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Fast technique. Fast reading technique with high retention rate

Speed reading is a fast reading technique, an acquired ability that increases speed by 3–20 times the average (which is 180–200 words per minute). With its help, you can speed up the perception of textual information and master the process of memorizing what you read.

There are many programs with which it is permissible to increase the level of reading, speed up the memorization process and achieve the expansion of memory cells. All training lessons of such programs are aimed at developing a person spiritually and, of course, intellectually.
Oleg Andreev is a well-known author, offers training according to his programs, which he compiles himself.

Learning to increase reading speed. Some were able to increase it 20 times, but the average achievement is an increase of 5 times.
Training provides a better and faster perception of text information.
Development of memory and, of course, attention.
The ability to develop your own intuition, which will not be superfluous in everyday life.
An opportunity to develop or improve creativity.
Full physical recovery of the body.
Learning affects the spiritual growth of a person.

To know, feel, realize all these points, you need to go through and study the 7 basic laws on which the technique of fast reading is based. These laws are the basis of all methods. The program "How to increase the speed of reading?" requires time, attention and, of course, the desires of a person, without which the implementation and achievement of a positive result is impossible.

Oleg Andreev, in turn, identifies 7 programs, each of which is aimed at working on oneself and developing one's intellectual abilities and spirituality.

Fast reading rules

No regression.

Regressions are eye movements that the reader involuntarily performs. The accessible wording is re-reading the text. This happens for several reasons:

the first is a complex text that requires sharpening of attention and, accordingly, re-reading;
the second reason is to rethink what you read.

Regressions are a kind of habit that slows down your fast reading technique. To get rid of regressions, you just need to exercise. The essence of the training is that the text must be read with the highest possible level of attention and concentration.

For the best result, get rid of all extraneous thoughts and distractions. In addition, one reading is efficient for memory. The memorization process works instantly, and repeated reading or sharpening on one word can confuse you with the main meaning.

No articulation.

Articulation is the reader's mimicry, which is accompanied by familiarization with textual information at a subconscious level. Articulation accompanies reading both aloud and to oneself. Many people think that reading to themselves speeds up the process, but this is a misconception.

This phenomenon has its own classification:

text accompaniment with mechanical movements;
speaking directly in the speech center is a much deeper and less controlled level.

The principle of operation is based on reading accompanied by a certain sound (we exclude music). It is necessary to use sound recordings with faster and slightly slower rhythms, which should be included when reading and at the same time tapping to the rhythm. Andreev devotes a whole program to master this process, in this teaching his opinion is fundamentally different from the lessons of foreign teachers.

Integral reading algorithm.

The essence of this rule is based on optimization and highlighting the main meaning that the text carries in itself. The semantic perception of the text can only be taught by a special program; it is impossible to cognize and master this rule on self-study.

Vertical eye movement.

Easy to say, harder to apply. This rule allows you to save the reader from unnecessary eye movements, which are spent on moving from one line to another. An ordinary person reads this way, which is due to a small field of view. Vertical eye movement is based on eye movement from top to bottom, but strictly through the center of the page. This method allows you to read the entire phrase, rather than individual words.

Isolation of the dominant.

This technique allows you to highlight the most basic semantic meaning of the text and cut off secondary information. This method has 2 principles:

definition and highlighting of central semantic points;
intuitive comprehension of the text.

In his book, Andreev explains this process in an accessible manner.

Development of memory and attention.

Attention, concentration and memory are the guides with the help of which it is possible to achieve high results in speed reading in practice.

The technique of fast speed reading allows you to master attention, it is such a vicious circle: you cannot read quickly without attention, but by reading quickly, you reach the highest level of attention and memory development.

An indispensable assistant in improving memory and attention is exercises with words, mentally reading them the other way around. Regular training gives results. It is worth starting with simple and short words and making it harder for yourself every day.

Mandatory daily minimum.

The development of fast reading requires special psychological costs and efforts from a person. Having embarked on the path of learning this program, you need to read several magazines, articles, newspapers and at least 50-100 pages of the book a day.

Oleg Andreev in his teachings prefers points: 1, 2, 3, 4, 6 and calls them not rules, but hindrances, which in one way or another slow down the reading technique, reduce the level of memorization. But with all this, Mr. Andreev proposes to study the volume of the readable text, which over time will provide a solid budget of time.

The program, which the author Andreev describes, offers a certain speed reading simulator, which will be entered into the table. The table called "Analysis of the volume of reading", which clearly demonstrates speed reading in practice, allows you to increase the tendency of its development, improve the processes of memorization and expansion of memory cells.

Reading Analysis Table

The table should clearly display the amount of text that is read during the day. At the same time, it is broken down separately according to the days and styles of the material read (textbooks, manuals, dictionaries, newspapers, magazines, etc.). The criteria are the volume of the text and the time spent on this text.

Measured units: the text must be counted in pieces, as for the style of the material, and the signs in each of the styles, the daily time spent on reading must be recorded in minutes, and the weekly result must be set in hours. The table is a kind of personal incentive, where a person, seeing the result of the previous day, tries to overcome it. Andreev claims that a week will be enough to see the result and set the pace of his development.

Teaching this technique allows you to develop five of the five types of reading. It is worth knowing that a person who has not studied speed reading has only two.

Reading types:

Concentrated reading, it is used when studying a narrow profile text (legal, medical, technical, etc.). This is a great training for developing memory.
Reading is unhurried, it is typical of fiction.
Advance reading or preliminary reading - with its help, they determine the essence of what is being read.
A quick scan is used to get an idea of the content.
Fast reading itself is fast reading.

Speed reading exercises

Read the text in a standard way, from top to bottom and in reverse order. This is the first training for memory and attention.
The second lesson trains attention. Learning is about finding one word that another person will point to. Any text for this exercise will work, be it a textbook or a novel.
The rapid reading technique and fluent reading program help develop logical thinking. Literary texts are suitable for this exercise. Learning consists in reading through a line or sentence. Such lessons are unacceptable for reading business documents, it obliges you to carefully and concentratedly read each word. This method displays the results in an indicative table that Andreev offers for training. Learning is aimed at speeding up reading, and at developing memory and improving the memorization of the information read.
Accelerated page browsing (20 seconds per page). During this time, you need to determine the main words that carry the main meaning and flip through the pages to compose a text that would not lose its general meaning. Such lessons are within the power of those who have already completed about half of the training and have basic memorization skills.
Read books at the same rhythm without slowing down and without stopping, do not re-read the same sentence several times.
Having mastered the previous point, complicate the task, the following lessons need to be covered with a sheet of the read text, observing the speed.
Acceleration occurs if you move your left finger across the page at a distance of 2-3 cm from the text being read.

These exercises will allow you to achieve results in speed reading and raise the level of memorization of information.

Do you want to speak and write Russian correctly, but have you made mistakes since high school? Lost your literacy in the race of networking? A unique method of increasing literacy under the Mikhail Shestov program is now available to the general public!
Mikhail Shestov is a linguist, international journalist, innovative teacher, author of his own method of teaching languages, recognized as one of the most successful in the world, an advisor to Earth Day and a number of other organizations of the UN system, is listed in the Guinness Book of Guinness Books - Divo books), consultant and instructor of Interpol in the field of improving the level of language proficiency, consultant to the Russian, American, Chinese and Israeli governments in the field of improving the effectiveness of teaching methods, head of the department of innovative methods of learning foreign languages at the International University of Moscow.
The book is intended for high school students, applicants, students, teachers and people who want to improve their literacy in the most effective way.

SPELLING AND MORPHOLOGY.

Lexeme is Greek for "word", and in the spelling section we will deal with the rules of spelling words without their connection in a sentence. The different forms of spelling of words will interest us when we move on to the section "Morphology".
So spelling. To understand its basic laws, you need to take a short trip into the past.
How did our alphabet come about? It appeared like this: in the 9th century, two Bulgarians - Cyril and Methodius - who lived in Greece, carried the Word of God to the Slavic people. They carried it to Eastern Europe, to the Dnieper, then inhabited by the ancient Russian people. This community had already developed by the 9th century, and the present-day Belarusians, Russians and Ukrainians were part of it. They spoke about the same. Cyril and Methodius, traveling through Ancient Russia, listened to the speech of the Eastern Slavs and, based on the Greek alphabet known to them, compiled a new alphabet for Russians. They composed it by the audible sounds: if there was a corresponding letter for them, they left the Greek, if not, they came up with a new, similar one. So we got many vowels: a, o, and (and). Then the letter didn’t exist for paz and it appeared from the nasal sound ep (this sound is still in some languages, for example, in Polish), it didn’t have - it was the nasal op; but there were special sounds (initial caps): b and b (by the way, these were once vowels denoting a very short sound, which still sounds in many unstressed syllables, where o or a is written instead of percussion).

Introduction
Part 1. SPELLING AND MORPHOLOGY
Part 2. SYNTAX AND PUNCTUATION
Part 3. STYLISM OF THE RUSSIAN LANGUAGE. THE CONCEPT OF BUSINESS AND SCIENTIFIC STYLES.
Exercises
Applications
Answers

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Practicing computational skills of students in mathematics lessons using the techniques of "fast" counting.

Kudinova I.K., teacher of mathematics

MKOU Limanovskaya secondary school

Paninsky municipal district

Voronezh region

“Have you ever observed how people with natural counting abilities are susceptible, one might say, to all sciences? Even all those who have a hard time understanding, if they learn this and practice, then even if they did not derive any benefit from it, they still become more receptive than they were before. "

Plato

The most important task of education is the formation of universal educational actions that provide schoolchildren with the ability to learn, the ability to self-development and self-improvement. The quality of knowledge assimilation is determined by the variety and nature of the types of universal actions. Formation of the ability and willingness of students to implement universal learning activities can improve the efficiency of the learning process. All types of universal educational activities are considered in the context of the content of specific academic subjects.

An important role in the formation of universal educational actions is played by teaching schoolchildren the skills of rational computing.No one doubts that the development of the skills of rational calculations and transformations, as well as the development of skills for solving the simplest problems "in the mind" is the most important element of the mathematical training of students. VThere is no need to prove the importance and necessity of such exercises. Their importance is great in the formation of computational skills, and the improvement of knowledge on numbering, and in the development of the child's personal qualities. The creation of a certain system of consolidation and repetition of the studied material gives students the opportunity to assimilate knowledge at the level of an automatic skill.

Knowledge of the simplified methods of oral calculations remains necessary even with the complete mechanization of all the most laborious computational processes. Oral calculations make it possible not only to quickly make calculations in the head, but also to control, evaluate, find and correct errors. In addition, mastering computational skills develops memory and helps schoolchildren to fully master the subjects of the physics and mathematics cycle.

Obviously, the methods of rational counting are a necessary element of the computational culture in the life of every person, first of all, the strength of their practical significance, and students need it in almost every lesson.

Computational culture is the foundation of the study of mathematics and other academic disciplines, because, in addition to the fact that calculations activate memory, attention, help to rationally organize activities and significantly affect human development.

In everyday life, in training sessions, when every minute is valued, it is very important to quickly and efficiently carry out oral and written calculations, without making mistakes and without using any additional computing means.

An analysis of the exam results in the 9th and 11th grades shows that students make the greatest number of mistakes when completing tasks for calculations. Often, even highly motivated students lose their oral counting skills before reaching the final certification. They think badly and irrationally, more and more often resorting to the help of technical means-calculators. The main task of the teacher is not only to preserve computational skills, but also to teach the use of non-standard methods of oral counting, which would significantly reduce the time of work on the assignment.

Let's consider specific examples of various techniques of fast rational computation.

VARIOUS ADD AND SUBTRACT METHODS

ADDITION

The basic rule for performing addition in the mind is as follows:

To add 9 to the number, add 10 to it and subtract 1; to add 8, add 10 and subtract 2; to add 7, add 10 and subtract 3, etc. For instance:

56+8=56+10-2=64;

65+9=65+10-1=74.

ADDITION IN THE MIND OF BINARY NUMBERS

If the number of units in the added number is greater than 5, then the number must be rounded up, and then the rounding error must be subtracted from the resulting amount. If the number of units is less, then we add tens first, and then units. For instance:

34+48=34+50-2=82;

27+31=27+30+1=58.

ADD OF THREE-DIGITS

We add from left to right, that is, first hundreds, then tens, and then ones. For instance:

359+523= 300+500+50+20+9+3=882;

456+298=400+200+50+90+6+8=754.

SUBTRACTION

To subtract two numbers mentally, you need to round off the subtraction, and then correct the answer.

56-9=56-10+1=47;

436-87=436-100+13=349.

Multiplying multidigit numbers by 9

1. The number of tens will increase by 1 and subtract from the multiplication

2. The result is attributed to the addition of the number of units to be multiplied to 10

Example:

576 9 = 5184 379 9 = 3411

576 - (57 + 1) = 576 - 58 = 518 . 379 - (37 + 1) = 341 .

Multiplication by 99

1. From the number we subtract the number of its hundreds, increased by 1

2. Find the complement of the number formed by the last two digits to 100

3. We attribute the addition to the previous result

Example:

2799 = 2673 (hundreds - 0) 13499 = 13266

27 - 1 = 26 134 - 2 = 132 (one hundred - 1 + 1)

100 - 27 = 73 66

Multiplication by 999 of any number

1. From the multiplied, subtract the number of thousands, increased by 1

2. Find the complement to 1000

23 999 = 22977 (thousand - 0 + 1 = 1)

23 - 1 = 22

1000 - 23 = 977

124 999 = 123876 (thousand - 0 + 1 = 1)

124 - 1 = 123

1000 - 124 = 876

1324 999 = 1322676 (thousand - 1 + 1 = 2)

1324 - 2 = 1322

1000 - 324 = 676

Multiplication by 11, 22, 33, ... 99

In order for a two-digit number, the sum of the digits of which does not exceed 10, to be multiplied by 11, it is necessary 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 11 by a two-digit number, the sum of the digits of which is 10 or more than 10, you need to mentally move 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:

94 × 11 = 9 (9 + 4) 4 = 9 (13) 4 = (9 + 1) 34 = 1034;

59 × 11 = 5 (5 + 9) 9 = 5 (14) 9 = (5 + 1) 49 = 649.

To multiply a two-digit number by 22, 33. ... 99, the last number must be represented as the product of a single-digit number (from 1 to 9) by 11, i.e.

44 = 4 × 11; 55 = 5 × 11, etc.

Then multiply the product of the first numbers by 11.

48 x 22 = 48 x 2 x (22: 2) = 96 x 11 = 1056;

24 x 22 = 24 x 2 x 11 = 48 x 11 = 528;

23 x 33 = 23 x 3 x 11 = 69 x 11 = 759;

18 x 44 = 18 x 4 x 11 = 72 x 11 = 792;

16 x 55 = 16 x 5 x 11 = 80 x 11 = 880;

16 x 66 = 16 x 6 x 11 = 96 x 11 = 1056;

14 x 77 = 14 x 7 x 11 = 98 x 11 = 1078;

12 x 88 = 12 x 8 x 11 = 96 x 11 = 1056;

8 × 99 = 8 × 9 × 11 = 72 × 11 = 792.

In addition, you can apply the law of the simultaneous increase in an equal number of times one factor and decrease the other.

Multiplication by a number ending in 5

To multiply an even two-digit number by a number ending in 5, apply the rule:if one of the factors is increased several times, and the other is reduced by the same amount, the product will not change.

44 x 5 = (44: 2) x 5 x 2 = 22 x 10 = 220;

28 x 15 = (28: 2) x 15 x 2 = 14 x 30 = 420;

32 × 25 = (32: 2) × 25 × 2 = 16 × 50 = 800;

26 × 35 = (26: 2) × 35 × 2 = 13 × 70 = 910;

36 x 45 = (36: 2) x 45 x 2 = 18 x 90 = 1625;

34 x 55 = (34: 2) x 55 x 2 = 17 x 110 = 1870;

18 × 65 = (18: 2) × 65 × 2 = 9 × 130 = 1170;

12 × 75 = (12: 2) × 75 × 2 = 6 × 150 = 900;

14 x 85 = (14: 2) x 85 x 2 = 7 x 170 = 1190;

12 × 95 = (12: 2) × 95 × 2 = 6 × 190 = 1140.

When multiplying by 65, 75, 85, 95, the numbers should be taken small, within the second ten. Otherwise, the calculations will become more difficult.

Multiplication and division by 25, 50, 75, 125, 250, 500

In order to orally learn to multiply and divide by 25 and 75, you need to know well the divisibility sign and the multiplication table by 4.

Those and only those numbers in which the last two digits of the number express the number divisible by 4 are divisible by 4.

For instance:

124 is divisible by 4 because 24 is divisible by 4;

1716 is divisible by 4 because 16 is divisible by 4;

1800 is divisible by 4 as 00 is divisible by 4

Rule. To multiply a number by 25, you must divide this number by 4 and multiply by 100.

Examples:

484 × 25 = (484: 4) × 25 × 4 = 121 × 100 = 12100

124 x 25 = 124: 4 x 100 = 3100

Rule. To divide a number by 25, you must divide this number by 100 and multiply by 4.

Examples:

12100: 25 = 12100: 100 × 4 = 484

31100: 25 = 31100: 100 × 4 = 1244

Rule. To multiply a number by 75, you must divide this number by 4 and multiply by 300.

Examples:

32 × 75 = (32: 4) × 75 × 4 = 8 × 300 = 2400

48 × 75 = 48: 4 × 300 = 3600

Rule. To divide a number by 75, you must divide this number by 300 and multiply by 4.

Examples:

2400: 75 = 2400: 300 × 4 = 32

3600: 75 = 3600: 300 × 4 = 48

Rule. To multiply a number by 50, you must divide this number by 2 and multiply by 100.

Examples:

432 × 50 = 432: 2 × 50 × 2 = 216 × 100 = 21600

848 × 50 = 848: 2 × 100 = 42400

Rule. To divide a number by 50, you must divide this number by 100 and multiply by 2.

Examples:

21600: 50 = 21600: 100 × 2 = 432

42400: 50 = 42400: 100 × 2 = 848

Rule. To multiply a number by 500, you must divide this number by 2 and multiply by 1000.

Examples:

428 × 500 = (428: 2) × 500 × 2 = 214 × 1000 = 214000

2436 × 500 = 2436: 2 × 1000 = 1218000

Rule. To divide a number by 500, you must divide this number by 1000 and multiply by 2.

Examples:

214000: 500 = 214000: 1000 × 2 = 428

1218000: 500 = 1218000: 1000 × 2 = 2436

Before learning how to multiply and divide by 125, you need to know the multiplication table by 8 and the divisibility by 8.

Sign. Those and only those numbers in which the last three digits express a number divisible by 8 are divisible by 8.

Examples:

3168 is divisible by 8 because 168 is divisible by 8

5248 is divisible by 8 because 248 is divisible by 8;

12328 is divisible by 8 because 324 is divisible by 8.

To find out if a three-digit number ending with the digits 2, 4, 6. 8. 8 is divisible, you need to add half the digits of ones to the number of tens. If the result is divisible by 8, then the original number is divisible by 8.

Examples:

632: 8, since i.e. 64: 8;

712: 8, since i.e. 72: 8;

304: 8, since i.e. 32: 8;

376: 8, since i.e. 40: 8;

208: 8, since i.e. 24: 8.

Rule. To multiply a number by 125, divide this number by 8 and multiply by 1000. To divide a number by 125, divide this number by 1000 and multiply

at 8.

Examples:

32 × 125 = (32: 8) × 125 × 8 = 4 × 1000 = 4000;

72 × 125 = 72: 8 × 1000 = 9000;

4000: 125 = 4000: 1000 × 8 = 32;

9000: 125 = 9000: 1000 × 8 = 72.

Rule. To multiply a number by 250, you must divide this number by 4 and multiply by 1000.

Examples:

36 × 250 = (36: 4) × 250 × 4 = 9 × 1000 = 9000;

44 × 250 = 44: 4 × 1000 = 11000.

Rule. To divide a number by 250, you must divide this number by 1000 and multiply by 4.

Examples:

9000: 250 = 9000: 1000 × 4 = 36;

11000: 250 = 11000: 1000 × 4 = 44

Multiplication and division by 37

Before learning how to orally multiply and divide by 37, you need to know well the multiplication table by three and the divisibility by three, which is studied in the school course.

Rule. To multiply a number by 37, you must divide this number by 3 and multiply by 111.

Examples:

24 × 37 = (24: 3) × 37 × 3 = 8 × 111 = 888;

27 × 37 = (27: 3) × 111 = 999.

Rule. To divide a number by 37, divide this number by 111 and multiply by 3

Examples:

999: 37 = 999: 111 × 3 = 27;

888: 37 = 888: 111 × 3 = 24.

Multiplication by 111

Having learned how to multiply by 11, it is easy to multiply by 111, 1111, etc., a number whose sum of digits is less than 10.

Examples:

24 × 111 = 2 (2 + 4) (2 + 4) 4 = 2664;

36 x 111 = 3 (3 + 6) (3 + 6) 6 = 3996;

17 × 1111 = 1 (1 + 7) (1 + 7) (1 + 7) 7 = 18887.

Conclusion. In order to multiply the number by 11, 111, etc., you must mentally move the digits of this number two, three, etc. steps, add the digits and write down between the expanded digits.

Multiplication of two adjacent numbers

Examples:

1) 12 × 13 =?

1 × 1 = 1

1 × (2 + 3) = 5

2 × 3 = 6

2) 23 × 24 =?

2 × 2 = 4

2 × (3 + 4) = 14

3 × 4 = 12

3) 32 × 33 =?

3 × 3 = 9

3 × (2 + 3) = 15

2 × 3 = 6

1056

4) 75 × 76 =?

7 × 7 = 49

7 × (5 + 6) = 77

5 × 6 = 30

5700

Examination:

× 12

Examination:

× 23

Examination:

× 32

1056

Examination:

× 75

525_

5700

Conclusion. When multiplying two adjacent numbers, you must first multiply the tens digits, then multiply the tens digit by the sum of the ones digits, and finally, multiply the ones digits. We will get the answer (see examples)

Multiplication of a pair of numbers in which the tens digits are the same and the sum of the ones digits is 10

Example:

24 × 26 = (24 - 4) × (26 + 4) + 4 × 6 = 20 × 30 + 24 = 624.

We round the numbers 24 and 26 to tens to get the number of hundreds, and add the product of ones to the number of hundreds.

18 × 12 = 2 × 1 honeycomb. + 8 × 2 = 200 + 16 = 216;

16 × 14 = 2 × 1 × 100 + 6 × 4 = 200 + 24 = 224;

23 × 27 = 2 × 3 × 100 + 3 × 7 = 621;

34 × 36 = 3 × 4 cells. + 4 x 6 = 1224;

71 × 79 = 7 × 8 honeycomb. + 1 × 9 = 5609;

82 × 88 = 8 × 9 honeycomb. + 2 × 8 = 7216.

You can solve orally and more complex examples:

108 × 102 = 10 × 11 honeycomb. + 8 × 2 = 11016;

204 × 206 = 20 × 21 honeycomb. +4 x 6 = 42024;

802 × 808 = 80 × 81 cells. +2 × 8 = 648016.

Examination:

× 802

6416

6416__

648016

Multiplication of two-digit numbers in which the sum of the tens digits is 10 and the ones digits are the same.

Rule. When multiplying two-digit numbers. in which the sum of the digits of the tens is 10, and the digits of the ones are the same, you must multiply the digits of the tens. and add the number of units, we get the number of hundreds and add the product of units to the number of hundreds.

Examples:

72 × 32 = (7 × 3 + 2) cells. + 2 × 2 = 2304;

64 × 44 = (6 × 4 + 4) × 100 + 4 × 4 = 2816;

53 × 53 = (5 × 5 +3) × 100 + 3 × 3 = 2809;

18 × 98 = (1 × 9 + 8) × 100 + 8 × 8 = 1764;

24 × 84 = (2 × 8 + 4) × 100 + 4 × 4 = 2016;

63 x 43 = (6 x 4 +3) x 100 +3 x 3 = 2709;

35 × 75 = (3 × 7 + 5) × 100 +5 × 5 = 2625.

Multiplying numbers ending in 1

Rule. When multiplying numbers ending in 1, you must first multiply the tens digits and to the right of the resulting product, write down the sum of the tens digits under this number, and then multiply 1 by 1 and write it even further to the right. By adding it in a column, we get the answer.

Examples:

1) 81 × 31 =?

8 × 3 = 24

8 + 3 = 11

1 × 1 = 1

2511

81 × 31 = 2511

2) 21 × 31 =?

2 × 3 = 6

2 +3 = 5

1 × 1 = 1

21 × 31 = 651

3) 91 × 71 =?

9 × 7 = 63

9 + 7 = 16

1 × 1 = 1

6461

91 × 71 = 6461

Multiplying two-digit numbers by 101, three-digit numbers by 1001

Rule. To multiply a two-digit number by 101, you must assign the same number to this number on the right.

648 1001 = 648648;

999 1001 = 999999.

The techniques of oral rational calculations used in mathematics lessons contribute to an increase in the general level of mathematical development;develop students' skill to quickly select from the laws, formulas, theorems they know, those that should be applied to solve the proposed problems, calculations and calculations;promote the development of memory, develop the ability of visual perception of mathematical facts, improve spatial imagination.

In addition, rational counting in mathematics lessons plays an important role in increasing children's cognitive interest in mathematics lessons, as one of the most important motives for educational and cognitive activities, the development of the child's personal qualities.Forming the skills of oral rational calculations, the teacher thereby educates students in the skills of conscious assimilation of the studied material, teaches them to value and save time, and develops the desire to search for rational ways to solve the problem. In other words, cognitive, including logical, cognitive and sign-symbolic universal educational actions are formed.

The goals and objectives of the school are changing dramatically, the transition from a knowledge paradigm to personally-oriented learning is being carried out. Therefore, it is important not only to teach how to solve problems in mathematics, but to show the operation of the basic mathematical laws in life, to explain how a student can apply the knowledge gained. And then the children will have the main thing: the desire and meaning to learn.

Bibliography

Minskikh E.M. "From game to knowledge", M., "Enlightenment" 1982.

B.A. Kordemsky, A.A. Akhadov The Amazing World of Numbers: A Student's Book, M. Enlightenment, 1986.

Sovaylenko VK. The system of teaching mathematics in grades 5-6. From work experience. - M.: Education, 1991.

Cutler E. McShane R. "Trachtenberg Quick Counting System" - M. Enlightenment, 1967.

Minaeva S.S. "Calculations in the classroom and extracurricular activities in mathematics." - M .: Education, 1983.

Sorokin A.S. "Counting technique (methods of rational calculations)", M, Znani ", 1976

http://razvivajka.ru/ Oral counting training

http://gzomrepus.ru/exercises/production/ Productivity exercises and quick verbal counting

Has it ever happened to you, scrolling through the negotiations just held in your head or your participation in a heated discussion, with annoyance to admit that, unfortunately, only now, after some time, the right argument for partners or an exact replica came into your head? to your opponent? And the train, as they say, has already left. What determines the speed of decision-making, and how to develop the speed of thinking?

Let's turn to a simple comparison. Have you noticed how the speed of information flow differs between a movie in the cinema and a TV series? When filming a film, directors have a good idea of the environment in which the audience will watch it, and depending on this, they choose the appropriate speed of the plot development. In the cinema, you are completely involved in what is happening on the screen.

The rate of information delivery is so high that, to facilitate perception, the rest of the stimuli are removed by turning off the light in the hall. On the contrary, at home you watch the series at a measured pace, you have the opportunity to run to the refrigerator for something tasty, be distracted by a phone call, and still stay in the loop of events on the screen.

The brain of different people also works at different tempo... Someone can easily navigate the information streams falling on him like shots of an action movie, while someone is able to process only the speed of the tempo of a soap opera. The speed of processing incoming information available to a person is called the speed of thinking.

The development of the speed of thinking is one of the directions for the development of a disciplined mind.

The speed of thinking is determined by the speed of the main nervous processes - excitation and inhibition. These are psychophysiological characteristics, and they cannot be influenced by a simple effort of will. But what can really be done is by training your mind to increase the speed of information processing.

So, here are 10 effective exercises for developing the speed of thinking.

Scenario "What if ..."

When preparing for difficult negotiations or a meeting where you are required to respond quickly to a rapidly changing situation, think over possible scenarios in advance. Ask yourself what you will say in response to such and such a question, or how you will act in such and such a situation, or how you will parry the reply of your opponent.

Such training is useful in that it encourages you to build probabilistic models of the future in your head. Use preventive calculation of possible events as a simulator, because when imagining a situation, you can arbitrarily speed up or slow down the speed of your reasoning.

As long as your vocabulary is littered with this verbal husk, the tempo of your thoughts will be slower than the tempo of which you are actually capable.

Practice thinking in another language

When you have the opportunity to reason outside the rigid time frame, force your brain to reason in a foreign language, not your native language. The process you initiate is similar to how Tibetan monks are trained. Performing various physical exercises with stress, they will then be able to perform these exercises without stress many times easier and faster.

The same principle works here: by forcing the brain to build the logic of reasoning in a foreign language, you train it so that it can then do the same in its native language much faster.

Reading with a stopwatch

Read a chapter of any book as quickly as possible. Time the time it took you to read. Now time again and quickly retell the basic information you just read. Do this exercise regularly, each time trying to reduce both the time for reading and the time for retelling. So you develop both the speed of perception and the speed of reproduction of information.

Speed Alphabet

Place a piece of paper with the letters of the alphabet in front of you. Come up with 3 words as quickly as possible, beginning with each letter of the alphabet: three words with "a", then three words with "b" and so on until the letter "i". Gradually increase the number of words to come up to 10.

To complicate this exercise, use the stopwatch again. Measure how long it takes you to find 30 words. Then try to shorten this time by speeding up the pace of the task.

With Wikium you can do exercises to develop the speed of thinking according to an individual program

Expensive calls

Sometimes abroad very quickly money is spent for international calls on a mobile phone. Imagine that every second of your conversation costs a lot of money. When recalling a conversation you just had with someone, make it a rule to mentally repeat it in such a way as to shorten its time as much as possible. Think about how you could cleanse this conversation of unnecessary information noise - unnecessary phrases and questions that could well be dispensed with.

Practice engaging in business dialogue with someone, if the situation permits. Imagine talking on a phone where calls are very expensive. Try to speed up the dialogue, speak and think faster than you usually do. Focus only on the essentials, choose only the most accurate words, do not get distracted from the topic, speak and respond quickly.

Define your priorities

Use prioritization practice to practice quick thinking. Everything you deal with, make contacts, surround you, you can rank from important to unnecessary and useless. The ranking habit structures your personal information space.

Just as it is easy for you to find the right things where they are located in a certain order you know, it will be easy for you to find the information you need to make a decision. While this recommendation is hardly a developmental exercise, following it means preparing your brain for quick decisions ahead of time.

Read humorous stories

Not just stories. You can also make it a rule to watch humorous drawings. A sense of humor is always associated with a high speed of response to a situation. Plus, this involves the ability to see a non-obvious contradiction and designate it in the most vivid and precise formulations. All this together is a quick thinking.

Don't just read or memorize witty anecdotes, but strive to understand what is the essence of the joke, why does it cause laughter?

Collecting a collection of puns will benefit your mind just as well. By accumulating such unusual experience of reaction, you train your brain at the right moment to produce something similar.

"Upside down"

This exercise has something in common with exercise 3, but it is much easier to perform. And more fun, too. When you pick up a magazine or book or newspaper, turn it over so as to change the top and bottom and flip through, looking at the pictures and photographs placed there.

Try to understand what is depicted there, and do it as quickly as possible. This is how you train your brain to recognize non-obvious signals, to navigate in the situation of "shape-shifters". And, most importantly, not to be satisfied with the first answer, but to delve into a deeper assessment of the situation. You can place a complex intricate picture upside down on your computer desktop.

Changing speeds

Since we are talking about the speed of thinking, it is worth practicing in controlling the speed of your processes. Do the same thing, changing the speed of its completion. For example, you can brush your teeth at different speeds, drink a glass of water, read a letter received in the mail. By deliberately speeding up and then slowing down your actions, you train your brain to work at different tempo and rhythms. Slow execution try to gradually make it even slower. Conversely, speed up fast execution every now and then.

These exercises will not work if not done regularly.... Doing one task each day will stimulate your brain to develop in the right direction.

If you really intend to get serious about solving a problem, how to develop the speed of thinking, the exercises suggested here will help you

promptly respond to a problem situation,
do not regret that the right decision came to mind with a delay,
protect your brain from early aging and destructive diseases such as Alzheimer's.

In the life of each of us, there have been situations when it was necessary to study certain material within a short period of time. The best solution to this problem is mastering. Moreover, it can be successfully applied not only for scientific, but also for fiction. At the same time, for any person, the technique of fast reading with a high level of memorization is especially relevant and significant. How to achieve the desired effect? To do this, you need to study the 7 basic rules for fast reading. What are they all about?

Reading without regression

Often, a person studying the material necessary for him makes return movements with his eyes. This is regression, the purpose of which is to repeat lines that have already been read. This is the most common flaw that can lead to slow learning.

Unbeknownst to themselves, many readers scan the text twice. It does not matter whether it is easy to perceive or not. Regression is performed for fidelity, resulting in a sharp decrease in reading speed.

However, there are returns that are deemed valid. A person makes these movements with his eyes when a new thought appears. They, in contrast to regression, are called reception. Such repetitions are quite reasonable, since they allow you to comprehend as deeply as possible what you have already read. Methods for quickly memorizing text do not recommend such return movements. In this case, repeated reading is possible only after the text has been completely passed through.

Remember that avoiding reciprocations and regressions is very important. He is able to double and triple the quality of his understanding.

Reading without articulations

Sometimes, when studying the material inwardly, a person makes involuntary movements with his tongue, lips and larynx elements. This is articulation. Its intensity is in direct proportion to the complexity of the text and the development of reading skills. Moreover, articulation is observed in everyone, even in fast-reading people. This is confirmed by special measurements and X-ray photography of pharyngeal modulations, made in the process of studying the text silently.

The technique of fast reading with a high level of memorization excludes the internal pronunciation of words. This is due to the fact that articulation is an important obstacle to quickly learning the material. Such should be excluded if the speed reading technique is mastered. At the same time, exercises for speed reading should be aimed at eliminating the pronunciation defect and depend on its type. So, if articulation is a mechanical movement of the tongue, lips, mumbling, etc., then it is necessary to exercise constant control over this process. How? Take something in your mouth or hold your tongue firmly with your teeth. Pain will be the most noticeable inhibiting factor.

It will be more difficult to eradicate the pronunciation of words in the speech center of the brain. The main method is to knock out the wedge with a wedge. He uses the fact that the centers of speech and control over movements are next to each other. It is recommended to record a non-musical rhythm (metronome) produced at different frequencies and combinations. This knock should be read.

Integral Algorithm

For people studying large amounts of information, the technique of fast reading with a high level of memorization of the necessary material is extremely important. How do you achieve this? It is necessary to develop an integral reading memorization algorithm. After all, many simply do not think about how to study the text. As a result, they read extremely slowly. The speed and reading technique that is used in the study of the material depends on the goals and objectives set by the reader. A person must develop appropriate programs, as well as flexibly and skillfully use them at the right time. This will largely determine his speed reading ability.

Vertical eye movement

This is the fourth rule of the fast assimilation technique. It presupposes the perception of a larger portion of the text than with ordinary reading. Expansion of the field of vision can significantly increase the efficiency of assimilation of the material. A person who reads quickly during one fixation of a gaze is able to perceive not just 2-3 words. It captures the meaning of an entire line, sentence, or even a paragraph.

Phrase comprehension is a fast reading technique with a high level of retention. Why is this happening? The fact is that, looking over large fragments of text, a person creates for himself visual-figurative representations of the material presented. They are a vivid explanation of the meaning of what you read. With this technique, the eyes move vertically, towards the top in the center of the text.

Highlighting the dominant

What accompanies the most effective perception of the material? First of all, it should be understood. This means nothing more than the establishment of logical connections between objects using the knowledge that a person already has.

Speed reading and understanding of text is a problem that psychologists have been successfully investigating for a long time. Sometimes the material we perceive is quite simple. In this case, his understanding goes next to perception. A person immediately remembers the knowledge he received earlier and associates it with the phrases he read. However, the text can be unfamiliar and difficult. In this case, its comprehension is a complex and lengthy process. How can you speed it up? To do this, you should be careful while reading, as well as possess a considerable baggage of knowledge, being able to apply them in a given situation. You will also need to use some techniques. One of them is to highlight the pivotal semantic points of the text. What is its meaning? To increase the perception of the text, it is divided into two parts, making a semantic grouping. At the same time, a dominant is highlighted, which deepens the understanding of the material and contributes to its more effective memorization. Also, thanks to this, it develops speed reading memory.

Fast reading in this case becomes possible when the text is perceived in the form of short and at the same time significant logical formulas. Each of these structural units has a concept that is basic in its meaning, which is associated with a certain image. Reading the entire text is the creation of a single logical chain of ideas. This is the essence of the method for identifying pivotal semantic points.

Another technique can be used to comprehend the material. It is called anticipation, or anticipation. This is a semantic guess, which is a psychological process of orientation towards the future, which is within the framework of the foreseen. Anticipation is based on knowledge of the logic of developing events, as well as the analysis of the existing signs of the phenomenon and the assimilation of its results. This speed reading technique is possible in the presence of a latent expectation reaction, when the reader is tuned in to certain actions that arise in the course of the text. At the same time, a person's thinking should work very productively, comprehending the idea of content and identifying the main intention of the author. Thus, anticipation during speed reading is the formation of a kind of flair for stereotypical phrases and the accumulation of an extensive dictionary of text stamps. It is also a prerequisite for the development of a semantic processing of the studied material brought to automatism.

Development of attention and memory

High-speed reading and memorization require a selective focus of consciousness to perform a certain work. This function represents attention. People are often incapable of self-organization. That is why they are not able to control their attention while reading. So, in a person who slowly perceives the material he needs, attention often switches to all sorts of extraneous objects and thoughts. This leads to a loss of interest in the text and misunderstanding of its meaning. Those who read quickly can control their attention.

One of the components of effective mental work is the ability to concentrate on the issue in question. This ability is best trained by mentally reading the words backwards. You can do this everywhere, for example, while traveling on public transport. Any word must be represented in the form of letters and read them backwards. For example, "water" - "hells". First, you can take words consisting of four letters, and then select them more authentic. This exercise is great for training attention.

Compliance with a mandatory norm

The seventh rule of fast reading implies daily reading of two newspapers, one popular science or scientific and technical journal, as well as a book volume of 50-100 pages. Why is it important? The fact is that in order to master the technique of fast reading, it is necessary to produce a complex effect on various aspects of the individual's mental activity.

This leads to the implementation of a program of technical re-equipment of the brain, which rebuilds consciousness and breaks the prevailing stereotypes of thinking.

Help in mastering speed reading

You can learn how to quickly and efficiently comprehend the material on your own. To help those wishing to master the technique of speed reading, various book publications are offered. Their authors describe a technique for effective perception and memorization of material. Here you can also familiarize yourself with exercises for mastering fast reading.

You can study the basic rules of speedy perception of the material at specially organized group sessions and trainings. This training option is the most effective.

Fast reading pace

Anyone who has mastered the technique of high-speed perception of the text processes information at different speeds, choosing it depending on the type of literature. Thus, news and newspapers are read with a speed that allows you to grasp their meaning. Fiction requires a special speed that includes imagination. Scientific publications require not only speed, but also thorough study of the material.