Extracurricular activity: "Mathematical Kaleidoscope." Extracurricular activity in mathematics

Natalina Alevtina Vasilievna, teacher, Novouralsk School No. 2, Novouralsk

Extracurricular activity "Mathematical Kaleidoscope"

Direction of spiritual and moral development and education: “Cultivating hard work, a creative attitude to learning, work, life”

Event name: "Mathematical Kaleidoscope"

Age of pupils: 4th grade

Equipment:

video projector;
PowerPoint presentation;
cards with tasks for each team;
applique samples, details, glue stick, album sheet (for each team)

Purpose of the event: to develop a positive attitude towards mathematics

promote the development of creativity and logical thinking of students;
foster feelings of camaraderie and mutual assistance;
improve the ability to rationally plan your activities;
relieve physical and psychological fatigue and stress.

Form of the lesson: game-competition

Progress of the lesson

Hello, dear guests. Let's welcome the young mathematicians who today will show us their mathematical knowledge and skills in the intellectual game "Mathematical Kaleidoscope" (participants, please take your seats).

"The subject of mathematics is such a serious subject that it is good to seize the opportunity to make it a little entertaining." These are the words of the great mathematician Pascal. You will often encounter his name in your further study of mathematics. Today I invite you to an exciting lesson, which we will call “Mathematical Kaleidoscope”.

– What is a kaleidoscope? (A children's toy is a tube with mirror plates and colored glass, which fold into various patterns when turned. A quick change of various phenomena and events).

– Our kaleidoscope will consist of interesting mathematical tasks, jokes, poems about mathematics, which means we will try to complete all tasks... (quickly and correctly).

Our class is divided into two teams “Plus” and “Minus” - representatives from each team come out.

1. Oh, earthly mathematics, be proud of yourself, beautiful.

You are the mother of all sciences and they value you.

2. Your calculations majestically lead ships to the planets,

Not for holiday fun, but for the pride of the Earth!

3. We glorify the mind of man, the works of his magical hands,

The hope of this century, the queen of all earthly sciences!

4. But to turn on the green light for the game

We need to give all the guys this advice:

Eyes become big from fear.

It is impossible to catch fish without difficulty

Knowledge will always help!

Remember that knowledge and work

Our difficulties will crush everything!

5. Now we ask everyone to stand up.

We ask you to take the Olympian oath!

The class stands up.

6. It is impossible to live in the world without mathematics.

We swear to love her!

Class in chorus: “We swear!”

7. Fight for the truth to the end,

Without sparing your belly!

Class in chorus: “We swear!”

8. Don’t be afraid of difficulties along the way,

Pass all the tests with dignity!

Class in chorus: “We swear!”

9. So, friends, it’s time for us to hit the road!

Try not to turn off the difficult road!

So that everything in the game goes without a hitch,

We will start it, of course, ... (with a warm-up!)

The first competition is Warm-up.

Proverbs: (I read out the first part of the proverb, and the participants show the number of the card under which its continuation is located. For each correct answer - a token.)

To seven troubles... the answer. (No. 3)
One head is good, but... better. (No. 1)
Measure seven times -...cut once. (No. 3)
Where two fools fight, there...they watch. (No. 4)
If you cut down one tree, then plant it. (No. 5)
One is plowing, and... they are waving their arms. (No. 2)
Whoever helped quickly... helped. (No. 1)

As quickly as possible, in each row, underline all the numbers that are multiples of the one at the end of the line:

answer

two,

twice

seven,

seven

one

three,

three

ten

Second competition: "In the land of numbers"

– A long time ago, many thousands of years ago, our distant ancestors lived in small tribes. Primitive people, just like modern small children, did not know counting. But children are taught to count by their parents and teachers. And primitive people had no one to learn from. Their teacher was life itself. Therefore, training went slowly. Life required learning to count. To get food, people had to hunt large animals: elk, bear. Our ancestors hunted in large groups, sometimes with the entire tribe. For the hunt to be successful, it was necessary to be able to surround the animal. Usually the elder placed two hunters behind the bear’s den, four with spears on the other side of the den, three on one side and three on the other side of the den. To do this, he had to be able to count, and since the name of numbers did not yet exist, he showed the number on his fingers.

Speech by group commanders:

Traces of counting on fingers have been preserved in many countries. At first there were special names for numbers only for one and two. Numbers greater than two were named using addition. In Ancient Egypt, the numbers of the first ten were written with the corresponding number of sticks.
The method of writing numbers in just a few signs (ten), which is now accepted throughout the world, was created in Ancient India. The Indian counting system then spread throughout Europe, and the numbers were called Arabic. But it would be more correct to call them Indian.
Man lives in a world of numbers. The child is born, and with it comes his date of birth. Everyone has their own home. It also has a number attached to it.
And sometimes our lives depend on numbers. For example, at 7 years old it’s time to go to school, at 14 it’s time to get a passport, at 18 you have the right to vote in elections, at 55 or 60 you have the right to retire.
Numbers make you happy and sad. Our mood depends on “2” or “5”.

- Guess what this number is? (for the correct answer 1 token)

Small, tailed, doesn’t bark, doesn’t bite, and won’t let you from class to class? (2)
What kind of figure is an acrobat? If it stands on its head, will it become exactly 3 less? (9)
Two rings, but without end, if I turn around, I won’t change at all. (8)

– And now the tasks for each team. On a piece of paper, within a certain time, write words containing the numbers 3 - for the plus team, 100 - for the minus team. For each word, the team receives a token. (Tights, erase, trilogy, Patricia, trillion, stroke, triton, table, haystack, dining room, feast, groan, capital, pillar, dentist, carpenter.)

“Training reaction speed” Each team has a card with mathematical operations. After completing these calculations, you can read the word you came up with.

3. Next competition "Mathematical puzzles"

(needle, knife)

(matches, iron)

4. Next competition "In the Land of Geometry"

1. Without end and edge,

The line is straight!

Walk along it for at least a hundred years -

You won't find the end of the road!

2. Once the line is straight

Came for my birthday

But for some reason I'm sad

In a terrible mood

The birthday girl nodded:

“I want to congratulate you,

Happy birthday!

My gift is very personal

It is limited on both sides -

Cutting myself out

And I give it to you lovingly!

Take it, catch it.

And call it a segment!”

3. Beam to beam was connected,

The top was fixed at the point.

So blunt, straight and sharp

It’s easy for us to build a corner!

– What geometric figures did you listen to the poem about? What other geometric shapes can you name?

– Count how many triangles (slide)

Today we tried to prove that man lives in a world of numbers. Books, songs, school subjects cannot do without numbers. And we cannot live without songs and books. This means we cannot live without mathematics.

Reflection

Each team has kaleidoscopes, open them and see what lies there (Faces). Now everyone take a face and draw a mouth, if you liked the tasks, then a smiling mouth, if not, then a straight mouth. Discuss.

We count the tokens. Rewarding. Well done everyone today!

Slide 2

I.MATHEMATICAL WARM-UP

Slide 3

CROSSWORD

Slide 4

II.IN THE WORLD OF NUMBERS

Slide 5

Task No. 1

After seven washes, the measurements of a piece of soap shaped like a rectangular parallelepiped decreased by 2 times. How many more washes will the remaining bar of soap last?

Slide 6

Task No. 2

What two numbers does the expression end with: 1*2*3*…*13? Answer: two zeros, because the product has factors of 2, 5 and 10.

Slide 7

Task No. 3

What number does the sum end with: Answer: 0.

Slide 8

Task No. 4

Kittens and goslings together have 44 legs and 17 heads. How many kittens and how many goslings? Answer: 5 kittens and 12 goslings.

Slide 9

Problem #5

Place the numbers 3, 4, 5, 6, 8, 9 in a square so that the total in horizontal, vertical rows and diagonals is 21. Answer:

Slide 10

III.MATHEMATICAL HEAVY WEIGHTS

Slide 11

Task No. 1

The vessel has the shape of a parallelepiped. How, without making any measurements and having no other containers, can you fill exactly half the volume of this vessel with water? Answer: tilt the parallelepiped so that the water level is along the diagonal section of the parallelepiped.

Slide 12

Task No. 2

Is there such a circle that its area and circumference are expressed by the same number? Answer: yes. If r=2, then S = π* r2, S = 4* π C = 2 * π * r, C = 4* π

Slide 13

Task No. 3

Of the 38 students, 28 attend the choir and 17 attend the ski section. How many skiers are in choir if there are no students in the class who are not in choir or ski club? Answer: 7 people. The choir is not attended by 10 people, they are all skiers. There are only 17 skiers. This means that 7 people must be “taken” from the choir.

Slide 14

Task No. 4

Two families went for a walk at the same time from the same place. Both families drove the same distances in cars and returned home at the same time. They rested along the way. The first family was on the road (traveling) twice as long as the second. The second was on the road (traveling) three times longer than the first one was resting. Which of these families drove the car faster? Solution: First family: 2 hours - time for driving, y hours - time for rest. Second family: 3y hours - time for driving, xhours - time for rest. We get: 2x + y = 3y + x x = 2y. Those. The second family vacationed 2 times more than the first. So she was going faster than the first.

Slide 15

IV. ANSWER QUESTIONS

Slide 16

1. What are two lines in a plane that do not intersect called? 1. Parallel 2. What is 1/3600 of an hour called? 2. Second 3. What is the name of the result of addition? 3. Amount

Slide 17

4. What is the volume of one 1 kg of water? 4. 1 liter 6. Can the sum of four consecutive natural numbers be a prime number? 6. No, it is divisible by 2 5. What geometric shapes are friendly with the sun? 5. Rays

Slide 18

7. 3 chickens will lay 3 eggs in 3 days. How many eggs will 9 chickens lay in 9 days? 7. 27 eggs 9. Smallest natural number? 9. 1 8. What is the difference between a number and a figure? 8. Number 10, many numbers

Slide 19

10. The hundredth part of a number is..? 10. Percentage 11. What do the equation and the plant have? 12. How many tens do you get if you multiply 2 tens by 4 tens? 11. Root 12. 80

Slide 20

13. Calculate: |-3.5 - 4.6|. 13. 8.1 15. What is the name of a fraction whose numerator is less than its denominator? 15. Correct 14. Which lines intersect at right angles? 14. Perpendicular

Slide 21

16. Surplus when finding a quotient is..? 16. Remainder 17. How many integers are there on the coordinate line between the numbers -4.1 and 12.9? 18. What is the name of the place where the digit appears in the notation of a number? 17. 17 18. Discharge

Slide 22

19. How many three-digit numbers can be made using the numbers 0, 5, 7? Each number can be used 1 time. 19. Four numbers 20. Draw two straight lines. On one of them 3 dots were marked, and on the other 5 dots. There are 7 points in total. Show in the picture how it happened? 21. How many times does the number 9 appear when writing numbers from 1 to 100? 21. 20 times 20.

Slide 23

V. FUN TASKS

Slide 24

1) In a tailoring workshop, 20 m were cut from a piece of cloth 200 m apart every day, starting from March 1. What date was the last piece cut? 1) March 9 Two diggers. 2) Two diggers dug a 2 m ditch in 2 hours of work. How many diggers does it take to dig 100 m of the same ditch in 100 hours?

Slide 25

3) To dress my sons warmly, two socks are missing. How many sons are there in a family if there are six socks in the house? 3) 4 sons. 4) One gray mouse 4) Vasya has 100 mice, some of them are white, some are gray. It is known that at least one mouse is gray, and out of every pair of mice at least one is white. How many gray mice does Vasya have?

Slide 26

5) Olya, her mother, grandmother and a doll are sitting on the bench. The grandmother sits next to her granddaughter, but not next to the doll. The doll does not sit next to its mother. Who sits next to mom? 5) Grandmother (doll - granddaughter - grandmother - mother) 6) 2: 4 * 6 = 3 * 3: 3 6) Place arithmetic signs and parentheses where you think necessary to get the correct equality. 2 4 6 = 3 3 3

When is Pi Day celebrated?
Pi has two unofficial holidays. The first one is March 14th because
this day in America is written as 3.14. The second is July 22, which is
in European format 22/7 is written, and the value of such a fraction is
a fairly popular approximate value of Pi.
What kind of drill can be used to drill a square hole?
The Reuleaux triangle is a geometric figure formed by the intersection
three equal circles of radius a with centers at the vertices of an equilateral
triangle with side a. A drill made on the basis of a Reuleaux triangle,
allows you to drill square holes (with an accuracy of 2%).
Who solved a difficult math problem by treating it as homework?

American mathematician George Danzig, while a graduate student at the university,
I was late for class one day and mistook the equations written on the board for homework.
exercise. It seemed more difficult to him than usual, but after a few days he was able
execute it. It turned out that he solved two “unsolvable” problems in
statistics that many scientists have struggled with.
What mathematician learned the basics of science from the wallpaper in his room?
Sofya Kovalevskaya became acquainted with mathematics in early childhood, when she
the room did not have enough wallpaper, instead of which sheets of lectures were pasted
Ostrogradsky on differential and integral calculus.
Where did they try to legally round the number Pi?
In Indiana in 1897, a bill was passed that legislated
setting the value of Pi to 3.2. This bill did not become law
thanks to the timely intervention of a university professor.

Rene Descartes (15961650)
French mathematician and philosopher. At the beginning of the Thirteen Years' War
served in the army. Later he settled in the Netherlands and, in solitude, began
science. At the invitation of the Swedish Queen he moved to Stockholm.
Laid the foundations of analytical geometry, gave the concept of force impulse, derived
law of conservation of momentum, created the coordinate method
(Cartesian coordinates). Descartes' curved ovals are known. At the heart of it
philosophy dualism of soul and body.
Blaise Pascal (16231662)
French mathematician, physicist, philosopher, writer. Born into a lawyer's family,
doing mathematics. He showed mathematical abilities early.
He has a treatise “An Experience on Conic Sections. Designed a summing
car. Has works on number theory, arithmetic, and probability theory.
I found a general algorithm for finding signs of divisibility of numbers. It has
treatise on the Arithmetic Triangle.
Leonhard Euler (17071783)

The greatest mathematician of the 18th century. Born in Switzerland. Lived for many years
and worked in Russia, member of the St. Petersburg Academy of Sciences. Enormous scientific
Euler's legacy includes brilliant results related to
mathematical analysis, geometry, number theory, variational
calculus, mechanics and other applications of mathematics.
His
They say
what in a three year old
his father with
10 years old) teacher
While he was dictating
task, from Gauss
written: 101*50=5050
Carl Gauss (17771855)
Mathematical talent manifested itself already in childhood.
age, he surprised those around him by correcting his calculations
masons. Once at school (Gauss was at that time
asked the class to add up all the numbers from one to one hundred.
the answer was already ready. On his slate was
Sofya Vasilievna Kovalevskaya
(18501891)
There was not enough wallpaper to cover the rooms, so the walls of the room were covered with sheets
lithographed lectures by M. V. Ostrogradsky on mathematical analysis.
Subsequently, she became the first woman mathematician, Ph.D. To her
belongs to the novel "Nihilist".
SQUARE
Parallelogram brother,
I'm called Square,
Rhombu is a close relative,
All areas are owned by the owner.
Triangle needs
"Pythagorean pants"
They are not knitted or sewn,
They make up of squares!
The circle is round, so what?!
Doesn't he look like me?
Only the area you will take
You will find a square in the formula!
STRAIGHT
Forward! Back! And not a step to the side
This is the most important principle of Direct.
Directness is needed here, courage is needed,
So as not to suddenly change yourself.
Every small schoolchild knows me
It was not in vain that this verse was composed,
After all, any polygon consists
From my little pieces.
Here is a bisector, a ray, a segment, a chord,
Diagonals... you can’t count them all.
My rays, segments... I know for sure
That my directness is definitely in them!
And if you, even for a moment,
You'll make me lose my head
If you want to change my direction...
I will become broken, but not crooked!

PARALLEL DIRECT
CORNER
Everyone knows these lines.
Keeping the direction
They run away together
To infinity from me.
We meet them often
It is impossible to name everything:
A pair of rails near the tram,
There are as many as five in the staff...
Even if there are many lines,
Do not mix one with the other:
They are very strict
Distance between each other.
Parallel Direct
Nice, polite people:
None of them are others
Will never cross it out.
We just find the angle
Here you just need a ruler.
We put a point, we move the beam
That's it, the side is ready.
And now this line
Turn around at the top
And from that peak of the meta
Extend the second ray.
It's very easy to use a protractor
We will measure your angle.
It is unfolded and sharp,
Convex, straight, blunt...
Having assessed Angle's nature,
We'll tell everyone a secret,
What's on the plane of a figure
It couldn't have been simpler.

Math kaleidoscope

Extracurricular activity

in mathematics for students

7 - 9 grades

Compiled by: Mytsykova E. N.

Event plan :

Blitz tournament.

Relay race.

Captains competition.

Problems from a barrel.

Mathematical kaleidoscope.

Pantomime competition.

Working with spectators:

(held between competitions, during breaks)

Decor:

Poster on the wall: “He who walks can master the road, but he who thinks mathematics can master it.”

Teams must prepare a team name, motto, and emblem in advance. The composition of the team can be of different ages, with the same distribution of students from different classes among the teams. The optimal number of people in a team is 6.

Blitz tournament.

(1 team)

A segment connecting a point on a circle to its center (radius).

Graph of a quadratic function (parabola).

A segment connecting the vertex of a triangle to the middle of the opposite side (median).

The ratio of the opposite side to the hypotenuse (sine).

An angle less than 90 degrees (acute).

How many numbers do you know? (10)

One hundredth of a number (percentage).

A device for measuring angles (protractor).

Smallest prime number.(2).

What part of an hour is 15 minutes? (1\4)

What is greater than 2 m or 201 cm? (201)

How many centimeters is 1% of a liter? (1 cm).

What is a hundredth of a meter called? (cm)

The result of addition (sum).

How many years are there in one century? (100).

(2nd team)

1. A segment connecting any two points on a circle (chord).

2. A statement that does not require proof (axiom).

3. Graph of a linear function (straight line).

4. A rhombus in which all angles are right (square).

5. The sum of the lengths of the sides of a polygon (perimeter).

6. What is the name of the result of subtraction? (difference).

7. Largest two-digit number (99).

8. A device for constructing a circle (compass).

9. What part of a minute is 20 seconds? (1\3)

10. What is greater than 2 dm or 23 cm? (23 cm).

11. Name the smallest natural number (1).

12. Find 10% of a ton (100 kg).

13. What is the hundredth part of a ruble called? (kopeck).

14. The diameter of the circle is 8 m, the radius is...? (4 m).

15. How many divisors does the number 43 have? (this is a prime number, 1 and 43)

Mathematical kaleidoscope.

Leading: Well, now, teams, stop!

Math kaleidoscope!

Who does not know the difficulty in terms,

He will write everything now without delay.

Exercise : Write mathematical terms, concepts, words related to mathematics using the given letters. (“P” and “S”)

Pantomime competition.

Using gestures and facial expressions, depict:

"adjacent angles" and "vertical angles".

Complete your task, guess the task of the opposing team.

Relay race.

Sheets with tasks are attached to the board, students, one by one, must run to the board, solve the proposed task and return back to the team. The speed and accuracy of completing tasks is taken into account.

1 . Underline the numbers that are divisible by the number written below

32, 36, 43, 54, 48, 13, 8, 24, 5, 36, 11,

10, 17, 21, 23, 30. 60,26, 100, 25.

3 4

2. y=kx , x=3,y=6 y=kx , x=3, k=2

k =? y=?

3 . Calculate:

2 2 2 2

111 – 11 = 19 – 9 =

4. From the given numbers, underline three numbers whose sum is equal to the number written below

3, 1, 9, 15, 20,7, 6. 11, 3, 7, 4, 17

31 2

5. Calculate:

2 2 2 2

36 – 2*36*16 + 16 25 + 2*25*15 + 15

6. S – path, t – time V – speed, t - time

V = ? S = ?

Troubles from a barrel

Teams take turns pulling out lotto barrels with task numbers and answering questions; you can give time to think about the answer.

Petya and Misha have the last names Belov and Chernov. What surname does each of the guys have if Petya is a year older than Belov? (Petya Ch., Misha B.)

What time is it now if the rest of the day is twice as long as the past? (8 hours)

Everyone knows that two squared is four, three squared is nine, and what is the angle in a square? (90 degrees)

A magnifying glass gives a magnification of four times, i.e., four times the magnification. What would be the 25 degree angle viewed through this lens? (25 degrees)

What should the next two numbers be in the sequence 10, 8, 11, 9, 12, 10, 13,... (14, 11)

What number must you divide two by to get four? (1\2)

What sign must be placed between the numbers two and three to make a number greater than two but less than three. (2.3)

How much is one and a half thirds of a kilometer? (half a kilometer)

Captains competition.

Leading: How a song cannot live without a button accordion,

The team cannot live without a captain!

Captains take turns naming literary works whose titles begin with numbers, for example, 3, 20, 7, 18, 1000.

The captains are shown a jar containing sweets. Players must judge by eye how many there are. The one who named the most accurate number receives candy as a reward and a point for the team.

Who will answer questions faster?

A pair of horses ran 40 km. How many kilometers did each horse run? (40)

Quickly count how many fingers there are on both hands; on 10 hands? (50)

One egg is boiled for 4 minutes. How many minutes should you boil 5 eggs? (4 minutes)

How many tens do you get if you multiply two tens by three tens? (60)

The area of the square is 100 sq.m. What is its perimeter? (40)

The father of one citizen is called Nikolai Petrovich, and the son of this citizen is Alexey Vladimirovich. What is this citizen's name? (Vladimir Nikolayevich)

Questions for fans.

The number 606 is written. What action must be performed to increase it by one and a half times? (turn over)

You entered a dark room. You only have one match in the box. In the room there is a candle, a kerosene lamp, and a stove ready to be lit. What will you light first? (match)

Where on earth is the longest day? (same everywhere)

Three light bulbs were on, one was turned off. How many light bulbs are left? (3)

A brick weighs 2 kg and another half brick. How much does a brick weigh? (4 kg)

You are probably familiar with I. A. Krylov’s fable “The Wolf and the Lamb.” The author states: “The powerful are always to blame for the powerless: we hear countless examples of this in history.” What number occurs and what meaning does it have? (Darkness. 10,000, a hundred hundreds, a lot, an unimaginable multitude)

Which word is missing?

Speed, time, path, area, meter, second;

Hectare, weaving, meter;

Yard, ton, hundredweight;

Cone, square, prism;

Triangle, rectangle, rhombus;

Straight line, segment, angle.

Fan competition.

Leading: Number, how much is in this sound

For math, friends!

But also in simple, ordinary life

We can't do anything without numbers.

Numbers invade our every day: get up at 7 o’clock, take the 2nd bus, be there by 9 o’clock. We are all accustomed to such things and do not attach much importance to it, but this was not always the case: ancient people considered numbers to be a special code and often gave them a fairy-tale and mythical meaning. For example, “7” was considered a magical, lucky number (7 colors of the rainbow, 7 tones of music); “13” is, on the contrary, an unlucky number (the devil’s dozen); “2” underlies the oppositions (life - death, cold - hot, day - night). The number “3” acquired the meaning of sacred. The ancient Pythagoreans considered it perfect, because it has a beginning and an end, and they denoted it in the form of a triangle.

So, our competition is about numbers, and it is a competition for fans.

Leading: Now we have a competition for the fans.

Let them show their wits and class.

The teams will support theirs with at least a point.

After all, they shouldn’t lag behind the teams.

I propose to name you, dear fans, lines from songs, proverbs, poems, fairy tales that contain numbers