Verbal counting? - No problem! How to make mathematics simple and accessible for a child and teach him to count? How to teach a child to add examples from 10

Mathematics. How to teach adding and subtracting numbers.

What should a child be able to do before starting to learn to add and subtract?

The game of hide and seek is also not superfluous: “One, two, three... ten. I’m going to look. It’s not my fault who didn’t hide!” 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 necessary to show the number of fingers, numbers were associated with the number of objects.

Knows numbers

I don't remember any special exercises that we did. Everything happened in passing.

“Which floor are we on? On the second. Look, his number is 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 guessed a little wrong. Here’s a three.”

In the store: “We have the key to box number 9. You see, there is a tag on the key. Which box has this number written on it?” Something similar with a wardrobe number.

In line to see the doctor: “What is the office number? Here’s the number.” - “Two” (as far as I understand, at random) - “No, this is the number “5”. Show 5 fingers. Okay!”

"When will daddy arrive?" - “In an hour. Look, now the short hand is at 6. When this hand is at 7, right here, then it will arrive.”

"Please switch to Channel 1. Bring the remote control. It says one here. Press this button. Thank you."

Many children, from an early age, are interested in numbers and counting.

First, the child masters ordinal counting; many children begin to take their first steps in this direction at the age of 2-2.5 years. A little later, at 3-3.5 years old, you can teach him to count backwards. This is also an important skill that will be needed a little later for learning addition and subtraction.

The next stage occurs at the age of 3.5-4 years. At this time, the baby can learn to perform simple arithmetic operations within 5, a little later and up to 10. However, at this age, abstract thinking in children is not yet developed, they do not know how to operate with numbers in their minds, generalize and draw conclusions, so it is very important that Learning to count took place on objects that can be seen and touched.

And finally, children are able to master addition and subtraction in their minds only after 5-6 years. All these figures are very conditional, they are presented as a guide and in each specific case they may differ in one direction or another. It is important to look at the child’s needs, follow his interest, without getting ahead of his time, so that learning is meaningful and not mechanical.

In addition to ordinal counting, the child masters the concepts of “more-less-exactly”, “first-then”, “it was-was”. All this is easy to do at home, during ordinary household chores and walks.

How to teach your child ordinal counting

This stage goes through quite easily for all children; children often develop an interest in counting quite early; already at the age of about two years, the baby can point with his finger and count after his mother “One, two, three...”. Of course, this is not yet a completely meaningful account; awareness will come a little later.

However, the first seeds are laid already at this age. Typically, young children begin their meaningful acquaintance with numbers with the concepts of “one” and “many.” Numbers are not immediately associated with the number of objects, but gradually an understanding comes: not just “three”, but “three apples”.

Through movement, memorization occurs much better, so you can, for example, hopscotch with your child on the street, taking turns counting the squares. Or count the steps when going outside: first down, then when we return home, count up.

You can count birds, fingers on your hands, passing cars, trailers next to a toy train, parts of a construction set - in a word, the whole the world in this case, a complete visual aid. It is very good to sing counting songs together or read short poems where there is ordinal counting. Gradually, the child will remember the numbers and count on his own.

Divide the cubes with him and count who has more and who has less. Now let's divide it equally?

How to teach your child to add up to 10

Once ordinal counting is well mastered, you can begin to learn addition. Adding is usually much easier for children than subtracting.

How to teach a child to subtract to 10

After addition is more or less mastered, you can move on to subtraction. To do this, you need to explain to the child that subtraction is the inverse action opposite to addition.

The principle is exactly the same as in addition: we clearly show it on objects: if we had 3 oranges, and we ate 1, how many are left? To ensure high-quality fixation of the material, you can eat the orange right there. And then count the remaining ones. Gradually the number of items increases and we move on to more complex examples.

Children really love the game “Look, what's missing?” It trains memory and teaches subtraction at the same time. There were 6 toys, I hid 3. How much is left? Which ones are missing?

How to teach a child to count in his head?

It is worth moving on to addition and subtraction in the mind after the child has mastered visual counting well enough.

Another important detail - at first it will be easier for the child to add more to less, then the terms can be swapped.

Training should take place unobtrusively, in a fun, playful way. The most important thing is that the baby is interested. Don't be nervous and rush time: some people learn very quickly, others need more time. If something doesn’t work out for the child, he doesn’t understand, go back a step and offer a simpler example. Do not put pressure on your child if he has no desire to engage: it is better to leave him a little intrigued than to continue to force an activity when he is no longer able to maintain attention.
There is no need to exercise if your child or you are tired or in a bad mood. This will definitely not benefit anyone.
As practice shows, it is much more interesting for a child to add and subtract where the situation is closely related to real life, he needs to understand why to count. If we are expecting guests, is the right number of cutlery on the table, is there enough for everyone? Or how many treats do you need to take so that everyone gets the same amount?
It is very useful to play a variety of counting games with children. Dominoes, lotto, all kinds of “adventure games” with dice rolling and chips, others Board games.

Some parents, when their baby is hardly even a year old, want to teach their child to count correctly and quickly. Others are not sure whether this should be done with a preschooler if they will teach it at school anyway.

Many experts say that this should be done only when kids show interest in counting, and not try to force it. Typically, children show interest in counting early, but parents need to nourish it and motivate it to develop in this regard in the form of games and exciting examples.

From time to time interest may fade, but you can warm it up, offering to count together steps while walking, toys or buttons on clothes.

Today you will learn how to teach a child to count, in some cases it can be done quickly, in other cases it will take time.

What parents need to understand

Some parents simply don't know how to start doing this.

Now there are many specialized books on how to teach a child to count. Psychologists claim that if you decide to start training, then you should follow these recommendations:

Teaching materials for counting

It is quite difficult to teach at the age of 3-5 years. For training at the initial stage You can use different visual materials, in particular:

Pictures;
numbers on a magnet;
cubes and so on.

When learning moves to addition and subtraction, then the following are used as visual materials:

fingers - invite the children to count the number of fingers on their hand, then bend them and ask how many are left;
sticks - by analogy with fingers;
ruler - show the numbers and divisions on the ruler, count them off if you want to teach your child addition.

However, many psychologists do not encourage the use of such devices to teach children to count, and believe that this provokes laziness and does not train thinking and memory. A number of experts suggest teaching children to count exclusively orally.

Examples for the little ones

Learning to count can begin as early as six months of age.. Naturally, we are not talking about allowing a child who cannot walk or talk to count objects, but this will allow parents to create a basis for future learning. A good example in this case is light rhymes where there is a count, for example, such as “1, 2, 3, 4, 5, the bunny went out for a walk.”

Already at the age of one, the examples will be more complex. You can take the cubes and tell your child where there is one cube and where there are many; it will be too early to teach counting to 5 or 10. And from this age, you need to teach your baby to show with his fingers how old he is.

How to teach a child to count to 10

From about three years of age, when children are already interested in numbers (and some may become interested at three years old, others closer to five), learning is based on the following principle:

go through the numbers from 0 to 10 with your baby;
teach your child to memorize them using cubes or other toys;
tell the difference between larger and smaller numbers, explain the concept of "half", use simple examples;
count household items at home or items on a walk, offer to count together.

Below we will look at methods for teaching children to count to 10 in more detail. To start Say numbers from one to 10 to your child, count the objects at hand. Good examples are simple addition of objects: for example, “here was one doll, now we will put the second one next to it, and there will be two of them.” Over time, the number of items counted needs to be increased.

As often as possible, ask your child how many plates are on the table, how many birds are sitting on a branch, or how many dogs are walking in the yard.

It is not recommended to ignore the number zero. First you need to learn the numbers from zero to two inclusive, and then all the rest - from three to 10. In terms of learning, zero is difficult in the sense that it is difficult for children to explain that emptiness can be designated as a separate number.

Something like this: draw two squares, put three dots in one, and not one in the second. Explain to your child that in digital equivalent this will mean “3” in the first case and “0” in the second.

Games, examples and rhymes for learning to count to 10

The simplest and in a fast way teach a child to count is counting on fingers, which we already talked about earlier. But fingers are good only at first; when you teach your child to understand numbers, you should wean him off the skill of counting with them. There are often cases when schoolchildren begin to solve examples on their fingers and cannot do it using any other method. The ruler, which was previously used to memorize numbers, is also not particularly welcome nowadays, as we also talked about.

Other examples and games include:

we see 10 paws of cats (dogs). Answer how many animals there are. You need to count in pairs: two, four, six, and so on until ten;
in the same way he calculates how many pairs of shoes a cat or dog needs;
Looking at your watch, count to 10 in fives.

How to teach your child to add and subtract numbers within ten

When your child has already learned number order, start solving problems with him. examples of their addition and subtraction. Examples could be:

There are four apples on one plate, and two on the second. How many of them are there in total?
There are six apples on the table, and three children. How to properly divide them between them?

Other problems might look something like this; for subtraction, everything will look the same. You should also teach your child in a playful way the rule that changing the terms does not change the sum.

To do this, place a plate with two apples on the table or ask your child to imagine it. Next to it, place another one with four apples. Count how many apples there are, then rearrange the plates and ask how many there will be now. The correct answer is the same.

IN primary school Students are explained what tens are using special sticks. Then they are taught to add and subtract numbers by moving through tens.

In the first grade, the student learns to count by full tens using bunches of sticks. And only after that he gets acquainted with the table of addition and subtraction with the transition through ten. If children show success, then this can be taught before school.

In first grade, mathematics instruction is based on three tables:

addition and subtraction up to 10;
examples with transition through ten;
multiplication table.

When a student masters these tables, then in the future he will not have problems with mathematics, even in high school when studying more complex calculations.

And so that the child does not have problems at school, and mathematics is only a joy, it is very important that parents are still in preschool age instilled a love of counting. Therefore, the first steps to learning mathematics should be in the form of a game and presented in an interesting way. And the more exciting this process is for the child, the faster he will master counting skills.

What should a child be able to do before starting to learn to add and subtract?

Can count to 10 or more

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

We didn’t count everything - the steps in the entrance, the Christmas tree in the yard, the bunnies in the book... It looked something like this. "How many bunnies? Point your finger. One, two, three. Three bunnies. Show three fingers. Good girl! That's right!" At first my son was not interested in counting; he liked searching more. The game of hide and seek is also not superfluous: “One, two, three... ten. I’m going to look. It’s not my fault who didn’t hide!” 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 necessary to show the number of fingers, numbers were associated with the number of objects.

Knows numbers

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

I don't remember any special exercises that we did. Everything happened in passing. “Which floor are we on? On the second. Look, his number is 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 guessed a little wrong. Here’s a three.” In the store: “We have the key to box number 9. You see, there is a tag on the key. Which box has this number written on it?” Something similar with a wardrobe number. In line to see the doctor: “What is the office number? Here’s the number.” - “Two” (as far as I understand, at random) - “No, this is the number “5”. Show 5 fingers. Okay!” "When will daddy arrive?" - “In an hour. Look, now the short hand is at 6. When this hand is at 7, right here, then it will arrive.” "Please switch to Channel 1. Bring the remote control. It says one here. Press this button. Thank you." Interesting. The numbers determine any color. In addition to learning colors and numbers, fine motor skills are trained. The numbers written in mirror by the child must be corrected. There is such a diagnosis as “dysgraphia”. To exclude it, you should contact a speech therapist.

Can sort (name) numbers in ascending-descending order

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

Until three or four years of age, a 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. Look for the smallest object, the longest... 2) combine objects: by color, shape and other characteristics (dishes, clothes, furniture, pets), find differences in the pictures. 4) remove an extra item in a row (for example, from several red apples there is one green one), continue the row (for example, ▷ ☐ ▷ ☐ ▷ ☐ ?), name the missing element (for example, ▷ ☐ ▷ ? ▷ ☐ ▷), distribute in pairs (for example, ▷ ☐ ▩ ☐ ▷ ▩), name what happened first, what came next (put on a sweater first, then a jacket, and not vice versa; first it’s autumn, then winter...). 5) fold a pyramid, a puzzle, place 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 talk through them. “Show all the fruits” - “Here” - “Well done!” (clap our hands) - “What kind of fruit is this?” - “Orange” - “Uh-huh. Are there any more?”... By the age of 4, you can and should introduce board games (there is already enough perseverance and attention): dominoes, cards, lotto, with chips (each player has a chip) and dice (the move is made based on the number of dots rolled on the dice), where the winner is the first one to reach the finish line according to the drawn map. We used standard options, not children's ones. The cards were played in “The Drunkard” with a full deck (with 2 and 3): the deck is divided equally between the players, in the piles the cards are turned face up and the top one is drawn, there are no suits, the one whose card is larger takes the bribe (7- ka beats a 4, 2 beats an ace, two more cards are placed on two equal cards: one face down, the other front side, for the second time, only the top cards are evaluated: “Who takes it?” - "I!" - “How?! What’s more: 5 or 10? Let’s count...”), she joins the general pile, the one who has the entire deck wins. Joy knows no bounds if the whole family sits down to play (with dad, grandma, grandpa...). The child learns not only to play, but also to correctly perceive defeat. It is better to be able to count numbers from 1 to 10, and back, 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 a relay race: “Who will collect the most cubes? Get ready! Ten, nine, eight... one. Start!” We organized such competitions when it was time to clean up scattered toys. Pictures where we need to connect the dots in ascending numbers helped us learn to count to one hundred. If you talk it out, it turns out good result. ""Forty-nine". Then what comes?" The appearance, pronunciation of the number and the sequence are remembered. You can interpret that the numbers in tens are the same, 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’s handy to consolidate the material on the way: “When will we arrive?” - “Not long left. Count to one hundred and we’ll arrive. Let’s go together. One, two...” We didn’t teach more than 100 before school. I answered questions only when the child himself was interested: “What comes after 100? And what is one thousand and one thousand?” Or if the numbers were encountered in everyday situations: “We are waiting for bus 205. Two zero five. Tell me when you see the 205th.” It is also useful to name the numbers before or after a given number or in a certain interval. The game will help with this: “I guessed a number from 1 to 20, try to guess it in 5 attempts, and I will tell you whether it is more or less than the number you named. I guessed.” — “Three” — “More” — “Seven” — “Less” — “Five” — “Well done! You guessed right! Now it’s your turn to guess the number.”

Knows the concepts of more and less

"Dad has 6 apples, mom has 8. Who has more apples?" - "Mom."

The clubs explain that the number 22 is greater than 18, since it is closer to 100. This is true, but at the same time we laid out piles of nuts and erected towers of cubes in order to connect the image of the number with the number of objects. More and less gradually become more complex, as does addition and subtraction. Almost simultaneously with the plus-minus-equal signs, the greater-than-less-equal signs are introduced. My son was just over 5 years old at the time. “There are a lot of apples on one side [intonation is required!], the distance between the fingers is large, there is a larger number next to the open side of the sign.” “On the other hand there are few apples, the distance between the fingers is tiny, the corner is looking at the smaller number.” “Equally”, “equally”, “at the same time”, “equally”, “as much” are the same: “You and dad have the same mugs”, “I have the same amount of soup”, “Share the candy equally with your sister”. There are no problems with this concept when there are two children in the family. next example

It is most difficult to compare numbers consisting of the same digits. Almost always we solved them. next example

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

Counting on fingers

"Dad has 3 apples. Unfold three fingers. Mom has 2 apples. Unfold 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 left? One, two. Dad has two apples left."

"Dad had 2 apples. Show two fingers. Dad got hungry and ate both apples. Take away two fingers. How many did 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 objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.

With objects on paper

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We had difficulties not with finding the answer, but with pronouncing the entire example with signs, with the correct declination of objects. "One, two, three. Three candies. PLUS. One candy. How much is it? One, two, three, four. Four candies. Let's do it again. Three candies PLUS one candy EQUALS four candies."

With numbers on paper

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Three examples a day is enough. In six months, their number can be increased to 5-7. The answers must not only be spoken, but also written down.

Number composition

change How many dots need to be added to make it work points?

The words “addition table,” which is crammed as “multiplication table,” make me itch. In my opinion, the child’s thinking and logic are completely switched off at this moment. 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, changing the places of the terms does not change the sum” (hmm, the last one came out automatically: I didn’t explain to my son what a “term” was). “Can you solve the examples: 2 + 3 = ? 1 + 4 = ?” - “Easy! Five. Oh, there’s five here too. And there and there are five!” You can also take seven spoons: “How many spoons are there?” - “One, two, three... seven.” Put one spoon aside: “How many spoons are in each pile?” - “One and one, two, three... six” - “And that’s all?” — “Seven” — “It turns out that 1 + 6 = 7.” Transfer another spoon: “Now how many spoons are in each pile?” - “Two and five” - “And that’s all?” — “Seven” — “Look, the number of spoons in the piles changes, but the total number remains the same.” Later in the club, he drew houses in which numbers live (without my participation). There are two apartments per floor. It is necessary to resettle all the residents 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 in total? There are already three. Stretch three fingers. Now two more. Three, four, five."

I myself didn’t notice how my son stopped counting all the items. She explained it a couple of times, but did not insist.

Based on 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’ve already played 5. How many unexplored games are there left?” - “Two” - “That’s right. It can be written as “7−5=2”. Interesting, Will you be able to write a similar problem yourself: “After dinner, you need to wash 10 dirty dishes. 4 have already been washed. How many more are in the sink?” - “Six” - “How to write it down?” - ""10−4=6"" - "Well done!"

Problems should be simple and ordinary, with objects from everyday life, with questions “how much”, “how much”. “You have 3 cars. They gave you 3 more for your birthday. How many cars do you have now?” (6) “You have 6 pencils, the girl you played with yesterday has 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 ball for everyone? How many balls are missing?” (no, 2) “2 pears and 4 bananas grow on a birch tree. How many fruits grow on a birch tree?” (0, since fruits do not grow on birch trees)

Relationship between addition and subtraction

Subtraction is the inverse operation of addition. In other words, in order to more conveniently find the unknown variable x (pronounced “x”) in the equation x +1 = 3, the entry is reduced to the form x = 3−1 (when the number is moved ahead, it changes its sign from plus to minus and vice versa ) .

Full example: x + 1 = 3 x = 3 - 1 = 2 This is the connection that needs to be conveyed to the child. That is, to show that 2+1=3 is the same as 3−1=2 and 3−2=1. For this purpose, you can ask him to come up with 3 conditions for the task based on what he saw (instead of dots there could be bows, houses, cars, etc.).

Change Total points

"What kind of examples do you think can be written? Let's say 6 + 2 = 8 or 2 + 6 = 8 “How many dots are there in total?” 8 - 2 = 6 “How many green dots?” 8 - 6 = 2 “How many pink dots?” Now it's your turn." next example

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Without counting fingers

When you have calculated quite a lot of examples, you simply already know that 2 + 3 = 5 and there is no need to double-check it with your fingers.

How to learn to count within 20

Counting by lines

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

Counting from 10 to 20

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

11 + 4 ----- 15

Counting in tens

Number composition

The statement that it is easier to count in tens was also transferred to the plane of trial and error. Why were 100 rubles exchanged 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 arrange the coins into piles of 10 coins, there will be fewer mistakes. "Ten, twenty, thirty, and in this pile there are seven. Thirty-seven in total." I also asked for some money for travel: “To get to the hospital and back I need 52 rubles. Count me out, please... Oh! There’s not enough for the trip back! How can I get back home?” Later, a problem was announced: “If you count how many steps up to the apartment, you will receive a prize” (there were exactly 10 steps between the flights).

Imaginary fingers (within 12)

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

I didn’t expect that I would like the proposed idea so much.

On fingers

"What is 8+9? Bend eight fingers"

“Two fingers are already straightened. Let’s straighten them some more to make it 9. Three, four, five... nine.”

“There are already ten fingers: these are 8 previously bent and 2 straightened from 9. Now let’s count the number of fingers before the bent one. Eleven, twelve, thirteen... seventeen. Answer: 17.”

On a piece of paper

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

“How much do you need to add to 7 to make 10?” - "3" - "That's right. And 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 happens?” — “4” — “Add 3”...

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

In my mind

Repetition is the mother of learning. The more examples there are, 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, lollipop, ice cream) with a given amount of money. But in such a way that he is the buyer, and you are just an outside observer. You should ask him if there is enough money to buy the thing [more or less]. It must be explained that the seller must give change if the amount of funds transferred exceeds the price [by how much/subtraction]. 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 to buy him a bottle of water himself. The following dialogue ensued with the seller: “Can I buy water?” - “Yes. It costs 8 rubles.” - “Are there any for 10?” That is, he did not think about whether he had enough money or not. If they had said that there was no bottle for 10 rubles, he would probably have turned around and left.

Mathematics for preschoolers: what else will be useful in 1st grade?

Orientation in space

"Where left hand? Close your right eye. Grab your left ear. Jump on your left leg. How many cars are there on your right? And on the left? And in front (in front)? And behind (behind)? What color is the car between gray and green? What's under the table? On the table? Over the table? Near? 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 leader (either me or my son) on the street gave instructions to the person who had closed his eyes: “Slow down, there’s a bump in front, two steps left, one, two, now raise your right leg high... A man is coming at you from behind, move to the left, a little more... "There's a cyclist coming towards you, quickly take two steps to the right." The presenter (either me or my son) drew a plan of the room, and on it marked with a cross where the toy was hidden, which the second player had to find using the plan. I laid out notes around the apartment indicating where the following piece of paper was located: “In the table in the kitchen”, “Under the sofa”, “Above your bed”... The last note said where the treasure was. The first one was given to my son. I gave (plus they did something at the club) to make sure that there were no problems with it: “From the point, two cells up, one diagonally, to the right...” And checked on a piece of paper: “Draw in the upper right corner a star. In the center there is a flower. To the left of the flower there is a circle. In the middle of the lower edge of the leaf, put a cross..."

Geometric figures

"What does a ball look like? What is the difference between an oval and a circle? What is the shape of a stool when you look at it from above?"

Even odd

“Please name 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, during a walk, I drew my son’s attention to the sign on the house “27 → 53”. "Do you know what she means?" - "..." - "It shows that the house numbers will increase if you go in this direction. But, since on this side there are only houses with odd numbers, they will increase like this: “27”, “29”, "31"... What number do you think will come 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 number is it, here it is?" - ““29”... By the way, I remember the question of a boy in the club, which puzzled the teacher: “Is zero an even or an odd number?” It is immediately clear that children do not memorize, but delve into it, their gray cells are working.

Preparing for Multiplication

At the age of six, it is useful to study how the minutes on the clock are grouped (by 5), why by pointing to “2” we talk about 10 minutes.

Problems involving groups of two are also interesting: “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 should you start learning mathematics?

The level of education in Russia is now such that it is the parent who will have to explain the basics of mathematics to a first-grader. In order to have time to maneuver, to enter into this process gradually (it’s not for nothing that first-graders’ eyesight declines), so that tasks are perceived as entertainment and not labor, one should begin before the child goes to school. If the baby doesn’t understand (doesn’t remember) some point, then it’s worth either trying to explain it differently, or quitting and returning to the material after a while, or finding a suitable incentive (“If you solve the example without my hint, you’ll get a prize”). It is better to write examples on paper rather than looking at the monitor.

We turned to problems at the moment when we felt like it. It turned out to be raids of 3-4 days (to consolidate the material) every two to four weeks. Why so rare? For comparison: we learned reading skills at least twice a week using N.B.’s manuals. Burakov (not advertising, mentioned because his approach satisfies). 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 the letters), and the second - to understand.

count examples up to 20

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

Stage 2

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

Stage 3

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

The study of the composition of numbers is traditionally carried out using so-called “houses”. Draw a house on checkered paper. There are always 2 cage rooms on one “floor”. The number of floors of a house is determined depending on the number of numerical pairs into which the number 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 create houses for the numbers 3, 4 and 5.

The child will have to memorize the distribution of “tenants” by floor. Start with small numbers. Ask your little one to carefully look at who lives with which neighbor, and then “populate” the numbers yourself.

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

Here here you can download this table and use it to master the number composition technique:

Stage 4

When the houses are completed, it is the turn of examples within 10. 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 place + or - signs between the “settlers”, having previously explained their purpose to the baby.

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

This is how we mastered counting within 10 with our child. As you can see, the technique is very simple, but it requires time and patience to work. Try to force your baby to count in his head first: written exercises slow down thinking.

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

Go ahead…

The time has come to introduce the baby to the second ten. To overcome arithmetic difficulties, we suggest 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. We explain that it is eleven. We say that the ending of the word “dtsat” means “ten”. To form the number from 11 to 19, you just need to add the number to the ending “twenty” and put the preposition “na” between them.

Part 2

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

Part 3

Now let's move on to the negative examples: we act in exactly the same way. Subtract the ones, then add the tens.

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 dozens. One way is to subtract three from six, subtract the remaining number from ten, i.e. 6-3=3, 10-3=7. After a few practices, your baby will be able to do subtraction in his head.

The child must clearly master the described skills: in 2nd grade 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 (learning with pictures is especially varied: you can simply count them, use coloring books with examples to reinforce counting skills);
any items at hand;
counting sticks;
abacus, etc.

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

We have looked at the sequence of teaching your little one to solve examples within 20 in stages. If the article was useful to you, leave a comment or share the article with your friends on social media. networks.

See you soon, dear friends!