Learning activities for math

Extracurricular event in mathematics for grade 11

“Mathematics and facts”

(Olympiad "Hope for success" math block)

The event was developed and conducted by Berchanskaya N.A.

22.03.2021 (10 people were present and took an active part: Shkamratov, Mukhin, Fedorov Vitaly, Anshakov, Passar, Ustenko, Kosachev, Kadushkin, Volkov, Yarosh)

03/23/2021 in the UKP at FKU IK-8 (people were present and took an active part: Egorov, Dmitriev, Malyushchak, Kovalenko, Pavlov, Raguzin, Kushnir)

03/25/2021 in UKP at FKU IK-11 (Nezhmakov, Sizov, Tuezov were present and took an active part)

03/26/2021 in the UKP at SIZO - 2 (attended and took an active part Ryabtsev, Ibrasov)

Event-Olympiad "Hope for success” is traditional and is included in the school-wide work plan and plan educational work of the school

Purposes of the event:

• stimulate interest in mathematics;

• promote development logical thinking, the ability to think quickly and accept

correct solution;

• promote development intelligence, intuition and resourcefulness of students,

manifestation of individual abilities of students and activation of their cognitive

activities.

Tasks of the event:

1. Educational (didactic) task: in a fun way to deepen knowledge of

mathematics, promote the development resourcefulness, ingenuity, speed of reaction.

2. Developing task: to develop intuition, erudition, broaden the horizons of students, interest in

mathematics.

3. Educational task: to educate culture of communication, culture of mathematical thinking.

Cabinet equipment

• personal computer;

• black box; items, related to mathematics: a) a compass, b) a clock.

Plan of the event:

1. Presentation of teams (name, emblem, slogan)

2. Warm-up (10 questions for each team)

3. "Black box"

4. "MIF-theater"

5. Competition "Do you know Are you his?"

6. Great people

7. Competition "Dark Horse"

8. Brainstorming

9. Competition "Mathematical compliment"

10. Competition "Letterhead"

11. Competition of captains "Who is ahead? "

12. Competition for teams fans

Summing up.

Summing up As a result, we can conclude that such events carry a huge educational potential.

First, every holiday is a perspective for learners. Knowing what's ahead of them waiting for some interesting event, students live this "tomorrow's joy", and every day of their life today is colored by this joyful prospect. Thanks to this, life becomes richer, more interesting.

Second, the event awakens in students the desire to improve their intellectual, creative and moral qualities, as well as contribute to formation of responsibility, organization, independence, discipline in students.

Third, a well-organized and brightly held event evokes feelings of pride students for their school, a respectful attitude towards both teachers and classmates.

On the event was attended by employees of the institution Semenikhin D.A. (IK-7), Vince P.Ya. (SIZO-2), Drozhzhin A. I. (IK-8), Mokhov S.S. (IK-11) and teachers of the Shukan school I.M., who highly appreciated the event. Held at the end of the event The reflection also showed that the students liked the event.

March 31st 2021 _________/ events:

Our jury: (jury presentation)

1.Team presentations.

Let's draw lots: from the word "HYPOTENUSE" you need to make words. That team

which has more words will be the first etc. One minute to think...

2. Warm-up slide 1

answer my questions. Each correct answer

earns you 1 point. Ready? Attention!

Questions for the first team

1. Who first drew the connection between the sides in a rectangular triangle? (Pythagoras)

2. What is the name of the author of the school geometry textbook. (Atanasyan)

3. Who said: “Mathematics is the queen of sciences, and arithmetic the Queen of Mathematics? (Gauss)

4. How many seconds are there in one hour? (3600)

5. What is the name of the ray that divides the angle in half? ( Bisector)

6. What is the name of a quadrilateral with all angles and sides equal? (square)

7. A kilogram of meat is cooked for 1 hour. How long does it take to cook 0.5 kg of meat? (in 1 hour)

8. What is 17

2

? (289)

9. What is the hundredth part of a number called? (percentage)

10. What is the largest number can be written in four units? (11

11

)

11. How many times longer is a kilometer than a centimeter? (100,000 times)

12. How many letters are there in the word "arithmetic"? (10)

Questions for the second

1. Who derived the formula for the roots of a quadratic equation? (Viet)

2. Which curve is the graph of a quadratic function? (parabola)

3. Who said: “Mathematics should be taught later, that she puts her mind in order"?

(Lomonosov)

4. How many days are there in a year? (365 or 366)

5. What is the name of the segment, connecting the apex of the corner with the midpoint of the opposite side

? (median)

6. What is the name of a quadrilateral whose angles are equal in pairs, and are the sides all

equal? (diamond)

7. Two people played chess for 2 hours. How many played each? (2 hours)

8. What is

16

2

? (256)

9. What is the fourth part of a number called? (quarter)

10. What is the smallest Can a number be written using four units? (1111)

11. How many times a kilometer more than a millimeter? (1000000)

12. How many letters are in the word "Mathematics"? (10)

Well done, the warm-up is over, and with what result, jury's word.

3. The next competition "BLACK BOX".

A compass is brought in the black box.

Clues

(80 points) There is a legend about the Greek inventor Daedalus (the master who made the wings

Icarus) and his nephew, a very talented young man who invented the potter's wheel,

the world's first saw and what is in this box. For this he paid his life, because

an envious uncle pushed him off a high city ​​rampart.

WHAT IS IN THE BLACK BOX?

1. (70 points.) The oldest object of this kind has lain in the ground for 2000 years.

2. (60 pts.) Under the ashes of Pompeii, archaeologists have discovered many such objects,

made of bronze. In our country this was first discovered during excavations in

Nizhny Novgorod.

3. (50 points.) For many hundreds of years, the construction of this object practically did not change,

was so perfect.

4. (40 pts.) In Ancient Greece, the ability to use this object was considered the height of perfection

, and the ability to solve problems with with his help - a sign of a high position in

society and a great mind.

5. (30 points) This item is indispensable in architecture and construction.

6. (20 points.) The well-known writer Yuri Karlovich Olesha, author of The Three Fat Men, wrote: “In

lies a velvet bed, tightly squeezing his legs, cold and sparkling. He has a heavy head. I

I intend to pick him up, he suddenly opens up and makes an injection in the hand.

7. (10 points) Needed to transfer dimensions from one drawing to another, for building

equal angles.

8. (0 points.) A riddle was invented about this object: "Two legs agreed to make arcs and circles."

(Answer: compass) slide 2

Teacher's comment (about the compass).

Each of us knows the story of Daedalus and his son Icarus. But few heard that

Daedalus also had a nephew Talos, son of his sister. They had a talent for invention in

blood: a nephew left after his death two rods connected to each other and

able to draw the ideal circle. This was the first circle.

Studying an ancient burial mound in France, archaeologists found an iron tool that was

at least 2 thousand years. The Greek city of Pompeii, buried under the ashes, became

a confirmation of the antiquity of the compasses: under the ashes there are many found these tools,

made of bronze. But also in the territory Russia made similar finds: during

excavations in Novgorod, archaeologists discovered compass - a cutter made of steel. What did they serve

Novgorodians tools? In ancient times in Rus' they were very fond of patterns from the correct

circles, and they applied them with this tool.

It is the architects and civil engineers who are the main users of the tool, without which

nothing can be built. The compass and square are drawing fixtures

which designers work with. Not without them arched buildings would be created,

stained glass windows on temples Middle Ages: at the Cathedral of Our Lady of Paris or the Cathedral of Saint

Vitta - in Prague.

The watch is brought in the black box.

Hints

(80 points) The history of this invention goes back thousands of years. Hardly

someone will take the liberty of naming the inventor. IN in ancient times they were called clepsydras.

WHAT IS IN THE BLACK BOX?

1. (70 points) Almost every one of you has this wonderful thing.

2. (60 pts.) This thing has been constantly improved over the centuries and endured

changes, decreasing in their sizes, becoming unified. At various times, in this

Galileo Galilei, dad Roman, engineer Kulibin.

3. (50 points) At the beginning of the 20th century. His Majesty's court supplier of this important thing was the owner of

a famous family. Years later, his grandson, famous sportsman playing in the NHL, went into

inheritance business.

4. (40 points) This thing does not have a singular number.

5. (30 points.) This is partly sung in the song:

just a moment, hold on to it. There is only a moment

between the past and the future, It is he is called life.

6. (20 points) In mathematics, it is difficult to do without this subject. Especially when solving problems for

movement.

7. (10 points.) This thing is characterized by epithets: solar, water, sand, mechanical,

electronic, waterproof, shockproof.

8. (0 points) The riddle is dedicated to this subject: “All day long mustache move and tell time to recognize

.

(Answer: hours) slide 3

Teacher's comment (about hours)

Pavel Bure, a famous hockey player, took up watch production, and one of the first copies

of his products was presented by B.N. Yeltsin.

It is about the transience of time that is sung in song "There is only a moment."

The very first clock on earth was solar.

Greek philosopher Plato invented the first alarm clock and school bell at the same time,

so that at the right time you can collect their students. The water clock, or clepsydra,

consisted of two vessels. Into the first vessel poured water, flowing out, it displaced the air from

the second vessel; air through the tube rushed to the flute, it began to sound and the children ran to

lesson, having heard a beep.

Then came sand, fire, mechanical watches. Today, apart from the time, the clock may

show month, day, day of the week, pressure, air temperature, can be an alarm clock,

be waterproof, shockproof.

The floor is given by the jury... Total score... explain: for reflection 1 min

1. perpendicularity of a line and planes.

2. parallel line and planes.

slide 4

5. Contest "Do you know him?"

Now let's test the teams' knowledge of the history of mathematics.

For each correct answer - 4 points. The hint "subtracts" 1 point. Each team has 2

questions.

Question 1. Long before our era the need for counting led a person to the concept of the natural number

. Gradually, the mathematicians of Babylon, Egypt, China, Greece, even before our

era laid the foundations of science - number theory. In Russia, the largest representatives of the theory numbers were

Chebyshev, Vinogradov and the person about whom further will be discussed.

Swiss by origin. However, more He lived in Russia for 30 years, where he was elected a member

of the St. Petersburg Academy of Sciences. He's so describes the role of Russia in his work: “His

royal majesty (Frederick II) recently asked where I learned what I know. I,

according to the truth, answered that I owe everything my stay at the St. Petersburg Academy of Sciences.

Name this person.

Hints:

hint 1 His name is associated with the designation of the ratio of the circumference of a circle to its diameter

Clue 2 He wrote the textbook "Complete Introduction" but algebra", following the model which in

further textbooks were written algebra.

What is your answer? slide 5 (Answer: Leonard Euler)

Question 2. From the age of 14, the life of this person was associated with Kazan University. Since the age of 22, he has been teaching at the university

: gives lectures on mathematics, physics, astronomy; in charge of the

observatory, head of the library.

This is what the poet Firsov said about him:

Once, here, on the wide square,

Along this Kazan pavement,

Thoughtful, unhurried, strict,

He was going to lectures - great and lively.

Give the person's first and last name.

Clues:

clue 1 - at the age of 35 he becomes Rector of Kazan University and

has been heading it for 19 years.

Hint 2 - he put forward new geometry, is the creator non-Euclidean geometry,

which in his time almost no one understood.

(Answer: Nikolay Ivanovich Lobachevsky). Slide 6

Question 3. This woman, who lived in the 5th century. before AD, was a professor of philosophy at

Alexandria Museum of the Egyptian city of Alexandria. In his the library had millions of

papyrus scrolls on which were written essays on history and geography, mathematics and

physics, philosophy and poetry. The woman mathematician of antiquity was engaged in mathematical research

and was very eloquent. Her advice was appreciated by both poets and the rulers of the city.

Clue - She lived in Athens for some time, constantly improving her education.

Upon returning home, starts work in the House of Muses, where he teaches mathematics and

philosophy. Poets wrote poems about her. Precisely because she kept the precepts of ancient science, Bishop Kirill hated her

. In 415 In the year

, lured by the bishop, a mob of Christian monks tore this outstanding woman to pieces. Name the first female mathematician.

What are your answers? (Answer: Hyp'atia Alexandria) Slide 7

Last (fourth) "historical" question:

Great need for literate people in military affairs, shipbuilding, in the mining

metallurgical industry led to the creation in Russia, a wide network of

general education and special schools and schools. For this purpose, in 1701, Peter the Great created the "School of Mathematical and Navigational Sciences"

. It was the first school in Russia, in which the main sections of mathematics were taught: arithmetic, algebra, geometry,

planar and spherical trigonometry…

In 1702 in school was assigned to teach arithmetic, geometry and trigonometry

mathematician, who then became a senior teacher and head of school. From 1714 he was instructed

to recruit teachers for the Digital Schools established by Peter I through

throughout Russia. State the name of this person.

Who is this interesting person? Your answer is…

Hint:

His textbook "Arithmetic, that is, numerical science" was published in 1703 in Moscow with a circulation of 2400

books. Mikhail Lomonosov highly appreciated this book and called it "the gate of learning". Lomonosov himself not only studied "Arithmetic", but also knew her by heart.

(Answer: Magnitsky Leonty Filippovich, comments of the jury ...) Slide 8

6. Great people

Teams will need after prompting name the person in question. The faster you are

do it, the better. There will be hints nine. If you guess right after the first clue, you

are awarded 9 points, then, for each subsequent clue, one point is deducted.

Teams answer in turn after each another hint.

/ The first team is offered a story about Archimedes. /

1. The English scientist John Willis said about this man like this: “He laid

the fundamental principles of almost all discoveries, by developing of which our age is proud. (9b)

2. This person owns a popular expression that signifies triumph of reason. (8 b)

3. He was the first to calculate the volume of a ball, the centers of gravity of a triangle, cone, parabola segment and

many others. (7 b)

4. His initial education was led by his father, a mathematician and astronomer Phidias. (6b)

5. One of his remarkable inventions in theoretical mechanics had a machine for

watering fields ("snail screw") (5 b)

6. One of this man's amazing inventions is a mechanical celestial globe -

a kind of planetarium that demonstrated all visible movements of celestial bodies and even phases

of the Moon, carried out with the help of special mechanisms located inside the globe. (4

b)

7. “Kill me, but don’t touch me, O barbarian of these drawings!” - this is the version of the last words of

people. And according to another version, he exclaimed: "Don't spoil my circles!" (3b)

8. An obelisk with engraved ball,

inscribed in a cylinder. (2 b)

9. An original monument was erected to this man with a medal from a concave mirror in

hands. (1 b) Slide 9

/ The second team is offered a story about Sofya Kovalevskaya. /

1. In childhood, relatives and friends called this person "Sparrow" for small stature and

thin figure. (9b)

2. Father - a large nobleman, artillery general. His family comes from the Polish

knight Krukovsky and the daughter of King Matei, patron of the arts and bibliophile. (8 b)

3. Early addicted to reading, this person first got carried away with poetry. At the age of 12, this

man firmly decided to become a poet. But those time with increasing force and

speed, mathematical gift. (7 b)

4. Man, who loved him, spoke of him like this: “Despite his 18 years, the sparrow is excellently educated, knows all languages ​​as his own, and is mainly engaged in mathematics. Works like an ant, from morning to evening. In general, this is a small phenomenon.” (6 b)

5. Him was not allowed to attend lectures at the University of Berlin, but then he became favorite student of the famous mathematician Karl Weierstrass. (5 b)

6. Council University of Göttingen, having considered three scientific works performed by by this

person, recognized them as outstanding and awarded him the academic degrees of Doctor of Philosophy in Mathematics

and Master of Fine Arts with best praise. (4 b)

7. Own the first lecture on the theory of partial differential equations this person, when its

invited to Stockholm University for reading higher mathematics, began like this: “Gentlemen,

among all the sciences that discover for man the path to the knowledge of the signs of nature, the most powerful,

greatest science is mathematics. (3 b)

8. This a person is the first to find a solution to the mathematical description of various points

solid body rotating around a fixed point - a top, a gyroscope, etc. Competitive commission

, after reviewing a dozen and a half works sent to the third competition announced on

Paris Association of Sciences, awarded the prize for work under the motto "Speak, What do you know;

do what you must: let it be, whatever may be” and even decreed increase premium 1.6

times « due to the greater importance results” (2 b)

9. This person, all heartily empathizing with the difficult struggle of the French Communards, he arrived in besieged Paris in

to care for the wounded. (1 b) Slide 10

7. Competition "Dark Horse" In this competition for the correct the answer is 2 points. Slide 11

/ on the sheet we answer with letters, then we hand over the commission /

1. What theorem was called in the old days the bride theorem?

a) Thales' theorem; b) the Pythagorean theorem; c) Vieta's theorem.

2. "Cone" translated from Greek means ...

a) Pine cone; b) spinning top; c) volcano.

3. Correct an octahedron is …

a) a tetrahedron; b) Octahedron; c) icosahedron.

4. What flower named after a woman - mathematician?

a) chrysanthemum; b) hydrangea; V) lily.

/Answer: in the name of the famous French calculator Gort'enzia Lekot (1723 - 1788)

is the name of the flower she brought from India. /

5. "Trapezium" translated from ancient Greek means…

a) the capital; b) sail; c) stairs; d) flat.

6. What the Greek word means "tight string"?

a) hypotenuse; b) leg; c) projection.

7. Quadrillion written with "1"

a) 15 zeros; b) 12 zeros; c) 9 zeros.

8. what the mathematical notation was introduced due to a typographical error.'

a) % sign; b) 3nak V.

9. how many times a kilometer is longer millimeter?

a) 1,000,000,000; b) 1,000,000; c) 1,000,000,000,000.

10. Who suggested the comma after the integer part of the decimal?

a) André Marie Ampère; b) Johann Bernoulli; c) Johannes Kepler.

8. Brainstorm

(Each team has 3 minutes to give as many correct answers as possible.

Command 1:

1. Does the decision equation

2. Solve the equation: 10x=1000

3. In what quarters is the sine positive?

4. Derivative of x

10

5. For what values ​​of x does the expression make sense?

4

1

sin =x

1+x

6. Calculate: sin - cosπ.

7. Calculate

8. Determine the sign of the value functions: sin 190

0

.

9. Which is greater: cos 0

0

or tg 45

0

10. Cube root of numbers 64

Command 2:

1. Is there a triangle with sides 7,8, 14?

2. Solve the equation: 5

x

= 1/25.

3. The area of ​​a square is 36. What is its perimeter?

4. Solve the equation cos x = 5

5. In what quarters is tg x negative?

6. Calculate: sin π + cos

7. Formula for even numbers?

8. Determine the sign of the value functions: sin (-120

°

).

9. Find the derivative functions: y = 6x

6

– 7

10. What is the root of the fifth degrees out of 32

After passing Slide 12

9. Competition "Mathematical compliment" Slide 13

Teams take turns complimenting their opponents using mathematical terms,

for example: “line of the shoulders, oval of the face,..”. Behind each compliment the team receives 3 points.

10. Competition "Book-eater"

From the given words by rearrangement letters, make up the names of famous scientists -

mathematicians. Use the letters completely, without a remainder and additions. For each correct answer

the team receives 20 points. Slide 14

1. OR + TANK

2. MILK + BOP + G

3. SCALP + A

4. CHIMERA+ D

5. KIY + HUMAN + BASS + V

Slide 15

11. Competition of captains "WHO FORWARD"

Captains answer questions. score credited to the first person to answer the question.

Slide 16

1. Statement accepted without proof.

2. Triangle with two equal sides is called...

3. With which instrument can draw a circle

4. How many people played on musical instruments in I. Krylov's fable "Quartet"?

5. The smallest natural number.

6. Line connecting vertex of a triangle with the midpoint of the opposite side.

7. How many seconds are there in three minutes?

8. Football sword shape.

9. How many faces does new hex pencil?

10. Quadratic chart functions?

Summing up the competition, congratulations winners, final word. Slide17

Well, here it is by the end of our game, the winners have been announced. And actually

defeated in our no game, each team showed worthy participation, knowledge of

mathematics, intelligence and ingenuity. I want to thank everyone and everyone for participation and wish

success. Thank you teams for participating. We thank the viewers for support. We thank the jury

for a fair trial.

And in conclusion I would like to say:

Mathematics is everywhere.

You can only look with your eyes

And there are a lot of examples at once

You will find around you.

Goodbye, see you soon!

Extracurricular event for grades 7-8 "Mathematical assault"

GOU "Snezhnyanskaya Special school boarding school No. 42"

Development 9000