How to teach a child to count: a few simple ways

When the first stages of mathematical science have been completed, basic knowledge about the first ten digits has been mastered, it’s time to start teaching a preschooler how to add and subtract second-order numbers. If the child is already fluent in single-digit numbers and can work with the first ten, distinguishes what is more and what is less, and knows the composition of the number, then further learning will not be difficult.

The most important requirement is to understand mathematics. Don’t memorize numbers like a rhyme, don’t count on your fingers, and don’t look at your neighbor’s notebook. Understanding is the basis of knowledge.

Count to 20

As a rule, counting to 10 for children 3 years old is not difficult. Things are a little different when it comes time to learn to count within 20. Difficulties can arise when counting to 10 is not entirely clear for children, which means that parents, in their desire to teach the baby to count, rushed and thereby confused him. You need to ask the question of how to teach a child to count to 20 only when he knows the numbers well, counting within 10.

When studying counting within 20 with children, they need to explain and confirm the main nuances, for example:

The number consists of 2 digits. The first is tens, the second is units. Counting material will help children master counting.
Without knowing how to teach a child to count to twenty, you should give him a clear example of what this number can look like. The best way to demonstrate this for preschoolers is to place two tanks in front of them.
Put 2 items in one of them, ten in the second. Using this example, the child will be able to understand what tens are and what units are.
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It is also necessary to explain that after 10 there are two-digit numbers, and their units follow each other (1,2,3 and so on).
After the baby has learned the first 20 numbers, you can figure out how to teach your child to count in his head. To do this, you can consider examples based on available items. We teach the child to count to 20 by asking him to put a certain amount of prepared material (sweets, bagels, pebbles) into a container. In this case, the first time the task should be performed out loud, and the second time the counting of objects should be pronounced in the mind.

How to teach a child to count quickly in his head? It’s a matter of time, and only regular classes and improvement of acquired knowledge will become a prerequisite for mastering the count up to 100, and at the age of 5 this is quite possible. In addition, this is the right age to explain to a preschooler how to do it correctly.

Mastering numbers

The topic of studying numbers can be divided into two components: memorizing the sequence (1, 2, 3, ....... 9, 10) and a graphic (visual) image. As a rule, children remember sequences of numbers much faster. When an adult often pronounces it, while simultaneously pointing at some objects in turn, the child quickly remembers by ear the names of numbers and their order, begins to repeat the same actions, and thus learns to count. However, there are many exercises to speed up this process and consolidate the skill. Here are some of them:

Count everything that catches your eye; You need to invite your child to count everything that surrounds him during the day: steps in the entrance, pigeons in the yard, pencils in a pencil case, cars in the parking lot, buttons on clothes, people in line at the checkout, and so on. The more often the child does this, the faster the information will fit into his memory, and an understanding of the relationship between the number (its name) and a specific quantity will appear.
Finger games; In learning numbers from 1 to 10, the best tool is your fingers. In addition to the fact that you can simply count them by unbending them one by one, there are also a large number of finger games aimed at both developing mental counting skills and training fine motor skills and imagination.
Poems, songs, counting rhymes; Memorizing a sequence of numbers with the help of songs, poems or counting rhymes allows you to perceive information not only auditorily, but also through visual images that the child’s imagination draws. This speeds up the learning process and develops imagination well. If a child has difficulties while learning numbers, most often they are associated with visual memorization. This is especially true for numbers that look similar to each other, such as 6 and 9, 1 and 7. To quickly remember the graphic image of a number, there are also many different secrets:
Associations; A simple and effective way to remember the appearance of a number is to find similarities with some object and come up with an association. For example, the number 8 looks like a nesting doll, a bow, a snowman or a teddy bear. The number 2 resembles a swan, 4 - an inverted chair or beak. There is no limit to imagination here, everyone will have their own associations.

Recognize by touch; The numbers must be voluminous. You can make them yourself from scrap materials or purchase ready-made ones. They need to be put in a bag or box, from which the child will take one at a time without looking and try to determine by touch what kind of number he came across.

Drawing on the back; It takes two to play. An adult draws a number on the child’s back with his finger, and the child must guess it. Then you can change places.

Toy figures; They can be magnetic, soft, drawn on cubes - depending on what you like best. From them you can build a sequence from 1 to 10, calling out each number out loud, arrange it in reverse order or randomly, finding the number that the adult calls.

Numbers around; Every day a child encounters different numbers: in the numbers of houses, cars, on various posters and advertisements.

If you pay attention to them and pronounce them, this will also contribute to memorization.

After the child has learned to count and memorized all the numbers, you can move on to studying the composition of numbers.

Learning to count to 20

To make the process of learning new numbers easier, you need to adhere to the following recommendations:

Children need to be introduced to each number separately.

It is necessary to write the number on paper, talk about it and illustrate it, for example, if we were talking about the number 12, you can draw 12 cars. Pay special attention to the number 20. Tell that this is the highest digit in the second ten. Pronounce each number separately, having learned several new numbers, start repeating over again. When learning to count, we must not forget to tell children about the meaning of numbers and what they are needed for. Start writing numbers

Ask the child to write down all the numbers in order and pronounce their names loudly when writing. This way the memorizing process will become more productive. Add items to activities. It will be much easier for children to understand new material if they are given blocks, sticks or pencils that they can touch. The lesson will become more interesting, because... children will count and use unusual objects.

How long does it take to learn to count?

As a rule, children learn to count to ten very quickly, especially if they are taught to count from infancy. Many children go to school knowing how to count to one hundred and backwards. Is it necessary to go beyond ten at all?

Write the numbers from one to ten on paper

Direct the child's special attention to the number 10. Show that it has a one in front and a zero at the end. Explain that two-digit numbers are formed from each digit.

For example, when writing the number 11, you need to replace the zeros with one, when writing 12, we change the zeros with two, and so on in order. Next, show the number 20. Explain that now we are changing the first one to a two, and with further counting we will need to change the zero to other numbers.

Write with your baby. Make up two-digit numbers, he must know them not only by ear and quantity, but also visually perceive the numbers.

How to properly consolidate the material covered?

In order for what you have gone through with your baby to find a response in his soul and mind, you need to apply patience, tact, imagination and your own interest in communicating with the baby

It is important not to overdo it and give the material in feasible doses that are accessible to the particular student.

You cannot cram the material and repeat the same thing several times in a row: knowledge must be digested in the child’s subconscious, and then it will become his property.

Training when consolidating material is mandatory, because they contribute to consistency in classes and the development of interest and respect for mental work.

In the following video, see examples for teaching your child to count numbers within 10.

Solving examples in a column

You need to move on to solving examples in a column only after becoming familiar with the digits of numbers: units, tens, hundreds and thousands. As a rule, this happens already at school (1st and 2nd grade).

The first training exercise is to write down different numbers under the lines of the corresponding category. For example, under 15 write 7. So, 7 should be under 5, not 1. In the future, the numbers must be increased.

It is much easier for a child to add numbers into a column than to subtract them. Important points to remember when training:

addition should be performed exclusively under the correct digit (the correct recording of the example is controlled);
Explain in detail the transition of a unit (or several units) to the tens digit. For example, when adding 29 and 8, the unit will go into the ten place and be added to 2, resulting in the number 37.

For your information! After mastering columnar addition, you need to move on to subtraction. No additional skills are required here, only great care and patience on the part of the parents. As a rule, kids do worse with subtraction.

In subtraction, the concept of borrowing a number from another, higher digit appears. It is worth bringing to the point of automaticity that you can only take a number from a larger digit.

To quickly teach your child to count in columns, you need to remember 3 main rules:

You can't rush the baby. Successful mastery of counting rules takes time. Every child is different and the pace of learning is different for everyone.
There is no need to overload the child's brain. Information should be dosed, with sufficient time for digestion and rest.
Correct answers should always be praised and encouraged. This will give your child an incentive to try harder and work harder.

Child counts, graphic recording

Teaching a preschooler to count mentally and in columns is not so difficult. By approaching this issue with responsibility and patience, with regular training you can achieve good results

It is important to remember that the learning process should take place in a playful way, then new knowledge will fit into the baby’s head much better

How to learn the table of addition and subtraction within ten?

After the child knows the order of numbers, it is useful to use tasks on the composition of numbers. You can, of course, memorize the composition of the number 5, for example, but it is better to use game actions with objects with a parallel focus on memorization.

For example:

There were 4 oranges in one plate and 2 in the other. How many oranges are there in total? (Task to find the sum)

There are only 6 apples, and three friends. Divide each equally, equally.

You can also combine small diagrams with simple tasks that are easy to use in the classroom and at home.

It is not difficult to give the following example of the commutative law of addition: one plate with two apples lies on the table, and another plate with four apples lies side by side; if you swap them, the total number of apples will still remain the same.

How can a child quickly learn the composition of numbers?

What you need for the lesson:

cards for composition of numbers;
many identical toys and other small items;
checkers or buttons of the same shape, but different colors.

Instructions

During the first lesson, use toys or household items. These can be cubes, pencils, cups, spoons. The type and size do not matter, the items should simply be the same. Start with the number 2. Ask your child to put 1 spoon on the table and ask what needs to be done to make 2 spoons. An older preschooler usually knows the answer, but you can tell a younger child. From what numbers can you add the number 2? If the child doesn’t understand right away, ask a leading question.
Repeat the task with other items. The child must understand that the number 2 in any case consists of two units, regardless of whether he places spoons, pebbles or cubes on the table.
When the child begins to answer confidently, move on to studying the number 3. Its composition can be presented in three versions. You can lay out 3 spoons one at a time, add one to two, or two to one. You can arrange objects in different ways. If you imagine the number 3 as consisting of three units, then pebbles or spoons can be placed at different distances from each other and even one pebble on top of another. Representing the same number as consisting of a pair of objects and one, put two together, and one at some distance.
Use checkers for practice. Invite your student to place 4 identical checkers on the board. What if you bet 3 red and 1 black? You will also get 4 checkers. And if you take two of different colors, there will still be four of them. That is, this number can be represented in several ways.
Get cards for number composition. They can be bought or made. They come in several types, and it is better if they are of two types. The cut card consists of two halves. One depicts 1 object, the other - 1, 2, 3 or more exactly the same objects. The halves can be connected by a “+” sign, but the “plus” sign can also be made separately. The second set is a set of pictures that depict the same objects in one set, without any division. When the child learns to compare numbers and numbers well, you can make the same cards with numbers. There may be several sets of them to represent each number in different ways.
Take classes regularly. Show your child a card that shows, say, 5 objects. Offer to choose the pictures so that they all have the same number of apples or circles. Change roles periodically. Let the child also give you tasks, and you diligently complete them. Make mistakes sometimes, your student must learn to control your actions.
Do similar tasks with numbers. Show, for example, the number 9 and, in the same way as in the previous case, offer to find several options for its composition. Explain to your child that the larger the number, the more opportunities there are to make it up.

Photo gallery: cards with numbers

Regular exercise will definitely give results. Move towards your goal step by step and everything will work out!

Methods of teaching counting

Smartum Training Center offers its unique method of teaching mental arithmetic. This technique is based on the ancient Japanese method of Mental Arithmetic, which was created more than 2000 years ago. It is aimed not only at learning to count, but also at developing mental abilities. In the learning process, traditional abacus (soroban) abacus is used, which will easily and quickly teach you not only to add and subtract, but also to multiply and divide complex numbers without using a calculator.

Training is aimed at developing both hemispheres of the brain, which contributes to the development of fantasy, memory, imagination, concentration, imaginative perception, and so on. The full course of training lasts 2-3 years, but the first amazing results can be seen after 3 months of regular classes. Help your child learn to do mental math quickly and easily. Contact us!

Simple games with numbers will help introduce your child to arithmetic operations

Cubes, magnets, cards, counting sticks - the most standard materials for teaching counting. But the child will quickly get bored with them. It will be much more interesting for him to play with what he makes with his own hands. You can get creative with your child and make your own games to learn numbers and practice simple mathematical operations.

There are interesting uses for shells brought from the sea. This game will help younger preschoolers quickly learn to add and subtract. Now abstract arithmetic operations can be seen with a clear example.

Don’t rush to throw away the egg tray and kinder capsules either, they can be turned into a fun game. The photo shows an option with addition, but it can be replaced with subtraction, multiplication or division. The good thing about the game is that the child can “disassemble” and “assemble” new examples with his hands.

Count to 100

Children as young as five years old can learn to quickly count to 10 or 20 in their head. But not all parents know how to teach a child to count to 100 at this age. Yes, a small preschooler may experience difficulties in the process of mastering new knowledge, especially since the number one hundred provides for a huge number of others, the mere thought of which shocks not only children, but also their parents. In fact, difficulties can be avoided and a preschooler can be taught to count to 100 without difficulty by choosing the right approach.

Learning to count to 100:

The easiest way to explain to children what “100” is is to give an example of the tens that it consists of (10, 20...90). At the same time, it is necessary to talk about the fact that between tens there are also ones. A preschooler who counts from 1 to 20 will know this.
Every day the child needs to be given a specific task - learning new numbers. You can limit yourself to ten. In this case, repetition should be carried out from 1 to the number that was learned last.
After each completed task in the form of mastering new numbers, you can conduct control games. For example, having written a number series, skip several values in it that the child must determine. You can also count any objects that surround it.
Counting to 100 for children is an incredible achievement for which they must be praised and encouraged, because this is the strongest incentive for achieving great heights.

Simple game - counting in steps

How to teach a child the composition of numbers? A simple and understandable example is to measure the distance to your house in steps. For example, let's take 20 steps.

When going for a walk, to a kindergarten, a store or any other place, count 20 steps from the entrance with your baby and make a mark, for example, with chalk. You need to start counting from one. Next, show that three more steps, and it will already be 23. Upon returning home, find the mark you set and count the steps from 20 - in reverse order. That is, you are 20 away from home, and now you are 20, 19, 18 and so on from home. The child will quickly understand what it means from home to home, and this is the composition of the number.

Adding and subtracting in your head

When the numbers are learned, parents are faced with the next task, namely, how to teach their child to add and subtract. There are also a large number of different techniques in this part. Let's talk about a few popular ones.

Gnomes in the house

Example: place two characters in the house, these can be animal figures or just cubes (the first option is more interesting), and then ask the child how many guests have come. Then add and remove elements within the first ten. Gradually, the task can be complicated by adding a roof to the house.

After the child has counted, reveal what was hidden so that the student can test himself.

Zaitsev's technique

Optimal for children 6-7 years old. The technique allows you to learn to add and subtract within 100 almost automatically, and in your head. To work with the equipment, you need to purchase special training material, as well as read the author’s recommendations. The essence of the technique is to show the child all the material, which is then, with constant viewing, systematized in the form of special tables.

Decomposition of numbers into composition

This option is so simple, since the child will have to learn several dozen different combinations (only for the first ten), but then the mental counting will be almost automatic.
How to use the technique: take any number, for example, 7. The student must remember that it “breaks down” into 5 and 2, 4 and 3, etc. For clarity, you can use any available material, for example, take 2 plates and 7 beans or colored candies, and then “divide” them into 2 parts.

Within the first ten, preschoolers can master the technique; older children are able to learn mental counting using the presented technique with numbers from 10 to 20.

Glen Doman Method

Ideal for preparing for school, as well as first graders. Instead of numbers, dots are depicted on a sheet of paper. According to the author of the technique, this allows children to memorize the principles of mental counting in just a few lessons.

When choosing a specific technique, it is important to evaluate the child’s reaction - if one does not arouse interest, it is worth trying another. You need to do the same if activities that previously brought you joy suddenly become boring.

When to start

Before a three-year-old can begin to count correctly, he must master basic mathematical concepts and learn certain skills:

Correctly and quickly select elements according to one given characteristic: (choose only red, only round, only green), and then several (put green and small things in a box).
Manipulate homogeneous groups using the concepts of “one”, “many”, “few”: show where there is one pencil, where there are many; make this box have a lot of pencils, etc.

Master the concept of “the same amount”, “equally”: bring the same number of cubes, divide equally (equally).
To develop mathematical thinking, games are played to master spatial concepts: show what is on the table, under the table, below the pyramid, above the plate, in the box, on the left, on the right, etc.
A three-year-old needs to be taught how to count to five correctly by pointing at each object with a finger.

The baby does not yet perceive abstract information by ear. He definitely needs to see and touch all the tasks with his hands: rearrange the pencils, distribute candy to the dolls, remove the excess, divide equally.

If preliminary mathematical concepts have been mastered, then by the fifth year of life the child can easily master counting and can quickly select the desired number for the resulting number. Five-year-olds should be taught how to obtain a new (“adjacent”) number by adding or subtracting one at a time. This method is easiest to learn by comparing two rows of parallel objects. For example, match cups to saucers, mushrooms to Christmas trees, etc.

A five-year-old needs to be taught not only to count to ten, but also to remember all the results of different variants of addition and subtraction within ten. In the future, this will help you quickly and automatically remember the correct answer, rather than calculating it “on your fingers.”

How to teach your child to add and subtract

When starting to teach mental arithmetic, you should first of all take into account the age characteristics of children.

If we are talking about a child of primary preschool age, it would be advisable to start studying the material with the simplest examples and problems, first explaining what a number is and what a figure is; Gradually explain addition and subtraction to your child.

For older preschoolers, more complex games and techniques are suitable - those in which you need to practice addition and subtraction skills, for example, the game “Shop”.

For children 2-3 years old

It will be easiest for children of this age group to learn to count using their fingers. For example, you need to sit next to the child, start bending his fingers one by one and count out loud.

For example, say: “Mom has one piece of candy. Extend one finger. Dad has three candies. Extend three more fingers. How many candies did you get? Count your fingers. One two three four. Right!"

Or like this: “Mom has five sweets. Extend your five fingers. Dad took two candies from mom. Bend two fingers. How many candies does mom have left? Count the remaining fingers. One two Three."

For children 4-5 years old

Children aged 4-5 years are most comfortable explaining the principles of addition and subtraction using educational material, which can be their favorite toys.

For example, you can put five dolls next to each other, then add two more, ask the child how many you got, then add one more, ask how many dolls you got now. Or put seven cars in a row, roll back three, ask what happened and how many cars are left now.

You can conduct training using any surrounding objects: cubes, sticks, cards. You can also purchase copybooks “Learning ordinal counting up to 5,10,20 and 100.”

For children 5-6 years old

To teach counting to children from 5 to 6 years old, the same game techniques are suitable as for four and five year olds.

Tasks can be complicated by giving the child compound examples to solve, for example 2 + 2 – 1; a counting ruler for preschoolers will help solve such problems. The main thing that parents should focus on is how to explain to their child what a plus and a minus are.

It is important to give a clear definition of these terms from the very first days of classes: plus is when something is added, and minus is when something is subtracted.

For 1st grade students

Children entering first grade is an important stage in their lives. At this time, the child’s field of activity changes, he tries on the role of a student

To achieve positive results, taking into account the age of schoolchildren, teachers practice learning mental arithmetic in a playful way:

Zaitsev's method. Gaining new knowledge occurs through the use of special cubes and tables.
Glen Daman method. Learning to count is carried out using cards on which a separate number of dots is located.
Polyakov's method. Children learn about numbers and numbers by arranging colorful cubes and filling boxes with holes.

For 2nd grade students

By this time, younger schoolchildren should already have mastered the basic skills of mathematical operations.

The use of gaming techniques fades into the background, the emphasis is on solving examples in notebooks and at the board. Children are given simple problems to solve that involve complex numbers and tens.

Counting materials

The choice of counting materials today is very rich. The most famous are counting sticks. Parents are attracted by their ease of use and affordability. However, simplicity does not lead to high efficiency. The child becomes dependent on the template and cannot translate such counting into oral.

There are many cards: “Composition of numbers”, “Number houses”, “Flower”, “Dominoes”. All of them are sets of composite counting material with variable characteristics. The child learns to find components in a number, that is, he learns that ten consists not only of two 5s, but also of 8 and 2, 7 and 3, and so on.

Wooden and plastic sets of numbers and calculation signs with sticks included are also an excellent way to develop visual memory by correlating the number of sticks and the number. Classic abacus and abacus with sound are also great for learning the composition of numbers. The method of decomposing numbers by adding up to ten and the remainder to obtain the answer is clearly expressed here.

Digital reels with numbers and signs are used for more experienced children. The principle is simple: the child turns wheels with numbers and signs and gets a clear example for solving. For the little ones - pyramids and pins. Simple counting and shifting will help in remembering numbers.

It is more interesting for the baby to create counting materials together with his mother. Draw together, create boxes with numbers and fill them with beads, count markers, pencils, make a number and, accordingly, peas or bagels. That is, combine different methods and methods of calculation for better memorization.

Introducing the Image of Numbers

When your baby has mastered counting to 5 properly, you can show him pictures of numbers. It is better to make or buy cards with large, colorful numbers in the store. It is advisable that their size be at least half an A4 sheet (this is a regular landscape sheet). Tell your child that each number has its own name. Next to the number, place a card depicting the number of objects corresponding to it. So, with the help of visual images, the baby will quickly remember how many objects a particular number corresponds to.

What else can you do to improve your memory:

make a number from plasticine;
buy magnetic numbers and hang them on the refrigerator, playing with them regularly;
draw a number on a large sheet of paper, all the time explaining to the child what you are doing, and hang it in a visible place;
start a tear-off calendar, telling your child every day that today is such and such a date, and what you are going to do today;
use a clock: a real wall clock or a toy one. Every hour you need to show your child the dial and say what time it is;
We use the children's store game, where you need to count toy money;
We play walking games with a toy cube on which we need to count dots;
we play children's dominoes with the image of numbers and objects that need to be counted;
always be in a good mood and often praise your child for his successes.

At the same time, show your child how to write numbers, studying no more than one per day. This is followed by the same algorithm with learning to count to 10. As a rule, children very easily master counting to this number. Then you can start counting to 20. What is the best way to explain to your child the pattern of such a count?

At what age should a child be able to handle numbers?

The mathematical mindset of a child does not affect the age at which he masters counting.

As a rule, all children master counting sooner or later, and this happens between the ages of three and six years:

At 4 years old, a child can be introduced to the formation of the first five numbers. At this age, children easily master direct quantitative counting up to five, and some even up to ten.
At the age of 5-6 years, preschool children become familiar with the principles of forming the natural series of numbers:
Each subsequent number is obtained by adding one to the given one, and the previous one is obtained by subtracting one from the given one.
At the 7th year, older preschool children can count objects in groups: twos, threes, fives.

We work with accounts

A child should be taught to count to ten before he enters school.
Then you need to develop computational skills. This can be done on your fingers or matches. Many experts advise using abacus. Such devices do not interfere with adding or subtracting numbers in the mind. Today, every person has a calculator at home. This device makes life easier, but does not develop mathematical and logical thinking. Therefore, you should not teach your child to use gadgets.

So the child will never learn to perform simple mathematical operations in his mind. Abacus should be used from the age of three. With such a device, you can teach your child to count to 10, 20, 100, and complicate the tasks as they master the material. This product develops fine motor skills and manual dexterity well.

Training in working with accounts should be based on the following algorithm:

set number . Align the knuckles to one edge. This location means zero. The bottom row is hundredths, the second row is tenths, the third is quarters. Next are units, tens, hundreds, thousands. To dial a number, move a certain number of dominoes to the other side;
addition _ Dial the first term on the abacus, and then the second, moving the required number of dominoes to the side, starting from the bottom row;
subtraction . All actions are carried out similarly to addition, but from top to bottom.

Multiplication action

If you understand that multiplication is adding identical numbers a certain number of times, there is nothing complicated in the action. For example, 4*7 = 4+4+4+4+4+4+4. As a result, they get 28. The multiplication table will simplify the action. Every schoolchild knows her.

To multiply numbers correctly, they are reduced to prime numbers. Let's look at multiplication techniques.

Multiplying 9 and 11

The rule when multiplying by 9 is to multiply by 10 and subtract 9. If multiply by 11, first multiply by 10, adding the original indicator.

Example:

15*9 = 15*10-15 = 150-15 = 135;
57*11 = 57*10+57 = 570+57 = 627.

Multiplying by 5 numbers up to 10

This technique will help you correctly multiply two- and three-digit numbers. The rule is simple - divide the multiplier by 2. Having received the result in the form of an integer, add 0 at the end, and if the number is not an integer, discard the remainder and add 5 at the end.

Example 1482*5 is solved like this:

(1482/2) _ (+0 or +5) = 741 _ (+0) = 7410 – the original indicator was divided by 2 without a remainder;
2269-5 = (2269/2) _ (+0 or +5) = 1134.5 _ (+5) = 11345 – the original indicator was divided by 2 with a remainder.

A technique for quickly learning how to count money by multiplying a number by 5, 25, 50, 125 using formulas:

A*5 = A*10/2;
A*50 = A*100/2;
A*25 = A*100/4;
A*125 = A*1000/8.

By putting a number in place of A, in the process of solving the formula, the desired result is obtained. For example, 25*25 = 25*100/4 = 2500/4 = 625.

Multiplying large numbers with one even number

In this case, the method of simplifying the factors is used. An even number is reduced by 2 times, and an odd number is increased by 2 times. For example, 48*125 = 24*250 = 12*500 = 6*1000 = 6000.

Multiplying a multi-digit number by a single-digit number

When figuring out how to learn how to quickly count money at the cash register, they use the technique of putting things into orders, as in the case of addition. Example 468*6 is solved like this:

Divide 468 into 400, 60, 8. Multiply each number by 6.
They get (400*6) = 2400 + (60*6) = 360 + (8*6) = 48. Total 2400+360+48 = 2808.

A more complex option with regrouping the final results looks like this: 2400+360+48 = 2000+400+300+60+48 = 2000+700+108 = 2808.

Multiplying Prime Numbers

The diagonal method is needed when looking for a technique for quickly learning to count orally. The method involves adding the number that is “not enough to reach 10.”

Example 7*8 is solved like this:

calculate the missing amount to 10 - in 7 it is 3, in 8 it is 2;
then 8-3 = 5;
3*2 = 6;
in the end they get 56.

Multiplying numbers from 10 to 20

The rule is that units of another are added to one number, and the sum is multiplied by 10. The sum of units is added to the result. For example, 13*15 = (13+5)*10 + 3*5 = 180+15 = 195.

Multiplying two-digit numbers

They simplify the process again by decomposing two-digit numbers into simple operations. Example 78*56 is solved like this:

The result should be adding the number 78 exactly 56 times. First, fold 78 fifty times, then 6 more times.
They count 78*5 = 70*5 + 8*5 = 350+40 = 390*10 = 3900.
78*6 = 70*6 + 8*6 = 420+48 = 468.
3900+468 = 3000+900+400+60+8 = (3000+1300+60+8) = 4368.

Using the principle of simplification and decomposition of large numbers into digits, multiply all two-digit numbers.

Multiply by 9, 99, 999

Take into account the rule of adding missing units. Example 154*99 is solved like this: 154*(100-1) = 15400-154 = 15246. Multiply by 9.999 in the same way.

Squaring

This is also multiplication, in which a number is broken down into its components. First, find the product of the first digit and the next one, the result will end with the square of the last digit. An example of squaring 75 is solved as follows: 7*8 = 56; 5*5 = 25. As a result, 75*75 = 5625.

Composition of numbers: explanation and cards

When we simply add different numbers, any result can come out. But when we find out the composition of a number, we seem to go in the opposite direction - from a result that is known in advance (for example, 8). We teach certain pairs of terms - each number has its own - so that we get exactly this result.

I propose to proceed in this order.

Explain clearly how, with the same amount, one term can increase and the second can decrease. It is very convenient to do this on objects that always have a fixed and familiar number to the eye: egg cartons (10), transparent packages of cookies or sweets (usually 6, 8, 12), calendar lines (7), packages of watercolors, plasticine are great and so on.
The child must write down in a notebook (or on a piece of paper) all possible options for the composition of the number, say them out loud, find and connect examples with the same terms (7+1 and 1+7, for example).
I highly recommend making cards like 7 + 1 = 8 6 + 2 = 8 5 + 3 = 8 4 + 4 = 8 to consolidate the composition of numbers.

A separate card for each example. For what? Number cards give us many opportunities to learn combinations. For example:

We arrange the cards in order.
We ask the child to name them all.
Turn over and place the cards face down.
We ask the child to remember them.
Open, check, praise!

Do this as many times as necessary for the child to name them all. You can practice for literally a few minutes at a time, in between times.

Count to 20

say that each subsequent number consists of two digits;
the first digit is tens, and the second is units, which go in order from 1 to 9, as in counting to 10;
We make sure to use clarity;
Practice more often: have a large number of small balls, toys, or use candies and fruits. Ask your child to take, for example, 15 balls from one box and put them in another. Draw and sculpt numbers, play with magnetic ones, let them visit each other and make two-digit numbers from each other;
ask your child to name the neighboring numbers: “Who lives next door to the number 17?”;
learn to recognize geometric shapes;
teach to recognize the concepts of “long-short”, “high-low”, “big-small”, “heavy-light”, “one-many”, “many-little”, etc., constantly commenting and comparing with each other other objects that surround you;
learn to recognize the concepts of “right-left”, “forward-backward”, constantly commenting on your movements and directions of action.

Learn to count correctly

After studying the numbers, you can begin counting operations. Show your child the “trick,” how two numbers turn into one by combining objects or, conversely, separating them. Next, show how you can count on your fingers and using different objects. Compare numbers. Learn to determine the smaller and larger of two numbers

It is important to study the operation signs and indicate their names

When it comes to the number ten, start introducing the concepts of “units” and “tens”.

Let the figure become a two-story house. Let's study the composition. Tens are a floor, and units are apartments. Explain the numbers of the second ten using identical toys lined up in two rows of ten - from 11 to 18. Next, note that the number 19 is the last in the second ten, which means you need to replace the number one by 2 - we get 20. It will be easier to remember if items will be numbered from 0 to 9.

You need to teach your child to form a number from two primes and name it. Offer two numbers and ask them to make a complex number. When the material is mastered, teach the opposite - to break down a number into ones and tens. Training should take place in a playful way. This way, the child’s interest will not be lost and the lesson will turn into a fascinating acquaintance with numbers. If you follow the rules, then oral counting will be easy.

How to get your child interested in counting?

Children's memory is very selective, and the child will remember exactly only what is interesting to him. It is useless to explain to your child that counting will be useful to him in school and everyday life. The learning process will bring effective results only if the parents were able to seriously interest the child.

Several ways to get your child interested in counting:

Mathematical basics should be presented to the baby in a playful way. Every time you play with your child, do not forget to count the toys and objects involved in the game.
You need to count everything, everywhere. While walking, you can count the houses around you, trees, passers-by and cars passing by.
List items when looking through books. All children love looking at book illustrations. While reading or viewing books, you need to count the drawn characters or read the rhymes.
Count kitchen utensils when setting the table or while preparing food.

As soon as your baby has learned to count to at least 10 without errors in following the sequence, you can start learning numbers.

“The language of numbers” and mathematical problems out of thin air

We adults think in numbers every day, but we don't always say them out loud. But children may be interested in the “language of numbers”: “What time did we wake up today? At 7 o'clock in the morning. What bus were you waiting for at the stop? 12th. How many minutes did it take? 10".

Gradually, just naming numbers will become boring. Show your child how interesting it is to count everything that surrounds him: entrances to the house, cars in the parking lot, trees near the playground, house numbers. If you're a resourceful parent, you can come up with little addition and subtraction math problems on the fly.

It has been noticed that the child will count what he likes with greater enthusiasm. Therefore, the well-known problems with candy act like a magnet.

At home, the child always has something to count. You can follow the clock hands and turn measuring your weight and height into a game. A tear-off calendar or a toy calendar in which you need to turn over cubes with numbers every day keeps children occupied for a long time.

But this Lego calendar needs to be disassembled and reassembled every month.

For children of senior preschool age

All of the above exercises can be made more difficult. Try writing word problems together based on what you saw during the day. Let your child count more in his head when solving applied problems.

In general, it will take time to come up with interesting problems on your own or find quality material on the Internet. The LogicLike team has already done all the methodological and other preparatory work for you!

2500+ tasks to develop logic and mathematical abilities. Voiceover of tasks, answers and explanations in your online account.

Why teach children mental arithmetic?

If you are sure that your child’s future activities will have nothing to do with calculations, you should not give up the skill of mental calculation. This ability plays a huge role in the formation of intelligence:

Regular practice with numbers stimulates thinking, improves memory, and promotes speech development.
Mental counting teaches children to think abstractly, find coincidences and patterns.
This skill helps children concentrate better, be attentive and observant.

Unfortunately, the age of high technology makes it difficult to appreciate the full importance of this skill. It is much easier to teach a child to use a calculator, which will quickly, accurately and accurately cope with the task.

However, it is necessary to develop children. The brain needs regular training. Otherwise, mental productivity decreases. So if you want your children to learn to use their full potential, be sure to teach them mental arithmetic.

Learning to count: where to start?

Children's interest in mental arithmetic awakens early, even in preschool age, and it must continue to be nourished so that it does not fade away. It can be stimulated through various educational games: start with simple counting toys, and in the elementary grades focus on the multiplication table, or as you progress, move on to learning mental arithmetic.

At the very beginning of the journey and even before school, you need to teach your child to count within 10, then move on to counting double-digit numbers. For learning, you can use pictures, toys or other similar objects that would be stored in the child’s memory and would help him in the future.

However, when teaching a child, it is important to control that he does not count with his fingers or sticks. This method is easy to master, but unlearning it will require effort, since the memory mechanism will not be used

It’s the same as with a calculator: people who are used to counting on it subsequently have a hard time unlearning it, and their ability to count in their head suffers as a result.

Notation

First, let's decide which numbers are considered two-digit in mathematics. From the word it is immediately clear that these are numbers that contain two significant characters. Significant positions are counted from units upward, according to the finished number from right to left.

Units come first, then tens, hundreds, and so on. In this case, the signs can extend to the left of units in the form of decimal fractions after the decimal point.

Such a system is called positional. Each number in it changes its meaning depending on the position occupied. For example, there is the number 23, and there is 32, and these are different numbers that were written using the same numbers. Thanks to this approach, you can write down any number using just 9 digits from 1 to 0.

Separately, it is worth saying that any position other than zero is considered significant. In any number of insignificant positions there are infinitely many. We write 23, but we understand that this number contains 0 hundreds and thousands, that is, we can write it as 0023.

At what age should a child be taught to count in their head?

Experts say that classes should begin as early as possible - from the age when the child learned to speak and began to show interest in counting. Usually this moment occurs between three and five years.

It is important not to miss the period when interest in numbers and counting appears, because if you do not notice the optimal time to start training, a little later it will be quite difficult to involve the baby in the process of training. A few rules that will help a parent teach their child to count:

A few rules that will help a parent teach their child to count:

classes should be systematic, that is, daily;
presenting the material exclusively in a playful way and if the child has a desire to practice;
tasks should be feasible for the child, and the increase in complexity should be gradual (when it is clear that the previous stage has been mastered and consolidated);
If the child has no visible interest, games will help. Some people don't like counting cubes, but they will happily do it while jumping up the stairs. The main thing is to find what a particular baby likes;
consolidation of material in everyday life. While walking you can count trees, cars, etc.;
Along the way, it is useful to teach the child such concepts as “more”, “less” and “equal”.

It is also important to set the correct duration of classes. For young children, it is better to exercise 2-3 times a day for 10 minutes than once for half an hour.

Easy learning to count: tips for parents

Rules for teaching preschoolers mathematics, which have already proven their effectiveness in practice:

exercise 20-30 minutes a day, dividing classes into 2-3 times;
do not focus on repetition if it is not required to solve new problems: repetition for the sake of repetition in mathematics only slows down the result;
move on to new material when the child has thoroughly mastered the previous one;
use the knowledge gained in everyday life: count steps, cats’ paws, money in a store;
trust your child to complete tasks independently - this will only increase your child’s self-confidence.

Be patient. Even if it’s hard and it seems like you’ve already explained it a hundred times, but the child still doesn’t understand anything. Gradually, even such a complex task as learning to count will fit into a child’s head and, perhaps, your child will become a future excellent student in mathematics!

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How to teach counting within 20

Teachers and parents provide recommendations and offer proven algorithms, thanks to which a small student will understand what tens are and how to master more complex concepts. Always test whether the “young mathematician” remembers the material covered, do not skip, even if the study takes not 2-3 days, but a week.

Where to start

Algorithm:

learn the names of the second ten numbers;
You will need two sets of cubes. Items must be the same;
the child must place 10 objects in a row, always from left to right;
say that 10 is ten, it is called “twenty”;
Place another one on top of the original row of cubes. It turned out - 11 or one plus “twenty” = eleven;
place two, then three, then four cubes on the “twenty”. It turned out: three - by - twenty, four - by - twenty and so on;
let the little student place the cubes himself, add a familiar number to ten;
Did the child clearly remember the scheme for constructing numbers from 11 to 19? Proceed to the next step.

How is a hundred formed?

Algorithm:

most children who have mastered the formation of numbers up to 20 quickly understand how to make two, three, four tens up to a hundred;
The beginning of the exercise is the same: lay out 10 cubes, say that it is ten or “twenty”;
Place the same row of ten cubes side by side, you get two rows. Name: two plus “twenty” = twenty, three plus “twenty” = thirty;
Leave 40 (forty) and 90 (ninety) for later, say: these round numbers have a different name. Show that ten always has a “0” at the end, therefore the number is round, the numbers 1, 5, 8 and so on are added to it;
50, 60, 70, 80 – even easier to remember. Ask how many tens there are in the number 50. That's right, five. Let the children name the first number, add the word “ten” - the result will be FIFTY. When the student understands the principle, ask: “How many tens did you find in 60, 70 and 80?” Of course, six, seven, eight. This will give you the new names: SIXTY, SEVENTY, EIGHTY.

Counting to 20 without passing through ten

Algorithm:

take out the same cubes again;
let the child line up a row of ten pieces;
Place two more cubes on top (necessarily from left to right). Got 12;
next to it, using the same principle, construct the number 15;
Explain to your little student how to quickly add 12 and 15. Add 1 + 1 ten, you get 2 tens or TWENTY;
add units: 2 + 5 = 7. Now there are TWENTY and SEVEN, together - TWENTY SEVEN;
support your explanation with cubes. Let the child count whether there really are 27 cubes on the table;
consolidate the task, let them try different options until the “young mathematician” understands the principle;
have you mastered addition? Start subtracting: the principle is the same;
move beyond ten only after you fully understand the material with any numbers from 10 to 100.

Recommendation! By the beginning of training, the child must clearly understand where the tens are and where the stakes are in two-digit numbers, and clearly know the concepts of “left - right”.

Counting rules with passing through ten

Use a table that shows the composition of the number. Children must figure out how to get numbers in different ways. For example, 8 = 3 + 5, 4 + 4, 6 + 2, 7 + 1, 8+ 0. Without the skills of quick counting, addition/subtraction from 0 to 10, you cannot move on to more complex exercises.

Parents' task: explain that one of the numbers must be divided by two to get 10, then add the remainder. The rule is easy to understand with an example.

See:

task: find how much 18 + 6 is;
18 is 10 and 8;
write it down in a new way (10 + + 6;
ask how many tens are missing from 6 to add to 8;
correct, 2 (the table “Composition of numbers” will be useful);
now write 6 as 2 and 4. The result is: 10 + 8 + 2 + 4 or 10 + 10 + 4. Two tens plus four ones equals TWENTY FOUR;
when the child remembers addition, explain subtraction in the same way;
Always keep the “Number Composition” table handy. Children will be less lost and it will be easier to navigate.

Constantly do “practice in between” to better remember the composition of the number. Speak more loudly, involve the child, let him finish the phrase: “There are 3 plates on the table on the left, I place 3 more plates on the right. How many items are there in total? That's right, 6." Show another way: “I will put 2 plates on the left, 4 plates on the right, again there are 6 plates” and so on (1 + 5).

Memory poems for learning counting

Berry count

A fox walked along the edge of the forest: - One, there is a strawberry in a basket, Two - blueberries like the sky, Three - ruddy lingonberries, And four - cloudberries, Five - a little currants, Six - like a viburnum bead, Seven - a rowan like the sun, Eight - in the paw blackberries, Nine - blue blueberries, Ten - juicy raspberries. Here's a full basket!

One - hand, two - hand - We are making a snowman! Three - four, three - four, Let's draw a wider mouth! Five - let's find carrots for the nose, Let's find coals for the eyes. Six - let's put our hat on askew. Let him laugh with us. Seven and eight, seven and eight, We will ask him to dance. Nine - ten - snowman Over the head - somersault! What a circus!

The fingers went for a walk, And the second fingers went to catch up, The third fingers ran, And the fourth fingers walked, The fifth finger galloped, And at the end of the path he fell.

Game "Name the neighbors of the number" .
For example, you need to name the neighbors of the number 4.
Exercise “The numbers got lost”
. You need to put the randomly arranged pictures with numbers in order. There is another interpretation of this exercise: Baba Yaga mixed up all the numbers. Help me arrange them correctly.

There were 10 chicken legs visible under the fence. Question: How many chickens are there in total? - Counting in twos: 2, 4, 6, 8, 10 - five chickens.
How many boots should three goslings be given? Similar to the previous problem.
The most convenient way to count in fives is by watching the clock.