forget to draw it.
And Dot decided to escape from the kingdom, because because of her there are always only problems. The student will get a bad mark because he forgot to put a full stop, or something else. She felt the dissatisfaction of others and was worried about it herself.
But where to run? Although the kingdom is large, the choice is small. And then Straight came to the aid of the Point and said:
Period, run on me. I am infinite, so you will run beyond the boundaries of the kingdom.
The point did just that. And as soon as she set off, chaos ensued in Mathematics. The numbers became agitated, huddled together, because now there was no one to determine their place on the digital beam. And the rays began to dissolve before our eyes, because they did not have a Point that would limit them and turn them into segments. The numbers stopped multiplying, because now the multiplication sign has been replaced with a slanting cross, but what can we take from it? He's oblique.
All the inhabitants of the kingdom became worried and began to ask Point to return. And just know that she is rolling like a bun along an endless straight line. But she heard the requests of her compatriots and decided to return. Since then, the Point not only has its place in space, but is very respected and revered, and even has its own definition.
What fairy tales can be read to sixth graders?
In sixth grade, children already know and understand a lot. These are already grown-up guys who are unlikely to be interested in primitive stories. For them, you can choose something more serious, for example, mathematical fairy tale problems. Here are a few options.
How the coordinate line was formed
This story is about how to remember and understand what numbers with negative and positive values are. A mathematical fairy tale (6th grade) will help you understand this topic.
A lonely Plusik walked and wandered the earth. And he had no friends. So he wandered through the forest for a long, long time until he met Straight. She was clumsy and no one wanted to talk to her. Then Plusik invited her to walk together. The direct one was delighted and agreed. For this, she invited Plus to sit on her long shoulders.
The friends went further and wandered into a dark forest. They wandered along the narrow paths for a long time until they came to a clearing where the house stood. They knocked on the door, and Minus, who was also lonely and not friends with anyone, opened it for them. Then he joined Direct and Plus, and they moved on together.
They went out to the city of Numbers, where only numbers lived. We saw the Plus and Minus numbers and immediately wanted to make friends with them. And they began to grab first one, then the other.
The king of the kingdom Null came out to hear the noise. He ordered everyone to line up along a straight line, and he himself stood in the middle. Everyone who wanted to be with a plus had to stand at the same distance from each other on the right side of the king, and those with a minus did the same, but on the left, in ascending order. This is how the coordinate line was formed.
Mystery
The themes of math stories can cover all the questions covered. Here is one good riddle that will allow you to generalize your knowledge of geometry.
One day all the quadrangles got together and decided that they needed to choose the most important one among them. But how to do that? We decided to conduct a test. Whoever reaches the kingdom of Mathematics first from the clearing will become the main one. That's what they agreed on.
At dawn, all the quadrangles left the clearing. They are walking, and a fast river crosses their path. She says:
Not everyone will be able to cross through me. Only those of you whose diagonals at the intersection point are divided in half will get to the other side.
Only those whose diagonals are equal can conquer my peak.
Again, the losing quadrangles remained at the foot, and the rest moved on. Suddenly there is a cliff with a narrow bridge, over which only one can pass, the one whose diagonals intersect at right angles.
Here are your questions:
Who became the main quadrangle?
Who was the main competitor and reached the bridge?
Who left the competition first?
Riddle of the isosceles triangle
Mathematical tales about mathematics can be very entertaining and already contain hidden questions in their essence.
In one state there lived a Triangle family: mother-side, father-side and son-foundation. The time has come to choose a bride for his son.
And the Foundation was very modest and cowardly. He was afraid of everything new, but there was nothing to do, he needed to get married. Then his mother and father found him a good bride - Mediana from the neighboring kingdom. But Mediana had a terribly nasty nanny who gave our fiance a whole ordeal.
Help the hapless Foundation solve the difficult problems of the nanny Geometry and marry Median. Here are the questions themselves:
Tell us which triangle is called isosceles.
How does an isosceles triangle differ from an equilateral triangle?
Who is Median and what is its peculiarity?
The riddle of proportions
In one direction, not far from the kingdom of Arithmetic, lived four dwarves. They were called Here, There, Where and How. Every New Year, one of them brought a small Christmas tree one meter high. They decorated her with 62 balls, one icicle and one star. But one day they all decided to go get the Christmas tree together. And they chose the most beautiful and tallest. They brought it home, but it turned out that there were not enough decorations. They measured the tree, and it turned out to be six times larger than usual.
Using a proportion, calculate how many decorations the gnomes need to buy.
Hero of the Planet Violet
As a result of research, it was discovered that intelligent beings live on the planet Violet. It was decided to send an expedition there. Kolya, a poor student, was included in the team. It so happened that only he managed to reach the planet. There is nothing to do, you need to carry out an important task from Earth.
As it turned out, all the inhabitants of the planet lived in round houses, because the population did not know how to calculate the area of rectangles. The earthlings decided to help them, and Kolya had to do it.
But the boy did not know geometry well. He didn’t want to study; he always copied his homework. There is nothing to be done, we need to figure out how to teach the residents of Violet to find the required area. With great difficulty Kolya remembered that one square with a side of 1 cm has an area of 1 square. cm, and a square with a side of 1 m is 1 sq. m. and so on. Reasoning this way, Kolya drew a rectangle and divided it into 1 cm squares. It contained 12 of them, 4 on one side and three on the other.
Then Kolya drew another rectangle, but with 30 squares. Of these, 10 were located along one side, 3 along the other.
Help Kolya calculate the area of the rectangles. Write down the formula.
Can you create your own mathematical tales or problems?
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 formulate, then I will give you a drink.” Everyone followed the river's orders. The lazy man 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 his 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. Its king was an intelligent and educated man: he knew arithmetic and 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, and 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
One day 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’m always in the retinue of the smartest 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 did not succeed in creating 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 took out living water and One and the imaginary One 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 business, 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.
It happened before. 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? 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 former starting point will become the ends of a small piece of the line and 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 dwarves. Their names were Pif, Paf, Poof and Pef. One New Year's Eve 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 a 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 Equal 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 considered 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 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?
Mathematical tales by students of grade 6b of MAOU Secondary School No. 26 of Veliky Novgorod.
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MAOU "Secondary school No. 26 with in-depth study of chemistry and biology"
Mathematic teacher:
Kelka Marina Leonidovna
Velikiy Novgorod
A tale of numbers.
In one town called "Fractions" lived the numbers from 10 to 20, as well as division, multiplication, addition and subtraction. One day, King Number 10 ordered the entire city to collect fruits and vegetables. Whoever did not bring them was severely punished by the king. Three sisters lived in the town: number 11, number 12 and number 13. They loved to walk in the beautiful park. In the park there were fractional trees - one quarter, two fifths and many others, there was also a fountain with the numbers 100 and 200. At the palace there were knights with weapons who guarded the king. The king awarded one of the knights a medal for saving a drowning figure on the water. This happened a long time ago. As always, the knight guarded the king's throne and heard someone scream. The knight saw that number 19 was drowning in the river, he rushed into the water and saved her. For this, the king awarded the knight a medal. There was a large forest near the city, but none of the residents went into it, because terrible numbers from 21 to 30 lived there. These numbers loved to scare the city residents and steal fruits and vegetables.
Friendship of numbers.
Once upon a time, long ago, there lived the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each of them lived alone and therefore was always bored. The smallest number, zero, could not mean anything. Zero meant emptiness. But even the big number 9 felt small because she was alone and could not compare with anyone.
Once the numbers 5 and 6 came across. At first glance, they were somewhat similar. 5 and 6 decided to play. But they not only wanted to measure their strength, but 6 turned out to be stronger, and 5 was weaker. This is how the “more than” and “less than” signs appeared. 7 and 9 also decided to play. But they wanted not only who was more, but also by how much. Thus, a minus sign appeared. The numbers 2 and 8 wanted to live together, so the plus sign appeared, and their little family received the value ten. This is how the first two-digit number appeared. Since then, the friendship of numbers began to be called Arithmetic.
Country of Numbers.
In the Land of Numbers there lived heroes 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. And then a dispute arose among them: who will rule?
Number 1 started this debate:
I am number 1 and therefore I must rule.
Number 2 was indignant:
I am number 2 and I must rule. After all, two heads are better than one.
Number 3 intervened:
I must rule because God loves the trinity.
Number 4 was even more indignant:
Am I not even there?
The number 5 fits in:
I must rule because my students love me and I am loved by everyone.
Number 6 said:
Kneel before me, I will rule.
Number 7 was in effect:
I am the most beautiful of all and therefore I will rule!
Number 8 was offended:
Why number 7 and not me (after all, she was jealous of number 7)?
Number 9 did not claim the throne and therefore said:
0 will rule!
All the figures agreed with this. And the number 0 began to rule the country of Numbers.
A tale about numbers.
There were two kingdoms. And only numbers lived in it, and King 7 ruled there. There were only positive numbers in this city. 7 has one enemy, he was jealous of him because he was not chosen as king. This enemy is -13. One day he turned - 13 into one of the king's servants 7 and went to the king. When he arrived at 7, there was no one near him. - 13 took a huge bag and stuffed 7 into it and disappeared from the city with it. A week passed, then another. Everyone started looking for the king. And then the smartest servants went to look for him throughout the kingdom. When they left the city, they heard sounds and recognized the voice of the king. The servants followed the voice. – 13 knew that they would look for the king. He placed traps everywhere, only the smartest scientists in the world could pass them.
The first trap for the servants was the appearance of a board in the air with a coordinate line drawn on it. It was necessary to find the distance between the numbers - 3 and 3. The servants easily realized that from positive 3 to negative - 3 there would be a distance of 6 units. They passed the first trap quickly.
The second trap was very close. It was necessary to divide the numbers. The servants also knew this and quickly solved the problems.
Walking along the corridor, they saw the king in a cage and immediately ran up to him. After 3 minutes, 13 came out and said: “If you answer my five questions, then I will release the king.” And he asked them these questions:
Compare numbers.
Perform operations with numbers.
What is the coordinate of a point?
What numbers are located on the coordinate line?
What is the modulus of a number?
The servants answered all the questions correctly, because in their kingdom all residents were required to attend classes. And then - 13 I realized that I would have to let the king go. The king and his servants went to the gate, but it suddenly closed. This was the last dirty trick - 13. It was necessary to solve a large example on operations with fractions. But the king and his servants managed quickly because they knew all the rules. As soon as they said the answer out loud, the gate opened.
The king and his faithful servants reached the kingdom, everyone was happy with them! King 7 gathered all the people to celebrate in his castle. He announced: “I reward my servants and appoint them as new teachers! So that children can be as smart!” Everyone was very happy.
A - 13 heard everything, he sat and thought: “What should I do?” And he went to the city to beg the next day. He was allowed to live in the city, but was told: “You will sit behind bars for 2 years for stealing the king and you will have to study.” And then in the city of King 7 all the inhabitants became educated.
Fairy tale "Reducing fractions."
Once upon a time there were three fractions: 3/6, 1/2, 6/12. They were twin sisters, but they didn't know it. One day the fraction 3/6 had a birthday. And she invited her girlfriends - fractions. I also invited a friend - Rule for reducing fractions. The girlfriends presented their gifts to the birthday girl and waited impatiently, what would Rule give? A friend said: “My gift will be this: I will make you redundant.” And the Rule read her spell, and then the fraction 3/6 became the fraction 1/2. Her friend 6/12 also asked her to reduce it. And then the Rule reduced the fraction by 6, and it became the fraction 1/2. And the third friend, the fraction 1/2, the Rule could not reduce, because it was irreducible. And the girlfriends realized that they were twin sisters.
A tale about triangles.
Once upon a time there was a Triangle. One day he flew on a rocket into space. He flew and flew, looking at the constellations Parallelepiped and Square. Triangle flew on a rocket for a long time. And suddenly bang! The rocket landed on a round white planet with a checkered pattern. Planet Nolikov. Triangle got out of the rocket and began to repair it. Nothing worked. Suddenly the Triangle turned around and saw that behind it were several hundred identical zeros.
Poor Triangle got scared and said: “Holy Squares!” But then I decided to get acquainted with the zeros. They helped him repair the rocket and fly home.
A tale about rational numbers.
A long time ago, in the kingdom of numbers and signs, rational numbers lived. Some of them were negative, others were positive. They were at odds with each other, and therefore divided the kingdom into two halves. They argued over who was in charge. The positive numbers said that they were in charge because they were kind to other numbers, and the negative numbers did not know why they were in charge, but they argued anyway.
One day, positive numbers decided to make peace with negative numbers because they are all important in mathematics. They were opposite numbers. Negative numbers agreed. The halves of the kingdom were united into one again. Since then, the numbers have never had a quarrel, and they have always been together.
Numbers and signs.
Previously, numbers were not friendly with signs. They interfered with each other. Once the number 10 went to visit the number 2, and the number 2 at that time went to visit the number 10. The number 10 encountered obstacles on the way, for example, commas, minuses, pluses and other signs. This time he came across a division sign on his way, which no one had ever been able to get around. He began to bypass the number 10 with cunning, but he failed. Number 2 did not know that his friend was in trouble and was in no hurry. But when it climbed a high mountain, it saw what was happening and ran to help. The number 2 jumped onto the back of the division sign and so they were able to unite with the number 10. The division sign now always served. In my life, numbers often encountered plus, minus, multiplication, and division signs. And already experienced and better numbers could, if necessary, make the signs serve them. For example, make a negative number from a positive number, and then add or subtract, multiply or divide them.
Country Digital.
Far, far beyond the mountains, seas and oceans was the country of Numbers. Negative and positive numbers lived in it. Four rivers flowed in the country - these are Multiplication, Division, Addition and Subtraction. And there were also mountains called Comparison.
All numbers were friendly and honest, and did not like only one Zero. He was angry and dishonest and didn’t want to be friends with anyone. He was a big lazy person.
Mathematics was the queen in the land of Numbers, and Zero always dreamed of taking her place. He told everyone that he would become king and change everything in the country of Numbers, but everyone just laughed at him.
For some time no one saw Null, everyone was very surprised. One went to Zero to check on him, maybe he was sick and needed help. She came to the door, knocked and asked:
Is anyone home?
Yes, come in One!
What happened to you? – she asked.
“Everyone is laughing at me,” he muttered.
Why do you think that everyone is laughing at you?
“I tell everyone that I will become a king and change everything here, but I will never become one, because I’m just a zero and don’t mean anything,” said Null.
Don’t be sad, you and I will go to Queen Mathematics, she’ll definitely come up with something! – Unity said in a cheerful voice.
And they went to Queen Mathematics. Zero and One entered the castle, saw the queen, and bowed to her. Mathematics greeted them warmly and asked them:
Why did you come to me?
The unit replied:
Your Majesty, Null says he means nothing, please help him!
Okay, I'll help you! – the queen answered and thought.
She was silent for a long time, and then continued the conversation:
I substituted different numbers to Zero, then multiplied, divided, subtracted, added, but nothing worked.
And then Unity exclaimed:
Queen, you forgot about the comparison!
Nothing will work out here either, Unity. If you compare the number 5 and 0, then 5 is always greater than 0.
And you forgot about negative numbers, for example, if you take the number - 5 and 0, then - 5 is less than 0.
Oh, I completely forgot about negative numbers. Thank you, you Unity was right.
And then One said to Zero:
You Zero still mean something!
Null was very happy, after that he changed a lot for the better. After this he made many friends.
Fairy tale "Comparison of numbers."
Many years ago, in a mysterious country there was a city called Mathematics, and numbers lived there. One day two decimal fractions argued with each other. One was called 0.7, and the other was called 5.3. They argued about which of them was greater and which was smaller. The one called 0.7 says:
I'm bigger than you because I have the number 0 in my name.
No,” says the one called 5.3, “more me.”
So they argued all day, quarreled, until finally one of them said:
Let's go to Uncle Coordinate Beam tomorrow and ask him.
The other agreed. And so in the morning the decimal fractions went to Uncle Coordinate Beam. He asked them what happened, and they said that they had been arguing for a long time and did not know which of them was greater and which was less.
Then Uncle Coordinate Ray called his daughter (her name was Coordinate Line) and asked her to draw herself on paper. She drew herself. It looked like this:
_________________________________________________
Then Uncle divided the straight line with a dot and drew Zero.
_________________________●_____________________________
After this he arranged the numbers:
_ ________________________●_________________________________
10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10
Then Uncle Coordinate Ray explained to the fractions that those numbers that are located to the right are larger. This rule is common to all numbers, not just decimals. The fractions made peace and went home together.
A tale about natural numbers.
In the kingdom of Mathematics there lived King Nine and he had a daughter, Unity. And she had no friends. The king ordered to collect all the natural numbers. Natural numbers and zero have arrived in the kingdom. Natural numbers laughed at zero all the time. But the princess really liked him. Then the king allowed zero to live in the castle. And zero asked the king that all natural numbers should live together. And then one day the natural numbers and zero went on a hike. On the way they met two brothers Plus and Minus. They couldn't decide which of them was more important. But zero stopped them and said: “Guys, let’s live together! You are both important, we numbers cannot do without you in the kingdom of Mathematics.” We went beyond numbers and reached the principality, where multiplication and division lived; zero was denied entry, because it is impossible to divide by zero. Then all the natural numbers went home along with zero. They could not live without zero, because some numbers do not exist without zero.
Straight line and segment.
In a certain kingdom, in a mathematical state, there lived a Straight Line and a Line Segment AC. Straight always ran away to her friends, and
The segment could not go anywhere. Because two points blocked his way. But one day one of the points wanted to see what was going on in the mathematical world. She rolled out and rolled. And at that time Otregok was thinking about how he could move from his place. And so he jerked from his spot and ran. So he became a happy ray.
The country of decimals and place value units.
One day I had a dream. It’s as if there is such a country in the world called “The Country of Decimal Fractions and Place Units.” This country was ruled by a queen whose name was 1000. Everyone loved her because she was very kind and generous. She multiplied everyone she rewarded by herself, and all the numbers became larger in value.
But then one day Queen 1000 fell ill and she became not 1000, but 0.001. Many doctors came to see her, but no one could help her, and for some reason all the doctors who came to her became fewer, not more. It was the queen, out of her habit, who began to reward them, but there was one doctor who was able to cure her. His name was 0.632. He was such a small number, but he came out as the number 632.
And then everyone realized that Queen 1000 was now healthy!
About dividing decimals. "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 considered 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.
Fairy tale "Journey to the city of "decimal fractions".
In a certain kingdom, in a certain state, in a distant country, Tsifiria lived and there was a zero. He was sad and boring, because everyone said that he didn’t mean anything and always stood in front of him, the inhabitants of this country-numbers never let him forward. They said:
You're still no use.
Here he is sitting on a bench and crying, suddenly someone comes up to him, he got scared:
Who is there? - he asked.
Is it me, comma, why are you crying?
Nulik replied:
Nobody loves me, they say I don't matter.
“Come with me to the city of decimal fractions,” said the comma, “they will respect you there.”
Nulik agreed, and they set off.
The comma led Nulik to street number 1. On this street live those who are less than 1 and there are a lot of them.
Why, do you allow zero forward? - asked Nulik.
Yes, if I’m standing next to you,” said the comma, “and you are treated the same as everyone else.”
Nulik really liked this city and stayed to live there.
Once upon a time there were two numbers O and 1.
One day they argued: which of them is more important. 1 says: “I am more important because the count starts with me. And you, O, mean nothing.” But Zero said: “If I stand in front of you, then you will decrease by 10 times - 0.1. And if I stand behind you, you will increase 10 times - 10. And the number ray begins with me.
Math lessons.
Once upon a time there lived Zero and Experienced Comma, they lived and did not grieve. One day they set off on another journey. They go and go, no one knows how much. And so
they approached the forest. They entered the forest and saw: two numbers 9,3 and 100 sitting on a stump and crying. Zero and Comma approached them and asked:
Why are you crying? The answer is 9.3!
How can you not cry? I was walking through the forest and came across the number 100. And we decided to multiply. I heard somewhere that to do this you need to move the comma, but I don’t know how to do this. And my comma doesn’t want to move anywhere, it’s getting capricious!
The comma is justified:
Firstly, I was sick today, and secondly, I’m an inexperienced comma, I’m in practice. And the number 9.3 doesn’t give me peace of mind, it keeps jumping somewhere.
Well, okay,” said Experienced Comma, “I’ll teach you.” So, Comma, look. How many zeros does the number 100 have?
That's why you jump two spaces to the right. It's clear?
Seems to be yes! It turned out to be 930.
Well done!
Dear Zero, if you don’t mind the number 100, come to it from the right, let’s multiply the resulting 1000 by 9.3,” asked the Experienced Comma.
Jump again! - Comma was scared.
Yes, you must learn.
OK. I jump three spaces to the right. Here's what happened - 9300. Thanks for studying, Old Comma.
Well, why are you shouting?
“Oh, I think that I am too big,” said the number 13,768, “I wanted to be smaller, for example, 100 times, and the number 100 asked for this. But nothing worked out for us, since my comma is in the 5th grade I talked a lot in math and listened to everything. Now we are arguing.
The experienced Comma began to explain.
How many zeros are there in 100?
- What action will we perform?
- Division.
- Listen now. Jump two signs to the left.
And the comma jumped two places to the left, and the result was the number 0.13768, which is 100 times less than the number 13.768.
And Zero and Experienced Comma returned home cheerful and happy. They began to live as before.
And the commas they taught came to visit them and talked about their affairs. From their stories we learned that they finished the practice with a “5” and became experienced commas who know how to behave when multiplying and dividing with digit units.
An unusual story.
In one sea, on the seabed, lived two families of octopuses. In each
the family had four octopuses and the octopuses in each made up the proportions - the true equality of the two ratios.
One day their dads went for a walk with them and forgot to give the kids cards with numbers written on them. The octopuses all got mixed up and this is what happened:
The octopus dads thought and remembered what they had talked about at their sea school about the basic property of proportion. It lies in the fact that If the product of the extreme terms is equal to the product of the middle terms, then the result is a proportion.
Dads tried and tried and finally they succeeded:
The children and parents went home and were happy that everything had turned out so well. The next day the octopuses went to maritime school. There the teacher explained what proportion is, the basic property of proportion. The octopuses also learned which quantities are called directly proportional.
Fairy tale
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 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.
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.
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.
Negative and positive numbers.
Once upon a time there were negative numbers and positive ones, and they built two houses. The right house is populated with positive numbers, and the left house is populated with negative numbers. Every day the chairman of the two houses, Nulik, whose name was the beginning of the numbers, went from house to house and looked to see if the negative ones had moved into the positive house, and the positive ones into the negative one. This went on every year, every month.
Geometry.
In a small geometric village, which stood on the bank of a river, lived an isosceles Triangle. But he himself did not know this and thought that no one needed him. In the village he was the only isosceles Triangle. All the figures, old people and children, laughed at him. But the time has come, and Triangle decided to go into the forest . He's tired of this bullying. Early in the morning, when everyone was still asleep, he got up, quickly got dressed and went out the gate.
The road was difficult and difficult. The triangle stopped on the way and remembered its village. The insult made him sad and offended, and he cried. Soon He wandered into a thick and dark thicket. He is there came across a hut. The old and wise Square lived in it. Triangle told him about his grief and burst into tears. The square quickly calmed him down and began to tell him about what he really is like. The Square told the Triangle that it was important and necessary, that it had sides that were always equal, a base and two angles at the base, which were also always equal.
You should be proud that your median is a bisector and an altitude!
About an 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. A 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 arranged for the Foundation three tests:
Before you marry Median, please answer:
- Which triangle is called isosceles?
- Which triangle is called equilateral?
- What is the median of a triangle?
For our Foundation, these questions turned out to be too complex.
Maybe you guys can answer?
Mathematical fairy tales collection of students of grade 3 “a” 2013 5 2
Kolobok's journey in the kingdom of Geometry. Once upon a time there lived Kolobok. One day he found himself in the kingdom of Geometry. He found out that he had a brother who looked like him, but he didn't know his name. Kolobok rolled and rolled and rolled into the valley of the Squares. All the figures looked nothing like Kolobok. He asked the squares how he could find his brothers. They told him to roll along the square path. Kolobok rolled and rolled towards the Mountain of Triangles. And his brothers were not here, he rolled further and rolled into Lake Krugov. Here all the inhabitants were equally round. -How can I tell my brother apart? - said Kolobok. “And we are all your brothers and sisters,” said the figures. Polina Svarchevskaya
New friendship Once upon a time there was a 9, she lived in a kingdom called Arithmetic. One day she was walking and wandered into the kingdom of Geometry. 9 saw the unusual inhabitants of this country and decided to get to know them. Krug was the first to approach the 9th, then his brother Oval. They chatted all evening, and then Circle and Oval introduced 9 to Square, Trapezium, Triangle and other inhabitants of the kingdom of Geometry. Since then, the numbers and figures have been very, very close friends and even communicate on Skype every evening. Sorokin Ilya
Magic story There were two cities - Arithmetic and Geometry. One day, 5 couldn't find the perimeter of the Square; only one side was known. 5 went to the country of Geometry to visit Square. The square told 5 that all its sides are equal and to find its perimeter you just need to add them up. 5 was delighted and invited Kvadrat to visit her. Sotrikhina Anastasia
How arithmetic operations became friends In the thirtieth kingdom, in the mathematical state, there lived arithmetic operations. But Minus and Plus always quarreled with Multiplication and Division because they do * and: first, and only then + and -. One evening the Good Fairy flew into their house and said: “Action, why are you quarreling, let me give you braces. When they are set, you + and – will be the first to be executed.” The actions thought and decided that this would be very good. They thanked the Fairy very much. Since then, arithmetic operations became friends and there was always joy and fun in their home. Khvorykh Sergey
Dispute between 6 and 9 Once upon a time, 6 and 9 lived next door. One day 6 went for a walk and saw 9. 6 asked 9 why she had a ponytail at the bottom? 9 replied that if 6 stood on his head, they would look alike. 6 and 9 were very friendly and never quarreled, they were almost like sisters. Saranina Valeria
The dispute between Zero and One Once upon a time there lived Zero and One. One day they argued, Zero said that he was greater than Unit, and Unit was smart, she knew that he was greater than Zero. But Null didn’t believe her; the next day he asked his mother Arithmetic which of them was bigger. Arithmetic said that Unit is greater, but if they are friends, they will be even larger and stronger - it will be 10. Then Unit took Zero by the hand and taught him to count! Myrzaeva Odina
Stubborn Problem Once upon a time there was a Problem. She was very, very stubborn. Her condition was: “Petya had 4 balls, and Anya had 5 times more.” And the question is: “How many balls did Anya have?” The Stubborn Problem said that it could be solved by addition, and the Teacher told her that it could be solved by multiplication. Now it's time to give grades, and the Stubborn Problem received a two. She sat and cried bitterly. A girl named Nastya approached her and offered to help her, and together they solved the Stubborn Problem. And now the Problem receives only A’s and remembers the girl Nastya with gratitude. Vershinina Polina
Poor 2 Once upon a time there lived 2 in a city of excellent students. Everyone didn't like her, they said she was bad. One day she met 5. 5 advised 2 to stand upside down, 2 turned over and became 5, everyone immediately loved her. Ivanov Dmitry
Arithmetic and the girl Masha One day the girl Masha went for a walk and met the Wizard. The wizard told Masha that she could make any three wishes. Masha ordered 10 ice creams, 5 chocolates and 1 big, big cake. The wizard said that he would grant wishes if Masha answered the following question: “How many sweets did she wish for?” Masha guessed right and received her sweets, and can you count how many sweets Masha wished for? Ivanov Evgeniy
Number 2 Once upon a time there was a number 2. She was always sad and sad. She had no friends. All the numbers laughed at her because no one liked her at school. One day she walked along the lake and saw a beautiful bird. Number 2 sat on the shore and began to admire the bird. How beautiful she was! And suddenly 2 realized that they were very similar. And then the swan swam to the shore and nodded its head. 2 understood everything, she was glad that she had found a true friend. Shmakalov Andrey