How to solve learning examples correctly. How to teach children to solve math problems: advice from eminent teachers and ordinary mothers

Good afternoon, dear readers! How much effort adults have to make to teach a child to count between 10 and 20. And not only count, but also solve examples, subtract and add! At the same time, this is not as difficult to do as it seems at first glance. We offer you non-standard play techniques on how to teach a child to count examples within 20.

Where to begin?

Stage 2

If you have learned to count, we get acquainted with the graphic representation of numbers. For this purpose, we use cubes with numerical images, cards.

Stage 3

The next step is very important: it prepares the foundation for quick mental arithmetic. This is the study of the composition of the number. If the baby knows exactly how numbers are decomposed, he will easily solve examples for addition and subtraction.

The study of the composition of the number is traditionally carried out using the so-called "houses". Draw a house on paper in a box. On one "floor" there are always 2 cell rooms. The number of storeys of a house is determined depending on the number of numerical pairs into which the digit can be decomposed.

For example, 4 can be decomposed into 3 and 1, 2 and 2. This means that the number 4 lives in a two-story house, etc. We will write it on the roof. The example clearly shows how to correctly make houses for the numbers 3, 4 and 5.

The child will have to memorize the resettlement of the “tenants” on the floors. Start with small numbers. Ask the baby to carefully look at who lives with which neighbor, and then “populate” the numbers on their own.

When the two and three are mastered, move on to more complex numbers. This technique gives the most solid results. Proven on my own experience.

Here you can download such a table and use it to master the methodology for the composition of a number:

Stage 4

When the houses are passed, the turn of examples within 10 came. In the first grade these examples will have to be solved in the first half of the year, so it is better to prepare in advance. Now all that remains is to put the + or - signs between the "settlers", having previously explained their purpose to the baby.

First, present addition or subtraction in the form of a game. For example, one left the four from the floor. Which of the neighbors will stay on the floor? Answer: three. Such exercises will help the little one quickly get used to mathematical examples. Gradually we change the words “left”, “came” to “plus” and “minus”.

So we mastered counting within 10 with the child. As you can see, the technique is very simple, but it takes time and patience to operate. Try to make the baby count in the mind first: written exercises slow down thinking.

Along the way, train the concepts of "more or less" (first use objects, spreading them out on different sides, then compare the numbers), neighbors of the number (write a series of numbers with missing numbers and ask the baby to complete the row by placing the neighbors correctly).

Move on…

It's time to introduce the kid to the second ten. To overcome arithmetic difficulties, we offer the following training algorithm:

Part 1

We introduce the concept of ten. To do this, lay out 10 cubes in front of the child and add one more. Explaining that this is eleven. We say that the end of the word "dtsat" means "ten". To form a number from 11 to 19, you just need to add the number to the end of "d" and put the preposition "on" between them.

Part 2

Since the baby is already familiar with the concept of ten, we introduce the category of units and, when adding, we operate with these concepts. For example, 13 + 5. First add the units: 3 + 5 \u003d 8. Now add the remaining ten and get 18.

Part 3

Now let's move on to examples for minus: we act in exactly the same way. Subtract units, then add ten.

Part 4

The most difficult stage is subtraction, in which the first unit is less than the second: 13-6. In this example, we cannot subtract six from 3. You have to deal with a dozen. One of the ways is to subtract three from six, subtract the remaining number from ten, i.e. 6-3 \u003d 3, 10-3 \u003d 7. After a few workouts, your child will be able to do mental subtraction.

The child must clearly master the skills described: in grade 2 he will need this to solve examples with two-digit numbers.

To brighten up the learning process, you can use various aids:

• cubes;
• magnets;
• pictures (teaching with pictures is especially diverse: you can simply count them, use coloring pages with examples to consolidate counting skills);
• any items at hand;
• counting sticks;
• abacus, etc.

The more you show your imagination, the sooner your child will be interested in mathematics.

We have considered the sequence of training crumbs to solve examples within 20 stages. If the article was useful to you, leave a comment or share the article with your friends in social. networks.

See you soon, dear friends!

With the entrance to primary school, a change in the main activity of the child takes place: more and more of his time is now occupied by educational activities. During this period, much attention began to be paid to teaching oral counting. And in this matter, the actions of the teacher and the parent should be the same: if the child is required to be able to count in his head during the lesson, and this process is not controlled at home, then the skill will take a very long time to develop.

How to develop the skill of oral counting?

Many teachers do not recommend it, because with this method they do not strive to memorize the result, because the necessary tool is always nearby. And if there are not enough fingers during the counting, then the child will have difficulty.

It is undesirable to constantly use sticks to find the result. When working with large numbers, a child can get confused and come to the wrong decision. Of course, you cannot completely ignore these methods, but it is better to use them to explain the material, and not constantly. Gradually reducing their use, you need to come to the skill of oral counting.

It is based on three components:

1. Abilities: a child, in order to learn to count in his mind, must first develop the ability to concentrate and memorize several things at the same time.
2. Knowledge of fast counting algorithms and the ability to choose the most effective in a particular situation.
3. Constant training , which will automate the solution of complex problems and improve the speed and quality of the account.

The last component is the main one, but the importance of the first two should not be underestimated: knowing a convenient algorithm and having the necessary mathematical skills, you can quickly solve the required example.

The development of the mental counting skill of younger students is based on two types of activities:

1. Speech - before performing an action, the child first says it out loud, then in a whisper, and then to himself. For example, solving the example “2 + 1”, he says: “to add 1, you need to name the next number,” and in his mind he determines that it is 3 and names the result.
2. Motor - first adds or removes objects (sticks, cars) to calculate the result, then does it with a finger, and at the last stage - with his eyes, performing the necessary actions in his mind.

You can invite your child to work with numbers using the manuals offered by different methods.

Zaitsev's technique

Allows you to educate a child who thinks logically, who can analyze information and generalize it, highlight the essential. For students in grades 1-2, these manuals will help you understand the arithmetic operations with numbers.

To study mathematical techniques, you will need special cards ("Stoscounting") with numbers 0 - 99 and tables that clearly show the composition of numbers (the required number of cells is filled in).

First, the child gets acquainted with the numbers of the first ten, determines the composition of his number, and then proceeds to arithmetic operations with the studied numbers.

A video lesson with children using his own methodology is conducted by N.A. Zaitsev.

The work is carried out with colored cubes and boxes with cells, where 10 cubes can fit ... With the help of a set, children are explained the concepts of "composition of a number" and "ten" and are taught the skill of oral counting.

Even a smart child may sometimes not understand the simplest things. This does not mean that he is incomprehensible or unintelligent, most likely it indicates a lack of interest.

After all, children can perceive information and remember it only when it evoked an emotional response in them. Children experience vivid positive emotions during an interesting game, therefore, it is better to teach the skill of mental counting in play activities.

For example, children imagine that the cubes are gnomes and the box is their house. There were 2 gnomes in the house, 3 more came to visit them. The task is clearly demonstrated, the lid of the box is closed and the question is asked: "How many gnomes are there in the box?" To answer the question posed, children will have to do it in their head, without relying on cubes.

Gradually, the tasks become more complicated, children learn to add and subtract with the transition through a dozen, and then two-digit numbers.

The video plot tells about teaching children according to the method of Sergei Polyakov

Algorithms

Knowledge of simple arithmetic rules and patterns will help you quickly find the result in your mind:

• To subtract 9 , you can first subtract 10, and then add 1. Similarly, subtract numbers 8 and 7, only then add 2 and 3, respectively.
• The numbers 8 and 5 are added as follows: first add 2 to 8 (to get 10), and then 3 (5 is 2 and 3). All examples of addition with a transition through ten are solved in a similar way.

For adding two-digit numbers, the following algorithms are suitable:

27+38=(27+40)-2=65
27+38=(20+30)+(7+8)=50+15=65

In the first case, the second term is rounded to tens, and then the added number is subtracted. In the second, the bit terms are added first, and then the results.

When subtracting, it is convenient to round the subtracted:

Workouts

For training, you can use special computer programs or games:

1. "Score" ... The child can play the role of both the seller and the buyer, all calculations must be carried out in the mind. The prices of goods are set according to the abilities of the student.
2. "Cheerful account" ... An adult throws a ball to a child and names an example to be answered. Thus, the account is brought up on the machine.
3. "Chains" ... A chain of examples is given, children need to find the final result without writing down intermediate results of calculations.

If the child regularly counts in his mind, then this skill will develop. Such classes will be a good basis for and with three-digit numbers.

The video plot will tell you how to teach a student to count quickly in the mind - not mental arithmetic

What a child should be able to do before learning to add-subtract

Can count up to 10 or more

"One, two, three ... there are six apples."

What we just didn’t consider - and the steps in the entrance, and the trees in the yard, and the bunnies in the book ... It looked something like this. "How many bunnies? Show your finger. One, two, three. Three bunnies. Show three fingers. Clever girl! Right!" At first, the son was not interested in counting, he liked to search more. The game of hide-and-seek is also not superfluous: "One, two, three ... ten. I'm going to look. Who didn't hide, I'm not to blame!" At 3 years old, we could not count to 10, instead of numbers we pronounced unknown words with a similar intonation. But later, due to the fact that it was often required to show the number of fingers, numbers were associated with the number of objects.

Knows the numbers

"One, two, three ... there are six apples. The number" six "is written like this" 6 "."

I don’t remember any special exercises that we would do. Everything happened in passing. "What floor are we on? On the second. Look, here is his number written on the wall." 2. Show two fingers. Well done. " In the elevator: "What floor does grandma live on?" - "On the 3rd" - "Which button should you press?" - "This one" - "I didn't guess a bit. Here is a three." In the store: "We have the key to the box at number 9. Here, you see, there is a tag on the key. On which box is this number written?" Something like a wardrobe number. In line to see the doctor: "What is the room number? Here is the number." - "Two" (as I understand it, at random) - "No, this is the number" 5. Show 5 fingers. Good! " "When is Dad coming?" - "In an hour. Look, now the short arrow is at 6. When this arrow is at 7, right here, then it will come." "Please switch to channel 1. Carry the remote control. One is written here. Press this button. Thanks." Interesting. The numbers define a color. In addition to studying color and number, fine motor skills are trained. The numbers written in mirror by the child must be corrected. There is a diagnosis of dysgraphia. To exclude it, you should contact a speech therapist.

Can expand (name) the numbers in ascending-descending order

"Baba Yaga came and mixed all the numbers. Can you arrange them correctly?"

Up to three or four years old, the child needs to be taught comparison, namely: 1) to distinguish between the concepts of big-small, high-low, long-short, heavy-light, wide-narrow, thick-thin, old-new, fast-slow, far - close, hot-warm-cold, strong-weak, etc. Search for the smallest object, the longest ... 2) combine objects: by color, shape and other characteristics (dishes, clothes, furniture, pets), find differences in pictures. 4) remove an extra item in a row (for example, from several red apples, one green), continue the row (for example, ▷ ☐ ▷ ☐ ▷ ☐?), Name the missing item (for example, ▷ ☐ ▷? ▷ ☐ ▷), distribute in pairs (for example, ▷ ☐ ▩ ☐ ▷ ▩), to name what happened first, what then (first put on a jacket, then a jacket, and not vice versa; first it is autumn, then winter ...). 5) fold a pyramid, a puzzle, put beads in a certain sequence. Only I have at least 20 books with similar tasks for kids. Previously with my son, now with my daughter we look through them with enthusiasm and pronounce them. "Show me all the fruits" - "Here" - "Well done!" (clap our hands) - "What is this fruit?" - "Orange" - "Uh-huh. Still there?" ... By the age of 4, you can and should introduce board games (you already have enough perseverance and attention): dominoes, cards, loto, with chips (each player has a chip) and dice (the move is made by the number of points dropped on the dice), where the first person who reaches the finish line on the drawn card becomes the winner. We used standard options, not childish ones. The cards were played in "Drunkard" with a full deck (with 2 and 3): the deck is divided into players equally, in the piles the cards are turned face down and the top is drawn, there are no suits, the one whose card is larger (7- ka beats 4-ku, 2-ka beats an ace, two more equal cards are put on two equal cards: one is face down, the other is face-down, the second time only the top cards are evaluated: "Who takes?" - "Me!" - " How ?! Which is more: 5 or 10? Let's count ... "), she joins the common pile, the one who has the whole deck wins. There is no limit to joy if the whole family sits down to play (with dad, grandmother, grandfather ...). The child learns not only to play, but also to perceive defeat correctly. It is better to be able to iterate over the numbers from 1 to 10, and vice versa, from 10 to 1, than to count to 100. When we were 5 years old, we confidently did both. The countdown can be said in the relay: "Who will collect the most cubes? Prepared! Ten, nine, eight ... one. Start! ". We arranged such contests when it was time to clean up the scattered toys. To learn how to count to a hundred we were helped by pictures, where we need to connect dots in ascending numbers. Speaking, it turns out a good result." Then what comes? "The appearance, the pronunciation of the number and the order of the sequence are remembered. You can interpret that in dozens of the numbers are the same, while writing the numbers as follows:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

And it is handy to fix the material along the way: "When will we arrive?" - "Not long left. You will count to a hundred and we will come. Come on together. One, two ..." We did not study more than 100 before school. She answered the questions only when the child himself was interested: "What comes after 100? And how much will be one thousand and one thousand?" Or if the numbers met in everyday situations: "We are waiting for the 205 bus. Two zero five. Tell me when you see the 205". It is also useful to name the numbers before or after a given number or in a certain interval. The game will help in this: "I have guessed a number from 1 to 20, try to guess it with 5 attempts, and I will say it more or less than the number you named. I wondered." - "Three" - "More" - "Seven" - "Less" - "Five" - \u200b\u200b"Well done! Guessed right! Now it's your turn to guess the number."

Knows more-less concepts

"Daddy has 6 apples, mommy has 8. Who has more apples?" - "Mom."

The clubs explain that the number 22 is greater than 18, as it is closer to 100. This is true, but we laid out heaps of nuts in parallel, erected towers of cubes to connect the image of the number with the number of objects. More-less is gradually becoming more complicated, as is addition-subtraction. Almost simultaneously with the plus-minus-equal signs, the more-less-equal signs are entered. The son was then a little over 5 years old. "On the one hand, there are many apples [intonation is required!], The distance between the fingers is large, next to the open side of the sign there is a larger number." "On the other hand, there are few apples, the distance between the fingers is tiny, the corner looks at a smaller number." "Equal", "equal", "at the same time", "the same", "the same amount" is the same: "You and dad have the same mugs", "I have the same amount of soup", "Share the sweets equally with your sister." There are no problems with this concept when there are two children in the family. next example

The most difficult thing is to compare numbers with the same digits. We have almost always solved them. next example

How to teach a child to add (subtract) to 10

Counting on fingers

"Dad has 3 apples. Unbend three fingers. Mom has 2 apples. Unbend two more fingers. How many apples are there? How many fingers? One, two, three, four, five. Mom and Dad have five apples."

"Dad has 3 apples. Unfold three fingers. He shared one apple with you. Bend one finger. How many apples does he have? One, two. Dad has two apples."

"Dad had 2 apples. Show me two fingers. Dad got hungry and ate both apples. Take two fingers away. How much does he have left?" - "Dad ate everything. Dad didn't give me an apple: (Dad needs to be put in a corner!" - "Uh-huh, Dad has no apples left. He has zero apples. Hee-hee, and yes, he needs to be put in a corner."

The child must count all the items. Do not rush, the understanding that 5 fingers on one hand does not come immediately.

With objects on paper

next example

+ =

next example

- =

We had difficulties not with finding an answer, but with pronouncing the whole example with signs, with the correct declension of objects. "One, two, three. Three candies. PLUS. One candy. How many? One, two, three, four. Four candies. Come on again. Three candies PLUS one candy EQUALS four candies."

With numbers on paper

next example

+ =

next example

- =

Three examples a day is enough. Six months later, their number can be increased to 5-7. The answers need not only be spoken, but already written down.

Number composition

change How many points need to be drawn to get it points?

From the words "addition table", which is crammed as "multiplication table", I start to itch. The child's reasoning and logic, in my opinion, at this moment is completely turned off. Therefore, I tried to put my son in such conditions that he himself would guess that the result of adding different numbers can be the same number. "One plus two?" - "Three" - "Two plus one?" - "Three" - "That is, the sum does not change from the change of the places of the terms" (hmm, the latter was pulled out automatically: what is the "term" I did not explain to my son). "Can you solve examples: 2 + 3 \u003d? 1 + 4 \u003d?" - "Lightweight! Five. Oh, there are five too. And there and there are five!" You can also take seven spoons: "How many spoons are there?" - "One, two, three ... seven." Set one spoon aside: "How many spoons are in each pile?" - "One and one, two, three ... six" - "And in total?" - "Seven" - "It turns out that 1 + 6 \u003d 7". Move one more spoon: "And now how many spoons are in each pile?" - "Two and five" - \u200b\u200b"And in total?" - "Seven" - "Look, the number of spoons in the piles changes, but the total remains the same." Further in the club, he painted houses in which numbers live (already without my participation). There are two apartments on the floor. It is necessary to resettle all the tenants so that on each floor their number is equal to the number indicated by the owner on the roof.

_ _ / \ / \ / \ / \ / 2 \ / 3 \ /_______\ /_______\ |_0_|_2_| |_0_|_3_| |_1_|_1_| |_1_|_2_| |_2_|_0_| |_2_|_1_| |_3_|_0_|

Without recalculating the first number

"Dad has 3 apples. Mom has 2 apples. How many apples are there? Three are already there. Bend three fingers. Now two more. Three, four, five."

She herself did not notice how the son stopped counting all the items. Explained a couple of times, but did not insist.

Under a given condition, formulate, write down and solve an example yourself

"Look. There is a problem." You have 7 games loaded on your tablet. You have already played 5. How many unexplored games are left? "-" Two "-" Right. It can be written as "7−5 \u003d 2". Interesting Will you be able to paint a similar problem yourself. "After dinner you need to wash 10 dirty dishes. 4 are already washed. How many more are in the sink?" "-" Six "-" How to write down? " - "" 10−4 \u003d 6 "" - "Well done!"

Problems should be simple and mundane, with objects from everyday life, with questions "how much", "how much." "You have 3 cars. They gave you 3 more cars for your birthday. How many cars have you got?" (6) "You have 6 pencils, the girl you played with yesterday - 2. How many more pencils do you have?" (4) "You are 5 years old, Nikita is three years older than you. How old is Nikita?" (8) "There are five dogs and three balls. Is there enough for everyone? How many balls are missing?" (no, 2) "There are 2 pears and 4 bananas growing on a birch. How many fruits are there on a birch?" (0, since no fruit grows on birch)

Relationship between addition and subtraction

Subtraction is the opposite of addition. In other words, in order to more comfortably find the unknown variable x (pronounced "x") in the equation x + 1 \u003d 3, the entry is reduced to x \u003d 3−1 (when the number is carried over early, it changes its sign from plus to minus and vice versa ).

Full example: x + 1 \u003d 3 x \u003d 3 - 1 \u003d 2 This is the connection that needs to be conveyed to the child. That is, to show that 2 + 1 \u003d 3 is the same as 3-1 \u003d 2 and 3-2 \u003d 1. Why can you suggest that he himself, on the basis of what he saw, come up with 3 conditions of the problem (instead of points there can be bows, houses, cars, etc.).

Change Total points

"What examples do you think can be written? Let's say 6 + 2 \u003d 8 or 2 + 6 \u003d 8" How many points are there? " 8 - 2 \u003d 6 "How many green dots?" 8 - 6 \u003d 2 "How many pink dots?" Now it's your turn. " next example

- =

− =
+ =
+ =

Without counting fingers

When you have calculated a lot of examples, you just already know that 2 + 3 \u003d 5 and there is no need to double-check on your fingers.

How to learn to count within 20

Counting by lines

"6 plus 8. First draw 6 lines, then add 8. How many lines are there? Six, seven, eight ... fourteen. Answer: 14"

Counting from 10 to 20

There were no problems, so I don't even remember how I explained. She also showed the solution in a column (tens under tens, units under ones). In order to keep the numbers from slipping, she outlined six cells with a pencil. Even when my son gave the correct answer, she sometimes asked him to write a column.

11 + 4 ----- 15

Account in ten

Number composition

The statement that it is easier to count dozens was also translated into the plane of trial and error. For what it was exchanged 100 rubles for 1 ruble. A handful of coins was taken. The child was asked to count the number of rubles. Even counting 37 coins is difficult. But if you put the coins in piles of 10 coins, then there will be fewer mistakes. "Ten, twenty, thirty, and in this heap there are seven. A total of thirty-seven." I also asked me to collect money for travel: "To get to the hospital and return back I need 52 rubles. Count me, please ... Oh! There is not enough money for the way back! How can I get home?" Later, a problem was voiced: "Count how many steps to the apartment - you will get a prize" (there were exactly 10 steps between the flights).

Imaginary fingers (within 12)

"How much is 6 + 6? Imagine that you have two more fingers on your right hand. Six, seven, eight ... twelve."

I didn't expect the proposed idea to be so good.

On fingers

"What is 8 + 9? Bend eight fingers"

"Two fingers are already unbent. Let's swing more to get 9. Three, four, five ... nine."

"There are already ten fingers: these are 8 previously bent and 2 unbent from 9. Now we count the number of fingers to bent. Eleven, twelve, thirteen ... seventeen. Answer: 17."

On a paper sheet

next example

+ =

next example

- =

7 + 8 = 7 + 3 + 5 = 10 + 5 = 15 ↙↘ 3+5

"How much do you need to add to 7 to make 10?" - "3" - "Right. Is eight minus 3?" - "5" - "We replaced 8 with 3 + 5. Where did 3 come from?" - "Out of 8" ...

13 - 6 = 10 + 3 - 6 = 4 + 3 = 7 ↙↘ 10+3

"Thirteen can be written as 10 plus 3. Subtract 6 from 10. What happened?" - "4" - "Add 3" ...

At the age of six, we solved such problems, but, as far as I saw, my son did it not meaningfully, but in the image and likeness. But if after, say, example 6 + 7 \u003d 13, you ask how much 6 + 8 will be, the child gives the correct answer "14". To the question "Why?" the laconic "Because 1" sounds.

In the mind

Repetition is the mother of learning. The more examples, the less often you turn to the above methods.

Practice!!!

You need to go with your child to the store for a single item (bread, pen, candy, ice cream) with a given amount of money. But so that he was the buyer, and you would be just an outside observer. He should be asked if there is enough money to buy a thing [more-less]. It is necessary to explain that the seller must give change if the amount of the transferred funds exceeds the price [by how much / deduction]. After a while, replace one coin with two, and then with three [addition].

My son had 10 rubles in one coin. I was thirsty and I offered him to buy a bottle of water myself. The following dialogue came out with the seller: - "Can I buy water?" - "Yes. It costs 8 rubles." - "Is there for 10?" That is, he did not begin to think whether he had enough money or not. If they said that there was no bottle for 10 rubles, he probably would have turned around and left.

Math for a preschooler: what else is useful in grade 1?

Orientation in space

"Where is your left hand? Close your right eye. Grab your left ear. Jump on your left foot. How many cars are on your right? And to your left? And in front (in front)? And behind (behind)? What color is the car between gray and green? is under the table? On the table? Above the table? Around? Near? Inside (in)? Outside (s / s)? Who got up from the table? What did I get from under the table? "

We played games like this. The presenter (either me or my son) on the street gave instructions to the one who closed his eyes: "Slow down, there is a bump in front, there are two steps left, one, two, now raise your right leg high ... A man is walking behind you, move to the left, a little more ... A cyclist is on the way, two steps to the right faster. " The presenter (either me or my son) drew a plan of the room, marked on it with a cross where the toy was hidden, which the second player had to find with the help of the plan. I laid out notes around the apartment indicating where the next piece of paper was: "In the kitchen table", "Under the sofa", "Above your bed" ... The last note said where the treasure was. The first was given to her son. I gave (plus they did something in the club) to make sure there were no problems with him: "From the point two cells up, one diagonally, to the right ..." And I checked on a piece of paper: "In the upper right corner draw A star. In the center is a flower. To the left of the flower is a circle. In the middle of the bottom edge of the leaf, put a cross ... "

Geometric figures

"What does a ball look like? What's the difference between an oval and a circle? What shape is the stool when viewed from above?"

Even odd

"Tell me, please, the even numbers? (2, 4, 6) And the odd ones? (1, 3, 5)" The definition that "Even numbers" are those that are divisible by 2 will not work here. Therefore, while walking, I drew my son's attention to the sign on the house "27 → 53". "Do you know what she means?" - "..." - "It shows that house numbers will increase if you go in this direction. But, since only houses with odd numbers stand on this side, they will increase like this:" 27 "," 29 ", "31" ... What do you think the number will be after "31"? " - "" 32 "" - "Nope," 33 ". This is the odd side. And after" 33 "?" - "" 35 "" - "Well done! Let's go check it out. So, this is" 27 ". And that one?" - "" 29 "" - "Let's see ... Well, what's the number, here it is?" - "" 29 "" ... By the way, I remember the question of the boy in the club, who puzzled the teacher: "Is zero an even or odd number?" It is immediately clear that children do not memorize, but delve into, their gray cells are working.

Preparing for multiplication

At six years old, it is useful to study how the minutes are grouped on the clock (by 5), why by showing "2" we are talking about 10 minutes.

There are also interesting tasks for associations of two: "Six legs are visible from under the fence. How many chickens are hiding behind the fence?" or "How many mittens do 4 kids need?" next example

Three flowers can stand in 4 vases, six fish can swim in 3 aquariums, etc.

At what age to start learning math

The level of education in Russia is now such that it is the parent who will have to explain the basics of mathematics to the first grader. In order to have time to maneuver, in order to enter this process gradually (it is not for nothing that first-graders have vision loss), so that tasks are perceived as entertainment, and not labor service, one should begin before the child goes to school. If at some point the baby does not understand (does not remember), then it is worth either trying to explain it in a different way, or quit and return to the material after a while, or find a suitable incentive ("If you solve an example without my prompting, you will get a prize"). It is better to write examples on paper, rather than looking at the monitor.

We turned to puzzles at the moment when there was a desire for it. It turned out in raids for 3-4 days (to consolidate the material) every two to four weeks. Why is it so rare? For comparison: we learned reading skills at least twice a week using the textbooks of N.B. Burakova (not advertising, she mentioned, because his approach suits him). There is one big difference between reading and counting. To learn the first, you need to memorize (if there is no periodicity, the child begins to confuse letters), and the second - to understand.

In children, visual-figurative thinking prevails. The problem is that most mathematical concepts are abstract and poorly understood or memorized by younger students. Therefore, any mathematical operations must be based on practical actions with objects.

Teachers use three main ways to teach a child to count in the head:

• based on knowledge of the composition of numbers;
• memorizing tables of mathematical actions by heart;
• using special techniques for performing mathematical operations.

Let's consider each of them.

Preparation for learning oral counting

Preparation for oral counting should begin with the first steps in learning mathematics. Introducing the child to numbers, it is imperative to teach him that each number represents a group with a certain number of objects. It is not enough, for example, to count to three and show the child the number 3. Be sure to ask him to show three fingers, put three candies in front of him, or draw three circles. If possible, connect the number with fairy-tale characters known to the child or other concepts:

• 3 - three pigs;
• 4 - ninja turtles;
• 5 - fingers on the hand;
• 6 - heroes of the "Turnip" fairy tale;
• 7 - gnomes, etc.

The child should form clear images attached to each number. At this stage, it is very useful to play math dominoes with the children. Gradually, pictures with dots that correspond to the corresponding numbers are imprinted in their memory.

You can also practice learning numbers with a box of cubes. Such a box should be divided into 10 cells, which are arranged in two rows. Getting acquainted with each number, the child will fill in the required number of cells and memorize the appropriate combinations. The benefit of these dice games is that the child will subconsciously notice and remember how many more dice are needed to complete the number to 10. This is a very important skill for verbal counting!

Alternatively, you can use Lego parts for such an exercise or apply the principle of pyramids from Zaitsev's method. The main result of all the described methods of acquaintance with numbers should be their recognition. It is necessary to ensure that the child, when looking at a combination of objects immediately (without recounting), can name their number and the corresponding number.

Verbal counting based on the composition of the number

Based on the knowledge of the composition of the number, the child can perform addition and subtraction. For example, to say how much “five plus two,” he must remember that 5 and 2 are 7. And “nine minus three” is six, because 9 is 3 and 6.

Without knowledge of the corresponding tables, a child is unlikely to be able to learn how to divide numbers in his head. Constant exercise in the use of tables greatly improves the speed of obtaining results when doing calculations in your head.

Using computational techniques for oral counting

The highest degree of proficiency in oral counting skills is the ability to find the fastest and most convenient way to calculate the result. Such techniques should begin to be explained to children immediately after familiarizing them with the actions of addition and subtraction.

So, for example, one of the first ways to teach a child to count in the mind in the 1st grade is the technique of counting and "jumping over". Children quickly learn that adding 1 is the next number, and subtracting 1 is the previous one. Then you need to offer to meet the best friend of the number 2 - a frog who can jump over a number and immediately name the result of adding or subtracting 2.

The explanation of the principle of performing these mathematical operations with the number 3. The example of a bunny who knows how to jump farther - immediately through two numbers will help in this.

Also, children need to demonstrate techniques:

• permutations of terms (for example, to count 3 + 68, it is easier to swap numbers and add);
• counting in parts (28 + 16 \u003d 28 + 2 + 14);
• reduction to a round number (74 - 15 \u003d 74 - 4 - 10 - 1).

The counting process facilitates the ability to apply combination and distribution laws. For example, 11 + 53 + 39 \u003d (11 + 39) + 53. In this case, children should be able to see the easiest way to count.

How to learn to count quickly in the mind of an adult

An adult can use more complex algorithms for oral counting. The most convenient way to quickly calculate in your head is to round and complete the numbers. For example, example 456 + 297 can be calculated like this:

• 456 + 300 = 756
• 756 - 3 = 753

Subtraction is performed similarly.

To perform multiplication and division, special rules have been developed for dealing with individual numbers. For example, such:

• to multiply a number by 5, it's easier to multiply it by 10 and then divide it in half;
• multiplying by 6 involves performing the previous steps and then adding the first multiplier to the result;
• to multiply a two-digit number by 11, you need to write the first digit in place of hundreds, and the second in place of units. In place of tens, the sum of these two digits is written;
• you can divide by 5 by multiplying the dividend by 2, and then divide by 10.

There are rules for calculating decimal fractions, calculating percentages, and exponentiation.

You can get acquainted with these techniques at school or find material on the Internet, but in order to learn how to quickly count in your mind on their basis, you need to train and train again! In the process of training, many of the results will be remembered by heart, and the child will name them automatically. He will also learn to operate with large numbers, decomposing them into simpler and more convenient terms.

Why do I call my method easy and even surprisingly easy? Yes, simply because I have not yet met a simpler and more reliable way of teaching kids to count. You will soon see for yourself if you use it to teach your child. For a child, this will be just a game, and all that is required from parents is to devote a few minutes a day to this game, and if you follow my recommendations, sooner or later your child will certainly start to count in a race with you. But is this possible if the child is only three or four years old? It turns out that it is quite possible. Anyway, I have been doing it successfully for over ten years.

I describe the entire learning process further in great detail, with a detailed description of each educational game, so that any mother can repeat it with her child. And, in addition, on the Internet on my site "Seven Steps to the Book", I posted videos of fragments of my activities with children to make these lessons even more accessible for playback.

First, a few introductory words.

The first question that some parents have is: is it worth starting teaching a child to count before school?

I believe that teaching a child is necessary when he shows interest in the subject of study, and not after this interest has faded. And interest in counting and counting is manifested in children early, it needs only to be slightly nourished and imperceptibly to complicate the games day by day. If for some reason your child is indifferent to counting objects, do not tell yourself: "He has no inclination for mathematics, I also lagged behind in mathematics at school." Try to awaken this interest in him. Just include in it what you've been missing so far: counting toys, buttons on a shirt, steps when walking, etc.

Initial lessons of the first stage. Counting training within five

For the initial lessons, you will need five cards with numbers 1, 2, 3, 4, 5 and five cubes with an edge size of about 1.5-2 cm, installed in a box. As bricks, I use "knowledge bricks" sold in educational game stores, 36 bricks per box. You will need three such boxes for the entire training course, i.e. 108 cubes. For the initial lessons, I take five cubes, the rest will be needed later. If you cannot find ready-made cubes, then it will not be difficult to make them yourself. To do this, you just need to print a drawing on thick paper, 200-250 g / m2, and then cut out cubes from it, glue them in accordance with the existing instructions, fill with any filler, for example, some kind of cereal, and glue it on the outside with tape. It is also necessary to make a box for placing these five cubes in a row. It is just as easy to glue it from a printed and cut-out pattern printed on thick paper. At the bottom of the box, five cells are drawn according to the size of the cubes, the cubes must fit freely in it.

You have already understood that learning to count at the initial stage will be carried out using five cubes and a box with five cells for them. In this regard, the question arises: what is the method of teaching with the help of five counting cubes and a box with five cells better than teaching with five fingers? Mainly because the teacher from time to time can cover the box with his palm or remove, due to which the cubes and empty cells located in it are very soon imprinted in the child's memory. And the child's fingers always remain with him, he can see or feel them, and memorization simply does not arise, the stimulation of the memory mechanism does not occur.

You should also not try to replace the box of cubes with counting sticks, other counting items, or cubes that are not in a row in the box. Unlike cubes lined up in a box, these objects are arranged randomly, do not form a permanent configuration, and therefore are not stored in memory in the form of a remembered picture.

Lesson number 1

Before the lesson, find out how many blocks the child is able to determine at the same time, without counting them one by one with his finger. Usually, by the age of three, children can tell right away without counting how many cubes are in a box, if their number does not exceed two or three, and only a few of them see four at once. But there are children who can only name one subject so far. In order to say that they see two objects, they must count them by pointing with their finger. The first lesson is intended for such children. The rest will join them later. To determine how many cubes the child sees at once, put different numbers of cubes in the box alternately and ask: "How many cubes are in the box? Don't count, tell me right away. Well done! Now? And now? Right, well done!" Children can sit or stand at the table. Place the box with cubes on the table next to the child parallel to the edge of the table.

For the tasks of the first lesson, leave the children who can only determine one cube for now. Play with them one at a time.

1. Game "Putting numbers to cubes" with two cubes.
   Put the card with the number 1 and the card with the number 2 on the table. Put the box on the table and put one cube in it. Ask your child how many cubes are in the box. After he answers "one", show him and tell the number 1 and ask to put it next to the box. Add a second cube to the box and ask to count how many cubes are in the box now. Let him count the cubes with his finger if he wants. After the child says that there are already two cubes in the box, show him and name the number 2 and ask him to remove the number 1 from the box, and put the number 2 in its place. Repeat this game several times. Very soon, the child will remember what two cubes look like, and will begin to call this number right away, without counting. At the same time, he will remember the numbers 1 and 2 and will move to the box the number corresponding to the number of cubes in it.
2. Game "Gnomes in the house" with two cubes.
   Tell your child that you are going to play Gnomes in the House with him. The box is a make-believe house, the cells in it are rooms, and the cubes are the gnomes who live in them. Place one cube on the first square to the left of the child and say: "One gnome came to the house." Then ask: "And if another one comes to him, how many gnomes will there be in the house?" If the child finds it difficult to answer, place the second cube on the table next to the house. After the child says that now there will be two gnomes in the house, let him put the second gnome next to the first on the second cell. Then ask: "And if now one gnome leaves, how many gnomes will remain in the house?" This time your question will not cause any difficulty and the child will answer: "One will remain."

Then complicate the game. Say: "Now let's make a roof for the house." Cover the box with your palm and repeat the game. Every time a child says how many gnomes there were in the house after one came, or how many of them are left in it after one left, remove the roof-palm and let the child add or remove the cube himself and make sure that his answer is correct ... This facilitates the connection not only of the visual, but also of the tactile memory of the child. You always need to remove the last cube, i.e. second from the left.