Why count in your head, if you can solve any arithmetic problem on a calculator. Modern medicine and psychology prove that oral counting is a trainer for gray cells. Performing such gymnastics is necessary for the development of memory and mathematical abilities.

Many techniques are known to simplify mental calculations. Everyone who has seen the famous painting by Bogdanov-Belsky "Oral Account" is always amazed - how peasant children solve such challenging task, how is the division of the sum of five numbers that must first be squared?

It turns out that these children are students of the famous teacher-mathematician Sergei Aleksandrovich Rachitsky (he is also depicted in the picture). These are not geeks - primary school students of a 19th century village school. But they all already know the tricks of simplifying arithmetic calculations and have learned the multiplication table! Therefore, these kids are quite capable of solving such a problem!

Secrets of Counting

There are oral counting techniques - simple algorithms that are desirable to bring to automatism. After mastering simple techniques, you can move on to mastering more complex ones.

Add numbers 7,8,9

To simplify the calculations, the numbers 7,8,9 must first be rounded to 10, and then subtract the increase. For example, to add 9 to a two-digit number, you must first add 10, then subtract 1, etc.

Examples of :

Add two-digit numbers quickly

If the last digit of a two-digit number is more than five, round it up. We carry out the addition, subtract the "addition" from the resulting sum.

Examples of :

54+39=54+40-1=93

26+38=26+40-2=64

If the last digit of a two-digit number is less than five, then we add up by place: first we add tens, then units.

Example :

57+32=57+30+2=89

If the terms are reversed, then first you can round the number 57 to 60, and then subtract 3 from the total:

32+57=32+60-3=89

Add three-digit numbers in your mind

Fast counting and adding three-digit numbers - is it possible? Yes. To do this, you need to parse three-digit numbers into hundreds, tens, units and add them one by one.

Example :

249+533=(200+500)+(40+30)+(9+3)=782

Features of Subtraction: Casting to Round Numbers

The deductible is rounded up to 10, to 100. If you need to subtract a two-digit number, you need to round it up to 100, subtract, and then add an amendment to the remainder. This is relevant if the amendment is small.

Examples of :

576-88=576-100+12=488

Mental subtraction of three-digit numbers

If at one time the composition of numbers from 1 to 10 was well mastered, then subtraction can be performed in parts and in the indicated order: hundreds, tens, units.

Example :

843-596=843-500-90-6=343-90-6=253-6=247

Multiply and divide

Mentally multiply and divide instantly? It is possible, but you cannot do without knowing the multiplication table. is the golden key to quick mental arithmetic! It applies to both multiplication and division. Let us recall that in the elementary grades of a village school in the pre-revolutionary Smolensk province (picture "Oral counting"), children knew the continuation of the multiplication table - from 11 to 19!

Although in my opinion it is enough to know the table from 1 to 10 to be able to multiply larger numbers. for instance:

15*16=15*10+(10*6+5*6)=150+60+30=240

Multiply and divide by 4, 6, 8, 9

Having mastered the multiplication table by 2 and 3 to automatism, it will be easier to do the rest of the calculations.

To multiply and divide two and three-digit numbers, we use simple techniques:

multiply by 4 is to multiply twice by 2;

multiplying by 6 means multiplying by 2, and then by 3;

multiply by 8 is to multiply by 2 three times;

multiplying by 9 is multiplying twice by 3.

for instance :

37*4=(37*2)*2=74*2=148;

412 * 6 \u003d (412 * 2) 3 \u003d 824 3 \u003d 2472

Similarly:

divide by 4 is twice divided by 2;

divide by 6 is first to divide by 2, and then by 3;

divide by 8 is to divide by 2 three times;

divided by 9 is twice divided by 3.

for instance :

412:4=(412:2):2=206:2=103

312:6=(312:2):3=156:3=52

How to multiply and divide by 5

The number 5 is half of 10 (10: 2). Therefore, first we multiply by 10, then we divide the resulting one in half.

Example :

326*5=(326*10):2=3260:2=1630

The rule of division by 5 is even simpler. First, we multiply by 2, and then divide the result by 10.

326: 5 \u003d (326 2): 10 \u003d 652: 10 \u003d 65.2.

Multiplication by 9

To multiply a number by 9, it is not necessary to multiply it twice by 3. It is enough to multiply it by 10 and subtract the multiplied number from the resulting number. Let's compare which is faster:

37*9=(37*3)*3=111*3=333

37*9=37*10 - 37=370-37=333

Also, particular patterns have long been noticed that greatly simplify the multiplication of two-digit numbers by 11 or 101. So, when multiplying by 11, the two-digit number seems to move apart. Its constituent numbers remain at the edges, and their sum is in the center. For example: 24 * 11 \u003d 264. When multiplying by 101, it is enough to assign the same to a two-digit number. 24 * 101 \u003d 2424. The simplicity and consistency of such examples is admirable. Such tasks are very rare - these are examples of entertaining, so-called little tricks.

Counting on fingers

Today you can still find many defenders of "finger gymnastics" and the method of oral counting on the fingers. We are convinced that learning to fold and subtract by bending and unbending fingers is very visual and convenient. The range of such calculations is very limited. As soon as the calculations go beyond the scope of one operation, difficulties arise: it is necessary to master the following technique. And bending your fingers in the era of iPhones is somehow undignified.

For example, in defense of the "finger" technique, the technique of multiplying by 9 is given. The trick of the technique is as follows:

• To multiply any number within the first ten by 9, you need to turn your palms towards you.
• Counting from left to right, bend the finger corresponding to the number to be multiplied. For example, to multiply 5 by 9, you have to bend the little finger on your left hand.
• The remaining number of fingers on the left will correspond to tens, on the right - to ones. In our example, 4 fingers to the left and 5 to the right. Answer: 45.

Yes, indeed, the solution is quick and clear! But this is from the area of \u200b\u200bfocuses. The rule is valid only when multiplying by 9. Isn't it easier to learn the multiplication table for multiplying 5 by 9? This trick will be forgotten, and a well-learned multiplication table will remain forever.

There are also many more similar techniques using fingers for some single mathematical operations, but this is relevant while you use it and is immediately forgotten when you stop using it. Therefore, it is better to learn the standard algorithms that will last a lifetime.

Verbal invoice machine

First, you need to know well the composition of the number and the multiplication table.

Secondly, you need to remember the techniques for simplifying the calculations. As it turned out, there are not so many such mathematical algorithms.

Thirdly, in order for a technique to become a convenient skill, it is necessary to constantly conduct short "brainstorming" sessions - to practice oral calculations using one or another algorithm.

Workouts should be short: solve in your head 3-4 examples using the same technique, then move on to the next. We must strive to use any free minute - both useful and not boring. Thanks to simple training, all calculations will be performed with lightning speed and without errors over time. It will be very useful in life and will help out in difficult situations.

Oral counting class 1-2

Godlevskaya Natalya Borisovna, student of group Sh-31 of the State Budgetary Educational Institution of Higher Education "Yeisk Pedagogical College"
Work description: this collection will be useful for primary school teachers for conducting oral counting in grades 1 and 2. Many tasks can be used in grades 3-4, complicating them accordingly, adding the necessary examples.

Assignments for oral counting in grade 1.

1. Russell tenants.
Purpose: 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.
Purpose: consolidation of computational techniques 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

Maple leaves cut out of colored paper with numbers and signs (2, 8, 10.9, +) and a drawing of a bear cub are pinned to the side. The children are offered a situation: the bear solved examples and wrote down the answers on maple leaves. The wind blew, and the leaves flew. Mishutka was very upset: how can he be 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 of answers to the place by clicking
3. Put the ball into the basket.
Purpose:
Drawings with basketball hoops and numbers on them are hung on the board. Assignment: come up with as many examples as possible, the answer to which will be the number above the basket.

4. Decipher the word.
Purpose: consolidation of computational techniques of addition and subtraction. Solve examples. Decipher the word by sorting the answers in ascending order.
4 + 3 \u003d u 7-2-1 \u003d n 3-2 + 6 \u003d u 7 + 0 + 1-4 \u003d 4 s
6-2 \u003d w 5-4 + 1 \u003d o 5 + 1 + 2 \u003d m 4-1 + 6-7 \u003d 2 o
2 + 6 \u003d e 4-1-2 \u003d s 9-3-3 \u003d q 7-5 + 1 + 3 \u003d 6 i
10-4 \u003d n 2 + 2 + 2 \u003d e 8-5 + 1 \u003d n 2 + 3 + 4-8 \u003d 1 p
7-4 \u003d o 3 + 4-2 \u003d q 4 + 3-2 \u003d a 9-9 + 5-0 \u003d 5 and
10-5 \u003d e 4-3 + 2 \u003d l 6 + 2-7 \u003d y 6-4 + 6-5 \u003d 3 s
5-3 \u003d l (Sun) (Clever) (Russia)
9-8 \u003d s
(Addition)
5. Tasks in poetic form.
Purpose: working out the skills of oral counting within 20. Problems are read aloud by the teacher.
Five baby cubs
Mom put me to bed.
One cannot sleep in any way,
How many have a good dream?
(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?
Only for sure!
(2+6=8)
There are seven grasshoppers in the choir
The songs were sung.
Soon two grasshoppers
Lost voice.
Count without further ado
How many voices are there in the choir?
(7-2=5)
The hedgehog went mushrooming,
I found ten saffron milk caps.
I put eight in a basket,
The rest are on the back.
How many saffron milk caps do you carry
On his pins and needles hedgehog?
(10-8=2)
What started to thunder like that?
Our bear builds hives.
He did only seven hives.
Two less than I wanted.
How many hives did the bear want to make?
(7+2=9)

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

The wind blew - the leaf was torn
And another one fell
And then five fell.
Who can count them?
(1+1+5=7)
They lie in my back.
Two mushrooms, five butter,
A pair of ruddy mushrooms,
How many mushrooms are there guys?
(2+5+2=9)
Amicably ants live
And they don't scurry about idle.
Two carry a blade of grass
Three carry a blade of grass
Five are carrying needles.
How many ants are under the tree?
(2+3+5=10)
The puppy ran into the chicken coop,
Dispersed all the roosters.
Three took off to roost,
And one climbed into the tub,
Two - through the open window.
How many were there in total?
(3+1+2=6)
They stand on my shelf
Two green frogs
Two bears and a mouse
And a wonderful cuckoo.
And there is also a baby elephant
And a puppy with a sewn-up ear
Pinky 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 the words by syllables.
Our girl became
In the yard of the crows, count:
“One sits in 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)
The kids fell in love
Adventure books.
I read a dozen Kolya,
Two books less - Olya,
Count, kids,
All books read.
(10+8=18)
Seven passengers were traveling in Gazik
Four came out at the bus station.
Two of them got on the bus at the station.
How many people are on that bus?
(7-4+2=5)
6. Tasks for the development of logical thinking.
Purpose:
Ivan Tsarevich rode on horseback to the Koscheevo kingdom. Three heroes were galloping towards him on horses. How many horses galloped to the Koscheevo kingdom? (1)
Kai and Gerda simultaneously built fortresses out of snow, but Gerda started building before Kai. Who worked faster? (Kai)
Dasha and Masha got A's at school: one in mathematics, the other in literature. In what subject did Dasha get an A if Masha got this mark not in mathematics? (Dasha in mathematics, Masha in literature)
Piero, Malvina and Buratino hid from Karabas Barabas in the house of Pope Carlo. One under the bed, the other in the closet, and the third in the stove. It is known that Buratino did not climb into the stove, Malvina did not hide under the bed and in the stove. Who is hiding where? (Malvina in the closet, Buratino under the bed, Pierrot in the stove)
On Monday Dunno drew one short man, on Tuesday - two, on Wednesday - three, and so on until the end of the week. How many short ones did Dunno draw on Sunday? (7)

A notebook is cheaper than a pen, but more expensive than a pencil. Which is cheaper? (pencil)
Yura and Petya came to the river. The boat, on which you can cross, can accommodate one person. And yet, without any help, the guys crossed over on this boat. How did they do it? (the guys approached the left and right banks of one river.)
7. Joke tasks.
Purpose: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 alone find if he went to the store? (3 rubles)
3 comrades went to school on the second shift and met two more comrades - students of the first shift. How many comrades went to school? (3 comrades)
7 candles were lit, 2 of them were extinguished. How many candles are left? (2 candles)
Which is heavier - a kilogram of cotton wool or a kilogram of iron? (the same)
7 brothers walked, each brother had one sister. How many people were walking? (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)
Purpose: consolidation of computational techniques 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.
Purpose: consolidation of computational techniques of addition and subtraction.
Students must go through two maze gates so that the total is 13.

3. Solve the puzzle.
Purpose: consolidation of computational techniques 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.
Purpose: strengthening the skills of subtraction and addition of round numbers.
The examples are chosen so that the number resulting from one of them is the beginning of the other. The answer of the last example is the same as the beginning of the first.

5. Connect the numbers with their sum of place terms.
Purpose: fixing the bit composition of two-digit numbers.
36 40 + 8
63 80 + 4
48 30 + 6
84 60 + 3
6. Concatenate expressions with the same value without evaluating.
Purpose: consolidation of knowledge about the displacement 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 examples with a 50 answer.
Purpose: consolidation of 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.
Purpose:
1. How are 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 numbers similar and 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 shapes:
a) triangle and quadrilateral;
b) circle and square;
c) rectangle and square;
d) rectangle and rhombus.
8. Mathematical expressions.
Purpose: develop the ability to find similarities or differences between objects on essential or insignificant signs.
1. Given mathematical expressions: 3 + 4 and 1 + 6
Compare them with each other.
Answer:
1) the same sign of 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 addition results are the same.
2. Given mathematical expressions, 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.
Purpose:develop the ability to find similarities or differences between objects on essential or insignificant signs.
1. Call 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. Call a group of numbers in one word:
a) 2, 4, 8, 12, 44, 56;
b) 1, 13, 77, 83, 95.
3. To name a group of objects in one word:
a) triangle, square, circle;
b) square, rectangle, rhombus.
10. Tasks for finding an extra number.
Purpose: develop the ability to find similarities or differences between objects on essential or insignificant signs.
1. Given numbers: 1, 10, 6.

For instance:
1) 1 may be superfluous, since this 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 one is used to write the numbers 1 and 10.
2. Given the numbers 6, 18, 81.
Combining two numbers in pairs, answer which number is superfluous.
For instance:
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 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 factors);
5) 6 is superfluous, since the numbers 18 and 81 are divisible by 9 (have a common divisor).
3. Given numbers: 48, 24, 9.
Combining two numbers in pairs, answer which number is superfluous.
4. Given numbers: 25, 5 36.
Combining two numbers in pairs, answer which number is superfluous.
5. From a number 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, deductible, sum, dividend.
11. Rebus.
Purpose: development of logical thinking, oral speech.
You 3, 100 l, 3 tone, 100 forehead, 2 l each, with 3 LCD, 100 faces, mustache 3 ts, mo 100, 3 cotage, for 100 leagues, smo 3 t, geome 3 i, ses 3 ts, 1 akovye, p 1 ka, about 100, s 3 f, about 5, on 100 th, for 1 ka, 1 order, 100 p, 2 jester, pa 3 from, kar 3 j.
12. Tasks that develop logical thinking.
Purpose: development of observation, abstract thinking.
1. Continue the series of numbers to the right and to the left (if possible), establishing a pattern in the recording 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. Rows of numbers are given. It is necessary to notice the peculiarity of drawing up 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 logical tasks
Purpose: development of logical thinking, attention, memory
A sliced \u200b\u200bloaf and a bag of sugar weigh more than the same loaf and a box of chocolates. Which weighs more - sugar or candy? (a pack of sugar weighs more than a box of chocolates)
How many times do you need to cut to cut a 10 cm long rope into pieces of 2 cm each? (4 times)

To use the preview of presentations, create yourself a Google account (account) and log into it: https://accounts.google.com

Slide captions:

Oral counting "With Hottabych" Mathematics Grade 4

O omnipotent ones! Oh, the smartest! Hope you know me! I prepared my friend Volka for the exam. I am sure that I can teach you how to count quickly and correctly. I conceived a word. To guess it, you need to solve examples. Rub my magic jug and tasks will appear in front of you. Good luck to you, dear youth!

(600 + 600) + 2800 \u003d 4000 (p) Check

2500+ 6500 - 8300 \u003d 700 (m) Check

1300 - (1500 - 700) \u003d 500 (o) Check

900 + 800 + 1700 \u003d 3400 (o) Check

(4000 - 3400) + 600 \u003d 1200 (and) Check

7000 - 3700 - 1300 \u003d 2000 (e) Check

2000 - (800 + 900) \u003d 300 (n) Check

300 (p) Check 4000 (p) 700 (m) 500 (o) 3400 (o) 1200 (i) 2000 (e) Arrange the answers in ascending order 300 (n) 4000 (p) 700 (m) 500 (o) 3400 (o) 1200 (i) 2000 (d)

Sources of images: http://gametherapy.ru/wp-content/uploads/starik_hottabych1.jpg -background https://2.bp.blogspot.com/-Qz5uF3WnKUY/Vx6j4JfFrrI/AAAAAAAAAyM/xy-J_nWazy16LAQ3CCLTV. -hand https://raw.githubusercontent.com/duboviy/minicache/master/logo.png -carpet http://cdn-nus-1.pinme.ru/tumb/600/photo/5f/c7/5fc788b541197492e05610d4fcfc74c3.png -jug

On the subject: methodological developments, presentations and notes

Oral counting within 100, multiplication table. Exercises for oral counting. 2nd grade

The presentation contains slides with chains of examples for oral counting. Click animation. The Shop slide is not animated ....

Verbal counting. How to organize and conduct oral counting in 2nd grade.

Verbal counting. How to choose it correctly for a particular topic of the lesson? How to make your math lesson interesting? How can you help students get involved in the new Croc theme? All these questions can be found in ...

Oral counting, as elsewhere, has its own tricks, and in order to learn how to count faster, you need to know these tricks and be able to apply them in practice.

Today we will do this!

1. How to quickly add and subtract numbers

Let's look at three random examples:

1. 25 – 7 =
2. 34 – 8 =
3. 77 – 9 =

Type 25 - 7 \u003d (20 + 5) - (5- 2) \u003d 20 - 2 \u003d (10 + 10) - 2 \u003d 10 + 8 \u003d 18

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

But there is an easier way:

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

It is much easier to subtract 10 from the number and add 3 than to fence complex calculations.

Let's go back to our examples:

1. 25 – 7 =
2. 34 – 8 =
3. 77 – 9 =

Optimizing the subtracted numbers:

1. Subtract 7 \u003d Subtract 10 Add 3
2. Subtract 8 \u003d Subtract 10 Add 2
3. Subtract 9 \u003d Subtract 10 Add 1

Total we get:

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

Now it is much more interesting and easier!

Count the examples below in this way now:

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 split 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 the numbers than to quadruple or eighty 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 method with the following examples:

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

3. Division of 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 enjoyable, because five is half of ten.

And how to quickly solve them?

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 trickier, but not too much, how would you solve the following examples?

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

It is not very pleasant to solve them without special chips, 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 which with zeros and add up the results.

To work out 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, take the number 732, imagine it as 7 + 3 + 2 \u003d 12. 12 is divisible by 3, which means that the number 372 is divisible by 3.

Check which of the following numbers is 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 is divisible by 5 (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, take the number 6732, represent it as 6 + 7 + 3 + 2 \u003d 18. 18 is divisible by 9, which means that the number 6732 is divisible by 9.

Check which of the following numbers is divisible by 9:

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

Fast addition game

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

An excellent simulator for developing fast counting. The screen shows a 4x4 table with numbers shown above it. The largest number to be collected in the table. To do this, click with the mouse on two numbers, the sum of which is equal to this number. For example, 15 + 10 \u003d 25.

Quick Counting Game

A quick score game 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 point of the game is to choose a mathematical sign for the equality to be true. There are examples on the screen, look carefully and put the required "+" or "-" sign so that the equality is correct. The "+" and "-" signs are located at the bottom of the picture, select the desired sign and click on the desired button. If you answered correctly, you collect points and keep playing.

Simplification game

Simplify develops thinking and memory. The main essence of the game must be completed quickly 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 an answer. There are three answers below, count and click the number you need with the mouse. If you answered correctly, you collect points and keep playing.

Task for today

Solve all examples and practice for at least 10 minutes in Fast Add.

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

Lesson taken from the course "Oral Counting in 30 Days"

Learn to quickly and correctly add, subtract, multiply, divide, square numbers and even extract roots. I will teach you to use easy tricks to simplify arithmetic operations. Each lesson has new techniques, clear examples, and helpful assignments.

Other development courses

Money and Millionaire Mindset

Why are there problems with money? In this course, we will answer this question in detail, look deeper into the problem, consider our relationship with money from a psychological, economic and emotional point of view. From the course you will learn what you need to do to solve all your financial problems, start accumulating money and invest it in the future.

Knowledge of the psychology of money and how to work with it makes a person a millionaire. 80% of people with an increase in income take more loans, becoming even poorer. On the other hand, self-made millionaires will make millions again in 3-5 years if they start from scratch. This course teaches the competent distribution of income and cost reduction, motivates to learn and achieve goals, teaches to invest and recognize a scam.

Speed \u200b\u200breading in 30 days

Increase your reading speed by 2-3x in 30 days. From 150-200 to 300-600 words per minute or from 400 to 800-1200 words per minute. The course uses traditional exercises for the development of speed reading, techniques that speed up the work of the brain, the method of progressively increasing the speed of reading, the psychology of speed reading and the questions of the course participants are discussed. Suitable for children and adults who read up to 5000 words per minute.

Development of memory and attention in a child 5-10 years old

The course includes 30 lessons with helpful tips and exercises for child development. In every lesson helpful advice, some interesting exercises, an assignment for the lesson and an additional bonus at the end: an educational mini-game from our partner. Course duration: 30 days. The course is useful not only for children, but also for their parents.

Super memory in 30 days

Memorize the necessary information quickly and for a long time. Wondering how to open a door or wash your hair? I am sure not, because this is part of our life. Light and simple exercises for memory training, you can make it a part of life and do it a little during the day. If you eat daily rate food at a time, but you can eat in portions throughout the day.

Brain fitness secrets, train memory, attention, thinking, counting

The brain, like the body, needs fitness. Physical exercises strengthen the body, mental develop the brain. 30 days of useful exercises and educational games for developing memory, concentration, intelligence and speed of reading will strengthen the brain, turning it into a tough nut to crack.

Well-developed oral counting skills among students are one of the conditions for their successful study in high school. The math teacher needs to pay attention to verbal counting from the very moment students move to it from elementary school. It is in the fifth or sixth grades that we lay the foundations for teaching mathematics to our pupils. We will not teach how to count during this period - we ourselves will experience difficulties in our work in the future, and we will condemn our students to constant offensive mistakes.

Mastering the skills of oral calculations is of great educational, educational and practical importance. They help to assimilate many questions of the theory of arithmetic operations, help to better assimilate the techniques of written calculations, and speed and correctness of calculations are essential in life. Verbal calculations contribute to the development of thinking, intelligence, mathematical vigilance, observation, initiative, etc. In addition, during oral exercises, students are prepared for work in the lesson, in particular, for the perception of new material, as well as a systematic repetition of what has been covered.

In the arsenal of every teacher, there are many types of oral counting exercises. However, all this variety comes down to finding the values \u200b\u200bof 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 closely follow each other's answers, and the teacher was 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 ratio in the application of oral and written methods of calculation, namely: calculate in writing only when it is difficult to calculate orally. Oral exercises should permeate the entire lesson. They can be paired with check homework; direct to consolidate and work 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 exercises of a developing nature (including non-standard tasks, logical, entertaining, exercises for quick wits).

In 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 designed to review previously covered material, to develop computational skills and prepare for learning new material, they are carried out at the beginning of the lesson. If the purpose of the exercises is to consolidate what was learned in the lesson, then oral counting is carried out after learning new material. It should not be held at the end of the lesson, as the children are already tired.

The number of exercises should be such that their implementation does not overwork the children and does not exceed the lesson allotted for this time. I always do verbal counting so that the guys start with an easy one, and then gradually take on more and more difficult calculations. If you immediately unleash difficult oral assignments on students, then the children will discover their own powerlessness, become 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 stage of warm-up before getting to know a new topic or at the stage of repetition of the material.

Secondly, the use of printed exercise books, where there are tasks that can be done orally, ignoring empty spaces for notes.

Third, the use of multimedia, which, unfortunately, is not always possible yet. Modern children are familiar with computers, and the perception of information in this form is familiar and understandable for them. Therefore, in this matter, it remains to be hoped that the modernization of schools will proceed faster and teachers will be able to fully use ICT. After all, multimedia tools help to solve a 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 unexpectedness necessarily generates interest, interest stimulates cognitive initiative, one's own motivation for learning is born, and therefore, the quality improves. learning.

Fourth, of course, the creativity of the teacher himself. In order to apply the method, technique, and even any kind of activity in the lesson, 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 oral counting feel like an interesting game for students. Conducted in a playful way, in the form of a competition, oral counting contributes to the creation of positive emotions in children, helps the effective mastery of knowledge, and forms an interest in mathematics.

Games for verbal counting.

"Guess the intended example"

Examples are written on the board. The teacher names the answer of one of them, and the students must find a conceived example by his answer. In this case, students solve all or almost all of the examples to find the one they need. The game can be conducted orally: students should have cards with example numbers, which they will pick up at the request of the teacher, or as a test.

"Move the comma"

Use this exercise to reinforce the actions of multiplying and dividing decimal fractions by digit units. 5-7 people go to the board, each receives a card with numbers from 1 to 9 and a moving point. At the teacher's request, children place a comma between the indicated numbers. The teacher names the example, and the students move the comma to the right or left by a certain number of characters. For example, the teacher dictates: "Set a comma between" 4 "and" 5 ". Multiply this number by 100. " The guys move the comma two characters to the right and show the result. Pupils sitting in workplaces signal by raising their hands if a mistake has been made.

"Sonya"

This game does not require any special preparation. The guys put their heads down on their folded hands on the desk, imitating a dream. The teacher slowly reads the example and names 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.

"Account-supplement"

The teacher writes down a number on the board, for example, 1.5. Then he slowly calls out a number that is less than 1.5. Pupils should answer in response to another number that complements the given one to 1.5. The numbers given by the teacher and those given by the students are not recorded. This provides a great exercise in memorizing numbers.

"Hurry, but don't be mistaken"

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

"Equal Score"

The teacher writes down examples with 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 guys should perceive the named numbers by ear and determine if the example is correct.

"Silent woman"

For the game, a geometric figure is taken, in the center of which and along the contour are written numbers. An arithmetic sign is placed near the number written in the center. The teacher points to the number written along the outline, and the children perform the indicated action. The student is called, he writes down the answer. The rest of the students raise their hands, signal 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 should become a component of the next, and so on. This game can be conducted in different forms. There are many such tasks in the textbooks "Mathematics" for grades 5, 6.

1. Restore the chain of calculations. It is useful to end such chains with the question: "How to get the initial 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 have already been given in the "windows".

"Do not snooze"

6 cards are made per class (2 for each row). For the first student in the column, the task is written down in full, and for all the rest, instead of the first number, there is an ellipsis. What is hidden behind the ellipsis, the student will find out only when his comrade, sitting in front, will cope 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 negates the work of everyone else. The column that fills the punch card faster wins.

"Magic and entertaining squares"

These are squares that consist of 9, 16 or 25 cells. The cells must contain such numbers that their sum is the same in all directions. In one case, the square is filled, you need to check if it is magic. In another, 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.

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 on the left (the result of some other example). Each takes three cards from the set. The double is laid 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 places his cards faster.

"Lotto"

A card is drawn up for each student. Their content differs only in the order of numbers. The teacher names an example, the children calculate and cover 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. Who will count faster last example, he wins. This game can be used to consolidate the knowledge of table 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 it is not an end in itself, but a means of enhancing the activity of students. It should be remembered that only that game will benefit, which makes it possible to perform the largest number of operations and cover all students.