In order to cultivate intellectual qualities in a child, to raise him as a versatile person with developed logical thinking, broad outlook and erudition, we must begin this from early childhood. But approach the process competently, according to the principle of consistency and systematicity.

One of the key components of a child’s intellectual development is learning mental arithmetic. For different ages, training should have an appropriate level of difficulty.

When to start learning?

You will need:

Basics of teaching mathematics

Geometry to help

Counting is not the only component of a child’s intellectual development in the direction of mathematics.

Children need to be taught the basic rules and concepts of geometry:

Sizes:

Simple geometric shapes

and their examples in everyday life;

Direction of movement:

left, right, back, forward, up, down.

Lessons in a playful way

For children of preschool age, training sessions should be carried out in a playful way, and for children of primary school age – with the inclusion of games and competitions in solving mathematical tasks against a time limit.

Take well-known games to help: lotto, dominoes, children's monopoly, the game “four on a line”... and specially designed manuals.

To master counting, many aids have been developed that are more like an entertaining game: graphical solving of labyrinths, similar to unwinding a ball, drawings of cells in normal and mirror images.

Illustrative examples are the key to success

Visibility and visualization are important teaching techniques for teaching young children. Count the items at hand, increasing their number, adding one at a time.

In the first stages of learning, do not focus on the mathematical concepts of “addition” and “subtraction”, “plus” and “minus”.

5 rules of early learning

Number of information submission

It is easier for children to learn new knowledge in doses, in small portions: conduct classes a day for 2-3 lessons, 10 minutes each. The child will remain interested, and the amount of information received will correspond to his age-related intellectual capabilities. It won't be a burden to him.

Don't go back to repeat

When studying the fundamentals of mathematics, you should not return to previously studied material, but repeat it when the completed section is the basis for solving problems at the next level.

Practical difficulty

Collaborate with your child to solve problems at his level. Under no circumstances should you be ashamed for misunderstanding, especially if you don’t shout or scold.

Fixing the material

Be sure to use examples of mathematics in everyday life:

• Count everything interesting, especially unusual ones: cats in the yard, daisy petals, red cars, fairy tale characters, buttons on a jacket.

Examples from counting problems at the primary school age level:

• From the price for an individual product and the required quantity, calculate the cost of this product;
• Calculate the total purchase price of all goods.

The principle of slowness in the learning process

Any training should be consistent and systematic. In order for the material to be assimilated and remembered, becoming the basis for the following knowledge, it is necessary that the child has time to go through all stages of mental development:

1. Getting used to terms, concepts and process.
2. Understanding the essence of the process.
3. Memorizing information.

Don't rush to submit new material. Constantly apply the acquired knowledge in everyday life, add, consolidate it.

Be sure to motivate with praise and recognition of his maturation. After all, instructing a person to place a certain number of cutlery on the table is to show trust and recognize his first steps on the path to independence.

How to teach a child to count in his head

To learn mental arithmetic, a certain level of development is required, which corresponds to the age abilities of a four-year-old child.

• Try to count with your child as much as possible and everything that is in sight and arouses interest. Teach your child to count objects without you. Constant training is important in activities of any kind;
• Help your child develop an understanding of concepts "less - more" through both quantitative comparison and visual comparison of length, height;
• It's time to explain what it is "equally".

The most intelligible explanation is a visual demonstration: compare an equal number of identical objects with the same number of the same objects. Ask your child to determine where there are more objects.

• It's time to introduce your child to a basic mathematical rule: “The sum does not change by changing the places of the terms”.

To explain, use the principle of visual demonstration: divide the objects, add them up, divide them again, but by a different quantity, and add them up again.

• To facilitate the learning process, and most importantly, to maintain its interest, use existing game aids for counting. Learn to count using counting sticks, cubes, tables, cards, etc.

How to quickly teach counting to 10 using a game

Start mastering counting not with the whole ten, but with the first five digits. So, first count within 5, only then take it to ten.

The learning process can be made much more effective if:

• Practice counting whenever possible, practicing the skill daily;
• Include fingers in activities;
• Include in lessons children's abacus and games designed to develop counting skills;
• Use watching educational programs to help;
• Learn nursery rhymes that rhyme counting.

Cards are especially useful teaching materials for counting. You should change the flashcard learning system from sequential to alternating to develop logic, not just memory.

Try to include counting in your first household chores, for this purpose set the following task:

1. Wash or arrange a certain number of dishes;.
2. Remember the quantitative list of necessary purchases, starting with 5.

Use the whole range of entertaining counting games, poetry and counting rhymes. Examples of which are given below.

Shop game

Prepare products and price tags for them. Also assign "monetary currency", for example, shells, pebbles, buttons, or prepare paper money, or maybe real coins.

The child should act as a cashier, you – the buyer. Get your child interested in counting, first quantitatively, without amounts: how many purchases you have and how much “currency” he has.

“Count with me!”

One two three four!
Who lives in our apartment?
Dad, mom, brother, sister,
Murka the cat, two kittens,
My puppy, cricket and me.
That's my whole family!
One two three four five!
I'll start counting everyone again!

“Guess what!”

Using either ready-made plastic numbers or homemade cardboard ones, invite your child to guess them.

Reward correct answers with his favorite treats or something interesting to him.

Modeling from plasticine

Let's give you the task of making two ears or four legs for a future plasticine animal.

Learning to count within 20

The starting point for increasing the counting difficulty level to 20 should be the following well-learned skills:

• Understanding counting to 9;
• Knowledge of the number 10.

Introduction to the concept of units and tens

Using the example of new two-digit numbers after 10, explain to your child the concepts of units and tens.

For a visual explanation, use two types of objects, for example, pencils and markers, apples and carrots. Assign one type as units, the other as tens.

Sequence of numbers

Explain the formula for the composition of a two-digit number and the sequence of changes in the second digit of ten, one, from 1 to 9, with which he is familiar.

Reinforce your understanding of tens and ones with visual expressions of double digits by choosing examples from the number line up to 20.

Example

The number 11 is 1 pencil and 1 felt-tip pen, 12 is 1 pencil and 2 felt-tip pens, respectively, and so on for all numbers up to 19 sequentially, without moving to the next ten.

How to learn to count to 100

The child’s consciousness must be ready for the next complex, labor-intensive and multifaceted level: if before the age of 5 the child received systematic and consistent knowledge about series of numbers, is familiar with the concepts of units and tens at the initial level of the number series up to 20.

Expand the number of tens

1. Introduce your child to the following rows of tens: from 20 to 29, from 30 to 39, from 40 to 49 and so on until 99.
2. Explain to him the algorithm for constructing a ten by increasing the units within the ten.
3. Reinforce concepts with clear examples.

New day - new numbers

1. Teach your child a new ten every day.
2. When you get to the middle of a hundred - 50, try looking for lost two-digit numbers from some ten.
3. Play this game every day.

This is a tablet for learning numbers from 1 to 100. The book is suitable for children over 4 years old.
Those who are familiar with Montesori training have probably already seen such a sign. It has many applications and now we will get to know them.
The child must have excellent knowledge of numbers up to 10 before starting to work with the table, since counting up to 10 is the basis for teaching numbers up to 100 and above.
With the help of this table, the child will learn the names of numbers up to 100; count to 100; sequence of numbers. You can also practice counting by 2, 3, 5, etc.

The table can be copied here

How to use the table

Examples of use:

1. He knows one girl who can help me. “He knows a girl who can help me.”
2. She has only two options. - She has only two options.
3. "Seven Psychopaths" is the best movie I have ever seen.– “Seven Psychopaths” is the best film I have ever seen.
4. You need another eight dollars to buy that necklace. “You need eight more dollars to buy that necklace.”
5. He called me eleven times in six minutes!“In eight minutes he called me eleven times!”
6. My wife paid twelve dollars for a souvenir. “My wife paid twelve dollars for the souvenir.”

Numbers in English from 13 to 19

The name of the numbers from 13 to 19 in English is quite simple - add the suffix –teen to one:

Six (6) + teen = sixteen (16)

Four (4) + teen = fourteen (14)

Examples of use:

1. Justin Bieber started his career in fourteen.– Justin Bieber began his career at the age of fourteen.
2. Our journey lasted sixteen days. “Our journey lasted sixteen days.
3. I wish I could be seventeen forever. “I wish I could always be seventeen!”
4. She just turned eighteen.– She recently turned eighteen.

Note:

Sometimes there are small changes in the figure, i.e. Simply adding the suffix –teen is not enough. In numbers 13 and 15 a different root word will be written.

He doesn't believe that number thirteen brings bad luck. “He believes that the number thirteen brings bad luck.”

I spent fifteen days trying to find him in Miami. “I spent fifteen days trying to find him in Miami.”

Features of the formation of tens in English

To get ten, you need to add the suffix –ty to one. Thus: seven (7) + ty = seventy (70).

Examples of use:

1. This mobile costs only sixty dollars. – This mobile phone costs only sixty dollars.
2. My grandmother died at the age of seventy.– My grandmother died at the age of seventy.
3. I should be there in about eighty minutes. “I should be there in about eighty minutes.”

Note:

In some cases, the spelling of tens changes. The numbers 30 and 50 change in much the same way as the numbers 13 and 15, and at 40 the letter "u" appears. The number 20 also changes, it is a bit like 12.

She asked twenty friends to her birthday party. She invited twenty friends to her birthday party.

Anna lost more than thirty thirty kilograms. – Anna lost more than thirty kilograms.

Michael was forty, but he appeared older. – Michael was forty, but he looked older.

There are fifty states in the USA. – The USA has fifty states.

How are compound numerals formed in English?

Two-digit numbers, as in Russian, are formed by adding one to ten. Please note that when writing between units and tens, you must add a hyphen.

For example:

Examplesuse:

1. Professor Jones has been studying linguistics for forty-five years.– Professor Jones has been studying linguistics for forty-five years.
2. Open your books at page fifty-nine. – Open the books to page fifty-nine.
3. Will you still need me when I’m sixty-four?“Will you still need me when I’m sixty-four?”
4. The man drove the taxi at eighty-seven kilometers an hour. The man was driving a taxi at a speed of eighty-seven kilometers per hour.
5. I’m ninety-nine percent sure about it.“I’m ninety-nine percent sure of this.”

Numbers in English up to 100: how to pronounce correctly?

If you look at the table, namely at the column where it is indicated how to pronounce numbers in Russian, you will notice two features:

1. The ":" sign is called a long read. It means that the vowel before this sign must be drawn out with the voice. For example, the number two. It should be read as “tu-u”, extending the “u” sound a little.
2. The second feature is the “’” sign, it means emphasis. , which follows after this sign should be emphasized. For example, the number eleven. It should be pronounced “ilEvn”, the word should sound with an emphasis on the sound “e”.

Speaking about numbers from 13 to 19, it is important to put the right emphasis here. If you look at the pronunciation table, you can see that the emphasis in a number always falls on the derived suffix –teen. What’s also important is that the “i” sound in the suffix should also be drawn out.

To pronounce tens correctly, it is enough to know units. The emphasis falls on the root of the word, as in units. Derivative suffix –ty does not stand out at all when speaking.

Note:

Particularly difficult for English language learners is the pronunciation of the letter combination “th”, which begins the numbers 3, 13, 30. The truth is that the sound should not be pronounced as “f” or “s”, it is something in between. When pronouncing this sound, the tip of the tongue must be inserted between the teeth. Be sure to listen to how these numbers are pronounced.

What is the difference between a hundred, a thousand, a million and a billion?

Hundreds, thousands, millions and billions can be counted. In order to get such a figure, you need to add a hundred, a thousand, etc. to one. If we are talking about hundreds of millions, the scheme remains the same.

For example:

1. Two (2) + one hundred (100)= two hundred (200)
2. Seventy-five (75) + one thousand (1.000)= Seventy-five thousand (75.000)
3. One hundred (100) + one million (1.000.000)= One hundred million (100.000.000)
4. Five hundred (500) + one billion (1.000.000.000)= Five hundred billion (5.000.000.000)

note that in such cases the plural ending is not added to hundreds, thousands, millions and billions in English. One billion or ten, it will still be “billion”.

Three-digit numbers are formed according to the scheme: hundred + ten + one.

There is a slight difference in the formation of three-digit numbers between British (Br.E.) and American English (Am.E.). The British put “and” between a hundred and ten, but Americans do not use this conjunction in three-digit numbers.

For example:

• One hundred (100) + eight (8)= One hundred and eight (Br.E.) or one hundred two (Am.E.) (102)
• Two hundred (200) + forty-three (43)= Two hundred and forty-three (Br.E.) or Two hundred forty-three (Am.E.) (243)

Conclusion

Now we can say with confidence that you know the order of formation of numbers in English up to 100. To consolidate your learning, you can count the counters or listen to the correct pronunciation of numbers in English up to 100.

After several trainings, it will not be difficult for you to learn, be able to write and name any number. We also advise you to perform various exercises or free ones, of which there are many on the Internet, as well as watch video tutorials online.

The topic of English numerals is quite complex, since the formation of English numerals differs from the formation of Russian ones. There are rules, and there are exceptions, and both have their own peculiarities. Let's look at English numbers with transcription and Russian pronunciation, give striking examples and focus on exceptions. Go ahead for new knowledge!

Numbers in English are formed in different ways. Numerals from 1 to 10 have some rules of formation, from 13 to 20 - others. Tens, hundreds and thousands also have peculiarities of education.

Features of the formation of numerals from 1 to 12

The table below shows the numerals from 1 to 12 with transcription, Russian pronunciation and examples:

• We wanted one cake, two bananas ang eight apples => We wanted one cake, two bananas and eight apples.
• We need to buy avocado fot this recipe. Or better two ones => For this recipe we have to buy an avocado. Or better yet, two.
• Three kilos of meat, four big tomatoes, five eggplants and garlic will make this evening much more better. I will prepare very delicious dish by my own recipe! => Three kilograms of meat, four large tomatoes, five eggplants and garlic will make the evening much better. I will prepare a very tasty dish according to my own recipe!
• Eleven foxes and twelve wolves were seen on this week at this place => Eleven foxes and twelve wolves were seen this week at this place.

Features of the formation of numerals from 13 to 20

The table shows that numerals from 13 to 19 (inclusive) are written according to the same rules; a particle is added to the cardinal number (one, two, three) –teen. And do not confuse cardinal numbers with ordinal numbers! in English they are formed in a completely different way!

On a note! It must be remembered that every rule has exceptions. In this case, the exceptions will be the numerals 13 and 15. Their roots three and five will have a modified form:

• Three => thirteen
• Five => fifteen.

Not threeteen/fiveteen!!!

Some examples:

• Seventeen girls were seen at this party while only eight boys came. — Seventeen girls were seen at the party, while only eight guys came.
• Seventeen pieces of cake were given to all those children. — All these children were given seventeen pieces of pie.
• There is a lot of fish in this river. Nineteen kinds were known 5 years ago. — There are a lot of fish in this river. Five years ago, nineteen species were known.

Tens of English numerals

The table clearly shows that tens of numbers are formed using a particle (suffix) –ty. These numerals are derivatives of cardinal ones, but you also need to add the suffix –ty.

Important! Remember that when forming the numbers 20,30, 40 and 50, the root of the quantitative digits, which serve as the basis for the formation of tens, will change:

• two – 20 twenty [ˈtwenti]
• three – 30 thirty [ˈθɜːti]
• four – 40 forty [ˈfɔːti]
• five – 50 fifty [ˈfɪfti]

And one more nuance: the number 80 [ˈeɪti] is characterized by the absence of repetition of the letter t: eight (eight) = eighty(eight+ty =eightty).

Examples:

• Thirty exotic animals were needed to make the idea of ​​the movie complete => Thirty exotic animals were needed to make the idea of ​​the movie complete.
• Sixty soldiers will come on parade in front of the palace => Sixty soldiers will come to the parade that will be in front of the palace.
• Fifty of them knew the road but only thirty agreed to follow us => Fifty of them knew the road, but only thirty agreed to follow us.

As for the stress of numerals that are formed with the help of –ty, then everything is simple - stress Always will be on the first syllable.

Reference: It happens that beginning students find it difficult to separate numerals with –ty and –teen in colloquial speech. And here stress comes to the rescue - if it is on the first syllable, then 100% we are dealing with tens of numerals.

Basics: How numbers are formed in English

When studying the formation of English numbers, it is important to remember that numbers from 1 to 12 are simple cardinal numbers. Their task is to indicate the number of objects. Such numerals consist of one word. It is very important to remember the spelling of the first twelve digits, since they are the basis for the formation of all other digits - from thirteen to a billion.

How to pronounce numerals that are formed by adding the particle –teen? Here you need to be very careful => the pronunciation of numerals (English numbers) will have two stresses: on the first and second syllable. At the same time, we immediately note that the stresses will not be equal in strength. One of them will be secondary, and the other will be primary.

For example, how do you pronounce thirteen? From the transcription of [ˌθɜːˈtiːn] it is clear that the word has two stresses. The bottom line indicates secondary stress, the top line indicates primary stress. The same goes for fourteen [ˌfɔːˈtiːn] and fifteen [ˌfɪfˈtiːn]. There are also two stresses here – main and additional.

What to do to avoid making mistakes with pronunciation? To do this, you should always look at the transcription. Each numeral, like any other word, should be studied according to the following scheme: transcription - translation - the presence of several meanings.

Note! In some dictionaries, the stress of numerals is determined by the presence (absence) of a noun after it. For example, if a numeral is next to a noun, then the stress falls on the first syllable =>

• fifteen rivers [ˈfɪftiːn ˈrɪvər z]
• sixteen cats [ˈsɪkstiːn ˈkæts]

But! If a numeral stands alone in a sentence, without a noun, then the stress falls on the second syllable (on the suffix –teen):

• fifteen
• sixteen

Examples:

• Fifteen cats were sold this week (emphasis is on the first syllable) => Fifteen cats were sold this week
• How many cats were sold this week? – Fifteen (emphasis on the suffix –teen) => How many cats were sold this week? - Fifteen.

A hundred, a thousand, a million: is there a difference?

First of all, it should be noted that before the numerals hundred (one hundred), thousand (thousand) and million (million) there will always be either the word one or the indefinite article a (meaning ‘one’).

• a/one hundred => One h’andrid [ə wʌn ˈhʌndrəd]
• a/one thousand => One Southend
• one million => One m'ilyan.
• One hundred and twenty => one hundred and twenty
• One hundred singers => one hundred singers
• One hundred thirty eight cars => one hundred thirty eight cars.

But! Other cardinal numbers are characterized by the absence of an article! =>

• Five dresses => Five dresses.
• Eight balls => Eight balls.

Important! The numerals hundred, thousand and million do not have the ending –s, which determines the plural.

• Two hundred => two hundred
• Five hundred => five hundred
• Nine hundred => nine hundred, etc.

If we are talking about thousands, then the same rule applies:

• thousand (one thousand) – one thousand or a thousand
• five thousand – five thousand
• seven thousand – seven thousand.

Millions are formed by the same principle:

• million (one million) – one million or a million
• seven million – seven million
• nine million – nine million.

But! English wouldn't be as fun to learn if it didn't have exceptions. What would it be like without them? Students will be interested to know that the ending –s in millions, thousands and hundreds is still used. When does this happen? When measures denote an indefinite number of these same millions, thousands and hundreds.

Examples

• Hundreds of pages to read for understanding => Read hundreds of pages to understand (something, a foreign language, for example).
• Five millions of tons of gold => Five million tons of gold.
• Thousands of kilometers to walk to win marathon => Walk thousands of kilometers to win the marathon.

From the examples it is clear that after hundreds, thousands and millions with the ending –s (when translated into English) comes a noun or verb. In most cases, the additional part of the sentence will still be a noun. And if it is present, it must be with the preposition of:

• Seven or eight thousand of specie were made of pure silver => Seven or eight thousand metal coins were made of pure silver.

A song about English numbers for children

Let's sum it up

Numbers in English are formed in a different way from the one we studied in Russian grammar. Tens and hundreds have their own peculiarities of education, in which, naturally, there will certainly be exceptions to the rules. At the same time, in order to learn numerals correctly, it is extremely important to learn how to pronounce them correctly.

When writing numerals, they also have their own nuances; you also need to know the subtleties of spelling. Therefore, we are learning the topic of English numbers with transcription and Russian pronunciation little by little and with examples (translation) in order to better understand the intricacies of the material. And don’t forget to regularly review the topics you’ve already studied so that you don’t forget them.

Good luck and new achievements! Remember that everything was not given to anyone at once. Start small and gradually develop your abilities. If you want, you will succeed! See you again and more interesting topics to study!

A couple more videos on the formation of English numbers from 1 to 100 and from 100 and above from an English-speaking teacher: