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1 Methodical manual "Entertaining mental counting" Chirkova Valentina Vasilievna, Honorary worker of general education of the Russian Federation, teacher of mathematics at GBOU SShI 68, Pavlovsk

3 In the fifth or sixth grades, it is very important not only to give children a solid knowledge of the principles of mathematics, but also not to scare away schoolchildren with the cold severity of the queen of sciences, to captivate them with this subject. Well-developed oral counting skills among students are one of the conditions for their successful education in high school. Mathematics teachers need to pay attention to mental counting from the very moment when students move to it from elementary school. It is in the fifth and sixth grades that we lay the foundations for teaching mathematics to our students. If we do not teach to count during this period, we ourselves will experience difficulties in the future in our work, and we will doom our students to constant offensive mistakes. To interest children, it is necessary to select a variety of tasks designed for both weak children and the strongest. These can be tasks of a computational nature, solving puzzles, tasks for attention, geometric tasks. To achieve the correctness and fluency of oral calculations during the entire period of study in elementary school, in each lesson, it is necessary to allocate 7-10 minutes for exercises in oral calculations. Oral exercises should be carried out not only regularly, but also in a certain sequence, which is determined by the primary school curriculum. Oral exercises are important not only because they activate the mental activity of students, but also because they play an educational role in learning - they discipline students, teach children patience and the ability to wait for lagging comrades, to help them.

4 Oral counting helps the teacher, firstly, to switch the student from one type of activity to another, secondly, to prepare students for studying a new topic, and thirdly, a task for repeating and summarizing the material covered can be included in the oral counting. By instilling a love for oral exercises, the teacher will help students to actively work with educational material, encourage them to strive to improve methods of computing and solving problems, replacing less rational ones with more economical ones. And this is the most important condition for the conscious assimilation of the material. The focus of the student's mental activity on the search for rational ways to solve the problem indicates the variability of thinking.

5 Come on, pencils aside. No bones. No pens. No chalk. Verbal counting! We do this work Only by the power of the mind and soul. The numbers converge somewhere in the darkness, And the eyes begin to glow, And all around are only smart faces, Because we count in the mind. V. Berestov

6 Calculate: 25 *4:20 *9-15:6

7 Find the missing numbers: a) b)

8 Restore the calculation chain: : 3 * 12-15

9 Restore the calculation chain: * 5: : 25:

10 Restore the calculation chain: * : 15: * 5: 2

11 Restore the calculation chain: *6-16: 15: 2 *

12 A) Restore the chain of calculations: : * + *. * + * : * B) 60 * : 80 * 30

13 : * *8

14 Calculate: + 38: *

15 Calculate: * 14:

16 Calculate: * 20 *

17 Calculate the sum of the answers of all chains: 72:8 +51:15 * :7 *5-13:8 * :9 +33:8 * :6 *7 +17: :9 +41:5 *7-17

18 "Circular" examples The result of one example is the beginning of the next * :

19 Find the roots of the equations: 1) X + 17 = 60 2) a 51 = 60 3) 60 = a) c 43 = 81 5) 62 = 100 y 6) 59 + X = 59 7) 78 a = 78 8) a + 45 = 45 9) X 0 = 82 10) 70 s = 68

20 Calculate the sum of the answers of all chains: 15*6:18 * : * :7 * : 23 * :8 *11 +22

21 For the expressions in the left column, find a pair from the right column: 55x + 3x -4 (5 + y) * 4 4a * 3 2a-a + 7a 12y-7y-2 4x * 6 * 2 9 * x * 5 8a 4x 45x 48x 8x y 12a 5y-2 3y

22 Calculate: = = 45*17+55*17 = = 50*76*2 = 79*34 69*34 =

23 Porcupine as a gift to his son Made a calculating machine. Unfortunately, it is not accurate enough. The results are in front of you We will quickly fix everything ourselves = = = = = 625

24 Calculate the sum of the answers of all chains: 8 2:4 +56:18 * *2:6 * *3:150 * :7 4 3:8 *9 +19:13 * *8:40 * :30

25 Insert missing "+" or "-" signs instead of "?": + *? = +?* - = -? * + = + - *? = +? * - = + - * + =? -*-=? +*? =-? * + = - + * + =? - *? = - + * - =?

26 Determine the sign of the product: 1) + * -* - * + * - * + * + * - 2) - * - * - * + * + * + * - * - 3) - * - * + * - * + * -* - 4) - * + * + *+ * - * + * - *-

27 Calculate: (-6) 5 (- 6) -5 + (-6) (- 5) -6 (- 5) 6 + (- 5) 5 + (- 6)

28 Determining the topic of the lesson Be careful, my friend, We begin the lesson. You have to decide again, guess, count. Mathematical charade: The preposition is at my beginning. At the end is a country house. And we all decided the whole Both at the blackboard and at the table.

29 Having solved all the examples, you can read the topic of the lesson 81:9 S 15*3 S 17-9 R 44*0 R 13*1 C 63:63 L 96*100 b 300:10 O 15*0 P 32:32 R 17*10 M 90:10 I A I L C U

30 You will read the topic of the lesson if you find the meanings of the expressions and insert the letters into the table 480:6 O 12*10 L 34:34 W E 18*0 M 51*2 And 75*1 N 14*6 B

31 Solve the equations and fill in the table s+13 M

32 Solve the crossword puzzle: Horizontally: Vertically you will read 1. The sum of the lengths of the sides of the polygon. key word of the topic. 2. Part of a straight line bounded by one point. 3.Component of the multiplication action. 4. Equality containing an unknown number. 5. The result of division.

33 Solve the equations and fill in 23*11 E 6*10 AND 77:1 O 61:61 A 400:10 L 47*9 D table 1313:13 H 1236:6 C 84:6 T 105:5 K 8*125 M

34 Solve the crossword puzzle: Horizontally: Vertically you will read 1. The sum of the lengths of the sides of a geometric figure. keyword. 2. A tool for measuring the length of a segment. 3. A rule written in letters. 4. Traveled path. 5. Arithmetic action.

35 Solve the mathematical charade, and name the topic of the lesson. The first one we find, we calculate, We know many formulas for it. On the second - rallies, parades, We are always happy to walk along it.

36 Find the meaning of the expressions and arrange the answers in descending order 15 * 11 A 24 * 83 Z 0 * 17 And 125 * 8 K 25 * 9 * 4 M 520:10 O 64:32 L 51:17 O 40 * 60 T 1000: 125 D

37 Solve the mathematical charade The first preposition. Second summer house. And the whole is difficult to solve. Everyone learns the first at school. Well, the second one is shot from a double-barreled shotgun. The third will be performed for us by two drums Or heels will beat it zealously.

38 Guess the riddle: He has known me for a long time. Every corner is right. All four sides are the same length.

39 Solve the examples and fill in the table 431.2 0.687 1.4 6.22 0.34 14.24 1.7

40 Solve the crossword puzzle: Horizontally: Vertically you will read 1. A tool for measuring the length of a segment. keyword. 2. Hundredth of a number. 3. Unit of mass. 4. Unit of time.

41 Solve the examples and fill in the table 5% of 600 And ¾ of 120 A 67 * 11 O 51.5: 5 C 0.8 * 7 P 9-0.99 T 12.8 + 7.02 R 4: 0.8 H 8.01 19.3 5.82 8.82

42 Find the roots of the equations, arrange them in ascending order and read the word 6.8x=13.6 6.5x+3.5x=40 0.01x=5 9x-1.8=7.2 4.2x-0.2x \u003d 20.4 x: 0.1 \u003d 60 7.5 x \u003d 0 15-3 x \u003d 5.1 3 x + 2 x = 15.5 A A A I M M D R G

43 Solve the crossword puzzle: Horizontally: Vertically you will read 1. It can be straight, curved and broken. keyword. 2. Part of the plane, bounded by a circle. 3. A tool for constructing a circle. 4. A quadrilateral with all right angles. 5. A segment connecting any two points of the circle. 6. Two radii. 7.Unit of length.

44 This is not an easy thing to count Triangles very quickly and skillfully. For example, in this figure How many are different? Consider. All carefully explore And on the edge and inside. A) B)

45 Guys, I invite you to a logical problem. Having solved it, you will know Success and good luck. a) How many squares do you see in the drawing? B)

46 How many segments do you see on the drawing? How many triangles?

47 How many rectangles do you see in the drawing? How many triangles do you see in the drawing?

48 How many triangles do you see in the drawing?

49 How many triangles do you see in the drawing?

50 Count the triangles: A) B)

51 How many triangles are in the picture? A) B)

52 What part of the square is shaded?

53 What geometric figure is missing in this picture? Choose the correct answer: A. Circle. B. Square. B. Triangle. G. Rectangle. D. All figures are there.

54 How many triangles are there?

55 How many rectangles are there?

56 We do not need to own a blade, We are not looking for loud fame. He wins who is familiar With the art of thinking, subtle. G. Wordsworth

57 Mathematical puzzles A) B)

58 Solve the puzzles: A) B) C) D) E) F) G) H)

59 Solve the puzzles: A) B) C) (Mountainous country) D)

60 Solve puzzles: A) B), a 3 C) D)

61 Solve the puzzles: A) B) E) C) D)

62 Solve the puzzles: A) B) C) D) D) E)

63 Tasks for the development of logical thinking In order to avoid offensive failures in mathematics, We will solve a series of Logical tasks with you. A chocolate bar costs a ruble and another half a chocolate bar. How much does a chocolate bar cost? How many times will a two-digit number increase if the same number is assigned to it on the right? The professor goes to bed at 8 o'clock in the evening and sets the alarm for 9 o'clock in the morning. How many hours will the professor sleep?

64 Solve the logic problem: A ship is standing near the shore with a rope ladder launched into the water. The stairs have 10 steps. The distance between the steps is 20 cm. The lowest step touches the surface of the water. The ocean is very calm today, but the tide begins, which raises the water by 15 cm per hour. How long will it take for the third step of the rope ladder to be covered with water?

65 Solve logical problems: How many tens do you get if two tens are multiplied by two tens? How much will it turn out if fifty is cut into half? One and a half fish cost 15 rubles. How much do 5 fish weigh? Instead of adding 27, Vasya subtracted 27. How much does his result differ from the correct one?

66 Solve logical problems: Kolya opened the book and found that the sum of the numbers of the left and right pages is 25. What is the product of these numbers? A bug is 6 times heavier than a cat, a mouse is 20 times lighter than a cat, a turnip is 720 times heavier than a mouse. How many times heavier is a turnip than a bug? The sum of the ages of the three friends is 29 years. How long will they be together in 5 years?

67 Solve logical problems: Baba Yaga brews a magic potion: to 1.5 kg of honey she added 100 g of crushed wolf claws, 100 g of tar and 300 g of kikimora tears. How many percent of kikimora's tears does the brew contain? A.20% B.17% C.16% D.15% E.6% My mother's birthday is on Sunday this year. What day of the week will dad's birthday be this year if dad is 55 days younger than mom? A. Sunday B. Wednesday C. Monday D. Saturday E. Friday

68 Solve logic problems: Librarians ask: “If 60 sheets of a book are 1 cm thick, what is the thickness of the book if it has 360 pages?” Canteen workers ask: “There are 3 apples left, 4 halves, 8 quarters. How many apples are left? An old man asks: “If he lives another half of what he lived, and one more year, then he will be 100 years old. How old is he now?

69 Solve the logic problems: A biology teacher asks, “A grasshopper ran a certain distance in 28 minutes. In how many minutes will a rabbit run 4 times the distance if its speed is 7 times the speed of a grasshopper? Question from the workers: “It is required to cut a log into 6 parts, each cut takes 2.5 minutes. How long does it take to complete this job? The watchmaker asks: “How many times faster does the end of the minute hand move than the end of the hour hand?”

70 Solve logical problems: Question from a literature teacher: “What number has as many numbers as letters in its name?” There are two fathers and two sons in one family. How many people is this? The striking clock strikes one beat in one second. How long does it take the clock to strike 12 o'clock? How much is three times forty and five? If tomorrow were yesterday, then there would be as many days left until Sunday as there were days from Sunday to yesterday. Name this day.

71 Solve logic problems: Two fathers and two sons carried three oranges. How much did each carry? The parents have six sons and each of them has a sister. How many children are in the family? A heron weighs 10 kg on one leg. And for two? Three people waited for the train for 3 hours. How long did each one wait? The rope was cut into 5 pieces. How many incisions were made? How many ends does a stick have? Have six sticks? Six and a half sticks?

72 Solve logical problems: Birds flew over the river: a dove, a pike, two tits, two swifts and five ruffs. How many birds? Answer quickly. 10 ducks flew. Two were killed. How much is left? There are 10 fingers on two hands. How many fingers are on 10 hands? How many nuts are in an empty glass? How many ends do 4 pencils have? What about four and a half? Two went 5 mushrooms found. Four will go, will they find many mushrooms?

73 Solve logic problems: If 2 roosters crow with all their might, then the person will wake up. How many roosters must crow to wake up 4 people? One girl wrote: "Two hundred and forty and two hundred and forty will be four hundred and forty." She wasn't wrong, but what's the matter? Hungry and well-fed elephants together eat 240 kg of grass in 3 hours. A well-fed eats 5 kg in 12 minutes. How much grass does a hungry elephant eat in an hour? A goose costs 20 rubles. and as much as half a goose costs. How much is a goose?

74 Solve logic problems: What is the female name consists of 30 pronouns? Which word has 100 negatives? The name of which bird consists of four dozen identical letters? In the name of which article of clothing is the English number 2 heard? In the name of which number is the name of the smaller number heard? Which aristocratic profession has a number in its name? In the name of which sport can you hear the English word?

75 Solve logical problems: What is the word, 100 identical letters of which can be found in the meadow? While walking through the forest, Masha found a mushroom every 40m. How far did she go from the first mushroom to the last, if she found 20 mushrooms in total?

76 Solve a logical problem: Three piglets Nif-nif, Nuf-nuf and Naf-naf were born one after the other after 4 years. The oldest of them is now 5 times older than the youngest. How old is the youngest pig?

77 Solve logical problems: Place 8 kids and 10 geese in 5 barns so that each barn contains both kids and geese, and the number of their legs is 10. An athlete jumps from a springboard into the water: first, the springboard throws him up 1 meter, then it flies down 6 meters and, emerging, rises 2 meters to the surface. How high was the springboard above the water? The boy replaced each letter of his name with the serial number of this letter in the Russian alphabet. It turned out the number What was the name of the boy?

78 Solve logic problems: If the red dragon had 6 more heads than the green one, then they would have 34 heads for two. But red has 6 goals less than green. How many heads does a red dragon have? Winnie the Pooh bought 12 jars of honey for his birthday and invited Piglet to visit. It is known that Piglet eats honey 2 times slower than Winnie the Pooh. After 2 hours, all the honey was eaten. How many jars of honey did Piglet eat?

79 Solve logic problems: In the dark Olya saw 6 pairs of cat's eyes. How many legs do these cats have? A square with a side of 6 cm was bent from a piece of wire. Then the wire was unbent and a triangle with equal sides was bent from it. What is the length of the side of the resulting triangle? Winnie the Pooh was given a keg of honey weighing 7 kg for his birthday. When he ate half of the honey, the mass of the barrel with the remains of honey became 4 kg. What is the mass of the barrel?

80 Solve logic problems: There are 15 plums in the basket. The hostess put a third of the plums into the compote. How many plums are in compote? 5 candles burned, two extinguished, how many candles are left? How many zeros will be at the end of the product of all digits? In which case the sum of two numbers is equal to the summand? When we look at 2 and say 10? Soft-boiled egg is boiled for 2 minutes. How long does it take to boil 5 eggs?

81 Solve logic problems: A first grade student lives on the 10th floor, but gets to the 7th, and then walks. Why? Two fathers and two sons bought 3 oranges. Divided so that everyone got an orange. How could this happen? The table top has 4 corners. One of them was sawn off. How much is left? The smallest natural number? How many plays are in P.I. Tchaikovsky? What number was called "darkness" in ancient times?

82 Solve logic problems: There are 10 spokes in a wheel. How many spaces between the spokes? What was the last number introduced into mathematics? A snail climbs up a tree 10 meters high. During the day it rises by 5 meters, and at night it drops by 4 meters. In how many days will she reach the top? How many edges does an unsharpened hex pencil have? How many years did Ilya Muromets sit on the stove?

83 Solve the logic problems: Lilies grew on the lake, and every day their number doubled. On the 20th day the lake was completely overgrown. On what day was half of the lake overgrown? Three horses ran 15 km in 1 hour. How fast was each horse running? How much do you get if 20 is divided by half? You are an airplane pilot. The plane flies to London via Paris. The flight altitude is 8 thousand meters, the temperature overboard is minus 40 degrees, the average speed is 900 km/h. How old is the pilot?

84 Solve logic problems: The motorcycle was going to the village. He was hit by 3 cars and a truck. How many cars were going to the village? If a chicken stands on one leg, it weighs 2 kg. How much will she weigh if she stands up on two legs? If it rains at 12 o'clock at night; then can it be that in 72 hours there will be sunny weather?

85 Solve logic problems: There were 4 apples on the table. One apple cut in half. How many apples are left on the table? 4 birches grew. Each has 4 large branches. Which big branch has 4 small ones. Each small branch has 4 apples. How many apples are there? The room has 4 corners. There is a cat in every corner. Opposite each cat are 3 cats. Each cat has one cat on its tail. How many cats are in the room. How to form a triangle on the table with only one stick?

86 Solve a logical problem: What weighs more 1 kg of cotton wool or 1 kg of iron?

87 Solve logical problems: From Moscow to St. Petersburg, the plane flies 1 hour 20 minutes. And from St. Petersburg to Moscow 80 minutes. Why is this happening? The school has 400 students. How can one prove, without looking at documents, without interviewing children or their parents, that among the students of the school there are at least 2 people who have the same date and month of birth? The two played chess for 2 hours. How many hours did each play?

88 Solve logic problems: A train left Moscow for St. Petersburg at a speed of 60 km/h. At the same time, another train left St. Petersburg for Moscow to meet him at a speed of 50 km/h. Which of the trains will be further from Moscow at the time of their meeting?

90 References: 1) Mathematics. Grade 5: lesson developments according to the textbook by N.Ya. Vilenkina and others / comp. Z.S. Stromov, O.V. Pozharskaya. Volgograd: Teacher, p. 2) Lesson development in mathematics: 5th grade / comp. L.P. Popova. M.: VAKO, p. 3) Lesson development in mathematics: grade 6 / comp. V.V. Vygovskaya. M.: VAKO, p. 4) Journals "Mathematics" 1. M .: S M .: S M .: S M .: S M .: S M .: S. 9, 14, 20, M .: S M .: S M .: S M.: S M.: S. 5.

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Oral counting grade 1-2

Godlevskaya Natalya Borisovna, student of group Sh-31, Yeysk Pedagogical College
Description of work: This collection will be useful for primary school teachers to conduct oral counting in grades 1 and 2. Many tasks can be used in grades 3-4, complicating them accordingly, adding the necessary examples.

Tasks for oral counting in grade 1.

1. Russell tenants.
Target: consolidation of knowledge about the composition of the number.
This is a number house. There are two apartments on each floor. The owner of the house lives in the triangle. As many residents can live on one floor as the number indicates - the owner of the house. Your task is to resettle the tenants.

2. Unlucky mathematician.
Target: consolidation of computational methods of addition and subtraction;

2+3=_ 3+_=4 _+8=9 4+_=7 4_3=1
_-4=4 7-_=2 9+_=9 _-6=3 7+_=1
9_2=7 5+_=9 2+_=5 3_5=8 3_3=0

A little to the side, maple leaves cut out of colored paper with numbers and signs written on them (2, 8, 10.9, +) and a drawing of a bear cub are pinned. The children are offered a situation: the bear cub solved the examples and wrote down the answers on maple leaves. The wind blew and the leaves scattered. Mishutka was very upset: what should he do now?
It is necessary to help the bear cub return the leaves with the answers to their places.

You can use this task on the slide. It is very convenient to return the necessary sheets with answers to their place with a click
3. Kick the ball into the basket.
Target:
Drawings with basketball baskets and numbers on them are hung on the board. Task: come up with as many examples as possible, the answer to which is the number above the basket.

4. Decipher the word.
Target: consolidation of computational methods of addition and subtraction. Solve examples. Unscramble the word by arranging the answers in ascending order.
4+3= and 7-2-1= n 3-2+6= and 7+0+1-4=4 s
6-2= W 5-4+1= O 5+1+2= M 4-1+6-7=2 O
2+6=e 4-1-2=c 9-3-3=c 7-5+1+3=6 i
10-4= n 2+2+2= e 8-5+1= n 2+3+4-8=1 p
7-4= o 3+4-2= c 4+3-2= a 9-9+5-0=5 i
10-5=e 4-3+2=l 6+2-7=y 6-4+6-5=3s
5-3= l (Sun) (Umnitsa) (Russia)
9-8= with
(Addition)
5. Tasks in poetic form.
Target: development of oral counting skills within 20. Tasks are read aloud by the teacher.
Five baby bears
Mom put me to bed.
One can't sleep
How many sleep well?
(5-1=4)
The heron walked on the water,
I was looking for frogs.
Two hid in the grass
Six - under the bump.
How many frogs survived?
Just for sure!
(2+6=8)
There are seven grasshoppers in the choir
Songs were sung.
Soon two grasshoppers
Lost voice.
Count without further ado
How many voices are in the choir?
(7-2=5)
The hedgehog went mushrooming
Found ten redheads.
Eight put in a basket,
The rest are on the back.
How many redheads are you bringing
On their needles hedgehog?
(10-8=2)
What started to rumble like that?
The hives are built by our bear.
Hive made it only seven-
Two less than expected.
How many hives did the bear want to make?
(7+2=9)

When solving more complex problems (in two steps), you can put up cards with numbers sounded in verses. And the children put signs of action on their own.

The wind blew - the leaf was torn off
And another one fell
And then five fell.
Who can count them?
(1+1+5=7)
They are in my back.
Two honey agaric, five oil,
A pair of ruddy saffron milk caps,
How many mushrooms guys?
(2+5+2=9)
Ants live together
And they do not scurry about without work.
Two carry a blade of grass
Three carry a blade of grass
Five carry needles.
How many ants are under the tree?
(2+3+5=10)
The puppy ran into the chicken coop,
Dispersed all the roosters.
Three flew up to the roost,
And one got into the tub,
Two - through the open window.
How many were there in total?
(3+1+2=6)
I have them on the shelf
Two green frogs
Two bears and a mouse
And a wonderful cuckoo.
And there is an elephant
And a puppy with a stitched ear
pink pig
With a red button on the belly.
And now I want to listen:
How many toys do I have?
(2+2+2+1+1+1+1=10)
Tired of our Lenochka
Read according to the syllables of the word.
Our girl has become
In the courtyard of the crows count:
One sits on a tree
Another one looks out the window
Three sit on the roof
To hear everything!
So tell me how many birds
Did our student count?
(1+1+3=5)
Loved by the kids
Adventure books.
I read a dozen Kohl,
Two books less - Olya,
Count, kids
All books read.
(10+8=18)
There were seven passengers in the Gazik
Four people got off at the bus station.
Two people boarded the bus at the station.
How many people were on that bus?
(7-4+2=5)
6. Tasks for the development of logical thinking.
Target:
Ivan Tsarevich rode on a horse to Koshcheevo's kingdom. Three heroes galloped towards him on horseback. How many horses galloped in Koshcheevo's kingdom? (1)
Kai and Gerda built snow fortresses at the same time, but Gerda started building before Kai. Who worked faster? (Kai)
Dasha and Masha got fives at school: one in mathematics, the other in literature. In what subject did Dasha get an A if Masha did not get this grade in mathematics? (Dasha in mathematics, Masha in literature)
Piero, Malvina and Pinocchio hid from Karabas Barabas in the house of Papa Carlo. One is under the bed, the other is in the closet, and the third is in the stove. It is known that Pinocchio did not climb into the stove, Malvina did not hide under the bed and in the stove. Who hid where? (Malvina in the closet, Pinocchio under the bed, Pierrot in the stove)
On Monday, Dunno drew one shorty, on Tuesday - two, on Wednesday - three, and so on until the end of the week. How many shorties did Dunno draw on Sunday? (7)

A notebook is cheaper than a pen, but more expensive than a pencil. What is cheaper? (pencil)
Yura and Petya approached the river. The boat, on which you can cross, can accommodate one person. And yet, without outside help, the guys crossed on this boat. How did they do it? (the guys approached the left and right banks of the same river.)
7. Tasks-jokes.
Target: development of critical and logical thinking.
Three boys, Kolya, Petya and Misha, went to the store. On the way they found 3 rubles. How much money would Misha find alone if he went to the store? (3 rubles)
3 comrades went to school for classes on the second shift and met two more comrades - students of the first shift. How many comrades went to school in total? (3 comrades)
7 candles were lit, 2 of them went out. How many candles are left? (2 candles)
What is heavier - a kilogram of cotton wool or a kilogram of iron? (same)
There were 7 brothers, each brother had one sister. How many people walked? (8 people)
How many nuts are in an empty glass? (not at all)
If you eat one plum, what is left? (bone)

Tasks for oral counting in grade 2.

1. Unlucky mathematician.(as in 1st grade)
Target: consolidation of computational methods of addition and subtraction; multiplication and division.
Examples with missing numbers and signs are written on the board:
66+21=_ 33_3=11 100_9=900 47_12=59
54_15=69 4_3=12 56_8=48 66_1=66
_+34=76 43-_=89 78+12=_ _+13=15
2. Labyrinth.
Target: consolidation of computational methods of addition and subtraction.
Students must pass through the two gates of the labyrinth in such a way that the value of the sum is 13.

3. Solve the puzzle.
Target: consolidation of computational methods of addition and subtraction, development of logical thinking.
_ _ - _ = 8
There are several possible answers to the rebus:
10 – 2 = 8
11 – 3 = 8
12 – 4 = 8
13 – 5 = 8
14 – 6 = 8
15 – 7 = 8
16 – 8 = 8
17 – 9 = 8
4. Circular examples.
Target: strengthening the skills of subtraction and addition of round numbers.
Examples are selected so that the number resulting from one of them is the beginning of another. The answer of the last example coincides with the beginning of the first.

5. Connect the numbers with their sum of bit terms.
Target: fixing the bit composition of two-digit numbers.
36 40 + 8
63 80 + 4
48 30 + 6
84 60 + 3
6. Connect expressions with the same values ​​without calculating.
Target: consolidation of knowledge about the commutative property of addition.
7 + 6 9 + 6
9 + 8 8 + 3
5 + 7 6 + 7
6 + 9 8 + 9
3 + 8 7 + 5
6. Read only the examples with answer 50.
Target: fixing actions on round numbers;
20 + 30 80 – 40
20 + 20 70 – 20
10 + 40 90 – 30
60 – 20 40 + 10
30 + 20 70 – 30
40 + 20 90 – 40
7. Tasks for comparison.
Target:
1. How are the numbers similar?
a) 7 and 71;
b) 77 and 17;
c) 31, 38, 345;
d) 24, 54, 624;
e) 5 and 15;
f) 12 and 21;
g) 20 and 40;
h) 333 and 444.
2. How are the numbers similar and how are they different?
a) 5 and 50;
b) 17 and 170;
c) 201 and 2010;
d) 8 and 800;
e) 14, 16, 20, 24.
3. Compare numbers:
a) 26 and 4;
b) 31 and 48.
4. Compare figures:
a) a triangle and a quadrilateral;
b) circle and square;
c) rectangle and square;
d) rectangle and rhombus.
8. Mathematical expressions.
Target: to develop the ability to find similarities or differences in objects according to essential or non-essential features.
1. Mathematical expressions are given: 3 + 4 and 1 + 6
Compare them to each other.
Answer:
1) the same sign of the action (addition);
2) the first terms are less than the second;
3) the first terms are odd numbers, and the second ones are even;
4) each expression has two terms;
5) the results of addition are the same.
2. Mathematical expressions are given, compare them with each other.
a) 7 - 2 and 9 - 4;
b) 15:3 and 25:5;
c) 5 6 and 15 2.
9. Comparison of numbers and figures.
Target: to develop the ability to find similarities or differences in objects according to essential or non-essential features.
1. Name a group of numbers in one word:
a) 2, 4, 7, 9, 6;
b) 12, 18, 25, 33, 48, 57;
c) 231, 564, 872, 954.
2. Name a group of numbers in one word:
a) 2, 4, 8, 12, 44, 56;
b) 1, 13, 77, 83, 95.
3. Name a group of objects in one word:
a) triangle, square, circle;
b) square, rectangle, rhombus.
10. Tasks for finding an extra number.
Target: to develop the ability to find similarities or differences in objects according to essential or non-essential features.
1. Numbers are given: 1, 10, 6.

For example:
1) 1 may be superfluous, since it is an odd number, and 6 and 10 are even;
2) 10 may be superfluous, since it is two-digit, and 1 and 6 are single-digit;
3) 6 may be superfluous, since a unit is used to write the numbers 1 and 10.
2. Numbers 6, 18, 81 are given.
By combining two numbers in pairs, answer which number is superfluous.
For example:
1) 6 is superfluous, since it is single-digit, and 18 and 81 are two-digit;
2) 81 is superfluous, since it is odd, and 6 and 18 are even;
3) 6 is superfluous, since the numbers 1 and 8 are used to write 18 and 81;
4) 81 is superfluous, since the numbers 6 and 18 are divisible by 2 and 6 (that is, they have common divisors);
5) 6 is superfluous, since the numbers 18 and 81 are divisible by 9 (they have a common divisor).
3. Numbers are given: 48, 24, 9.
By combining two numbers in pairs, answer which number is superfluous.
4. Numbers are given: 25, 5 36.
By combining two numbers in pairs, answer which number is superfluous.
5. From a series of numbers or mathematical concepts, select four that have a common property. The fifth element does not have this property.
a) 4, 6, 8, 7, 35;
b) 2, 44, 22, 8, 9;
c) 3, 5, 44, 7, 13;
d) 300, 35, 44, 37, 29;
e) square, rhombus, rectangle, triangle, circle;
f) ray, rhombus, square, polygon, rectangle;
g) sum, difference, product, term, quotient;
h) term, divisor, subtrahend, sum, dividend.
11. Puzzles.
Target: development of logical thinking, oral speech.
You 3, 100 l, 3 tone, 100 lb, 2 l each, from 3 zhka, 100 faces, mustache 3 tsa, my 100 vay, 3 cotage, for 100 leagues, sm 3 t, geome 3 I, ses 3 tsa, 1 stock, r 1 ka, about 100, with 3 f, about 5, for 100 th, for 1 ka, 1 number, 100 p, 2 jester, pa 3 from, car 3 j.
12. Tasks that develop logical thinking.
Target: development of observation, abstract thinking.
1. Continue the rows of numbers to the right and left (if possible), establishing a pattern in the notation of numbers:
a) ...5, 7, 9, ...;
b) …5, 6, 9, 10, …;
c) ...21, 17, 13, ...;
d) …6, 12, 18, …;
e) ...6, 12, 24, ...;
f) 0, 1, 4, 5, 8, 9, ...;
g) 0, 1, 4, 9, 16, ...;
Answers:
a) 1, 3, 5, 7, 9, 11, 13, 15, ...;
b) 1, 2, 5, 6, 9, 10, 13, 14, 17, ...;
c) 29, 25, 21, 17, 13, 9, 5, 1;
d) 0, 6, 12, 18, 24, 30, 36, 42, ...;
e) 3, 6, 12, 24, 48, 96, 192, ...;
f) 0, 1, 4, 5, 8, 9, 12, 13, 16, 17, ...;
g) 0, 1, 4, 9, 16, 25, 36, 49, ...;
2. Series of numbers are given. It is necessary to notice the peculiarity of the compilation of each row and write down the following 4 numbers in it:
a) 6, 9, 12, 15, 18, 21, ...;
b) 5, 10, 15, 20, 25, 30, ...;
c) 3, 7, 11, 15, 19, 23, ...;
d) 16, 12, 15, 11, 14, 10, ...;
e) 25, 24, 22, 21, 19, 18, ...;
Answers:
a) 24, 27, 30, 33;
b) 35, 40, 45, 50;
c) 27, 31, 35, 39;
d) 13, 9, 12, 8;
e) 16, 15, 13, 12.
13. Logic tasks
Target: development of logical thinking, attention, memory
A sliced ​​loaf and a pack of sugar weigh more than the same loaf and a box of chocolates. What weighs more - sugar or candy? (a pack of sugar weighs more than a box of chocolates)
How many times do you need to cut it in order to divide a rope 10 cm long into pieces of 2 cm each? (4 times)

In mental counting, as elsewhere, there are tricks, and in order to learn how to count faster, you need to know these tricks and be able to put them into practice.

Today we will do this!

1. How to quickly add and subtract numbers

Consider three random examples:

1. 25 – 7 =
2. 34 – 8 =
3. 77 – 9 =

Type 25 - 7 = (20 + 5) - (5- 2) = 20 - 2 = (10 + 10) - 2 = 10 + 8 = 18

Agree that such operations are difficult to turn in your head.

But there is an easier way:

25 - 7 \u003d 25 - 10 + 3, since -7 \u003d -10 + 3

It's much easier to subtract 10 from 10 and add 3 than it is to do complex calculations.

Let's go back to our examples:

1. 25 – 7 =
2. 34 – 8 =
3. 77 – 9 =

Optimizing subtracted numbers:

1. Subtract 7 = subtract 10 add 3
2. Subtract 8 = subtract 10 add 2
3. Subtract 9 = subtract 10 add 1

In total we get:

1. 25 – 10 + 3 =
2. 34 – 10 + 2 =
3. 77 – 10 + 1 =

Now it's much more interesting and easier!

Now count the examples below in this way:

1. 91 – 7 =
2. 23 – 6 =
3. 24 – 5 =
4. 46 – 8 =
5. 13 – 7 =
6. 64 – 6 =
7. 72 – 19 =
8. 83 – 56 =
9. 47 – 29 =

2. How to quickly multiply by 4, 8 and 16

In the case of multiplication, we also break numbers into simpler ones, for example:

If you remember the multiplication table, then everything is simple. And if not?

Then you need to simplify the operation:

We put the largest number first, and decompose the second into simpler ones:

8 * 4 = 8 * 2 * 2 = ?

It is much easier to double numbers than to quadruple or eight them.

We get:

8 * 4 = 8 * 2 * 2 = 16 * 2 = 32

Examples of decomposing numbers into simpler ones:

1. 4 = 2*2
2. 8 = 2*2 *2
3. 16 = 22 * 2 2

Practice this with the following examples:

1. 3 * 8 =
2. 6 * 4 =
3. 5 * 16 =
4. 7 * 8 =
5. 9 * 4 =
6. 8 * 16 =

3. Divide a number by 5

Let's take the following examples:

1. 780 / 5 = ?
2. 565 / 5 = ?
3. 235 / 5 = ?

Division and multiplication with the number 5 is always very simple and pleasant, because five is half of ten.

And how to solve them quickly?

1. 780 / 10 * 2 = 78 * 2 = 156
2. 565 /10 * 2 = 56,5 * 2 = 113
3. 235 / 10 * 2 = 23,5 *2 = 47

In order to work out this method, solve the following examples:

1. 300 / 5 =
2. 120 / 5 =
3. 495 / 5 =
4. 145 / 5 =
5. 990 / 5 =
6. 555 / 5 =
7. 350 / 5 =
8. 760 / 5 =
9. 865 / 5 =
10. 1270 / 5 =
11. 2425 / 5 =
12. 9425 / 5 =

4. Multiplication by single digits

Multiplication is a little more difficult, but not much, how would you solve the following examples?

1. 56 * 3 = ?
2. 122 * 7 = ?
3. 523 * 6 = ?

Without special counters, solving them is not very pleasant, but thanks to the Divide and Conquer method, we can count them much faster:

1. 56 * 3 = (50 + 6)3 = 50 3 + 6*3 = ?
2. 122 * 7 = (100 + 20 + 2)7 = 100 7 + 207 + 2 7 = ?
3. 523 * 6 = (500 + 20 + 3)6 = 500 6 + 206 + 3 6 =?

We just have to multiply single-digit numbers, some of them with zeros, and add the results.

To work through this technique, solve the following examples:

1. 123 * 4 =
2. 236 * 3 =
3. 154 * 4 =
4. 490 * 2 =
5. 145 * 5 =
6. 990 * 3 =
7. 555 * 5 =
8. 433 * 7 =
9. 132 * 9 =
10. 766 * 2 =
11. 865 * 5 =
12. 1270 * 4 =
13. 2425 * 3 =

Divisibility of a number by 2, 3, 4, 5, 6 and 9

Check the numbers: 523, 221, 232

A number is divisible by 3 if the sum of its digits is divisible by 3.

For example, let's take the number 732 and represent it as 7 + 3 + 2 = 12. 12 is divisible by 3, which means that the number 372 is divisible by 3.

Check which of the following numbers are divisible by 3:

12, 24, 71, 63, 234, 124, 123, 444, 2422, 4243, 53253, 4234, 657, 9754

A number is divisible by 4 if the number consisting of its last two digits is divisible by 4.

For example, 1729. The last two digits form 20, which is divisible by 4.

Check which of the following numbers are divisible by 4:

20, 24, 16, 34, 54, 45, 64, 124, 2024, 3056, 5432, 6872, 9865, 1242, 2354

A number is divisible by 5 if its last digit is 0 or 5.

Check which of the following numbers are divisible by 5 (the easiest exercise):

3, 5, 10, 15, 21, 23, 56, 25, 40, 655, 720, 4032, 14340, 42343, 2340, 243240

A number is divisible by 6 if it is divisible by both 2 and 3.

Check which of the following numbers are divisible by 6:

22, 36, 72, 12, 34, 24, 16, 26, 122, 76, 86, 56, 46, 126, 124

A number is divisible by 9 if the sum of its digits is divisible by 9.

For example, let's take the number 6732 and represent it as 6 + 7 + 3 + 2 = 18. 18 is divisible by 9, which means that the number 6732 is divisible by 9.

Check which of the following numbers are divisible by 9:

9, 16, 18, 21, 26, 29, 81, 63, 45, 27, 127, 99, 399, 699, 299, 49

Game "Fast Addition"

1. Speeds up mental counting
2. Trains attention
3. Develops creative thinking

An excellent simulator for the development of fast counting. A 4x4 table is given on the screen, and numbers are shown above it. The largest number you need to collect in the table. To do this, click on two numbers with the mouse, the sum of which is equal to this number. For example, 15+10 = 25.

Game "Quick Score"

The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer "yes" or "no" to the question "are there 5 identical fruits?". Follow your goal, and this game will help you with this.

Game "Guess the operation"

The game "Guess the operation" develops thinking and memory. The main essence of the game is to choose a mathematical sign so that the equality is true. Examples are given on the screen, look carefully and put the desired “+” or “-” sign so that the equality is true. The sign "+" and "-" are located at the bottom of the picture, select the desired sign and click on the desired button. If you answer correctly, you score points and continue playing.

Game "Simplify"

The game "Simplify" develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and continue playing.

Task for today

Solve all the examples and practice for at least 10 minutes in the Quick Addition game.

It is very important to work out all the tasks of this lesson. The better you perform the tasks, the more you will benefit. If you feel that there are not enough tasks for you, you can make up examples for yourself and solve them and train in mathematical educational games.

The lesson is taken from the course "Oral counting in 30 days"

Learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even take roots. I will teach you how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

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Knowing the psychology of money and how to work with them makes a person a millionaire. 80% of people with an increase in income take out more loans, becoming even poorer. Self-made millionaires, on the other hand, will make millions again in 3-5 years if they start from scratch. This course teaches how to properly distribute income and reduce costs, motivates you to learn and achieve goals, teaches you how to invest and recognize a scam.

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Bibliographic description: Vladimirov A. I., Mikhailova V. V., Shmeleva S. P. Interesting ways of fast counting // Young scientist. - 2016. - No. 6.1. - S. 15-17..04.2019).



Introduction

Mental counting is gymnastics for the mind. Mental counting is the oldest way of calculating. Mastering computational skills develops memory and helps to assimilate subjects of the natural and mathematical cycle.

There are many ways to simplify arithmetic operations. Knowledge of simplified calculation techniques is especially important in cases where the calculator does not have tables and a calculator at his disposal.

We want to dwell on the methods of addition, subtraction, multiplication, division, for the production of which it is enough to count or use a pen and paper.

The motivation for choosing the topic was the desire to continue the formation of computational skills, the ability to quickly and clearly find the result of mathematical operations.

The rules and techniques of calculations do not depend on whether they are performed in writing or orally. However, mastering the skills of oral calculations is of great value not because they are used more often in everyday life than written calculations. This is also important because they speed up written calculations, gain experience in rational calculations, and give a gain in computational work.

In mathematics lessons, we have to do a lot of oral calculations, and when the teacher showed us the method of fast multiplication by the numbers 11, we had an idea if there were still methods of fast calculation. We set ourselves the task of finding and testing other methods of fast calculation.

b) to do well in school; (sixteen%)

c) to decide quickly; (sixteen%)

d) to be literate; (52%)

2. List, when studying, which school subjects you will need to count correctly ?

a) mathematics; (80%)

b) physics; (fifteen%)

c) chemistry; (5%)

d) technology;

e) music;

3. Do you know how to count quickly?

a) yes, a lot;

b) yes, a few (85%);

c) no, I don't know (15%).

4. Do you use fast counting techniques in calculations?

b) no (85%)

5. Would you like to learn quick counting techniques to quickly count?

b) no (8%).

They say that if you want to learn how to swim, you must enter the water, and if you want to be able to solve problems, you must start solving them. But first you need to master the basics of arithmetic. You can learn to count quickly, count in your mind only with a great desire and systematic training in solving problems.

But the methods of fast mental counting have been known for a long time. The excellent mental arithmetic abilities of such brilliant mathematicians as Gauss, von Neumann, Euler or Wallis are a real delight. Much has been written about this. We want to tell and show some well-known computational secrets. And then a completely different math will open before you. Lively, useful and understandable.

1. Methods for fast multiplication

1. COUNTING ON FINGERS

A way to quickly multiply numbers within the first ten by 9.

Let's say we need to multiply 7 by 9.

Let's turn our hands with palms facing us and bend the seventh finger (starting to count from the thumb to the left).

The number of fingers to the left of the bent one will be equal to tens, and to the right - units of the desired product.

Rice. 1. Finger counting

2. MULTIPLICATION OF NUMBERS FROM 10 TO 20

It is very easy to multiply such numbers.

To one of the numbers it is necessary to add the number of units of the other, multiply by 10 and add the product of units of numbers.

Example 1. 16∙18=(16+8) ∙ 10+6 ∙ 8=288, or

Example 2. 17 ∙ 17=(17+7) ∙ 10+7 ∙ 7=289.

Task: Multiply quickly 19 ∙ 13. Answer 19 ∙13=(19+3) ∙10 +9 ∙3=247.

3. MULTIPLY BY 11

To multiply a two-digit number whose sum of digits does not exceed 10 by 11, you need to move the digits of this number apart and put the sum of these digits between them.

72 ∙ 11 = 7 (7 + 2) 2 = 792;

35 ∙ 11 = 3 (3 + 5) 5 = 385.

To multiply by 11 a two-digit number whose sum of digits is 10 or more than 10, you must mentally push the digits of this number, put the sum of these digits between them, and then add one to the first digit, and leave the second and last (third) unchanged.

Example .

94 ∙ 11 = 9 (9 + 4) 4 = 9 (13) 4 = (9 + 1) 34 = 1034.

Task: Multiply quickly 54 ∙ 11 (594)

Task: Multiply quickly 67∙ 11 (737)

4. MULTIPLYING BY 22, 33, ..., 99

To multiply a two-digit number by 22, 33, ..., 99, this multiplier must be represented as a product of a single-digit number (from 2 to 9) by 11, that is, 44 \u003d 4 11; 55 = 5 ∙ 11 etc. Then multiply the product of the first numbers by 11.

Example 1. 24 ∙ 22 = 24 ∙ 2 ∙ 11 = 48 ∙ 11 = 528

Example 2. 23 ∙ 33 = 23 ∙ 3 ∙ 11= 69 ∙ 11 = 759

Task: Multiply 18∙44

5. MULTIPLY BY 5, BY 50, BY 25, BY 125

When multiplying by these numbers, you can use the following expressions:

a ∙ 5=a ∙ 10:2 a ∙ 50=a ∙ 100:2

a ∙ 25=a ∙ 100:4 a ∙ 125=a ∙ 1000:8

Example1. 17 ∙ 5=17 ∙ 10:2=170:2=85

Example 2. 43 ∙ 50=43 ∙ 100:2=4300:2=2150

Example 3. 27 ∙ 25=27 ∙ 100:4=2700:4=675

Example 4. 96 ∙ 125=96:8 ∙ 1000=12 ∙ 1000=12000

Task: multiply 824∙25

Task: multiply 348∙50

&2. Ways to quickly divide

1. DIVISION BY 5, BY 50, BY 25

When dividing by 5, by 50, by 25, you can use the following expressions:

a:5= a ∙ 2:10 a:50=a ∙ 2:100

a:25=a ∙ 4:100

35:5=35 ∙ 2:10=70:10=7

3750:50=3750 ∙ 2:100=7500:100=75

6400:25=6400 ∙ 4:100=25600:100=256

&3. Ways to quickly add and subtract natural numbers.

If one of the terms is increased by several units, then the same number of units must be subtracted from the resulting amount.

Example. 785+963=785+(963+7)-7=785+970-7= 1748

If one of the terms is increased by several units, and the second is reduced by the same number of units, then the sum will not change.

Example. 762+639=(762+8)+(639-8)=770 + 631=1401

If the subtrahend is reduced by several units and the minuend is increased by the same number of units, then the difference will not change.

Example. 529-435=(529-5)-(435+5)=524-440=84

Conclusion

There are ways to quickly add, subtract, multiply, divide, exponentiate. We have considered only a few ways to quickly count.

All the methods of mental calculation we have considered speak of the long-standing interest of scientists and ordinary people in playing with numbers. Using some of these methods in the classroom or at home, you can develop the speed of calculations, achieve success in the study of all school subjects.

Multiplication without a calculator is a training of memory and mathematical thinking. Computer technology is improving to this day, but any machine does what people put into it, and we have learned some tricks of mental counting that will help us in life.

We were interested in working on the project. So far, we have only studied and analyzed the already known methods of fast counting.

But who knows, perhaps in the future we ourselves will be able to discover new ways of fast computing.

Literature:

1. Arutyunyan E., Levitas G. Entertaining Mathematics. - M .: AST - PRESS, 1999. - 368 p.
2. Gardner M. Mathematical miracles and secrets. - M., 1978.
3. Glazer G.I. History of mathematics at school. - M., 1981.
4. "First of September" Mathematics No. 3 (15), 2007.
5. Tatarchenko T.D. Methods for quick counting in the classroom, "Mathematics at School", 2008, No. 7, p.68.
6. Oral account / Comp. P.M. Kamaev. - M .: Chistye Prudy, 2007 - Library "First of September", series "Mathematics". Issue. 3(15).
7. http://portfolio.1september.ru/subject.php

Well-developed oral counting skills among students are one of the conditions for their successful education in high school. Mathematics teachers need to pay attention to mental counting from the very moment when students move to it from elementary school. It is in the fifth and sixth grades that we lay the foundations for teaching mathematics to our students. If we don’t teach counting during this period, we ourselves will experience difficulties in the future in our work, and we will condemn our students to constant insulting mistakes.

Mastering the skills of oral calculations is of great educational, educational and practical importance. They help to learn many questions of the theory of arithmetic operations, help to better master the techniques of written calculations, and the speed and accuracy of calculations are necessary in life. Oral calculations contribute to the development of thinking, ingenuity, mathematical vigilance, observation, initiative, etc. In addition, during oral exercises, students are preparing for work in the classroom, in particular, for the perception of new material, as well as the systematic repetition of what has been learned.

In the arsenal of every teacher, there are many types of exercises for oral counting. However, all this diversity comes down to finding the values ​​of mathematical expressions, comparing numbers and mathematical expressions, solving equations and problems. The main task of the teacher is to create such conditions, to conduct oral counting in such a way that the students themselves carefully follow each other's answers, and the teacher is not so much a controller as a leader who comes up with more and more interesting tasks.

In order for the skills of oral calculations to be constantly improved, it is necessary to establish the correct balance in the use of oral and written methods of calculation, namely: to calculate in writing only when it is difficult to calculate orally. Oral exercises should permeate the entire lesson. They can be combined with homework checks; focus on consolidating and working out the current material. It is necessary to include tasks with elements of creativity (for example, to prepare for the perception of new material), as well as developmental exercises (including non-standard tasks, logical, entertaining, quick wit exercises).

At each lesson, you can specifically set aside 5-7 minutes for oral calculations. Assignments should correspond to the topic and purpose of the lesson. Depending on this, the teacher determines the place of oral counting in the lesson. If the exercises are intended to repeat the previously covered material, to form computational skills and prepare for the study of new material, they are carried out at the beginning of the lesson. If the purpose of the exercises is to consolidate what has been learned in the lesson, then the oral count is carried out after studying the new material. It should not be done at the end of the lesson, as the children are already tired.

The number of exercises should be such that their performance does not overwork the children and does not exceed the time allotted for this lesson. I always conduct mental counting in such a way that the guys start with an easy one, and then gradually take on more and more difficult calculations. If you immediately bring down difficult oral tasks on students, then the guys will discover their own impotence, they will be confused, and their initiative will be suppressed.

It is quite easy for a modern teacher to organize the oral work of students. Firstly, within each topic of any textbook there are always a number of tasks for oral calculations. These tasks are convenient to use at the warm-up stage before getting acquainted with a new topic or at the stage of reviewing the material.

Secondly, the use of printed notebooks, where there are tasks that can be performed orally, leaving empty spaces for notes without attention.

Thirdly, the use of multimedia tools, which, unfortunately, is not always possible. Modern children with a computer on "you", and the perception of information in this form is familiar and understandable to them. Therefore, in this matter, it remains to be hoped that the modernization of schools will be faster and teachers will be able to fully use ICT. After all, multimedia tools help to solve the whole range of educational, developmental and educational tasks quickly and efficiently, since the perception of information is at a high emotional level, there is an effect of surprise, and surprise necessarily generates interest, interest stimulates cognitive initiative, one’s own motivation for learning is born, and therefore, quality improves. learning.

Fourth, of course, the work of the teacher himself. In order to apply the method, technique, and even any type of activity in the classroom, it is necessary to take into account the characteristics of the personality of the students, the team, the circumstances of the real life environment and the characteristics of the teacher himself.

I try to make mental counting perceived by students as an interesting game. Carried out in the form of a game, in the form of a competition, oral counting contributes to the creation of positive emotions in children, helps to effectively acquire knowledge, and forms an interest in mathematics.

Games for conducting oral counting.

"Guess the conceived example"

Examples are written on the board. The teacher names the answer of one of them, and the students must find the intended example according to his answer. In this case, students solve all or almost all examples to find the right one. The game can be played orally: students should have cards with numbers of examples that they will raise at the request of the teacher, or in the form of a test.

"Move a comma"

This exercise is used when fixing the actions of multiplying and dividing decimal fractions into bit units. 5-7 people come to the board, each receives a card with numbers from 1 to 9 and a moving comma. At the request of the teacher, the children set a comma between the indicated numbers. The teacher calls an example, and the students move the comma to the right or left by a certain number of places. For example, the teacher dictates: “Place a comma between '4' and '5'. Multiply the resulting number by 100. The guys move the comma two places to the right and demonstrate the result. Pupils sitting at their workplaces signal by raising their hands if a mistake is made.

"Sonya"

This game does not require special training. The guys lower their heads on their hands folded on the desk, imitating a dream. The teacher slowly reads the example and calls his answer. If the answer is correct, the children continue to “sleep”, but if a mistake is made, they “wake up”, raise their hand and correct the mistake.

"Supplement Account"

The teacher writes a number on the board, for example, 1.5. Then he slowly calls out a number that is less than 1.5. In response, students must name another number that complements the given one up to 1.5. Those numbers that the teacher calls, and those that the students give, are not written down. This provides a great training in memorizing numbers.

"Hurry, don't make a mistake"

This game is actually a mathematical dictation. The teacher slowly reads the task after the task, and the students write the answers on the sheets of paper.

"Equal Score"

The teacher writes answers on the board. Students should come up with their own examples with the same answer. Their examples are not written on the board. The children must listen to the named numbers and determine whether the example is correctly composed.

"Silence"

For the game, any geometric figure is taken, in the center of which and along the contour numbers are written. Near the number written in the center, the sign of the arithmetic operation is placed. The teacher points to the number written along the contour, and the children perform the specified action. The student is called, he writes down the answer. The rest of the students raise their hands, signaling if a mistake is made. All work is done in silence.

"Circular Examples"

Circular examples are composed as follows: the first example is taken arbitrarily, the result of this example must become a component of the next one, and so on. This game can be played in various forms. There are many such tasks in the textbooks "Mathematics" for grades 5 and 6.

1. Restore the chain of calculations. It is useful to end such chains with the question: “How to get the original number from the last result?”

2. The task is based on the same principle: restore the chain of calculations by substituting the missing numbers above the arrow. In this case, the numbers in the "windows" are already given.

"Do not snooze"

6 cards are made per class (2 for each row). The first student in the column has the task written down in full, and all the rest have an ellipsis instead of the first number. What is hidden behind the ellipsis, the student will know only when his friend, sitting in front, copes with his task. This answer will be the missing number. In such a game, everyone should be extremely careful, since the mistake of one participant crosses out the work of all the others. The column that fills the punch card the fastest wins.

"Magic and Entertaining Squares"

These are squares that consist of 9, 16 or 25 cells. The cells should contain such numbers that their sum in all directions is the same. In one case, the square is filled, you need to check if it is magic. In the other, not all numbers are given, and the amount is indicated; you need to fill in the square. In the third - not all numbers are given and the amount is not indicated.

The scheme of drawing up a magic square.

In the specified sequence, numbers are inserted in order (starting with any).

"Domino"

Each pair of students receives a set of "dominoes" (10 cards). An example is written on the right side of the card, and a number (the result of some other example) is written on the left. Everyone takes three cards from the set. The double is laid out first, and then, as in a regular game: the cards are laid out so that the correct numerical equalities are obtained. The winner is the one who lays out his cards the fastest.

"Lotto"

A card is drawn up for each student. Their content differs only in the order of numbers. The teacher calls an example, the children calculate and close the corresponding numbers with chips. If all students counted correctly, then by the time the game ends, one of the rows on each card will be closed. Whoever calculates the last example faster wins. This game can be used to consolidate the knowledge of tabular multiplication, the ability to perform actions with natural numbers and fractions. It all depends on what numbers will be written on the cards, and what examples the teacher will make.

When choosing a game, the teacher should be guided by the fact that this is not an end in itself, but a means of activating the activity of students. At the same time, it must be remembered that only that game will be useful, which makes it possible to perform the largest number of operations and cover all students.