Slide 2
Once upon a time there was a king. The tsar had three sons: Fedor, Yegor and Ivan. The tsar's wealth was innumerable. Yes, he began to get sick. So he sends his sons for living water and rejuvenating apples. The sons set out.
Slide 3
The sons drove for a long time, and they met a passer-by. "Is it far to the village?" You have covered a third of the entire distance, and if you still drive 2 versts, you will be exactly in the middle - a passer-by answered. How many miles still need to be covered by the sons? Solution: 2 versts is 1/2 - 1/3 = 1/6 of the total distance between villages, which means that the entire distance is 1 i.e. 6/6 is equal to 2۰6 = 12 (versts). 1 / 3–4 versts, and 12-4 = 8 (versts) remain. Answer: 8 versts
Slide 4
The sons arrived at the village and went to the inn to rest. We ordered the hostess to cook potatoes, but they themselves fell asleep. The hostess cooked it, put it on the table and left. Fedor woke up, ate the third part and fell asleep again. Then Yegor woke up, counted the potatoes, ate the third part and also fell asleep. Ivan woke up and ate a third of the remaining potatoes. Then all the brothers woke up and saw that there were 8 potatoes left in the cup. How many pieces did the hostess cook and how much more should each of the brothers eat so that everyone gets the same amount?
Slide 5
Solution: Ivan left the brothers 8 potatoes, i.e. 4 each, so he ate 4. It turns out that Yegor left 12 for the brothers, 6 for each and ate 6 himself. It follows that Fedor left the brothers 18 potatoes, 9 for each, and ate 9 of them himself. So, the hostess served 27 potatoes on the table. The answer is 27 potatoes
Slide 6
The brothers wandered for a long time until they reached the hut of Baba Yaga. They told where and why they were going. "Guess my riddles, then I will tell you where to find living water and rejuvenating apples," said Baba Yaga
Slide 7
Answer: 1) 3 2) the same 3) 100 Ducks flew: one in front and two behind, one behind and two in front, one between two and three in a row. How many ducks flew? Which is heavier: a pound of iron or a pound of fluff? Divide half a dime in half
Slide 8
The brothers guessed all the riddles and Baba Yaga showed them the way to her middle sister, and left Fedora so that he could cut wood for her. Sawing off one piece takes 1 minute. How many minutes will it take for him to cut a log five meters long? Answer: 4 minutes
Slide 9
Meanwhile, Yegor and Ivan reached the dense forest. In that forest there is a hut on chicken legs. The middle sister of Baba Yaga lived in that hut. She had 20 girls in her service
Slide 10
In the evenings, she went around the house and checked if everything was in order? There were 7 girls on each side of the room. 3 3 2 2 3 2 3 2
Slide 11
But one day 4 girlfriends came to the girls and stayed overnight with them. There were 24 of them. They were placed so that on each side there were again 7 girls. How did the 24 girls fit if there were 7 girls on each side? 24 girls were placed like this: 1 1 1 1 5 5 5 5
Slide 12
The next day 4 girlfriends left, 4 more girls went to see them off. There are 16 girls left. And they were positioned so that on each side there were again 7 girls. How did the 16 girls fit if there were 7 girls on each side? Here's how they fit: 3 3 3 3 1 1 1 1
Slide 13
The middle sister of Baba Yaga found out what the brothers were going for, and decided to help them. She sent them to her younger sister. They drove, drove, they saw - there was a hut on chicken legs, turning. And in the hut is Baba Yaga's younger sister.
Slide 14
She has a cow, a goat and a sheep. The younger sister is sitting, wondering how to feed her animals? A cow eats a cart of hay in a month, a goat in 3 months, a sheep in 6 months. How many days will a hayload of hay last for these animals?
Slide 15
Solution: If there are 30 days in a month, then in 1 day the cow eats 1/30 of the hay load, the goat - 1/90 of the cart, and the sheep - 1/180 of the cart. Together they eat 1/30 + 1/90 + 1/180 hay in 1 day. 1/30 + 1/90 + 1/180 = 1/20 This means that in 20 days they will eat 20/20 carts, i.e. 1 or all of the hay. And for a month you need 30/20, that is, 1.5 wagons. Answer: for 20 days.
Slide 16
The brothers helped Baba Yaga's sister, dung hay for her animals, and she told them how to get to Kashchei the Immortal, who had living water and rejuvenating apples. So they drove along the road again. Ahead is the river. They see a peasant sitting on the bank of the river, who needs to transport a wolf, a goat and a cabbage.
Slide 17
Only one person can fit in the boat, and he is either a wolf, or a goat, or a cabbage. If you leave a wolf with a goat without a man, then the wolf will eat the goat. If you leave the goat with the cabbage, the goat will eat the cabbage. In the presence of a man, a goat cannot eat a cabbage, and a wolf cannot eat a goat. The peasant asked the brothers for advice on how to transport his cargo across the river?
Slide 18
Solution: First, the peasant needs to transport the goat to the other side, leaving the wolf with cabbage, then return, take the wolf, transport him to the other side, and take the goat back with him. Leaving the goat on the shore, it is necessary to transport the cabbage to the wolf, then transport the goat.
Slide 19
The brothers helped the peasant, and then Fedor caught up with them. And they went together to Kashchei the Immortal. But it's not easy to cope with Kashchei. He does not want to give away living water and rejuvenating apples. He began to set tasks. Tasks of Kashchei Bessmertny: Task 1. The miller came to the mill. In each of the four corners, he saw three sacks of flour. There were three cats on each bag, and each cat had three kittens with her. The question is, were there many feet in the mill?
PROJECT:
Mathematical Tales
Performed:
student of grade 3-A
Lisyak Anastasia
Objective of the project:
Find out what role numbers play in our life.
Once an unpleasant story happened to the numbers.
What happened?
We learn about this from a fairy tale.
"Important figures"
There were numbers in the realm of mathematics
0 to 9. Digits as digits.
Some of them
were thin
such as, and Some are full, rounded.
These included
Some of the numbers were with a ponytail,
such as,
and Someone with a circle like
In general, they were different, unlike each other.
Despite this, the numbers were very amicable.
between themselves
But then one day, at a holiday, the letters told the numbers that they are more important. Without letters and words, no one would understand anything. And the numbers were offended and scattered in all directions. And such chaos began!
Letter A , for example, stands on 1 place in the alphabet,
letter D - on 5 and the letter I AM - on 33 location.
And now, when there are no numbers, it is not clear where
them to get up.
Such a confusion!
- ? - ? - ? - ?
In the mathematical realm, no one could really count anything, and panic began.
Then the letters apologized to the numbers, and asked them to continue to fulfill their digital duties.
And everything fell into place.
Quiz
Solve examples:
A * D = D L + M = U K-B = I H: D = D
__*__=__ __+__=__ __-__=__ __:__=__
The work was performed by a student of grade 5B Kosenkova Natasha
Introduction
Mathematics is a real magic kingdom.And numbers, numbers, geometric shapes,
if you really want to, they can
turn into amazing fabulous
characters.
Baby's first mathematical concepts
learns from fairy tales: 1) numbers (Snow White and
seven dwarfs, Three little pigs), 2) counting
(Mitten), 3) comparison (Three bears,
Thumbelina), 4) geometric shapes
(Gingerbread man)
Mathematics puts the mind in order,
Mathematics finds the unknown
Mathematics makes us happy
the senses,
Mathematics is a science - an art.
Purpose of work:
- Prove what a concept like fairy tales in mathematics is,has a right to exist.
- Give specific examples of the relationship
mathematics and fairy tales.
- Prove that mathematics and fairy tales can
exist together without contradicting each other.
Plan:
- Introduction
-Numbers in fairy tales
-Math problems in fairy tales
- Literary mathematicians
Literary and math quiz
-Conclusion Fairy tales in mathematics. Sounds
unusual and somehow strange.
We are used to fairy tales
collide in lessons
literature. Fairy tales are
adventure, we're not serious
treat them.
And mathematics is the queen of all sciences. WITH
elementary school we are taught to be
attentive, hardworking and
serious with this lady. We
accustomed that mathematics is a science
dry and not always interesting
speaking her own language of formulas,
equations,
reasoning,
evidence, graphs ... But this
at all
not
means,
what
the words
"Fairy tale" and "mathematics" cannot
stand next to. Of course they can!
Numbers in fairy tales
The presence of numbers in fairy tales is observed everywhere and almostalways they appear as sacred and deep
symbolic. The number one is found in the Russian tradition.
rarely. However, the image of Anika as a warrior who travels to
Pure Field to fight the enemy alone, as well as a symbol
spears and unicorns found in the texts of the annals and the ancients
legends say otherwise. The number two represents the idea of a couple.
and oddness, expresses the ratio of right and wrong principles.
The Slavic tale is permeated with the idea of the struggle of such principles as Life
and Death, living and dead Truth and Krivda.
Much more often in Russian fairy tales and folklore they talk about the number seven.
These are the seven gods of the ancient Russian pantheon, and the god Semargl, obviously
leading his name from the number 7, and the seven heavens, and many
other septenary symbols scattered over the numerous
legends, fairy tales and traditions. "7 is a human number - (seven
holes in the human head), seven ages, seven
virtues.
Favorite fairy number
Who among us does not remember the famous fabulous beginning: “For distant lands in the distant kingdom lived ... ”And who of us, reading fairy tales in childhood.
Didn't come across the mysterious number three.
The peasant has three sons:
The elder was smart,
Middle son - this and that,
The youngest was a fool at all.
And this youngest, beloved by all Ivanushkudurochka, fate always tests three times.
And what about proverbs and sayings? After all, literally
interspersed with the number three: "in three pines", "in three
streams "," with three boxes ".
So where did this magical "three" come from?
It is curious that the number 3 was considered not only as
happy ("God loves the trinity"), but also how
unhappy ("damned").
The number 9 is in direct connection and
depending on the number three. From 3 x 3 = 9 a step is made to 3
x 9 = 27. This number also has magical power. From
it is the famous fabulous "far away
lands ".
Special number
The most, perhaps, mysterious and eventhe magic number in mathematics is
number zero. With its special properties, we
we collide already in primary and secondary
school. You cannot divide by zero. At the first
acquaintance with the number line, it turns out
that zero is not the same as empty
to the multitude. This number not only has its own
coordinate on the number line, but from it
originate from the frame of reference. Can
say zero is borderline
point separating positive and
negative numbers, upward directions and
down, right and left, forward and backward.
fairy tale we meet
a heroine whose characteristics resemble
us the characteristics of this number. She always
lives on the border of two worlds, being like
would be a door between them. Baba Yaga's hut
is never part of those
worlds that she shares, but always
only - by the border. So, Baba Yaga's hut -
this is the point of initiation. Unworthy or not
allowed or perished. The worthy can
cross this border and return back to
the material world alive .. ABOUT ZERO
Once upon a time many believed
That zero means nothing.
And oddly enough, they believed
That zero is not a number at all.
But on the axis among other numbers
He still got a place.
And all the real numbers
Divided into two categories.
If you add zero to the number,
Or you take away from him
In response, you immediately receive
Again the same number.
Caught, like a multiplier, among the numbers
He brings everything to naught in an instant.
And therefore in the work
One for all bears the answer.
And regarding division
First, you need to remember
What a long time in the scientific world
It is not allowed to divide by zero.
The reason is obvious to everyone
And the reason is
That there is no point in such a division
The contradiction is in itself.
Mathematical Tales
. “Lived - there were three fractions: 3/6, 1/2 and 6/12.They were twin sisters, but about this
did not know. 3/6 once had a day
birth. And she invited her girlfriends fractions: 1/2 and 6/12. I also invited a friend:
the rule for reducing fractions. Girlfriends
presented their gifts to the birthday girl and with
waited impatiently, but what will give
rule? A friend said, “My gift will be
like this: I'll cut you down. " And read her
spell-rule: “Division of the numerator and
denominator by their common divisor, excellent
from one, is called the reduction of the fraction. " AND
then 3/6 became 1/2. Girlfriend
6/12 also asked, the rule reduced her
by 6, and it also became a fraction 1/2. And the third
girlfriend, fraction 1/2, the rule could not
cut because this fraction was
irreducible. And the girlfriends realized that they
twin sisters. ("Reducing fractions",
Khammatov Ruslan, grade 6).
TRIANGLE AND SQUARE
TRIANGLE AND SQUAREOnce upon a time there were two brothers:
Triangle with square
Senior - square
Good-natured, pleasant
The youngest is triangular,
Always dissatisfied.
I began to ask the square:
- Why are you angry, brother?
He shouts to him: - Look,
You are fuller and wider than me
I only have three corners
You have four of them!
But the square answered: - Brother!
I'm older, I'm a square:
I said even more tenderly:
- It is not known who is more needed!
But night came, and to my brother,
Bumping into tables
The younger climbs stealthily
Cut corners to the elder.
Leaving he said:
- I wish you pleasant dreams!
Know, went to bed - was square,
And wake up without corners!
But the next morning the little brother
I was not happy with a terrible revenge.
He looked - there is no square,
Numb, stood without words ...
That's revenge! Now brother
Eight brand new corners.
How mathematicians tell fairy tales
What parts does a fairy tale consist of? It turns out that the answer to this question can beformulate strictly mathematically - for this you just need to compose
fabulous equation with pictures instead of variables
Guess these tales!
Problem from a fairy tale
One woman went to the gardencollect apples. To exit from
garden, she had to go through 4
doors, each of which stood
guard. Guard at the first
the woman gave half of the doors
the apples she collected. Reaching
the second guard, the woman gave
half of the remaining apples to him. So
she did the third
guard, and when she shared
apples with a guard at the fourth
doors, then she has only 10
apples. How many apples did she collect in
garden?
Problem from the collection of fairy tales "1001
night"
Solution: 10x2x2x2x2 = 160.
Mathematicians - writers
Why among mathematicians it turns outso many talented writers?
Seemingly violent fantasy and strict
figure - things are incompatible, inherent
antipodes. But how to explain the phenomenon
Lewis Carroll, Alexander
Solzhenitsyn, Sophia Kovalevskaya,
Alexandra Sukhovo-Kobylina, Isaac
Azimov, our contemporary
Alexandra Kabakov, not to mention
figures of lesser renown? Too much
many names for it to be
by chance. At a Canadian university
Waterloo conducted research,
which proves that following
manifested in childhood abilities
a good storyteller is found and
bright mathematical giftedness.
PUSHKIN AND MATHEMATICS
There is an inextricable connection between Pushkin and mathematics.Pushkin received his first knowledge of mathematics rather
in all, in childhood from frequently changing French governors.
At the Lyceum, mathematics was studied thoroughly: in the program
mathematics included arithmetic, geometry, applied
mathematics, pure mathematics, even mathematics with
differentials and integrals. But, Pushkin at the Lyceum
"I was lazy and lagged behind." Nevertheless, I believe that Pushkin
received good mathematical training.
Therefore, subsequently in his work are
some interesting points related to mathematics
Some data related to the calculations are available in the tale
"About Tsar Saltan". Having calculated the possible distance from
the kingdom of Saltan to the island of Buyan, to the city-palace,
justified by Prince Guidon, to which she could swim
barrel with the queen and his son, concluded that the queen with
son were at a sufficiently large distance that
the news of the wonders of this city reached Tsar Saltan
the passing merchants are not so fast and not so long.
This means that Pushkin's poetry was based on deep knowledge
subject, coverage of all its sides and turned out to be more reliable
simplified primitive mathematical models.
Hence, the words “The tale is a lie, but there is a hint in it, kind
a lesson for the good fellows ”- non-empty words in Pushkin's tales. except
Moreover, the winged words of Pushkin “In geometry it is necessary
inspiration, as in poetry "," I believed in algebra
harmony ”, etc. have a deep mathematical meaning
A.P. Chekhov "Problems of a Crazy Mathematician"
A.P. Chekhov "Tasks of a Madmanmaths"
I was chased by 30 dogs, of which 7 were white, 8 were gray, and
the rest are black. The question is, which leg did the dogs bite me for?
right or left?
We bought 20 cibics of tea. Each tsibik had 5 poods,
each pood was 40 pounds. Of the horses carrying tea, two fell into
road, one of the carters fell ill, and 18 pounds fell apart. The pound has
96 spools of tea. The question is, what's the difference between cucumber
brine and bewilderment?
English has 13,7856738 words, French 0.7 times
more. The British got along with the French and combined both languages
together. The question is what is the third parrot and how much
did it take time to conquer these peoples?
On Wednesday, June 17, 1881 at 3 a.m. I was supposed to leave
station A train the railway, so that at 11 o'clock. evenings
arrive at station B; but at the very departure of the train received
there was an order for the train to arrive at station B at 7 pm.
Who loves longer, man or woman?
My mother-in-law is 75 years old and my wife 42. What time is it?
Literary - Math Quiz
¥ Which Russian poet do these mathematicallines: "We regard all as zeros, and ourselves as ones"?
(To A.S. Pushkin.)
¥ What Pushkin hero said:
“... I believed
I algebra harmony ... "
(Salieri in Mozart and Salieri.)
¥ Whose lines are these?
“We love everything - and the heat of cold numbers,
And the gift of divine visions
Everything is clear to us - and the sharp Gallic meaning,
And the gloomy German genius ... "
(A. Block "Scythians".) ¥ Which poet sang numbers?
“I bow to you, I wish you, numbers!
Free, disembodied like shadows
You are hanging like a rainbow binder
To meditation from the top of inspiration! "
(V. Bryusov "Numbers".)
¥ What books did the professor of mathematics, logician Charles Lutwidge write
Dodgson, aka Lewis Carroll?
("Alice in Wonderland", "Through the Looking Glass".)
¥ What did Lewis Carroll invent as a mathematician?
(Methods for checking the divisibility of numbers by 17 and 19. Reception of memorization
a number of digits of the infinite fraction 3.14 ..., thanks to which he could
write the number p to 71 decimal places. Anticipated some
ideas of mathematical logic.)
¥ How many residents were there in the Florida village of Missouri, in
which the future writer Mark Twain was born, if in his autobiography
the writer says: “I have increased the population by exactly one percent. Not
every historical figure can boast of having done more
for the hometown "?
(100 people.) ¥ In the story of I.S. Turgenev "Mumu" is told that Gerasim was
"Twelve inches of growth." One inch is approximately 4.4 cm.
It turns out that Gerasim's height was about 53 cm, which contradicts
the description of the mighty figure of the hero in the story. Did Turgenev have
bad with math?
(No. It's just that in the time of Turgenev it was indicated how many vershoks
human height exceeds 2 yards. One arshin is equal to 71 cm,
therefore Gerasim's real height is 195 cm.)
¥ What number received the name Scheherazade (Scheherazade) and what are its
wonderful properties?
(1001 is the Scheherazade number, it can be seen in the title of the immortals
fairy tales "A Thousand and One Nights". Mathematically speaking, the number 1001
possesses a number of interesting properties:
a) This is the smallest natural four-digit number that can
represent as the sum of cubes of two natural numbers: 1001 =
103+13;
b) The number 1001 consists of 77 ill-fated damn dozen (1001 =
77x13), out of 91 elevens or out of 143 sevens (remember that the number
7 was considered a magic number);
c) The method for determining divisibility is based on the properties of the number 1001
numbers at 7, at 11 and at 13.)
¥ Which prose genre is the arithmetic mean of a story
and a novel?
(Story.) ¥ The record holder among writers with a score of 27,000 is L.N. Tolstoy, and
in second place - A.S. Pushkin from 24000. For what nomination?
(According to the vocabulary of used words.)
¥ According to scientists, the heroes of Shakespeare's works pronounce this word
2259 times. What is this word?
("Love".)
¥ "Mathematical" children's folklore is ... What?
(Readers, counting rhymes.)
¥ What "literary value" of a work is both positive and
negative?
(Hero, character of a literary work.)
¥ Which line can be found in a literary work?
(Storyline.)
¥ What does an unkilled bear like to do “divisible”, according to Russian
proverb?
(Skin. To split the skin of an unkilled bear.)
¥ What mathematical law, known to everyone from elementary school, has become
popular proverb?
(The sum does not change from the change of the places of the terms. It is translocative, or
commutative law, property of addition and multiplication expressed by formulas
a + b = b + a, ab = ba.)
¥ Who is taller: a fabulous Russian-shorty Man-with-a-fingernail or
Thumbelina?
(Thumbelina, because Thumbelina's height is 2.54 cm, which is larger than the size of a marigold.)
Conclusion
It is a lie that there is no poetry in science.In the reflections of the great world
The poet will catch hundreds of colors from sounds
And the magic lyre will repeat.
Behind the halls of formulas, forgetting about spring,
In the world of numbers, wandering like a sleepwalker,
Suddenly, the harmony of conclusions gives the string,
A mathematician clinging to a sonorous violin.
A real scientist, he is also a poet,
Ever hungry to know and to foresee.
Who said that there is no poetry in science?
You just need to understand and see.
Bromley.
So I tried to prove that mathematics and fairy tales can exist side by side, enriching and helping each other. Wild fantasy
literary and strictmathematical thinking - things are quite
compatible.
And in a math lesson, a fairy tale can
become a helper and a good friend.
In a certain kingdom, in a certain state, there lived a king. And he had a son, Ivan Tsarevich. Once, when Ivan became an adult, the tsar said to his son:
Son, it's time for you to get married.
Here's what you take….
- How can I marry a frog?
- If you complete my tasks, then I will turn into a red maiden!
Six funny cubs
They rush to the forest for raspberries, but one of them is tired,
He lagged behind his comrades. Now find the answer: How many bears are ahead?
Tasks in verse
Seven funny pigs They stand in a row at the trough. The two decided to go to bed, How many pigs does the trough have?
Four goslings and two ducklings They swim in the lake, shout loudly. Well, count it quickly - How many babies are there in the water?
The seagull warmed up the kettle, I invited nine seagulls
"Come all for tea!" How many seagulls, answer!
Ivan Tsarevich completed the tasks of the frog. The frog jumped, threw off the frog skin and turned into Vasilisa the Beautiful.
Look for me in the distant lands, in the thirtieth Kingdom at Koshchei the Immortal
“ I'll show you where Koschey the Immortal lives if you complete my assignments. "
“I will not fight with you, I know that you will defeat me anyway, I read this tale as a child. Let's agree, if you can get to Vasilisa the Beautiful, I will free her, let you go in peace. If not, blame yourself. I will take Vasilisa as my wife, and I will imprison you in prison. "
“ I will not fight with you, I know that you will defeat me anyway, I read this tale as a child. Let's agree, if you can get to Vasilisa the Beautiful, I will free her, let you go in peace. If not, blame yourself. I will take Vasilisa as my wife, and I will imprison you in prison. "
Tasks of Koshchei the immortal:
Name the items. Use the first letters to form a word.
Think and solve problems:
Who will reach the nest faster than a caterpillar or a sparrow?
Who will swim faster to the bank of a goose or a rooster?
