Didactic material on mathematics. Number "7. Children's poems about numbers and numbers What animal does the number 7 look like?

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Introduction

The theme of my work is “The Amazing Number 7”.

I chose this topic because I was interested in the ancient origins of natural numbers, and I decided to find more information about numbers. While reading books on entertaining mathematics, fairy tales, proverbs, I noticed that I often came across the number 7. Every day in mathematics lessons we learn about the properties of numbers, solve problems and equations with their help. A textbook is a great help; you can learn a lot from it. But about who and when numbers were invented, why people needed them, what amazing properties some numbers have, what works on mathematics have come down to us, how mathematics is used in various games and much more, you can find out if you read additional literature on mathematics.

Target my job is to analyze the number 7 from a mathematical, philosophical, magical point of view.

I visited libraries, read as many books as possible and to achieve the goal the following were set: tasks:

1. Find interesting facts, problems related to the number 7.

2. Understand the meaning of proverbs and sayings associated with this number.

3. Reveal the magical, philosophical meaning of the number 7.

Object research became the number 7.

Item research: frequency of appearance of the number 7 in mathematical problems, puzzles, and various literary genres.

Hypothesis: a number of interesting facts suggest that the number 7 is one of significant numbers in our lives.

Chapter 1. From the history of the number 7

The series of numbers 1,2,3,4,5,6,7,8,9... is called natural. And these numbers themselves are natural. This series arose in ancient times, when people had a need to count objects. With the advent of the natural series, the first step towards the creation of mathematics was taken. Now everyone understands that the natural series of numbers is infinite. In ancient times people did not know this. The natural series was very short. It is believed that the term “natural number” was first used by the Roman statesman, philosopher, author of works on mathematics and music theory, Boethius (480 - 524). The initial ideas about numbers appeared a long time ago, in the Stone Age, when people not only collected food for themselves, but also began to actively produce it, approximately 100 centuries BC. e. Numerical terms were difficult to conceive and came into use slowly.

Food production grew, objects were added that needed to be taken into account in everyday life, in connection with which new numbers were invented: “three”, “four”... For a long time The limit of human knowledge was the number seven. Let's talk about him. “What’s so interesting about the number seven?” - you say. A number is like a number. However, let's look at the most interesting facts related to it. About the incomprehensible they said that this book was “locked with seven seals”; healers in fairy tales gave the patient “seven knots with medicinal herbs, which had to be infused in seven waters for seven days and taken seven spoons every day.”

The Greek Pythagoras, who was born on the island of Samos in the 6th century BC, was the first to talk about numbers. e. First he took up music. He managed to establish a connection between the length of the string of a musical instrument and the sound it produces. And then Pythagoras decided that not only the laws of music, but in general everything in the world can be expressed using numbers. “Numbers rule the world!” - he declared.

The Pythagoreans viewed the number seven as an image and model of the divine order and harmony in nature. It was a number that contained two sacred triplets, or “triads”, to which was added a “one” - the divine monad: 3+1+3.

In Egyptian and Babylonian philosophy and astronomy, it was considered the sum of two “life” numbers: three and four. Three people - father, mother, child - form the basis of life; and four is the number of cardinal directions and wind directions from where rain comes, the life-giving moisture of which makes the earth fruitful. According to Pythagoras, the sum of the numbers 3 and 4 (symbolizing a triangle and a square) was considered a manifestation of completeness and perfection. That is why the number 7, the sum of three and four, was perceived as sacred.

Chapter 2. Secrets of the number 7

We all didn’t think about the fact that the number seven is found almost throughout the entire path of human development. The history of the number 7 dates back to the times ancient egypt. It was the Egyptians who chose 7 gods to worship, based on the fact that they saw seven planets in the sky. And they connected their entire history and religion with this mysterious number, believing that this would bring them eternal and happy life. In the night sky only visible to the naked eye seven "wandering luminaries": Sun, Moon, Mars, Venus, Mercury, Jupiter, Saturn. All incomprehensible natural phenomena were attributed to the gods, and gradually the idea of ​​gods was combined with the seven "wandering luminaries". Venus was considered by the Romans to be the goddess of beauty, Mercury - the god of trade, Mars - the god of war, Jupiter - the god of thunder, and Saturn was the god of sowing, plus the Sun and Moon. They began to count time using them. Thus was born seven day week.

In the Old Testament it is written that the Lord created the earth, sea, sky and everything in them in six days. And on the seventh day he rested. And since then, for all Christians, seven is a sacred number. And Sunday is the seventh day of the week - a day off, on which, according to Christian customs, you cannot do anything.

The Flood lasted 7 days.

Lent lasts for Christians 7weeks.

There are many cities on seven hills: Rome, Moscow, Istanbul, Khanty-Mansiysk, Prague, Kyiv and Barcelona. And these are only the most famous and largest cities. But in reality there are many more of them. Generally anyone locality they are trying to bring 7 hills under this figure. 7 hills,on which Rome was built- these are the Palatine, Capitol, Aventine, Quirinal, Viminal, Esquiline and Caelium. During the heyday of Ancient Rome, the hills took centuries to build on.

7 hills on which Moscow is built: Borovitsky (Kremlevsky), Sretensky, Tverskoy, Trekhgorny, Shvivaya Gorka, Lefortovo and Vorobievsky. They wrote about Moscow: “You stand, holy Moscow, on your seven hills.” In reality there are many more hills, but for the red word there are seven hills: different researchers have different ones. But they began to mention the Moscow hills only from the end of the 15th century, when they started talking about Moscow as the Third Rome.

Seven notes on the staff (do, re, mi, fa, sol, la, si);

Surely, each of us has seen a rainbow at least once and can easily name seven colors of the rainbow in order. Remember colors of the rainbow in order we were taught as children. There is a famous phrase: Every Hunter Wants to Know Where the Pheasant Sits? But this is nothing more than the most popular mnemonic phrase for remembering the colors of the rainbow in order. The first letter of each word in this phrase corresponds to the first letter of the color name. That's why, colors of the rainbow in order sound like this: red, orange, yellow, green, blue, indigo, violet.

The seven most outstanding works of architecture and art were named " seven wonders of the world": Egyptian pyramids at Giza; Hanging Gardens of Babylon in Babylon 7th century BC; Temple of Artemis at Ephesus around 550 BC; giant statue of Zeus at Olympia around 430 BC; Mausoleum of Halicarnassus in Asia Minor, mid-4th century BC; Colossus of Rhodes (statue of Helios in Rhodes), around 292 - 280 BC; Pharos lighthouse in the port of Alexandria, 143 m, around 280 BC.

In Christianity there are seven deadly sins- intemperance, pride, envy, stinginess, gluttony, laziness, despondency.

7 virtues- moderation, courage, wisdom, justice, faith, hope and love.

Seven Sacraments— the sacrament of baptism, communion, repentance, confirmation, unction, marriage, priesthood. AND number 777 is the number of the Christian Trinity.

7 ancient sciences- grammar, rhetoric, dialectics, arithmetic, geometry, astronomy, music.

7 main rapids on the Dnieper: “Don’t sleep”, “Island”, “The noise of the threshold”, “Insatiable”, “Backwater”. "Boiling". "Small threshold".

An ancient Chinese proverb says: “For life it is necessary seven items: firewood, oil, salt, soybeans, vinegar, tea and rice."

7 body parts(head, neck, torso, two legs and arms).

7 main life manifestations of a cell(reproduction, respiration, nutrition, metabolism, growth, development, movement).

7 structural levels(atomic, molecular, cellular, tissue, individual organs, organ systems, whole organism).

Seven types of people psychologists distinguish: dominant, analytical, aesthetic, independent, inert, stable, satellite.

In relation to innovations in life, people are divided into the following 7 types: innovators, enthusiasts, rationalists, neutrals, skeptics, conservatives, retrogrades.

IN periodic table seven periods.

Hindus have a custom of giving gifts for good luck. seven elephants.

7 pairs of human ribs reach his sternum, the rest are wandering.

7 stars in the constellation Ursa Major - a symbol of the North.

IN Ancient Greece revered 7 wise men who lived in the 7th-6th centuries. BC, who left behind sayings based on experience and observations. These are Salon, Thales, Periander, Cleobull, Chilo, Bian and Pittacus.

It was found that the period of gestation in humans lasts 280 days (7x40), in mice - 21 days (7x3), in hares and rats - 28 days (7x4), in cats - 56 days (7x8), in dogs - 63 days ( 7x9), for a lioness - 98 days (7x14), for a sheep - 147 days (7x21).

In Islam the number 7 symbolizes perfection. It is believed that the Universe consists of 7 heavens, 7 seas, 7 lands, 7 steps leading to hell, and 7 doors to heaven.

During the annual Hajj to Mecca, the pilgrim must Walk around the sacred stone of the Kaaba 7 times.

A person perceives all surrounding phenomena - light, sound, smell, taste - through seven holes in the head: through two eyes, two ears, two nostrils and a mouth. Moreover: people tend to assimilate incoming information if it does not exceed 7 categories. If the number of characters, for example, dots on paper, is less than seven, then the person, without counting, immediately intuitively names the number. If the number of such points is more than seven, then the mind begins to count.

Among many peoples, the seventh son in the family was considered a future miracle worker. He was credited with the ability to heal a number of diseases with one touch of his hand. The Slavs had a legend about 7 tribes and 7 ancestors (5 brothers and 2 sisters).

Ancient hunters and farmers watched the sky. Their attention was attracted by the change in the lunar disk. They noticed that 7 days after the new moon, half of this disk was visible in the sky. And after another 7 days, the entire moon shines in the sky. Another 7 days pass and again half of the disk remains, and after another 7 only stars shine in the night sky, and the Moon is not visible at all. This is how they came to the concept of a lunar month consisting of four seven days. One phase of the moon lasts 7 days.

The number seven was especially revered in the Ancient East. Several thousand years ago, the Sumerian people lived between the Tigris and Euphrates rivers. They designated the number seven with the same sign as the entire universe. Some scientists think that they expressed with this number the six main directions (up, down, forward, backward, left, and right) and also the place from which this countdown comes. The stars in the sky also attracted their attention, in particular the constellation Ursa Major.

An interesting description of the number 7 is given by H.E. Kerlot: “Seven symbolizes perfect order, a complete period or cycle. It contains the union of trinity and fourfoldness and is therefore endowed with exceptional value. It corresponds to the seven directions of space (i.e., the six existing dimensions: north, west, south, east, top, bottom plus center); seven-pointed star; reconciling the square with the triangle, by superimposing the latter on the previous one (like heaven on earth) or by inscribing one into the other.

They also say that every person has a life cycle, which is exactly 7 years. During the “seven-year” period, each person undergoes a renewal and transformation of his inner world.

The “septenary” nature of the world manifested itself, as they thought, in seven ages human life: infancy - up to 7x1 = 7 years; adolescence - up to 7x2 = 14 years; youth - 7x3 = 21 years; young man - up to 7x4 = 28 years; man - up to 7x7 = 49 years; elderly man - up to 7x8 = 56 years.

Chapter 3. Number 7 in fairy tales, proverbs and poems

Mathematicians have long noticed that 7 is the largest prime number in the top ten. This mathematical explanation sheds light on the ancient deification of the number seven, the largest of the simple digits. Many ancient Russian proverbs and sayings, which include the number seven, are related in meaning to size.

In the fairy tale “Seven Underground Kings,” the heroes, together with the girl Ellie, help the inhabitants of a magical land get rid of the seven kings by re-educating them.

In the fairy tale “The Seven-Year-Old Daughter,” a seven-year-old girl turned out to be smarter than the king himself and was able to help her poor father.

In the fairy tale “The Wise Maiden and the Seven Thieves,” a young girl saved her entire family from death by deceiving evil and treacherous robbers.

In the fairy tale “Snow White and the Seven Dwarfs,” Snow White lived with 7 dwarfs behind 7 mountains.

In the fairy tale “The Seven Simeons,” seven twin brothers owned a wonderful craft and traveled across distant seas in order to bring a bride for the king.

This magic number was widely used in the fairy tales “The Wolf and the Seven Little Goats”, “About the Dead Princess and the Seven Knights” by A.S. Pushkin, “Seven Brave Men” by the Brothers Grimm, “Flower - Seven Flowers” ​​by V. Kataev, “Seven Brothers” adapted by M. Afanasyev, “Seven Underground Kings” by A. Volkov, “Seven-Year-Old Archer” Sami fairy tale, “Journey in Seven seas."

I think in Russian sayings and proverbs the word “seven” often acts as the word “many”: “Measure seven times, cut once”, “Garlic plagues seven ailments”, “After bread and salt - rest for seven hours”, “Seven with a spoon - one with a bipod”, “Seven do not wait for one”, “Seven nannies have an unattended child”, “She drained seven rivers, did not wet the canvas”, “The fox will guide seven wolves”, “The onion cures seven ailments”, “Seven feet under the keel,” etc.

The meaning of the popular expressions is instructive: “To be in seventh heaven,” denoting the highest degree of bliss; “Beyond the seven seas” means far; “Seven spans in the forehead” - a very smart, wise, outstanding, talented person; “Seventh water on jelly” or “Seventh kvass on thick” is a very distant relative; “A week without a year” - recently; “Seven miles to heaven” - to promise and say a lot; “To sip jelly seven miles away” - to walk far and in vain, drive, trudge; “To the seventh generation” - to the most distant generations; “Seven Fridays in a week” is a figurative designation of human impermanence; “By leaps and bounds” - very quickly; “Working up a sweat” - to work, toil, to the point of extreme fatigue, complete exhaustion; “Behind seven seals” - secret; The “Seven Deadly Sins” are bad, unforgivable actions.

We meet the number 7 in poems:

The number seven is known to everyone.

What can we say about the number seven?

Seryozha turned seven.

He became smarter and stricter.

Year after year will fly by,

He will go to seventh grade!

G. Kaytukov

In the crowded sky on a starry night

I found seven bright spots.

Found seven burning eyes

Called a bucket

And the name is Bear...

I don't understand what's going on here?

And my father answered me:

You son, well done!

The year will fly by unnoticed,

And it will be seven years -

Will you be at school to study?

And you will find the answer to everything.

G. Kaytukov

Maria Konopnitskaya refers to the number 7 in her poems

Urbs Avinionensis

“Seven is the number of the best

For everything that is dear to the heart.

Avignon in the seven scooped

Faith, truth and strength.

He had seven gates in his walls,

Seven consonances in a chime.

Seven sins were committed in a day

In good Avignon..."

and Rasul Rza

Seven plane trees

...The whole region, fields and rivers

Autumn in the midday heat

Seven plane trees, seven plane trees.

Who grew these trees?

Centuries fly by day by day...

And it always stands at dawn

Tree of life. Gift of life -

Seven plane trees, seven plane trees...

Why are you, wind, so furious?

One blow will break

Emeralds of tender leaves,

But seven plane trees will not break...

Chapter 4. Number 7 in problems

Everything that has been said, of course, is interesting for general development, but I don’t think this is the most important thing. The ancient Romans said: “Words fly away, but what is written remains.” And “what is written with a pen cannot be cut down with an ax.” Many manuscripts specifically devoted to mathematics have survived to this day. The papyrus of the scribe Ahmes, which is kept in London, provides solutions to 84 problems involving various calculations that may be needed in practice. Most of the problems relate to arithmetic. Among them there is a problem related to the number 7: “There are 7 cats in the house, each cat eats 7 mice, each mouse eats 7 ears of corn, each ear produces 7 plants, each plant grows 7 measures of grain. How many are there together?" From this problem it is clear that the author is not interested in what objects are being discussed, whether they are homogeneous or not - only the total quantity is important to him.

Several thousand years have passed since the time of Ahmes, and in the 13th century, the Italian mathematician Leonardo of Pisa, nicknamed Fibonacci, cited a similar problem in his book: “Seven old women went to Rome. Each old woman has seven donkeys, each donkey carries seven bags, each bag has seven loaves of bread, each loaf has seven knives, each knife has seven sheaths. How many items are there in total?

Similar problems were solved in Rus'. In the 19th century, people in villages said: “Seven elders walked. Each elder has seven crutches. There are seven knots on each crutch. There are seven wallets on each knot. Each bag contains seven pies. There are seven sparrows in each pie. How much in total? But this is the same task of Ahmes, which has lived for thousands of years and has come down to us.

I was interested in problems in which the number 7 is used. There are many of them in books on entertaining mathematics.

I found many more problems, problems in poems, sayings, riddles.

I found seven interesting questions related to the number 7:

A unit of time equal to seven days? (week)

What is the name of a measure of length equal to 7 feet? (fathom)

An ensemble of seven instruments? (septet)

What is the name of a team of seven horses? (seven)

There were seven subjects in the medieval school. They were called the “Seven Liberal Arts”: grammar, dialectics, music, geometry, rhetoric, astronomy, arithmetic.

Chapter 5. Tangram Puzzle

As a child, I was fond of playing puzzles, but now I got acquainted with a more interesting game.

The ancient Greeks were engaged in geometry, not only measuring land plots and distances to ships at sea. They loved geometric games. One of them was called "Stomachion". In this game you had to put together various shapes from 14 parts of a square. People were so keen on this game that the great scientist Archimedes himself wrote an essay about it. The ancient Chinese also entertained themselves with a similar game. Only they divided the square not into 14, but into 7 parts and called their game “Chi-chao-chu”. Now this game is called "Tangram". The first known ancient book on tangram is "A Collection of Figures in Seven Parts" (China 1803). There are a number of versions and hypotheses of the origin of the tangram game. The most common and famous is that the tangram game dates back about 4000 years. One of the fans of the game was Edgar A. Poe. The tangram he owned was made of ivory and is currently kept in the New York Public Library.

The essence of the game is to construct various object silhouettes on a plane. Diversity and varying degrees the complexity of geometric constructors makes it possible to take into account the age characteristics of children, their inclinations, capabilities, and level of training

All assembled figures have an equal area, because assembled from identical elements. It follows from this that: each assembled figure must certainly include all seven elements; When composing a figure, the elements should not overlap each other, i.e. located only in one plane; elements of the figures must be adjacent to one another.

The basic element of tangram is tan. Tans can be obtained by cutting the square initially into two large equal triangles, then according to the figure. There are various problems associated with the tangram.

According to M. Gardner: “The charm of tangram lies in the simplicity of the material and in its apparent unsuitability for creating figures with aesthetic appeal.” The game "Tangram" develops logic, thinking, and erudition. The minimum number of basic figures equal to seven leads to the ingenious simplicity of combinations, Pythagoras believed. The “Pythagorean puzzle” has reached us, with the help of which geometric figures are assembled from 7 parts.

Chapter 6. The magic of numbers

"The world is built on the power of numbers..."

Numbers are the key to understanding human behavior, one of the simple methods to study and train human intuitive gifts and to comprehend the depths of the human personality.

The ancients believed that numbers have a mysterious, magical meaning and influence a person and everything he does. Each person has his own “master numbers”. Seven is a symbol of mystery and mystery. People of this number have increased spirituality. They have fantastic dreams, smell unknown smells, and they interpret all this in their own way. They are interested in history, art, the mysteries of the human soul and do not care about earnings. In the business that the “sevens” are involved in, they, as a rule, achieve a lot. The number 7 is considered to be the sign born on the 7th, 16th or 25th of any month. Seven is the number of luck, the personification of wisdom.

Personality traits: diligence and a poetic soul, a penchant for analytical thinking and strong intuition. Rich imagination, lively and vivid imagination. Composers and musicians, writers and poets, philosophers and hermits, thinkers and hermits are born with this number. Owners of 7 are talented, emotional and inquisitive, have a good sense of humor and a penchant for invention.

It is believed that the following people were born under the sign of the number 7: Charles Dickens, Oscar Wilde, Brad Harte, Newton, Picasso, Tchaikovsky P.I., Nosov N.N., Lobachevsky N.I., Vavilov N.I., Aivazovsky I.K. ., Plushenko E.I., Nikulin Yu.V., Mironov A.A.

Chapter 7. Test for divisibility by 7

A number is divisible by 7 if and only if the result of subtracting twice the last digit from that number without the last digit is divisible by 7.

For example: 364 is divisible by 7, since 36 - (2 × 4) = 28 is divisible by 7.

In order for a natural number to be divisible by 7, it is necessary and sufficient that the algebraic sum of numbers forming odd groups of three digits (starting from ones) taken with the “+” sign and even numbers with the “-” sign is divisible by 7.

For example: the number 689255. The first group is with a “+” sign (689), the second with a “-” sign (255). Hence 689-255 = 434. In turn, 434: 7 = 62.

Another sign is to take the first digit, multiply by 3, add the next one (here you can take the remainder of the resulting number when divided by 7). And then - first: multiply by 3, add the next one, etc. For 364: 3 * 3 + 6 = 15. The remainder is 1. Then 1 * 3 + 4 = 7.

Conclusion

So, it turns out that the number seven follows us almost everywhere. Over many centuries, people have developed a constant value, a memory capacity that was concentrated specifically on seven. A person could think about only seven things at a time and no more. But this, of course, is only philosophy. Seven was considered in many sciences, and they came to a version that is more or less close to the truth - everything is connected with fundamental mathematics and the microcosm. All attention and all meaning are focused on the number seven. In every science, in every field, in every sphere of activity and human life, there is a place for seven - it is completeness and integrity.

Doing this work helped me develop the skill of a creative approach to tasks in mathematics, understand some methods and ways of solving problems, and learn to independently select necessary information, draw conclusions. I realized that mathematics is an interesting science about numbers and their application, and I agree with what Pythagoras believed - everything in the world can be expressed using numbers.

The object of study was the number 7. I found interesting problems related to it. I understood the meaning of proverbs better. I saw its use in puzzles and concluded that for the Tangram game the main requirement for a person is logical thinking, and for the puzzle game it is just perseverance and patience. Now it will be easier for me to study further and work with other numbers.

The information contained in this work also interested my classmates and helped them discover new facts and tasks. Based on this information, you can do conclusion: The world of numbers is so mysterious and fascinating that if each of the students paid more attention to it, they would find a lot of useful and interesting things for themselves.

As a result of the study The magical and philosophical meaning of the number 7 was confirmed.

All these facts prove the significance of the number 7 in support of the hypothesis I put forward. And I, as a student, are allowed to be successful in solving non-standard problems in mathematics lessons.

Amazing number seven! No matter how they consider it: sacred, divine, magical, and happy. He was revered for many centuries BC, in the Middle Ages, and is still revered today.

Literature

The emergence and development of mathematical science: book. for the teacher. M: "Enlightenment", 1987.

Depman I.Ya., Vilenkin N.Ya. Behind the pages of a mathematics textbook. M: "Enlightenment", 1989.

Kordemsky B.A. Amazing world numbers. / Book for students, M: “Enlightenment”, 1995.

Kotov A.Ya. Evenings of entertaining arithmetic. M. "Enlightenment", 1967.

Nagibin F.F., Kanin E.S. Math box. M: "Enlightenment", 1988.

Neihardt A. A. Seven Wonders of the Ancient World. - M., 1966.

Savin A.P., Stanzo V.V., Kotova A.Yu. Children's encyclopedia "I explore the world." Authors and compilers M.: AST, 1998

Yakusheva G.M. and others. Great mathematical encyclopedia. M: “WORD”: OLMA-PRESS, 2005.

Information resources:

http://kod-imeni.ru/

Sergey Furs. About geometric constructors. http://www.pxpict.com/

"Interactive mathematics grades 5 - 9." Bustard - DOS Multimedia.

1C: Educational collection “Planimetry 7 - 9”.

Appendix 1

Proverbs and sayings

And you, seventh, stand at the gate.

It can be seen that the town is great because it has seven governors.

For a mad dog, seven miles is not a circle.

For a beloved friend, seven miles is not a suburb.

Wait a year and seven Saturdays.

To sip jelly seven miles away.

Behind seven seals.

Onion - from seven ailments.

Bow to Makar, and Makar to seven sides.

Martok, put on seven parkas.

Not a big town, but seven governors.

One with a bipod, and seven with a spoon.

Seventh water on jelly.

Seven gates and all into the garden.

Seven do not wait for one.

Seven birds with one stone, but no skin.

Seven on the benches.

Seven deaths cannot happen, but one cannot be avoided.

Seven troubles - one answer.

Seven miles to heaven and all through forest.

Seven years is trouble, nine years is misfortune.

Seven wise men are cheaper than one experienced man.

Seven sweats dropped.

Seven spans in the forehead.

Seven Fridays a week.

Measure seven times and cut once.

We ate seven times, but did not sit at the table.

There were seven villagers, one ox, and even that one was naked, and ten police officers.

Seven axes lie together, and two spinning wheels are apart.

Seven feet under the keel.

Seven, eight - let's discard laziness.

A secret sealed with seven seals.

Three women are a bazaar, and seven are a fair.

The mare has at least seven foals, and she has her own collar.

One sheep has seven shepherds.

All of us will go - we will go far.

Seven can barely pull uphill, but even one can be pushed downhill.

For a mad dog, seven miles is not a circle.

For a beloved friend, seven miles is not a suburb.

They were looking for a mosquito seven miles away, but the mosquito was on their nose.

Onion - from seven ailments.

Appendix 2

Counting books

Once the guys went to the river,

They carried two oars in their hands.

Three sheep meet them

And four turkeys.

They got scared and ran away.

The oars were thrown into the bushes,

And you must find them.

One, two - the ducklings walked,

Three, four - we went home.

The fifth trudged after them,

The sixth man ran ahead

And the seventh fell behind everyone,

Frightened, he squeaked:

Where are you? Where are you?

We're nearby... look for it.

Tongue twisters

Seven waxwings sat and whistled.

In seven sleighs

Seven to a sleigh

Sit down yourself.

Stepan has sour cream.

Curdled milk and cottage cheese,

Seven kopecks.

Riddles

There are exactly seven of these brothers.

You all know them.

Every week around.

Brothers walk after each other.

The last one will say goodbye -

The front one appears.

(Days of the week)

We are a flock, seven rams,

Protects from snowstorms.

The sun ordered: “Stop”

The Seven Color Bridge is steep.

7 Ya (Family)

Appendix 3

Problems in verse

There is a rainbow in the sky - an arc

Closes the banks

Blooming more and more clearly

Miracle - the colors shine

Let him answer

How many colors

Plays in it

Illuminating the surface of the sea?

The fishermen are sitting

Guard the floats.

Fisherman Korney

I caught three perches

Fisherman Evsey -

Four crucian carp.

How many fish are the fishermen

Dragged from the river?

In Sashka's pocket

Candies in paper.

He gave me some candy

Sveta and Pete,

Irina and Galina,

Marina and Nina,

And I ate the candy myself

But no more.

(How many candies were there?)

Tongue twister task

Sasha walked along the highway

He carried drying things in a bag.

Drying - Grisha,

Drying - Misha.

There are dryers Proshe,

Vasyusha and Antosha.

Two more dryings

Nyusha and Petrushka.

(How many sushi bags did Sasha carry?)

Appendix 4

Problems with number 7

Problem 1

What natural number is 7 times greater than its units digit? Answer: number 35

Problem 2

How can 7 apples be divided equally among 12 boys without cutting any apple into more than 4 pieces?

Problem 3

A collective farmer brought a basket of eggs to the market to sell. She sold them at the same price. After selling the eggs, the collective farmer wanted to check whether she received the money correctly. But here's the problem: she forgot how many eggs she had. She only remembered that when she transferred eggs 2 at a time, there was only one egg left. One egg also remained when she transferred eggs by 3, 4, 5, 6. When she transferred eggs by 7, there was not a single one left. Help the collective farmer figure out how many eggs were in the basket. Answer: 301 eggs

Problem 4

The number VII (seven) is made from 4 matches. How can you rearrange two matches to make the number 5?

Problem 5

The can, the capacity of which is 10 liters, is filled with kerosene. There are also empty vessels of 7 and 2 liters. How to pour kerosene into two vessels of 5 liters each?

Solution: First, 7L must be poured from the first vessel into the second, and then 2L from the second into the third.

Problem 6

What digit ends in the usual notation of a number? Answer: 3

Problem 7

Place mathematical symbols and brackets between some numbers to obtain correct equalities.

7 7 7 7 7 7 7=6 Answer: (7+7+7+7+7+7):7=6

7 7 7 7 7 7 7=7 (7 7-7 7+7 7):7=7

7 7 7 7 7 7 7=8 777:777+7=8

7 7 7 7 7 7 7=10 7:7+7:7+7:7+7=10

7 7 7 7 7 7 7=49 7+7+7+7+7+7+7=49

7 7 7 7 7 7 7=107 (777-77):7+7=107

7 7 7 7 7 7 7=140 ((7+7):7+7) 7+77=140

Task 8.

Prove that numbers of the form aba are divisible by 7 if a+b is divisible by 7.

Solution: write aba = 100a + 10b +a = 101a +10b

By condition, a+b =7k, where k N. Then aba = 91a + 10a + 10b = 91a + 10(a+b) = 91a + 10*7k = 7(13a + 10k), this number is divisible by 7.

Appendix 5

How to calculate a person's number

To do this, you need to add all the numbers included in your date of birth to a single digit! For example: 05/26/1961. 2+6+5+1+9+6+1=30. 3+0=3.

Now you can see the interpretation of the lucky number:

1 - the number of leaders, energetic, straightforward people.

2 - number of diplomats. These people are soft and tactful.

3 - three endows people with talent, a sharp mind, and developed intuition.

4 - reliable, persistent, honest people.

5 - they are characterized by mobility, freedom, love of adventure and everything unusual.

6 - people of this number of fate are honest, frank, reliable, kind, cheerful.

7 - they are born philosophers, not interested in the material side of life.

8 - the number of leaders, inventors, humane and strong people.

9 - people of this destiny number are smart, creatively gifted and have a strong will.

That's it!

1 - Sun

Strength, individuality, creation. People of this number are born leaders. “Ones” are active, aggressive and ambitious, they always strive to take first place, they can be completely ruthless and are capable of sacrificing everything for the sake of their career, including relationships with others. This is the number of winners, but also of tyrants. The lucky day of the week for number 1 is Sunday.

Number 2 people are usually gentle, artistic and charming, and can easily adapt to circumstances. They are often characterized by passivity and detachment. They are characterized by ingenuity and intuition, but they do not often succeed in implementing their plans. They are more prone to thinking than to action. These people are often susceptible to depression. They establish very good relationships with people of number 1. The lucky day of the week for number 2 is Monday.

3 - Jupiter

Three is the number of trinity. Usually people of this number are energetic, talented, disciplined, which almost always allows them to achieve great success in their chosen fields of activity. As a rule, they are never satisfied with little. By nature they are very proud and independent, they like to control the situation, command and order. Most often, they have the best relationships with those whose number is 3, 6 or 9. The lucky day for this number 3 is Thursday.

4 - the number of seasons, the number of cardinal directions, the number of elements. People of this number usually look at things from their own special point of view, which allows them to find details hidden from others. At the same time, this usually becomes the reason for their disagreement with the majority and clashes with others. They rarely strive for material success, being not very friendly, they are often lonely. They have the best relationships with people of numbers 1, 2, 7 and 8. The lucky day of the week for number 4 is Sunday.

5 - Mercury

5 is the number of feelings. And people of this number are indeed extremely sensitive. Usually by nature they are very lively, impulsive, frivolous, prone to risk, and value pleasure very much. As a rule, they are easily excitable and are often susceptible to nervous disorders. In business, people of number 5 tend to succeed and recover very quickly from failures. They usually have the best relationships with those with the same number. A lucky day of the week for number 5 is Wednesday.

6 - Venus

6 is a number that is considered one of the happiest, since it is the sum of its divisors: 6 = 1 + 2 + 3. People of number 6 are harmonious and balanced, they are conducive to trust, although sometimes they are too stubborn. They are most often very romantic and amorous, their interests are usually focused on home and family. They have good taste, they are very attractive, and they easily get along with other people. Lucky day of the week for number 6 is Friday.

7 - Neptune

The number seven is a symbol of good luck and occult knowledge. People of this number most often become philosophers and thinkers. They are usually immersed in their own thoughts and therefore somewhat disconnected from those around them. They also have a love for all kinds of travel. The undertakings of these people most often end successfully. The lucky day of the week for number 7 is Monday.

8 - Saturn

8 is the strangest and most difficult number. On the one hand, it can be represented as the sum of 4 + 4, which suggests that the character of its people is doubly characterized by the qualities of people of the number 4. On the other hand, the number 8 also has its own properties. For example, it can mean grief, sadness and, at the same time, success, sometimes of world significance. People of number 8 are distinguished by great willpower and a pronounced individuality; usually in communication they are characterized by external coldness and detachment, although in fact they are capable of the most ardent feelings. The lucky day of the week for the number 8 is Saturday.

The number 9 is often considered the main number of numerology, with a special, sometimes even sacred meaning. This is due to the fact that when multiplied by any number, nine reproduces itself. For example, 9 x 4 = 36 => 3 + 6 = 9. Usually people with number 9 are born fighters, they are active, courageous and purposeful, which is why they usually win. At the same time, people of number 9 often find themselves in all sorts of unpleasant situations. These people are capable of the best feelings towards loved ones. The lucky day of the week for number 9 is Tuesday.

Let's get acquainted with the number and number "7", we use various didactic materials to get acquainted.

Didactic material on mathematics.

Number "7"

Funny poems

Riddles

Fun puzzles

Proverbs and sayings

• Seven troubles - one answer.
• Seven do not wait for one.
• Measure seven times, cut once.
• One with a bipod, seven with a spoon.
• Seven Fridays a week.
• Too many cooks spoil the broth.
• Onion from seven ailments.

Tongue twisters

• Seven waxwings sat and whistled.
• We sat in seven sleighs ourselves.
• Stepan has sour cream, curdled milk and cottage cheese, seven kopecks - tuesok.

Physical education minute

How many green Christmas trees?

Let's perform so many bows (7).

How many circles do we have here?

We will do so many jumps (7).

How many knitted balls.

Let's clap so much (7).

Graphics tasks

Task 1. Divide the ducklings.

Seven ducklings in a pond quarrel all the time. How to divide them into three lines to stop quarrels?

Task 2. Find the circles.

Find 7 circles in each figure.

Task 3. Help Snow White find the way.

Snow White decided to give a treat to the seven dwarfs who were working in the forest. How to get to the gnomes without going to each one twice?

Rebus

7 i

“Number and figure 8” - Check. The figure eight has two rings - without beginning and end. What is shown in front of you? What does the number 8 look like? Place the balls into 2 groups according to color. How to get the number 8? Calculate. Number and figure 8. Arrange the numbers of the pictures. What does the number look like? What number follows the number 7 when counting? Let's check. Goals and objectives.

“Seven Wonders of the World Lesson” - To introduce students to the history of the Seven Wonders of the World. Continue to develop students' creative abilities. Egyptian pyramids. Colossus of Rhodes. Halicarnassus Mausoleum. Work on the 35-meter statue lasted 12 years. “Seven Wonders of the World” Lesson-tour on the history of the Ancient World in 5th grade. In 220 BC. the statue was destroyed by an earthquake.

“Heroes of Bunin’s Numbers” - a description of the heroes of the work by I.A. Bunin "Numbers". 8. The attitude of other characters towards this hero. Bunin shows the relationship between the boy and his uncle in this situation. We found facts in the text of the story that confirmed the identified causes of the conflict. 1. The place occupied by the hero in the work. We got acquainted with the materials of comparative analysis of the characteristics of the heroes of the work.

“History of numbers” - We still use Roman numerals and letters. Many thousands of years ago, our distant ancestors lived in small tribes. And these are Egyptian numbers from 1 to 10. For example, the clock on the Spasskaya Tower of the Moscow Kremlin. At first they counted on their fingers. The name “Arabic numerals” is a tribute to the historical role of Arabic culture in mathematical science.

“Numbers Lesson” - Some tasks can be completed interactively. Lesson objectives: Systematize and generalize children's knowledge about numbers and numbers. Lesson topic: “Numbers and figures. Working with number series. “My mathematics” 1st grade. Tips for the teacher. Roman numerals. Calendar of the ancient Mayan people. Arabic numerals. Mathematics. Addition table.

“Number and number” - Name the numbers from which you can make the number 9. Number and number 7. Insert the missing numbers. Number and figure 1. Make up a problem based on the picture and solution. Number and figure 6. Number and figure 5. 6 – 1. Number and figure 9. Name the “neighbors” of the number. = 5. Number and figure 4. 6 – 5. Insert the missing number. Make up examples of addition and subtraction.

Additional materials
Dear users, do not forget to leave your comments, reviews, wishes! All materials have been checked by an anti-virus program.

Teaching aids and simulators in the Integral online store for 1st grade
Manual on Moro M.I. Manual by Peterson L.G.

Getting to know the number and number 7

Listen! The bell is ringing!
This is the beginning of the lesson.
You and I are setting off on our journey today.
To the country that is called “Mathematics”.
Numbers and mathematical signs live there.
They can tell us a lot.
The main thing is to listen carefully and remember.

Together with us, the Smart Gnome and the Little Fox are going to the land of Mathematics.
“I want to learn so much,” said the Little Fox to the Smart Dwarf, “I just don’t know if I can.”
Guys, can you help Little Fox? So here we go. Is everyone ready to go? Has anyone forgotten pens, pencils, notebooks, textbooks?

Let's practice counting to 7

Look at the picture and tell me what the number will be: blue square, green square, red square, red circle, yellow circle, red circle?

Look at the picture and count how many squares, circles, and triangles are there in total? Compose and write the inequalities.

Look at this picture and write down in numbers the number of kittens you see.

You couldn't write down the number of kittens in the last picture? No problem. Today we are going to visit the number and number

Let's remember all the numbers we know.

Look at the picture and tell me which numbers are in the wrong house?

Have you noticed that one house is empty? And this is because its resident is waiting for us to visit and meets us at the doorstep. What's his name?

That's right, this is the number SEVEN.

I'm a daring seven.
Among the numbers, mischievous.
It’s impossible without me.
Look around
You will see that I am right.

See where the number 7 is on the number line?

All numbers to the left of the number 7 are less, and all the numbers to the right of the number 7 are greater.

Think about where we can find seven?

The braid looks like SEVEN.
when the mower goes to the meadow,
He takes her with him.

Look at the poker.
Her grandmother stirs the coals in the stove.
If you stand upside down,
Then SEVEN will be with us.

There are exactly SEVEN of these brothers.
Equal for years, but different names.
They are known to everyone.
Every week around
The brothers follow each other.
As soon as the last brother says goodbye,
Then the first brother appears again.

The sun ordered:
"Wait,
The Seven-Color Bridge - in an arc!
I'll walk on you
And I can reach the stars with my hand.

Seven guys on a ladder

Songs started playing.
After all, it’s impossible without them:
Not a melody to listen to,
Not to play a symphony.

Seven thought and said:
I want to fly into the sky like a bird.
I thought and became a boomerang.
What more could she want?

On a starry night,
On a dark night, look at the sky.
You will see seven beautiful bright stars.
They call them a ladle
or "Big Bear".

Proverbs and sayings about the number seven:

• Seven troubles, one answer.
• Seven do not wait for one.
• Measure seven times, cut once.
• One with a bipod, seven with a spoon.
• Seven Fridays a week.

Let's try to solve the examples that the smart Dwarf asked the Little Fox.

Put the correct sign. Which entry is missing here?

Mathematicians who come to the country are sure to solve problems. Can you handle the decision? Help Little Fox.

On the lawn in the yard
Six puppies play hide and seek.
Mom Laika is looking for them.
Try to count it:
How many dogs are there in the yard?

Ants live together.
And they don’t scurry around idle.
Two carry a blade of grass.
Two - carry a blade of grass.
Three - they carry needles.
How many are there under the tree?

To Little Fox for his birthday
All the forest people came to visit:
Hedgehog, Teddy Bear, little Raccoon,
Hare, Squirrel and Badger.
And the last Tiger is a friend.
Quickly count:
How many guests were there?

Well done, I knew that you would quickly complete the tasks. Now let's remember what we learned in class today?
We met the number SEVEN.
We remembered inequalities, solved complex problems and examples.

So the lesson flew by.
Listen! The bell rings for recess.
We'll take a little rest
And again we will begin our journey to the land of Knowledge.

Natalia Nikulina
Lesson summary “Travel to the country of Mathematics. Number 7. Number 7"

Abstract GCD in the preparatory group

Subject: « Number 7. Number 7.« Journey to the land of knowledge»

Program tasks:

Educational:

1. Strengthen ideas about the composition numbers 6;

2. Continue to form temporary representations (days of the week);

3. Introduce education and composition number 7 and number 7;

4. Strengthen the ability to correlate the number of objects with number;

5. Strengthen the ability to recognize shapes, regardless of their spatial depict positions, arrange on a plane, arrange by size, classify, group by color, shape, size;

6. Improve quantitative and ordinal counting skills within 10.

Developmental:

1. Develop logical thinking;

2. Develop fine motor skills;

3. Develop imaginative imagination.

Educating:

1. Develop the ability to focus on the task at hand.

2. Develop the ability to work in a team, perseverance, the ability to understand and independently carry out the teacher’s tasks

3. Cultivate a kind, respectful attitude towards others, work independently with handouts material.

Methodical techniques:

1. artistic word;

2. questions for children, answers; guessing riddles;

3. independent work on cards;

4. ball games, counting out loud;

5. work with benefits;

6. surprise moment;

7. encouragement and praise of children.

Material for GCD: magnetic board, envelopes with a set of geometric shapes for each child, counting sticks, cards with in numbers"7", "6"; number series with numbers from 1 to 10; pictures of wild animals (hare, squirrel, wolf, bear, elk, hedgehog, pictures of objects, what does it look like number 7(scythe, poker, hockey stick, house "Compound number 7» , cards with squares for the house, red squares 10 x 10 cm in the amount of 6 pieces, squares blue 1 piece, simple pencils according to the number of children, sheets of paper with number 7(by points) For independent work children, serving plates material by number of children, ball, magnets for securing benefits, stickers for encouraging children, song "Blue Car", music for physical exercises.

Progress of the lesson.

Artistic word:

Someone threw it to me at the window,

Look, the letter.

Maybe it's a ray of sunshine

What's tickling my face?

Maybe it's a sparrow

While flying, did you drop it?

Maybe the wind is like a leaf,

Did you lure the letter to us?

V. – Who could the letter be from? Let's read it.

“Hello, children! I know that you are skillful and smart and love travel. I invite you to my country. Mathematics»

V. - Guys, what is possible? travel?

D. - By bus, plane, boat, train, bicycle.

V. - You and I are going to our train travel.

To do this we must buy tickets.

1. Game exercise with a ball "Train Ticket"

To get on the train, you need to know how to count forward and backward to 10.

As you pass the ball to each other, you count.

V. - Well done, you counted well, and we can all take our seats on the train.

Music is playing "Blue Car", the children go to their places at the table.

In order not to get bored on the way, we will play with you (we raise our hand when answering)

2. Game task "Neighbours numbers»

V. I call number and you are his neighbors

Name your neighbors numbers 2; neighbors numbers 4; neighbors number 5; neighbors numbers 6.

"Funny puzzles"

The task is carried out based on visual material In the process of reading the conditions of the problems, place mugs and counting sticks on the table.

The hedgehog went mushroom picking

I found ten saffron milk caps.

Eight put in the basket,

The rest are on their backs.

How many saffron milk caps will you take?

On your needles, hedgehog (2)

The puppy has 10 balls, and the kitten has 3. How many balls do the puppy and kitten have together? Tell me where the condition and where the question is in this problem.

V. - Well done! Now we have reached the first stop.

V. - The first stop is the station "Lesnaya". Guess the riddles and find out who lives at this station. The teacher asks riddles, the children guess them. Pictures of the guessed animals are displayed on the board at the same time.

Riddles:

1. In a dense forest under the fir trees, covered with leaves, lies a ball of needles, it snorts - alive! (hedgehog)

2. He sleeps in a den in winter,

Little by little he snores,

And if he wakes up, well, cry.

What's his name? (Bear)

3. Gray, toothy, howls in the forest, prowls the field, looking for lambs, calves.

(wolf)

4. Gray Column stood in the forest.

Afraid of wolves and foxes.

He plays hide and seek with them -

Running without looking back.

(hare)

5. He is tall, he is horned, he is strong

The wool is shiny - just glossy

Eats bark and branches in winter,

Walks through the snowdrifts

(elk)

6. I walk around in a fluffy fur coat,

I live in a dense forest.

In a hollow on an old oak tree

I'm gnawing nuts.

(squirrel)

V. - How can you call these animals in one word? (wild animals). How many animals are there in total? (6) Animals are preparing for winter, they have a lot to do, and we will move on (music). While the music is playing, prepare the squares on the board.

Next station « Digital»

Here we are. What an interesting task they have prepared for us

V. - Guys, there are red and blue squares on the board in front of you.

How many squares are there in total? (5)

Q. How many red squares? (5) how many blue? (1)

How did we get number 6? to 5 +1=6

And now you and I will play a game "Day-Night"

IN. - Attentively look at the squares on them and remember.

The children close their eyes, night has fallen.

The teacher changes the blue square to a red one.

The day has come, open our eyes “What has changed?”

D. - Blue was changed to red. How many blue squares are there? (6)

Night, close our eyes. The teacher adds one red square.

IN. - Number seven is designated like this number.

(Exhibited on the board number 7)

What does it look like number seven?

Here is the seven-poker, she has one leg. (S. Marshak)

Sevens are very similar to sticks for a hockey player and for an old lady.

Seven - exactly sharp braid, mow, braid. Bye sharp. (G. Vieru)

What to say about number 7? You know the days of the week, count them quickly!

If you don't miss the mark, you'll get exactly seven days.

Children name the days of the week in the correct sequence. The teacher lays out 7 strips of colored paper - according to the number of colors rainbows: Monday – red, Tuesday – orange, etc.

Children draw number 7 by hand, then on the sheet by points (working with a notebook)

Physical education minute.

V. - You are probably tired?

Well, then everyone stood up together.

They stomped their feet,

Hands patted

We reached our socks,

Turned right, left

Everyone sat down quietly.

Close our eyes tightly

We count to 7 together

Open, blink

And we continue to work.

Compound number 7

"House" on a board with circles.

V. - What is the number of this house? (7)

How to split number 7 by 2 smaller numbers?

How many circles do you need to add to make it work? number 7?

The teacher shows a table with squares and discusses with the children options: 6 and 1; 5 and 2; 4 and 3; 3 and 4; 2 and 5; 1 and 6.

Conclusion: teacher speaks: can be composed in different ways and lists all options according to tables 1 and 6; 2 and 5; 3 and 4; 4 and 3; 5 and 2; 6 and 1; how many composition options we have number 7

V. - Well done! We did well.

We arrived at the station - "Geometric Shapes".

Game "Geometric Lotto"

Each child is given "letter" with a set of geometric figures:

Let's see what's in yours "letters"!

Children name how many and what geometric shapes they have in their envelopes. It turns out that everyone has 1 large green triangle, 2 small green circles, 1 small red circle and 4 small red triangles.

What groups can we divide these figures into? (Red and green - by color, triangles and circles - by shape, large and small - by size.)

What geometric shapes do you know? (Children call).- Which one? geometric figure in my hands?

Work in a notebook.

Draw a square in the upper right corner. In the lower left - draw a triangle, in the upper left - an oval, in the lower right - a rectangle, in the middle - a circle.

V. - Congratulations! You've done your job well and it's time for us to return to kindergarten. (music)

V. - Today we did something exciting. traveling around the country"Knowledge". Did you like it journey? What did you like? What was interesting? From what number and number met. I want to give you stickers that you can stick on your notebooks.

The teacher praises the children.