With the help of this lesson, we will study the digits of countable terms. First, let's repeat the ratio of counting units. Recall what digits are, what category hundreds, tens and ones belong to. We will solve many different and interesting tasks to consolidate the material. After this lesson, you can easily determine what category the units, tens and hundreds belong to in a three-digit number. You will also easily convert length units to smaller or larger units. Don't waste a minute. Forward - to study and comprehend new horizons!

When writing a number, each counting unit is written in its place (Table 1).

Table 1. Writing three-digit numbers

The digits are counted from right to left, starting with the first digit - one. The second digit is tens. And the third digit is hundreds.

Write down the numbers set aside on the accounts (Fig. 2, 3, 4) and read them.

Rice. 2. Numbers

Rice. 4. Numbers

Rice. 3. Numbers

Solution: 1. Seven units, two tens and three hundreds are set aside on the accounts. It turns out the number three hundred twenty-seven.

2. There are no units in the next number (Fig. 3). If there is no digit, you can put zero. The whole number is three hundred and twenty.

3. In Figure 4, there are seven units, no tens and three hundreds. It turns out the number three hundred and seven.

2. In the second magnitude, five hundred and forty centimeters. In this number, 5 hundreds - 5 m and 4 tens - 4 dm, and there are no units, therefore, there will be no centimeters.

540 cm = 5 m 4 dm

3. Eighty-six millimeters. There are ten millimeters in one centimeter, which means that this value will be eight centimeters and six millimeters.

86mm = 8cm 6mm

4. In the last number (42 dm), four tens are visible and it is known that in 1 m - 10 dm.

42 dm = 4 m 2 dm

Express these quantities in smaller units:

2. 2 dm 8 mm

Solution: 1. To solve the task, we will use Figure 5, which shows the relationship between units of length.

1 m 75 cm = 175 cm

2. Let's translate the second number.

2 dm 8 mm = 208 mm

Bibliography

1. Maths. Grade 3 Proc. for general education institutions with adj. to an electron. carrier. At 2 h. Part 1 / [M.I. Moro, M.A. Bantova, G.V. Beltyukova and others] - 2nd ed. - M.: Education, 2012. - 112 p.: ill. - (School of Russia).
2. Rudnitskaya V.N., Yudacheva T.V. Mathematics, 3rd grade. - M.: VENTANA-GRAF.
3. Peterson L.G. Mathematics, 3rd grade. - M.: Juventa.

1. All-schools.pp.ua ().
2. Urokonline.com ().
3. Uchu24.ru ().

Homework

1. Maths. Grade 3 Proc. for general education institutions with adj. to an electron. carrier. At 2 h. Part 2 / [M.I. Moro, M.A. Bantova, G.V. Beltyukova and others] - 2nd ed. - M.: Education, 2012., pp. 44, 45 No. 1-7.
2. Express in millimeters

In the primary grades, children study "Digits and Classes of Numbers", but this topic raises many questions from parents.

In this article, you can “refresh” your knowledge and explain this topic to your child.

Numbers and numbers

NUMBERS are units of account. With the help of numbers, you can count the number of objects and determine various quantities (length, width, height, etc.).
Special characters are used to write numbers - NUMBERS.
Number ten: 1 2 3 4 5 6 7 8 9 0

Integers

INTEGERS are the numbers used in counting.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …,
1 is the smallest number, and there is no largest number.
number 0 (zero) indicates the absence of an object. Zero NOT is a natural number.

Discharges and classes of natural numbers

Used to write numbers DECIMAL NUMBER SYSTEM. In the decimal number system, units, tens of units, tens of tens - hundreds, etc. are used.
Each new count unit is exactly 10 times greater than the previous one:

Decimal number system- positional. In this number system, the value of each digit in the notation of a number depends on its positions(places).

The position (place) of a digit in a number entry is called DISCHARGE. The youngest rank - UNITS. Then follow TENS, HUNDREDS, THOUSANDS etc.

Every three digits of natural numbers form CLASS.

Do-it-yourself poster Grade 3-4 https: // site

The main question that parents often ask is: why does a child need this knowledge? The answer to this question is very simple - after studying this material, children move on to topics such as addition and subtraction in a column, where it is necessary to know the digits of a number in order to correctly calculate examples.

And if the child does not master this topic, then he will not be able to correctly solve in a column.

Add and subtract through digits

Column addition

A) Adding units: 4 + 3 = 7.
We write under the units.
B) Add up the tens: 4 + 3 = 7.
We write under tens.
C) Add hundreds: 4 + 3 = 7.
We write under the hundreds.

An easy way to explain the digits and classes of a number to a child. Even a preschooler understands. The method of adding and subtracting multi-digit numbers by children without problems and clearly. Teaching mathematics in a playful way. Simple and fun math for kids.

How easy it is to explain to a child the digits and classes of a number.

My son has been able to count to 10 since the age of 2.5, he mastered tens and counting up to 20 at 3, and hundreds at 4. Board, mathematical and logic games helped us a lot in this. But, it's only verbal. Visually, he always confused the numbers 43 and 34. He could say that he had “two hundred hundred toys”, that is, the names of the classes, he knew, but the composition of the number itself was a mystery to him for a long time. Started looking how to explain simply and intelligibly, I found several methods, but we liked the most and this one came up.

On the sheet I drew a table like this

The child already knew the names of tens and hundreds in turn. I just reminded that one zero is ten, two zeros is a hundred, three zeros is a thousand, and if two zeros and three more zeros, then this is respectively ten thousand.

She gave the child buttons and offered to arrange them in columns as he wanted.

It turned out like this.

She asked me to count the buttons in the column, and put the desired number below. (we have a set of wooden numbers, but just drawn numbers on cardboard squares will do).

And then we just read what happened TWO THOUSAND (first by 2, and then by 1000, then I say that zero is empty, which means we just miss it, 13. Here, with 13, they messed around a little, 23, 33, 59 was easier to understand. Together they voiced that it turned out, then it helped a little, and then the child began to cope on his own.When I began to read the number correctly, I wrote the number on a sheet, and he laid it out in columns from buttons, the next step I just called the number, slowly, pausing between digits, and with each time it got better.

Simple addition and subtraction with transition through the category for children.

After playing like this for half a year, we moved on to addition and subtraction using the same tablet. For example 2013+224=2234 . Blue buttons put then purple

There were no problems with the transition through the category, by that time we had long and successfully played “Superfarmer” from Granna. She simply explained that as we changed 6 hares for a sheep, we also change 10 buttons in a column for one more button. The child understood. And at the age of 5, he successfully adds and subtracts arbitrarily significant numbers, and sometimes even in his mind. As he explained to me, he simply presents a sign in front of his eyes. I hope our experience will be useful.

Try it and write your impressions in the reviews.

1. Numbers of the second ten (twenties).

2. Numbers of the first hundred.

3. Numbers of the first thousand.

4. Multi-digit numbers.

5. Number systems.

1. Numbers of the second ten (twenties)

The numbers of the second ten (11, 12, 13, 14, 15, 16, 17, 18, 19, 20) are two-digit numbers.

Two digits are used to write a two-digit number. The first digit on the right in a two-digit number is called the digit of the first digit or units digit, the second digit on the right is called the digit of the second digit or tens digit.

The numbers of the second ten in all mathematics textbooks for elementary grades are considered separately from other two-digit numbers. This is because the names of the numbers of the second ten contradict the way they are written. Therefore, many children for some time confuse the order of writing numbers in the numbers of the second ten, although they can name them correctly.

For example, when recording the number 12 (two-twenty) by ear, the child hears “two (a)” as the first word, so he can write the numbers in this order 21, but read this entry as “twelve”.

The formation of the concept of two-digit numbers is based on the concept of "digit".

The concept of a digit is basic in the decimal number system. A digit is understood as a certain place in a number entry in a positional number system (a digit is the position of a digit in a number entry).

Each position in this system has its own name and its conventional meaning: the number in the first position on the right means the number of units in the number; the figure in the second position from the right means the number of tens in the number, etc.

The numbers from 1 to 9 are called significant, and zero is an insignificant digit. At the same time, its role in writing two-digit and other multi-digit numbers is very important: zero in the notation of a two-digit (etc.) number means that the number contains a bit designated by zero, but there are no significant digits in it, i.e. the presence of zero on the right in number 20, means that the number 2 should be perceived as a symbol of tens, and at the same time the number contains only two whole tens; writing 23 will mean that in addition to 2 integer tens, the number contains 3 more units, in addition to integer tens.

The concept of "digit" plays a big role in the system of studying numbering, and is also the basis for mastering the so-called "numbering" cases of addition and subtraction, in which actions are performed by whole digits:

27 - 20 365 - 300

The ability to recognize and highlight digits in numbers is the basis for the ability to decompose numbers into bit terms: 34 \u003d 30 + 4.

For numbers of the second ten, the concept of "digit composition" coincides with the concept of "decimal composition". For two-digit numbers containing more than one ten - these concepts do not match. For the number 34, the decimal composition is 3 tens and 4 ones. For the number 340, the bit composition is 300 and 40, and the decimal is 34 tens.

Acquaintance with the numbers of the second ten (11-20) is convenient to start with the way they are formed and the names of the numbers, accompanying it first with a model on sticks, and then reading the number according to the model:

Memorizing the names of two-digit numbers in this case will not be difficult for children with a record that contradicts the name: 11, 13.17. (After all, in accordance with the tradition of reading in European scripts from left to right in the name of these numbers, first the tens digit, and then the units digits!) hearing and reading by writing. The early introduction of symbolism plays a negative role in this case, both for remembering the names of the numbers of the second ten, and for understanding their structure. To form a correct idea of ​​the structure of a two-digit number, you should always put tens on the left and ones on the right. Thus, the child will fix in the inner plan the correct image of the concept, without special verbose explanations that are not always clear to him.

At the next stage, we offer the child the correlation of the real model and the symbolic notation:

one-on-twenty three-on-twenty seven-on-twenty

Then we move on to graphical models and to reading numbers according to the graphical model:

and then a symbolic notation of the bit composition of the numbers of the second ten:

Later, the concept of a category is introduced at school and children are introduced to the concept of "bit terms":

37 = 30 + 7; 624 = 600 + 20 + 4.

Using a decimal model instead of a bit model to get acquainted with all two-digit numbers allows, without introducing the concept of "digit", to introduce the child both to the method of forming these numbers, and to teach him to read a number according to the model (and vice versa, build a model by the name of the number), and then write :

When children study second-order numbers, we recommend that the teacher use the following types of tasks:

1) on the method of forming the numbers of the second ten:

Show thirteen sticks. How many dozens and how many more individual sticks?

2) on the principle of formation of a natural series of numbers:

Draw a picture for the problem and solve it orally. “There were 10 cinemas in the city. They built 1 more. How many cinemas are there in the city?”

Decrease by 1: 16, 11, 13, 20

Zoom in 1:19, 18, 14, 17

Find the value of the expression: 10+ 1; 14+1; 18-1; 20-1.

(In all cases, one can refer to the fact that adding 1 leads to the next number, and decreasing by 1 leads to the previous number.)

3) on the local value of the digit in the notation of the number:

What does each digit in the number entry mean: 15, 13, 18, 11, 10.20?

(In the entry for the number 15, the number 1 indicates the number of tens, and the number 5 indicates the number of ones. In the entry for the number 20, the number 2 indicates that there are 2 tens in the number, and the number 0 indicates that there are no ones in the first digit.)

4) in place of a number in a series of numbers:

Fill in the missing numbers: 12.........16 17 ... 19 20

Fill in the missing numbers: 20 ... 18 17.........13 ... 11

(When completing a task, they refer to the order of numbers when counting.)

5) for the digit (decimal) composition:

10 + 3 = ... 13-3 = ... 13-10 = ...

12=10 + ... 15 = ... + 5

When performing a task, they refer to a bit (decimal) model of a number from a dozen (a bunch of sticks) and units (individual sticks),

6) to compare the numbers of the second ten:

Which number is larger: 13 or 15? 14 or 17? 18 or 14? 20 or 12?

When completing a task, you can compare two models of numbers from sticks (a quantitative model), or refer to the order of the numbers when counting (the smaller number is called when counting earlier), or rely on the process of counting and counting (counting two units to 13 we get 15, which means 15 more than 13).

Comparing the numbers of the second ten with single-digit numbers, one should refer to the fact that all single-digit numbers are less than two-digit ones:

What is the largest and smallest of these numbers: 12 6 18 10 7 20.

When comparing the numbers of the second ten, it is convenient to use a ruler.

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Comparing the lengths of the corresponding segments, the child clearly determines the setting of the comparison sign: 17< 19.

To remember how much they harvested or how many stars in the sky, people came up with symbols. In different areas, these symbols were different.

But with the development of trade, in order to understand the designations of another people, people began to use the most convenient symbols. We, for example, use Arabic symbols. And they are called Arabic because the Europeans learned them from the Arabs. But the Arabs learned these symbols from the Indians.

The symbols used to write numbers are called figures .

The word digit comes from the Arabic name for the number 0 (sifr). This is a very interesting number. It is called insignificant and denotes the absence of something.

In the picture we see a plate with 3 apples on it and an empty plate with no apples on it. In the case of an empty plate, we can say that there are 0 apples on it.

The remaining numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 are called meaningful .

Bit units

Notation which we use is called decimal. Because it is ten units of one rank that makes up one unit of the next rank.

We count in units, tens, hundreds, thousands, and so on. These are the bit units of our number system.

10 units - 1 ten (10)

10 tens - 1 hundred (100)

10 hundreds - 1 thousand (1000)

10 times 1 thousand - 1 ten thousand (10,000)

10 tens of thousands - 100 thousand (100,000) and so on ...

A digit is the place of a digit in a number notation.

For example, among 12 two digits: the units digit consists of 2 units, the tens digit consists of one dozen.

We talked about the fact that 0 is an insignificant number, which means the absence of something. In numbers, the number 0 means the absence of ones in the discharge.

In the number 190, the digit 0 indicates the absence of a units digit. In the number 208, the digit 0 indicates the absence of a tens digit. Such numbers are called incomplete .

And the numbers in the digits of which there are no zeros are called complete .

The digits are counted from right to left:

It will be clearer if you depict the bit grid as follows:

1. In list 2375 :

5 units of the first category, or 5 units

7 units of the second digit, or 7 tens

3 units of the third category, or 3 hundreds

2 units of the fourth category, or 2 thousand

This number is pronounced like this: two thousand three hundred seventy five

1. In list 1000462086432

2 pieces

3 dozen

8 tens of thousands

0 hundred thousand

2 units million

6 tens of millions

4 hundred million

0 units billion

0 tens of billions

0 hundred billion

1 unit trillion

This number is pronounced like this: one trillion four hundred sixty-two million eighty-six thousand four hundred thirty-two .

1. In list 83 :

3 units

8 tens

Pronounced like this: eighty three .

Bit , call numbers consisting of units of only one digit:

For example, numbers 1, 3, 40, 600, 8000 - bit, in such numbers of zeros (insignificant digits) there can be as many as you like or not at all, and there is only one significant digit.

Other numbers, for example: 34, 108, 756 and so on, non-digit , they are called algorithmic.

Non-bit numbers can be represented as a sum of bit terms.

For example, number 6734 can be represented like this:

6000 + 700 + 30 + 4 = 6734