We study the number 7. Proverbs and sayings

The purpose of the lesson: Introduction of the concepts “Number 7 and number 7”

Tasks:

• introduce the number and number 7;
• study the composition of the number 7;
• improve computing skills;
• develop speech, attention, memory, thinking.

Equipment: a sample of writing the number 7, drawings with the number 7, plates with the terms “1 term; 2 term; sum ”, students have cards for working in pairs, a digital “fan”. Computer presentation. Appendix 1 , Appendix 2 .

During the classes

I. Organizational moment

It rang, friends, a call,
The lesson starts.
Did you all wake up?
Now let's get down to business.
Math is waiting for us
Let's start counting.

II. Updating of basic knowledge

1. Numbering of numbers within 20.

• Count from 1 to 20:

- straight - boys
– reverse – girls

• Name the numbers from 2 to 9; 8 to 3. Slide 1. Appendix 1.
• Name the neighbors of the number 9; to the right of; on the left of; between numbers;
• Name the previous number; the next number. slide 2
• How to get the previous number? How to get the next number? slide 3

2. “Lost number”

• Let's read a series of numbers; is everything okay?
• Between what numbers is the number 7? Your correct answer helped bring the fugitive back to her place.

slide 4

III. Setting the topic of the lesson

Guess what number we will study today?

slide 5

IV. Learning new material

1. Opening a new one. Historical information.

The number 7 was surrounded in antiquity with great honor and was considered magical. Ancient Rome had 7 main gods Ancient Greece- 7 wonders of the world, Kyiv and Rome are built on 7 hills, and in India 7 elephants are given for happiness. And in our modern world, there are many objects in which the number 7 is always present. Name them. (7 days of the week, 7 notes, 7 colors of the rainbow.)

2. Statement of the problem. Lesson goals. Mystery.

Over the forests, over the river
Seven-colored bridge with an arc.
If I could stand on the bridge
I would reach for the stars. ( Rainbow.)

There are actually 7 colors in the rainbow. And who knows the magic phrase that helps to remember the order of the colors in the rainbow? (Every hunter wants to know where the pheasant sits.)

But in our rainbow, all the colors are gone. Do you like colorless rainbows? slide 6

Let's fix everything as soon as possible, if we complete all the tasks correctly and together, then the rainbow will again become colorful and bright.

3. Acquaintance with the number 7. Writing the number 7.

With what number do we write the number 7? What does the number 7 look like? (Visibility.)

Here is a seven - a poker,
She has one leg.

Seven is like a sharp scythe,
Mow, spit while dew.

(Work in the textbook - p. 62, No. 2.)

See what the number 7 looks like. Find the number 7 among the signs, tick it off. How many times did the number 7 appear? Write it down.

(Work in the textbook - p. 63, No. 4.)

We will now learn how to write the number 7.

Number 7, number 7, ( visibility)
The number is very easy.
How will I present the scythe -
The number 7 is easy to write.

Slide 7

4. Correlation of the number, quantity of objects and graphic image.

(Work on the card, in pairs.) Slide 8

(Check on the slide.)

5. Physical education "Dance of ducklings"

If you solve the problem, then its heroes will help you spend a physical minute.

A group of baby ducklings want to swim and dive,
Five sailed far, two dived deep.
How many ducklings are in the pond, I cannot count. ( Slides 9, 10)

6. The composition of the number 7.

1) Tasks in verse:

Three books at Pavlushka,
Four - at Andryushka.
How many books do the children have?
Well, count quickly.
3 + 4 = 7

Five tits sat on a branch,
Two jackdaws flew towards them.
Count quickly kids
How many birds are on the branch?
5 + 2 = 7

I have a purchase in hand:
Six knives and a meat grinder.
How many items did I bring
Tell me about it.
6 + 1 = 7

Slides 11, 12, 13

2) "Let's move into the house." Slides 14, 15

V. Consolidation of the studied material. Repetition of the past

1. Logic task. Proverb.

Arrange the numbers in ascending order and read the saying. How do you understand it? (“Measure seven times, cut once” - before proceeding to important business, you need to think it over.)

Slides 16, 17

2. Days of the week. Repetition of the composition of the number 7.

• What kind of person is said to have “seven Fridays in a week”? (about who promises and does not keep promises)
• But we are not like that, we promised to paint the rainbow, and soon we will complete all the tasks.
• Do you know the days of the week in order? Name them soon, if we don’t go astray in the account, we’ll get exactly seven days.
• Which day is first; last; today; yesterday; tomorrow?

(Work in the textbook - p. 62, No. 1)

• Why are some days black and others red?
• How did you get 7 days? (5 and 2)
• The older brother loves to study, but he is also happy on Sunday. School days there are six in a week - and there is one day for rest.
• How did you get 7 days? (6 and 1)
• Four times a week we have math lesson, and how many days are missing?
• How else to get 7?

3. Additional physical education

One - get up, stretch.
Two - bend, unbend.
Three - in the hands of 3 claps,
Head 3 nods.
Four - arms wider.
Five - wave your hands.
Six - sit quietly at the desk.
Seven - open notebooks to everyone.

4. Solution of examples. Rule for rearrangement of terms

(Work in a notebook according to options) Slide 18

• What is the result of your examples?
• Compare the examples in each line, what interesting thing did you notice?
• What rule do we know about the permutation of terms?

Slide 19

5. Comparing the sum of numbers

(Working with a fan.)

Read the written sums of numbers and put the signs “>”, “<”, “=”.

Slide 20

6. Additional task in a notebook

• Let's draw 10 circles in a row through the cell.
• Color the 7th circle from the left with a red pencil.
• And what will it be on the right side?
• How many circles need to be completed so that he is 7th from the right in a row?

slide 21

VI. Summing up the lesson

So we painted our rainbow in seven colors. Let's list all the colors in order. Who remembers the magic phrase? And in France, colors are remembered with the help of such a phrase: “How once Jacques the city bell ringer broke a lantern.” What was the main number in today's lesson? Name the composition of the number 7.

VII. Homework

Whoever liked the lesson, you can play with the number 7 and draw objects in which the number 7 is hidden. Also, remember sayings and proverbs with the number 7 with your parents.

The text of the work is placed without images and formulas.
The full version of the work is available in the "Job Files" tab in PDF format

Introduction

The theme of my work is "The Amazing Number 7".

I chose this topic because I was interested in natural numbers, ancient in origin, and I decided to find more information about numbers. Reading books on entertaining mathematics, fairy tales, proverbs, I noticed that I often come across the number 7. Every day in mathematics lessons we learn about the properties of numbers, solve problems and equations with their help. A great helper is a textbook, you can learn a lot from it. But about who and when numbers were invented, why a person 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 mathematical, philosophical, magical points 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, tasks related to the number 7.

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

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

object research became the number 7.

Subject research: the frequency of occurrence of the number 7 in mathematical problems, puzzles, in various literary genres.

Hypothesis: a number of interesting facts makes it possible to assume that the number 7 is one of the 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 the number appeared a very long time ago, in the Stone Age, when people not only collected food for themselves, but also began to actively produce it, about 100 centuries BC. e. Numerical terms were hard to come by and slowly came into use.

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, consider the most interesting facts related to it. They said about the incomprehensible that this book was “with seven seals”, healers in fairy tales gave the patient “seven bundles with medicinal herbs, which had to be infused with seven waters for seven days and taken seven spoons every day.”

The first to talk about numbers was the Greek Pythagoras, who was born on the island of Samos in the 6th century BC. 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 makes. 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 proclaimed.

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

In Egyptian and Babylonian philosophy and astronomy, it was considered as the sum of two "life" numbers: three and four. Three people - father, mother, child - are the basis of life; and four is the number of cardinal points and directions of the wind, whence comes the rain, 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. Therefore, the number 7, the sum of three and four, was perceived as sacred.

Chapter 2

We all did not think about the fact that the number seven is found in almost the entire path of human development. The history of the number 7 dates back to the time of 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 it would bring them eternal and happy life. In the night sky, the naked eye can only see seven "wandering lights": Sun, Moon, Mars, Venus, Mercury, Jupiter, Saturn. All incomprehensible phenomena of nature were attributed to the gods, and gradually the concept of the gods was combined with the seven "wandering lights". Venus was considered by the Romans as the goddess of beauty, Mercury was the god of trade, Mars was the god of war, Jupiter was the god of thunder, and Saturn was the god of sowing, plus the Sun and Moon. They began to count time. So was born seven-day week.

It is written in the Old Testament that the Lord created the earth, the sea, the 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 - the seventh day of the week - is a day off, on which, according to Christian customs, nothing can be done.

The Flood lasted 7 days.

Lent for Christians lasts 7 weeks.

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. In general, they try to bring any settlement under this figure - 7 hills. 7 hills,on which Rome was built are Palatine, Capitol, Aventine, Quirinal, Viminal, Esquiline and Caelius. During the heyday of ancient Rome, the hills were built up for centuries.

7 hills on which Moscow is built: Borovitsky (Kremlin), Sretensky, Tver, Trekhgorny, Shvyvaya Gorka, Lefortovsky and Vorobevsky. They wrote about Moscow: “You are standing, holy Moscow, on your seven hills.” In reality, there are many more hills, but seven hills are distinguished for the red word: they are different for different researchers. 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 stave (do, re, mi, fa, salt, la, si);

Surely, each of us has seen a rainbow at least once and can easily name seven colors of the rainbow in order. memorize rainbow colors in order we were taught from childhood. 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 in order to remember the colors of the rainbow in order. The first letter of each word in this phrase corresponds to the first letter in the color name. That's why, rainbow colors in order sound like this: red, orange, yellow, green, blue, blue, purple.

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

Ancient Chinese wisdom says "Life requires seven items: firewood, oil, salt, soybeans, vinegar, tea and rice.

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

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

7 structural levels(atomic, molecular, cellular, tissue, separate 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 7 following types: innovators, enthusiasts, rationalists, neutrals, skeptics, conservatives, retrogrades.

AT periodic table seven periods.

Hindus have a custom of giving 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 they worshiped 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, Chilon, 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 a cat - 56 days (7x8), in a dog - 63 days ( 7x9), for a lioness - 98 days (7x14), for a sheep - 147 days (7x21).

In Islam 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 the 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.

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

Ancient hunters and farmers watched the sky. Their attention was drawn to the change in the lunar disk. They noticed that 7 days after the new moon, half of this disk is visible in the sky. And after another 7 days, the whole 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. So they came to the concept of a lunar month, consisting of four seven days. 7 days lasts one phase of the moon.

The number seven was especially honored in the Ancient East. Several thousand years ago, the Sumerians lived between the Tigris and Euphrates rivers. They denoted the number seven with the same sign as the whole universe. Some scholars think that they expressed by this number the six main directions (up, down, forward, backward, left, and right) and even the place from which this countdown comes. Also, their attention in the sky was attracted by the stars, 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 the trinity and the quaternary and therefore is endowed with exceptional value. It corresponds to the seven directions of space (i.e., the six existing dimensions: north, west, south, east, up, down plus center); seven-pointed star; reconciliation of a square with a triangle, by superimposing the latter on the previous one (like heaven on earth) or by inscribing one into the other.

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

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

Chapter 3

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 single digits. It is with the size, the size, that many old Russian proverbs and sayings, which include the number seven, are connected in meaning.

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

In the fairy tale “The Daughter of Seven Years,” a seven-year-old girl turned out to be smarter than the king himself, and by this she 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 the evil and insidious robbers.

In the fairy tale "Snow White and the Seven Dwarfs" Snow White lived with 7 dwarfs over 7 mountains.

In the fairy tale "Seven Simeons", seven twin brothers owned a wonderful craft, 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 Kids”, “About the Dead Princess and the Seven Heroes” by A.S. Pushkin, "Seven Brave Men" by the Brothers Grimm, "Flower - Seven-Colored" by V. Kataev, "Seven Brothers" in the processing of M. Afanasiev, "Seven Underground Kings" by A. Volkov, "Seven Year Old Archer" Sami fairy tale, "Journey for seven seas".

I think in Russian sayings and proverbs the word “seven” often acts as the word “many”: “Measure seven times, cut once”, “Garlic brings 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 a child without supervision", "Drained seven rivers, did not moisten the canvas", "The fox of seven wolves will hold", "Onion heals seven ailments", "Seven feet under the keel, etc.

The meaning of popular expressions is instructive: “To be in the 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” - promise a lot, say a lot; “For seven miles of jelly to slurp” - go far and in vain, go, drag; "Until 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; “Until the seventh sweat” - to work, work, to extreme fatigue, complete exhaustion; "Behind seven seals" - secret; The "seven deadly sins" are bad, unforgivable deeds.

We meet the number 7 in poems:

The number seven is known to all.

What about the number seven?

Seryozha turned seven.

He became smarter and stricter.

Year after year will fly by

He's going to seventh grade!

G. Kaitukov

In the close sky on a starry night

I found seven bright dots.

I found seven burning eyes

Are called a bucket

And she's called Bear...

I don't understand what's wrong here?

And my father answered me:

You are a son, well done!

Imperceptibly the year will fly by

And it will be seven years old -

Will you study at school

And you will find the answer to everything.

G. Kaitukov

The number 7 is addressed in her poems Maria Konopnitskaya

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 power.

He had seven gates in the walls,

Seven consonances in chime.

Seven sins were committed in one day

In good-natured Avignon ... "

and Rasul Rza

Seven plane trees

... A 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. Life is a gift -

Seven plane trees, seven plane trees ...

What are you, wind, so frantic?

Shatter one blow

Emeralds of delicate leaves,

But it will not break seven plane trees ...

Chapter 4

All of the above, of course, is interesting for the general development, but I do not consider this to be the most important thing. The ancient Romans said: "Words fly away, the written remains." And “what is written with a pen cannot be cut down with an axe.” Many manuscripts specially devoted to mathematics have survived to our time. In the papyrus of the scribe Ahmes, which is kept in London, solutions are given to 84 problems for various calculations that may be needed in practice. Most of the tasks relate to arithmetic. Among them there is a task related to the number 7: “There are 7 cats in the house, each cat eats 7 mice, each mouse eats 7 ears, each ear gives 7 plants, each plant grows 7 measures of grain. How many together? It is clear from this problem that the author is not interested in what objects are being discussed, whether they are homogeneous or not - only the total number is important to him.

Several millennia 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 contains seven loaves, each loaf contains seven knives, each knife in seven sheaths. How many items are there?"

And similar problems were solved in Russia. In the 19th century, in the villages they thought: “Seven elders were walking. Each elder has seven crutches. There are seven knots on each crutch. Each bitch has seven purses. Each bag contains seven pies. There are seven sparrows in each pie. How many?" But this is the same task of Ahmes, which has lived for millennia and has come down to us.

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

I found many more tasks, tasks in verses, sayings, riddles.

I found seven interesting questions related to the number 7:

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

What is a unit of length equal to 7 feet called? (sazhen)

An ensemble of seven instruments? (septet)

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

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

Chapter 5

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

The ancient Greeks were engaged in geometry, not only measuring land and the distance to ships at sea. They loved geometric games. One of them was called "Stomachion". In this game, it was necessary to add various figures from 14 parts of the square. This game was so addicted that the great scientist Archimedes himself wrote an essay about it. The ancient Chinese also played 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 about the origin of the tangram game. The most common and famous is that the game of tangram is about 4000 years old. One of the fans of the game was Edgar A. Poe. His tangram is made of ivory and is currently in the New York Public Library.

The essence of the game is to construct various subject silhouettes on a plane. The variety and varying degrees of complexity of geometric designers allows you to take into account the age characteristics of children, their inclinations, capabilities, level of training

All collected figures have an equal area, because. assembled from the same elements. It follows from this that: all seven elements must certainly enter into each assembled figure; when drawing up a figure, the elements should not overlap each other, i.e. be located in only one plane; the elements of the figures must adjoin one another.

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

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

Chapter 6

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

Numbers are the key to understanding human behavior, one of the simple methods for learning and training the intuitive gifts of man and for comprehending the depths of the human personality.

The ancients believed that numbers have a mysterious, magical meaning and affect a person and everything that he does. Each person has their own "master numbers". Seven is a symbol of mystery and mystery. People of this number have increased spirituality. They have fantastic dreams, strange smells seem to them, 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 engaged in, they, as a rule, achieve a lot. It is believed that the number 7 is the sign of those born on the 7th, 16th or 25th of any month. Seven is the number of luck, the personification of wisdom.

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

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

Chapter 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 with the “-” sign is divisible by 7.

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

Another sign - we take the first digit, multiply by 3, add the next one (here you can take the remainder of the division by 7 from the resulting number). 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 developed a constant value, the amount of memory, which was concentrated precisely on seven. A person could only think about seven things at the same time and no more. But this, of course, is only philosophy. The seven was considered in many sciences, and they came to a version more or less close to the truth - everything is connected with fundamental mathematics with the microcosm. All attention and all meaning is focused on the number seven. In every science, in every field, in every sphere of activity and human life, there is a place for the seven - it is completeness and integrity.

The performance of this work helped me to form the skill of a creative approach to tasks in mathematics, to understand some methods and ways of solving problems, to learn how to independently select the necessary information, and 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 research was the number 7. I found interesting problems related to it. Better understood the meaning of the proverbs. I saw its use in puzzles and concluded that for playing Tangram the main requirement for a person is logical thinking, and for playing a puzzle - 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, helped them discover new facts and tasks. Based on this information, you can 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 significance of the number 7 was confirmed.

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

The amazing number seven! Whatever they consider him to be: both sacred, and divine, and magical, and happy. He was revered for many centuries BC, in the Middle Ages, and is 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. The wonderful world of 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 know the world." Authors-compilers M.: AST, 1998

Yakusheva G.M. and others. Great Mathematical Encyclopedia. M: "WORD": OLMA-PRESS, 2005.

Informational resources:

http://kod-nameni.ru/

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

"Interactive Mathematics Grade 5 - 9". Bustard - DOS Multimedia.

1C: Educational collection "Planimetry 7 - 9".

Attachment 1

Proverbs and sayings

And you, the seventh, stay at the gate.

It can be seen that the town is large, that there are seven governors in it.

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.

For seven miles of jelly slurp.

For seven seals.

Onions - from seven ailments.

Bow to Makar, and Makar to seven sides.

Martok put on seven desks.

Not a big town, but seven governors.

One with a bipod, and seven with a spoon.

Seventh water on jelly.

Seven gates and all in the garden.

Seven do not wait for one.

Seven for hares, but no skins.

Seven on benches.

Seven deaths - do not happen, but one cannot be avoided.

Seven troubles - one answer.

Seven miles to heaven and all the forest.

Seven years is trouble, nine years is misfortune.

Seven wise men are cheaper than one experienced person.

Seven sweats gone.

Seven spans in the forehead.

Seven Fridays in a week.

Seven times measure cut once.

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

Seven villages, one ox, and that goal, and ten officers.

Seven axes lie together, and two spinning wheels apart.

Seven feet under the keel.

Seven, eight - let's discard laziness.

Secret behind seven seals.

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

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

One sheep has seven shepherds.

Seven of us will go - we will go far.

Uphill seven barely pull, and downhill and one will push.

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

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

They searched for a mosquito for seven miles, and a mosquito on the nose.

Onions - from seven ailments.

Appendix 2

Rhymes

Once the guys went to the river,

They carried two oars in their hands.

Three sheep meet them

And four turkeys.

Frightened, they fled.

The oars were thrown into the bushes,

And you must find them.

One, two - there were ducklings,

Three, four - went home.

Behind them trailed the fifth,

The sixth ran ahead

And the seventh lagged behind everyone,

Frightened, he squealed:

Where are you? Where are you?

We are here nearby ... look.

Tongue Twisters

They sat and whistled seven waxwings.

In seven sledges

Seven per sleigh

Sat down yourself.

Stepan has sour cream.

Yogurt and cottage cheese

Seven kopecks tuesok.

Puzzles

There are exactly seven of these brothers.

You all know them.

Around every week.

The brothers follow each other.

Say goodbye to the last -

The front appears.

(Days of the week)

We are a flock, seven sheep,

Protects from storms.

The sun ordered: "Stop",

The Seven Colored Bridge is steep.

7 I. (Family)

Annex 3

Tasks in verse

In the sky, a rainbow is an arc

Closes the coast

Blooming clearer

Miracle - colors shine

Let him answer

How many colors

plays in it,

Illuminating the sea surface?

The fishermen are sitting

Guard floats.

Fisherman Roots

Caught three bass

Rybak Yevsey -

Four carp.

How many fish are fishermen

Dragged from the river?

Sasha in a pocket

Candy in paper.

He gave candy

Sveta and Pete,

Irina and Galina,

Marina and Nina

And I ate candy

And no more.

(How many sweets were there?)

Task tongue twister

Sasha walked along the highway

Carry dryers in a bag.

Drying - Grisha,

Drying - Misha.

There are drying Proshe,

Vasyusha and Antosha.

Two more dryers

Nyusha and Petrushka.

(How many dryers did Sasha carry?)

Appendix 4

Problems with the number 7

Task 1

What natural number is 7 times the digit of its units? Answer: number 35

Task 2

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

Task 3

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

Task 4

The number VII (seven) is composed of 4 matches. How can you move two matches so that you get the number 5?

Task 5

A can with a capacity of 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, 7 liters must be poured from the first vessel into the second, and then 2 liters from the second into the third.

Task 6

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

Task 7

Between some numbers, place mathematical signs and brackets to get the 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.

Annex 5

How to calculate the number of a person

To do this, add up all the numbers included in the 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 - the number of diplomats. These people are soft and tactful.

3 - the three endow people with talent, a sharp mind, 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 number of fate are smart, creatively gifted and have a strong will.

That's all!

1 - Sun

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

Number 2 people are usually soft, artistic and charming, and can easily adapt to circumstances. Often they are characterized by passivity and detachment. They are characterized by ingenuity and intuition, but they do not succeed very often in the implementation of their plans. They are more inclined to think than to act. These people are often prone to depression. They have very good relations with people of number 1. The lucky day of the week for number 2 is Monday.

3 - Jupiter

Three is the number of the 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 small things. By nature, they are very proud and independent, they like to control the situation, command and order. Most often, they have the best relationship 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 points, 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 the rest. 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 too friendly, they are often lonely. They have the best relationship 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 really extremely sensitive. Usually by nature they are very lively, impulsive, frivolous, prone to risk, very much appreciate pleasure. As a rule, they are easily excitable and often subject to nervous disorders. In business, people of the number 5 usually succeed and recover very quickly after failures. The best relationship usually develops with them with the owners of the same number. A lucky day of the week for the 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 \u003d 1 + 2 + 3. People of the number 6 are harmonious and balanced, have confidence, although sometimes they are too stubborn. They are most often very romantic and amorous, their interests, as a rule, are focused on home and family. They have a good taste, they are very conducive to themselves, they easily converge with other people. The lucky day of the week for the 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. Usually they are immersed in their own thoughts and therefore somewhat detached from others. 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 the number 7 is Monday.

8 - Saturn

8 is the strangest and most difficult number. On the one hand, it can be represented as a sum of 4 + 4, which indicates that the character of its people is doubly characteristic of the qualities of people of the number 4. On the other hand, the number 8 has its own properties. For example, it can mean grief, sadness and, at the same time, success, sometimes of world significance. People of the 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 hottest feelings. Lucky day of the week for 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 \u003d 36 \u003d 3 + 6 \u003d 9. Usually people of the number 9 are born fighters, they are active, courageous and purposeful, due to which they usually win. At the same time, people of the 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 the number 9 is Tuesday.

Getting to know the number number "7", we use various didactic material for acquaintance .

Didactic material in mathematics.

Number "7"

Merry Poems

Puzzles

funny puzzles

Proverbs and sayings

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

Tongue Twisters

• They sat and whistled seven waxwings.
• In seven sledges, seven in a sleigh sat themselves.
• Stepan has sour cream, yogurt and cottage cheese, seven kopecks - tuesok.

Physical education minute

How many green trees

So many bows (7).

How many circles do we have here

So many jumps (7).

How many knitted balls.

We will make so many claps (7).

Graphics tasks

Task 1. Separate the ducklings.

The seven ducklings in the pond fight all the time. How to separate them with three lines to stop quarrels?

Task 2. Find the circles.

Find 7 circles in each figure.

Task 3. Help Snow White find her way.

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

Rebus

7th

A new interesting educational game for kids "Learning the number seven 7" is completely free. Meet the graceful heroine of our new nursery math game is the number seven. In order for you to better understand it, we have prepared for you a short educational presentation that will teach you how to write this number correctly, remember how it looks and understand what, after all, it means. Do you think you can deal with game tasks? Then welcome to new level. Assemble the image of the number "seven" from the cubes, turning them over with the mouse. As soon as you do it, count and say how many hardworking bees you see in the picture in front of you. Did you complete the task flawlessly? Well done! Now you can count to seven!

As school begins with a desk, so mathematics begins with the most important and simple number - the number "One", or one. Remembering it is very simple, because it looks like the most ordinary stick with a small tail on top. Did you manage? Then go to the next task and look for cubes


Educational game "Learn the number five 5" for kids and children 3-4-5 years old. So you got to the five, or, as it is called in mathematics, the number "Five"! A pot-bellied number, consisting of two lines and an arc, and next to it are five dinosaurs, see? And to make it easier for you, remember


Kid, you have reached the last level of our exciting math game. Now that you know almost all the numbers, it's time for the last of them - the numbers "Nine 9". This wonderful game is dedicated to her. She looks exactly like an inverted tormash


In a new educational game for toddlers and children, the main character will be the number "Eight 8". Did you say bagels? Quite right! It is the two round bagels that you love to eat with tea while visiting your grandmother, and this figure reminds you! And next to this wonderful figure are scattered


Ready for a new adventure in the world of fascinating numbers? Then get acquainted with the number "Six" and learn it 6 times! Doesn't it remind you of anything? She's like a circle with a ponytail to the top, don't you agree? And next to this unusual number, multi-colored birds fly, and there are exactly six of them too. As soon as good

Under each task, for learning the number 7, you will find a picture that can be printed out and used as didactic material for teaching a child.

Exercise 1. Write down the number 7.

Task 2. Find all the numbers 7 in the picture and circle them.

Task 3. Connect the numbers in order and color the resulting picture. (numbers from 1 to 7)

Task 4. Color the fragments of the picture with the number 7 with a blue pencil. What happened.

Task 5. Lead the frog to the swamp, following the numbers 7.

Task 7. Enter the missing numbers in the digital rows (from 1 to 7 and from 7 to 1)

- Consider domino bones and add the number of points on the empty half to make 7. On their basis, paint the composition of the number in the form of addition examples.

- Settle in a house. (composition of the number 7)

- Opposite each example, paint over the required number of cells with two different colors (Take a blue and red pencil. Opposite the example 6 + 1 = 7 - 6 red cells and without skipping 1 blue cell. 7 + 0 = 7, 6 + 1 = 7, 5+ 2=7, 4+3=7, 3+4=7, 2+5=7, 1+6=7, 0+7=7)

- Solve funny examples. Write the result in squares. (examples for adding and subtracting identical objects, based on the composition of the number 7)

- Color the mushrooms, the sum of the numbers on which is equal to 7

- Solve problems using counting material (the result should be 7)

• 5 birds were sitting on the apple tree, 2 more magpies flew to them. How many birds were in the tree?
• The dog gnawed 6 bones, then 1 more. How many bones did the squirrel gnaw?
• Dasha had 7 balloons, 2 balloons burst. How many more balls does Dasha have left?

- List the days of the week. What is the name of the seventh day?
What are more flowers or butterflies? (butterflies 7, flowers 6. Connect with lines. What is more, less. How many flowers were not enough?)

- Color 7 bananas yellow and the rest green.

Find the number 7 and color it.

- Count the number of animals in the frame. Enter the appropriate number.

- In each row, number the items in order, starting with the smallest.

- Solve the example and connect the squirrel with the corresponding nut. (an example is written on a squirrel, an answer is on a nut)

- Count the number of bananas, oranges, pineapples in the picture. Record the result in the appropriate boxes. Compare. (bananas 6, oranges 7, pineapples 8)

- Solve examples on apples and pears. Connect the apples and pears with lines that have the same answers.

Video task, "Write the number 7 correctly"