In everyday life, most people operate with fairly small numbers. Tens, hundreds, thousands, very rarely - millions, almost never - billions. A person’s usual idea of quantity or magnitude is limited to approximately these numbers. Almost everyone has heard about trillions, but few have ever used them in any calculations.
What are they, giant numbers?
Meanwhile, numbers denoting powers of a thousand have been known to people for a long time. In Russia and many other countries, a simple and logical notation system is used:
Thousand;
Million;
Billion;
Trillion;
Quadrillion;
Quintillion;
Sextillion;
Septillion;
Octillion;
Quintillion;
Decillion.
In this system, each subsequent number is obtained by multiplying the previous one by a thousand. Billion is usually called billion.
Many adults can accurately write numbers such as a million - 1,000,000 and a billion - 1,000,000,000. A trillion is more difficult, but almost everyone can handle it - 1,000,000,000,000. And then begins territory unknown to many.
Let's take a closer look at the big numbers
However, there is nothing complicated, the main thing is to understand the system of formation of large numbers and the principle of naming. As already mentioned, each subsequent number is a thousand times greater than the previous one. This means that in order to correctly write the next number in ascending order, you need to add three more zeros to the previous one. That is, a million has 6 zeros, a billion has 9, a trillion has 12, a quadrillion has 15, and a quintillion has 18.
You can also figure out the names if you wish. The word "million" comes from the Latin "mille", which means "more than a thousand." The following numbers were formed by adding the Latin words "bi" (two), "tri" (three), "quad" (four), etc.
Now let's try to visualize these numbers clearly. Most people have a pretty good idea of the difference between a thousand and a million. Everyone understands that a million rubles is good, but a billion is more. Much more. Also, everyone has the idea that a trillion is something absolutely immense. But how much more is a trillion than a billion? How big is it?
For many, beyond a billion the concept of “incomprehensible to the mind” begins. Indeed, a billion kilometers or a trillion - the difference is not very big in the sense that such a distance still cannot be covered in a lifetime. A billion rubles or a trillion is also not very different, because you still can’t earn that kind of money in your entire life. But let's do a little math using our imagination.
Russia's housing stock and four football fields as examples
For every person on earth there is a land area measuring 100x200 meters. This is approximately four football fields. But if there are not 7 billion people, but seven trillion, then everyone will only get a piece of land 4x5 meters. Four football fields versus the area of the front garden in front of the entrance - this is the ratio of a billion to a trillion.
In absolute terms, the picture is also impressive.
If you take a trillion bricks, you can build more than 30 million one-story houses with an area of 100 square meters. That is, about 3 billion square meters of private development. This is comparable to the total housing stock of the Russian Federation.
If you build ten-story buildings, you will get approximately 2.5 million houses, that is, 100 million two- and three-room apartments, about 7 billion square meters of housing. This is 2.5 times more than the entire housing stock in Russia.
In a word, there are not a trillion bricks in all of Russia.
One quadrillion student notebooks will cover the entire territory of Russia with a double layer. And one quintillion of the same notebooks will cover the entire landmass with a layer 40 centimeters thick. If we manage to get a sextillion notebooks, then the entire planet, including the oceans, will be under a layer 100 meters thick.
Let's count to a decillion
Let's count some more. For example, a matchbox magnified a thousand times would be the size of a sixteen-story building. An increase of a million times will give a “box” that is larger in area than St. Petersburg. Enlarged a billion times, the boxes would not fit on our planet. On the contrary, the Earth will fit into such a “box” 25 times!
Increasing the box gives an increase in its volume. It will be almost impossible to imagine such volumes with further increase. For ease of perception, let's try to increase not the object itself, but its quantity, and arrange the matchboxes in space. This will make it easier to navigate. A quintillion boxes laid out in one row would stretch beyond the star α Centauri by 9 trillion kilometers.
Another thousandfold magnification (sextillion) would allow matchboxes lined up to span the entire length of our Milky Way galaxy. A septillion matchboxes would stretch over 50 quintillion kilometers. Light can travel such a distance in 5 million 260 thousand years. And the boxes laid out in two rows would stretch to the Andromeda galaxy.
There are only three numbers left: octillion, nonillion and decillion. You'll have to use your imagination. An octillion boxes form a continuous line of 50 sextillion kilometers. This is more than five billion light years. Not every telescope installed on one edge of such an object could see its opposite edge.
Shall we count further? A nonillion matchboxes would fill the entire space of the known part of the Universe with an average density of 6 pieces per cubic meter. By earthly standards, it doesn’t seem like a lot - 36 matchboxes in the back of a standard Gazelle. But a nonillion matchboxes would have a mass billions of times greater than the mass of all the material objects in the known Universe combined.
Decillion. The size, or rather even the majesty, of this giant from the world of numbers is difficult to imagine. Just one example - six decillion boxes would no longer fit in the entire part of the Universe accessible to humanity for observation.
The majesty of this number is even more striking if you do not multiply the number of boxes, but increase the object itself. A matchbox, magnified a decillion times, would contain the entire part of the Universe known to mankind 20 trillion times. It’s impossible to even imagine this.
Small calculations showed how huge the numbers are, known to mankind for several centuries. In modern mathematics, numbers many times greater than a decillion are known, but they are used only in complex mathematical calculations. Only professional mathematicians have to deal with such numbers.
The most famous (and smallest) of these numbers is the googol, denoted by one followed by one hundred zeros. A googol is greater than the total number of elementary particles in the visible part of the Universe. This makes googol an abstract number that has little practical use.
Countless different numbers surround us every day. Surely many people have at least once wondered what number is considered the largest. You can simply say to a child that this is a million, but adults understand perfectly well that other numbers follow a million. For example, all you have to do is add one to a number each time, and it will become larger and larger - this happens ad infinitum. But if you look at the numbers that have names, you can find out what the largest number in the world is called.
The appearance of number names: what methods are used?
Today there are 2 systems according to which names are given to numbers - American and English. The first is quite simple, and the second is the most common throughout the world. The American one allows you to give names to large numbers as follows: first, the ordinal number in Latin is indicated, and then the suffix “million” is added (the exception here is million, meaning a thousand). This system is used by Americans, French, Canadians, and it is also used in our country.
English is widely used in England and Spain. According to it, numbers are named as follows: the numeral in Latin is “plus” with the suffix “illion”, and the next (a thousand times larger) number is “plus” “billion”. For example, the trillion comes first, the trillion comes after it, the quadrillion comes after the quadrillion, etc.
Thus, the same number in different systems can mean different things; for example, an American billion in the English system is called a billion.
Extra-system numbers
In addition to the numbers that are written according to the known systems (given above), there are also non-systemic ones. They have their own names, which do not include Latin prefixes.
You can start considering them with a number called a myriad. It is defined as one hundred hundreds (10000). But according to its intended purpose, this word is not used, but is used as an indication of an innumerable multitude. Even Dahl's dictionary will kindly provide a definition of such a number.
Next after the myriad is a googol, denoting 10 to the power of 100. This name was first used in 1938 by the American mathematician E. Kasner, who noted that this name was invented by his nephew.
Google (search engine) got its name in honor of googol. Then 1 with a googol of zeros (1010100) represents a googolplex - Kasner also came up with this name.
Even larger than the googolplex is the Skuse number (e to the power of e to the power of e79), proposed by Skuse in his proof of the Rimmann conjecture about prime numbers (1933). There is another Skuse number, but it is used when the Rimmann hypothesis is not valid. Which one is greater is quite difficult to say, especially when it comes to large degrees. However, this number, despite its “hugeness,” cannot be considered the very best of all those that have their own names.
And the leader among the largest numbers in the world is the Graham number (G64). It was used for the first time to carry out proofs in the field of mathematical science (1977).
When it comes to such a number, you need to know that you cannot do without a special 64-level system created by Knuth - the reason for this is the connection of the number G with bichromatic hypercubes. Knuth invented the superdegree, and in order to make it convenient to record it, he proposed the use of up arrows. So we found out what the largest number in the world is called. It is worth noting that this number G was included in the pages of the famous Book of Records.
I once read a tragic story about a Chukchi who was taught by polar explorers to count and write down numbers. The magic of numbers amazed him so much that he decided to write down absolutely all the numbers in the world in a row, starting with one, in a notebook donated by polar explorers. The Chukchi abandons all his affairs, stops communicating even with his own wife, no longer hunts ringed seals and seals, but keeps writing and writing numbers in a notebook…. This is how a year goes by. In the end, the notebook runs out and the Chukchi realizes that he was able to write down only a small part of all the numbers. He weeps bitterly and in despair burns his scribbled notebook in order to again begin to live the simple life of a fisherman, no longer thinking about the mysterious infinity of numbers...
Let's not repeat the feat of this Chukchi and try to find the largest number, since any number only needs to add one to get an even larger number. Let us ask ourselves a similar but different question: which of the numbers that have their own name is the largest?
It is obvious that although the numbers themselves are infinite, they do not have so many proper names, since most of them are content with names made up of smaller numbers. So, for example, the numbers 1 and 100 have their own names “one” and “one hundred,” and the name of the number 101 is already compound (“one hundred and one”). It is clear that in the final set of numbers that humanity has awarded with its own name, there must be some largest number. But what is it called and what does it equal? Let's try to figure this out and find, in the end, this is the largest number!
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"Short" and "long" scale
The history of the modern system of naming large numbers dates back to the middle of the 15th century, when in Italy they began to use the words “million” (literally - large thousand) for a thousand squared, “bimillion” for a million squared and “trimillion” for a million cubed. We know about this system thanks to the French mathematician Nicolas Chuquet (c. 1450 - c. 1500): in his treatise “The Science of Numbers” (Triparty en la science des nombres, 1484) he developed this idea, proposing to further use the Latin cardinal numbers (see table), adding them to the ending “-million”. So, “bimillion” for Schuke turned into a billion, “trimillion” became a trillion, and a million to the fourth power became “quadrillion”.
In the Schuquet system, the number 10 9, located between a million and a billion, did not have its own name and was simply called “a thousand millions”, similarly 10 15 was called “a thousand billions”, 10 21 - “a thousand trillion”, etc. This was not very convenient, and in 1549 the French writer and scientist Jacques Peletier du Mans (1517-1582) proposed naming such “intermediate” numbers using the same Latin prefixes, but with the ending “-billion”. Thus, 10 9 began to be called “billion”, 10 15 - “billiard”, 10 21 - “trillion”, etc.
The Chuquet-Peletier system gradually became popular and was used throughout Europe. However, in the 17th century an unexpected problem arose. It turned out that for some reason some scientists began to get confused and call the number 10 9 not “billion” or “thousand millions”, but “billion”. Soon this error quickly spread, and a paradoxical situation arose - “billion” became simultaneously synonymous with “billion” (10 9) and “million millions” (10 18).
This confusion continued for quite a long time and led to the fact that the United States created its own system for naming large numbers. According to the American system, the names of numbers are constructed in the same way as in the Chuquet system - the Latin prefix and the ending “million”. However, the magnitudes of these numbers are different. If in the Schuquet system names with the ending “illion” received numbers that were powers of a million, then in the American system the ending “-illion” received powers of a thousand. That is, a thousand million (1000 3 = 10 9) began to be called a “billion”, 1000 4 (10 12) - a “trillion”, 1000 5 (10 15) - a “quadrillion”, etc.
The old system of naming large numbers continued to be used in conservative Great Britain and began to be called “British” throughout the world, despite the fact that it was invented by the French Chuquet and Peletier. However, in the 1970s, the UK officially switched to the “American system”, which led to the fact that it became somehow strange to call one system American and another British. As a result, the American system is now commonly referred to as the "short scale" and the British or Chuquet-Peletier system as the "long scale".
To avoid confusion, let's summarize:
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The short naming scale is now used in the US, UK, Canada, Ireland, Australia, Brazil and Puerto Rico. Russia, Denmark, Turkey and Bulgaria also use a short scale, except that the number 10 9 is called "billion" rather than "billion". The long scale continues to be used in most other countries.
It is curious that in our country the final transition to a short scale occurred only in the second half of the 20th century. For example, Yakov Isidorovich Perelman (1882-1942) in his “Entertaining Arithmetic” mentions the parallel existence of two scales in the USSR. The short scale, according to Perelman, was used in everyday life and financial calculations, and the long scale was used in scientific books on astronomy and physics. However, now it is wrong to use a long scale in Russia, although the numbers there are large.
But let's return to the search for the largest number. After decillion, the names of numbers are obtained by combining prefixes. This produces numbers such as undecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion, novemdecillion, etc. However, these names are no longer interesting to us, since we agreed to find the largest number with its own non-composite name.
If we turn to Latin grammar, we will find that the Romans had only three non-compound names for numbers greater than ten: viginti - “twenty”, centum - “hundred” and mille - “thousand”. The Romans did not have their own names for numbers greater than a thousand. For example, the Romans called a million (1,000,000) “decies centena milia,” that is, “ten times a hundred thousand.” According to Chuquet's rule, these three remaining Latin numerals give us such names for numbers as "vigintillion", "centillion" and "millillion".
So, we found out that on the “short scale” the maximum number that has its own name and is not a composite of smaller numbers is “million” (10 3003). If Russia adopted a “long scale” for naming numbers, then the largest number with its own name would be “billion” (10 6003).
However, there are names for even larger numbers.
Numbers outside the system
Some numbers have their own name, without any connection with the naming system using Latin prefixes. And there are many such numbers. You can, for example, remember the number e, number “pi”, dozen, number of the beast, etc. However, since we are now interested in large numbers, we will consider only those numbers with their own non-composite name that are greater than a million.
Until the 17th century, Rus' used its own system for naming numbers. Tens of thousands were called "darkness", hundreds of thousands were called "legions", millions were called "leoders", tens of millions were called "ravens", and hundreds of millions were called "decks". This count up to hundreds of millions was called the “small count”, and in some manuscripts the authors also considered the “great count”, in which the same names were used for large numbers, but with a different meaning. So, “darkness” no longer meant ten thousand, but a thousand thousand (10 6), “legion” - the darkness of those (10 12); “leodr” - legion of legions (10 24), “raven” - leodr of leodrov (10 48). For some reason, “deck” in the great Slavic counting was not called “raven of ravens” (10 96), but only ten “ravens”, that is, 10 49 (see table).
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The number 10,100 also has its own name and was invented by a nine-year-old boy. And it was like this. In 1938, American mathematician Edward Kasner (1878-1955) was walking in the park with his two nephews and discussing large numbers with them. During the conversation, we talked about a number with a hundred zeros, which did not have its own name. One of the nephews, nine-year-old Milton Sirott, suggested calling this number “googol.” In 1940, Edward Kasner, together with James Newman, wrote the popular science book Mathematics and the Imagination, where he told mathematics lovers about the googol number. Googol became even more widely known in the late 1990s, thanks to the Google search engine named after it.
The name for an even larger number than googol arose in 1950 thanks to the father of computer science, Claude Elwood Shannon (1916-2001). In his article "Programming a Computer to Play Chess" he tried to estimate the number of possible variants of a chess game. According to it, each game lasts on average 40 moves and on each move the player makes a choice from an average of 30 options, which corresponds to 900 40 (approximately equal to 10,118) game options. This work became widely known, and this number became known as the “Shannon number.”
In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, the number “asankheya” is found equal to 10,140. It is believed that this number is equal to the number of cosmic cycles required to achieve nirvana.
Nine-year-old Milton Sirotta went down in the history of mathematics not only because he came up with the number googol, but also because at the same time he proposed another number - the “googolplex”, which is equal to 10 to the power of “googol”, that is, one with a googol of zeros.
Two more numbers larger than the googolplex were proposed by the South African mathematician Stanley Skewes (1899-1988) when proving the Riemann hypothesis. The first number, which later became known as the "Skuse number", is equal to e to a degree e to a degree e to the power of 79, that is e e e 79 = 10 10 8.85.10 33 . However, the “second Skewes number” is even larger and is 10 10 10 1000.
Obviously, the more powers there are in the powers, the more difficult it is to write the numbers and understand their meaning when reading. Moreover, it is possible to come up with such numbers (and, by the way, they have already been invented) when the degrees of degrees simply do not fit on the page. Yes, that's on the page! They won't even fit into a book the size of the entire Universe! In this case, the question arises of how to write such numbers. The problem, fortunately, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked about this problem came up with his own way of writing, which led to the existence of several unrelated methods for writing large numbers - these are the notations of Knuth, Conway, Steinhaus, etc. We now have to deal with some of them.
Other notations
In 1938, the same year that nine-year-old Milton Sirotta invented the numbers googol and googolplex, a book about entertaining mathematics, A Mathematical Kaleidoscope, written by Hugo Dionizy Steinhaus (1887-1972), was published in Poland. This book became very popular, went through many editions and was translated into many languages, including English and Russian. In it, Steinhaus, discussing large numbers, offers a simple way to write them using three geometric figures - a triangle, a square and a circle:
"n in a triangle" means " n n»,
« n squared" means " n V n triangles",
« n in a circle" means " n V n squares."
Explaining this method of notation, Steinhaus comes up with the number "mega" equal to 2 in a circle and shows that it is equal to 256 in a "square" or 256 in 256 triangles. To calculate it, you need to raise 256 to the power of 256, raise the resulting number 3.2.10 616 to the power of 3.2.10 616, then raise the resulting number to the power of the resulting number, and so on, raise it to the power 256 times. For example, a calculator in MS Windows cannot calculate due to overflow of 256 even in two triangles. Approximately this huge number is 10 10 2.10 619.
Having determined the “mega” number, Steinhaus invites readers to independently estimate another number - “medzon”, equal to 3 in a circle. In another edition of the book, Steinhaus, instead of medzone, suggests estimating an even larger number - “megiston”, equal to 10 in a circle. Following Steinhaus, I also recommend that readers break away from this text for a while and try to write these numbers themselves using ordinary powers in order to feel their gigantic magnitude.
However, there are names for b O larger numbers. Thus, the Canadian mathematician Leo Moser (Leo Moser, 1921-1970) modified the Steinhaus notation, which was limited by the fact that if it were necessary to write numbers much larger than megiston, then difficulties and inconveniences would arise, since it would be necessary to draw many circles one inside another. Moser suggested that after the squares, draw not circles, but pentagons, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written without drawing complex pictures. Moser notation looks like this:
« n triangle" = n n = n;
« n squared" = n = « n V n triangles" = nn;
« n in a pentagon" = n = « n V n squares" = nn;
« n V k+ 1-gon" = n[k+1] = " n V n k-gons" = n[k]n.
Thus, according to Moser’s notation, Steinhaus’s “mega” is written as 2, “medzone” as 3, and “megiston” as 10. In addition, Leo Moser proposed calling a polygon with the number of sides equal to mega - “megagon”. And he proposed the number “2 in megagon”, that is, 2. This number became known as the Moser number or simply as “Moser”.
But even “Moser” is not the largest number. So, the largest number ever used in mathematical proof is the "Graham number". This number was first used by the American mathematician Ronald Graham in 1977 when proving one estimate in Ramsey theory, namely when calculating the dimension of certain n-dimensional bichromatic hypercubes. Graham's number became famous only after it was described in Martin Gardner's 1989 book, From Penrose Mosaics to Reliable Ciphers.
To explain how large Graham's number is, we have to explain another way of writing large numbers, introduced by Donald Knuth in 1976. American professor Donald Knuth came up with the concept of superpower, which he proposed to write with arrows pointing upward:
I think everything is clear, so let’s return to Graham’s number. Ronald Graham proposed the so-called G-numbers:
The number G 64 is called the Graham number (it is often designated simply as G). This number is the largest known number in the world used in a mathematical proof, and is even listed in the Guinness Book of Records.
And finally
Having written this article, I can’t help but resist the temptation to come up with my own number. Let this number be called " stasplex"and will be equal to the number G 100. Remember it, and when your children ask what the largest number in the world is, tell them that this number is called stasplex.
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Have you ever thought how many zeros there are in one million? This is a pretty simple question. What about a billion or a trillion? One followed by nine zeros (1000000000) - what is the name of the number?
A short list of numbers and their quantitative designation
- Ten (1 zero).
- One hundred (2 zeros).
- One thousand (3 zeros).
- Ten thousand (4 zeros).
- One hundred thousand (5 zeros).
- Million (6 zeros).
- Billion (9 zeros).
- Trillion (12 zeros).
- Quadrillion (15 zeros).
- Quintilion (18 zeros).
- Sextillion (21 zeros).
- Septillion (24 zeros).
- Octalion (27 zeros).
- Nonalion (30 zeros).
- Decalion (33 zeros).
Grouping of zeros
1000000000 - what is the name of a number that has 9 zeros? This is a billion. For convenience, large numbers are usually grouped into sets of three, separated from each other by a space or punctuation marks such as a comma or period.
This is done to make the quantitative value easier to read and understand. For example, what is the name of the number 1000000000? In this form, it’s worth straining a little and doing the math. And if you write 1,000,000,000, then the task immediately becomes visually easier, since you need to count not zeros, but triples of zeros.
Numbers with a lot of zeros
The most popular are million and billion (1000000000). What is the name of a number that has 100 zeros? This is a Googol number, so called by Milton Sirotta. This is a wildly huge amount. Do you think this number is large? Then what about a googolplex, a one followed by a googol of zeros? This figure is so large that it is difficult to come up with a meaning for it. In fact, there is no need for such giants, except to count the number of atoms in the infinite Universe.
Is 1 billion a lot?
There are two measurement scales - short and long. Around the world in science and finance, 1 billion is 1,000 million. This is on a short scale. According to it, this is a number with 9 zeros.
There is also a long scale that is used in some European countries, including France, and was formerly used in the UK (until 1971), where a billion was 1 million million, that is, a one followed by 12 zeros. This gradation is also called the long-term scale. The short scale is now predominant in financial and scientific matters.
Some European languages, such as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use billion (or billion) in this system. In Russian, a number with 9 zeros is also described for the short scale of a thousand million, and a trillion is a million million. This avoids unnecessary confusion.
Conversational options
In Russian colloquial speech after the events of 1917 - the Great October Revolution - and the period of hyperinflation in the early 1920s. 1 billion rubles was called “limard”. And in the dashing 1990s, a new slang expression “watermelon” appeared for a billion; a million were called “lemon.”
The word "billion" is now used internationally. This is a natural number, which is represented in the decimal system as 10 9 (one followed by 9 zeros). There is also another name - billion, which is not used in Russia and the CIS countries.
Billion = billion?
A word such as billion is used to designate a billion only in those states in which the “short scale” is adopted as a basis. These are countries such as the Russian Federation, the United Kingdom of Great Britain and Northern Ireland, the USA, Canada, Greece and Turkey. In other countries, the concept of a billion means the number 10 12, that is, one followed by 12 zeros. In countries with a “short scale”, including Russia, this figure corresponds to 1 trillion.
Such confusion appeared in France at a time when the formation of such a science as algebra was taking place. Initially, a billion had 12 zeros. However, everything changed after the appearance of the main manual on arithmetic (author Tranchan) in 1558), where a billion is already a number with 9 zeros (a thousand millions).
For several subsequent centuries, these two concepts were used on an equal basis with each other. In the mid-20th century, namely in 1948, France switched to a long scale numerical naming system. In this regard, the short scale, once borrowed from the French, is still different from the one they use today.
Historically, the United Kingdom used the long-term billion, but since 1974 official UK statistics have used the short-term scale. Since the 1950s, the short-term scale has been increasingly used in the fields of technical writing and journalism, although the long-term scale still persists.
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
It consists of two parts (two-sided). On one side of the sheet we copy a table with numbers up to 100, and on the other side we copy empty cells where we can practice. Laminate the table so that the child can write on it with markers and wipe it off easily.
How to use the table
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1. The table can be used to study numbers from 1 to 100. Starting from 1 and counting to 100. Initially the parent/teacher shows how it is done. It is important that the child notices the principle by which numbers are repeated. |
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2. Mark one number on the laminated chart. The child must say the next 3-4 numbers. |
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3. Mark some numbers. Ask your child to say their names. The second version of the exercise is for the parent to name arbitrary numbers, and the child finds and marks them. |
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4. Count in 5. The child counts 1,2,3,4,5 and marks the last (fifth) number. |
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5. If you copy the number template again and cut it, you can make cards. They can be placed in the table as you will see in the following lines In this case, the table is copied on blue cardboard so that it can be easily distinguished from the white background of the table. |
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6. Cards can be placed on the table and counted - name the number by placing its card. This helps the child learn all the numbers. This way he will exercise. Before this, it is important that the parent divides the cards into 10s (from 1 to 10; from 11 to 20; from 21 to 30, etc.). The child takes a card, puts it down and says the number. |
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7. When the child has already progressed with the counting, you can go to the empty table and place the cards there. |
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8. Count horizontally or vertically. Arrange the cards in a column or row and read all the numbers in order, following the pattern of their changes - 6, 16, 26, 36, etc. |
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9. Write the missing number. The parent writes arbitrary numbers into an empty table. The child must complete the empty cells. |