Numbers greater than a thousand are considered multi-digit. Multi-digit numbers are numbers in the thousands class and in the millions class. Multi-digit numbers are formed, named, and written based not only on the concept of rank, but also on the concept of class.
The class combines three categories.
Class of units - units, tens hundreds. This is first class.
Class of thousands - units of thousands, tens of thousands, hundreds of thousands. This is second class. The unit of this class is thousand.
Class of millions - units of millions, tens of millions, hundreds of millions. This is third grade. The unit of this class is million.
Table of Class I ranks:
The table contains the number 257. Table of Class II ranks:
The table contains the number 275,000,000.
Multi-digit numbers form the second class - the class of thousands and the third class - the class of millions.
Ten hundred is a thousand. Numbers from 1001 to 1,000,000 are called thousand numbers.
Thousands class numbers are four, five and six digit numbers.
Four-digit numbers are written with four digits: 1537, 7455, 3164, 3401. The first digit on the right in writing a four-digit number is called the first digit or units digit, the second digit on the right is the second digit or tens digit, the third digit on the right is the third digit or hundreds digit , the fourth digit from the right is the digit of the fourth digit or thousand digit.
The fifth digit is a tens of thousands figure, the sixth digit is a hundreds of thousands.
The table contains the number 257,000. Table of Class III ranks:
Whole thousands: 1000,2000,3000,4000,5000,6000,7000,8000,9000.
Read multi-digit numbers from left to right. For numbers 1001 and beyond, the order of naming their constituent digit numbers and the order of writing are the same: 4,321 - four thousand three hundred twenty-one; 346 456 - three hundred forty-six thousand four hundred fifty-six.
Rule for reading multi-digit numbers: multi-digit numbers are read from left to right. First, they divide the number into classes, counting three digits from the right. Reading begins with high school units (left). High school units are read immediately as a three-digit number, then adding the class name. Grade I units are read without adding the class name.
For example: 1 234 456 - one million two hundred thirty-four thousand four hundred fifty-six.
If some class in a number notation does not contain significant digits, it is skipped when reading.
For example: 123 000 324 - one hundred twenty-three million three hundred twenty-four.
The concept of “class” is basic for the formation of multi-digit numbers. All multi-digit numbers contain two or more classes.
The class combines three digits (units, tens and hundreds).
In writing, when writing a multi-digit number, it is customary to place a space between classes: 345,674, 23,456, 101,405.12,345,567.
Rule for writing multi-digit numbers: multi-digit numbers are written by class, starting with the highest. To write down a number in numbers, for example, twelve million four hundred fifty thousand seven hundred forty-two, do this: write down the units of each named class in groups, separating one class from another by a small gap (digit): 12,450,742.
Class composition - selection " class numbers"(class components) in a multi-digit number.
For example: 123,456 = 123,000 + 456
34 123 345 - 34 000 000 + 123 000 + 345
Bit composition - highlighting digit numbers in a multi-digit number:_____
Based on the bit composition, cases of bit addition and subtraction are considered:
400 000 + 3 000 20 534 - 34 340 000 - 40 000
534 000 - 30 000 672 000 - 600 000 24 000 + 300
When finding the values of these expressions, reference is made to the bit composition of three-digit numbers: the number 340,000 consists of 300,000 and 40,000. Subtracting 40,000 we get 300,000.
Place terms are the sum of the digit numbers of a multi-digit number:
247 000 - 200 000 + 40 000 + 7 000
968 460 - 900 000 + 60 000 + 8 000 + 400 + 60
Decimal composition is the selection of tens and ones in a multi-digit number: 234,000 is 23,400 des. or 2,340 cells.
When studying the numbering of multi-digit numbers, cases of addition and subtraction are also considered, based on the principle of constructing a sequence of natural numbers:
443 999 +1 20 443 - 1 640 000 + 1 640 000 - 1
10599+1 700000-1 99999 + 1 100000-1
When finding the meaning of these expressions, they refer to the principle of constructing a natural series of numbers: adding 1 to a number, we get the next number (subsequent). Subtracting 1 from the number, we get the previous number.
Here are the main types of tasks performed by children when learning multi-digit numbers:
1) to read and write multi-digit numbers:
Divide the number into classes, say how many units of each class are in it, and then read the number:
7300 29608 305220 400400 90060
7340 29680 305020 400004 60090
When completing the task, you should use the rule for reading multi-digit numbers.
Write and read the numbers in which: a) 30 units. second class and 870 units. first class; 6) 8 units. second class and 600 units. first class; c) 4 units. second class and 0 units. first class.
When completing the task, you should use the table of ranks and classes.
Write down the numbers in numbers: “The shortest distance from the Earth to the Moon is three hundred and fifty-six thousand four hundred and ten kilometers, and the greatest is four hundred and six thousand seven hundred and forty kilometers.”
The students wrote down the number nine thousand and forty like this: 940, 900 040, 9 040. Explain which entry is correct.
When completing tasks, you should use the rule for writing multi-digit numbers.
2) on the digit and class composition of multi-digit numbers:
Replace these numbers with the sum according to the example: 108201 = 108000 + 201
360 400 = ... + ... 50070 = ... + ... 9007 = ... + ... Task on the class composition of a multi-digit number.
Replace each number with the sum of its digit terms:
205 000 = ... + ... 640 000 = ... + ...
200 000 + 90 000 + 9 000 299 000 - 200 000
4 000 + 8 000 408 000 - 8 000
How many units of each digit are there in the number 395,028, and in the number 602,023? How many units of each class are there in these numbers?
When completing tasks, use the scheme of the bit composition of multi-digit numbers.
3) on the principle of formation of a natural series of numbers:
Find the meaning of the expressions: 99 999 +1 30 000 - 1
100000-1 699999 + 1
In all cases, we can refer to the fact that adding 1 leads to obtaining the number of the subsequent one, and decreasing by 1 leads to obtaining the number of the previous one.
4) on the order of numbers in the natural series:
The three tractors have the following serial numbers: 250 000, 249 999, 250 001. Which one came off the assembly line first? Second? Third?
Write down all six-digit numbers that are greater than 999,996.
5) on the place value of a digit in a number notation:
What does the number 2 mean in each number: 2, 20, 200, 2,000, 20,000, 200,000? Explain how the meaning of the digit 2 in the notation of a number changes when its place changes.
What does each digit in the notation of numbers mean: 140,401, 308,000, 70,050?
(In writing the number 140401, the number 4, standing in third place from the right, indicates the number of hundreds, the number 4, standing in fifth place from the right, indicates the number
tens of thousands. The number 1, standing in the first place from the right, indicates the number of units in the number, and the number 1, standing in the sixth place from the right, indicates the number of hundreds of thousands. The number 0, standing second from the right and fourth from the right, means that there are no ones in the second and fourth digits.)
Write one thing using the numbers 9 and 0 five digit number and one six-digit number. Using the same numbers, write down other multi-digit numbers.
6) to compare multi-digit numbers:
Check if the equalities are true:
5 312 < 5 320 900 001 > 901 000
Compare the numbers:
a) 999 ... 1000 b) 9 999 ... 999 c) 415 760 ... 415 670
d) 200,030 ... 200,003 d) 94,875 ... 94,895
When comparing the first pair of numbers, they refer to the order of numbers in the natural series: the subsequent number is greater than the previous number.
When comparing the second pair of numbers, reference is made to the number of digits in the number record: a three-digit number is always less than a four-digit number.
When comparing the third, fourth and fifth pairs of numbers, use the rule for comparing multi-digit numbers: To find out which of two multi-digit numbers is greater and which is less, do this:
Compare numbers bit by bit, starting with the highest digits.
For example, from two numbers 34,567 and 43,567 more second, since in the tens of thousands place it contains 4 units, and the first one in the same place contains three units.
Of the two numbers 415,760 and 415,670, the first is greater, since the thousands class in both numbers contains the same number of units -415 units. thousand, but in the hundreds of thousands place the first number contains 7 units, and the second - 6 units.
Of the two numbers 200,030 and 200,003, the first is greater, since the thousand class in both numbers contains the same number of units - 200 units. thousand, in the hundreds place both numbers contain zeros, in the tens place the first number contains 3 units, and the second number in the tens place does not have significant figures(contains zero), so the first number is greater.
For greater clarity, when completing a task, you can compare two models of numbers from seeds on an abacus (quantitative model).
When comparing multi-digit numbers, you can refer to the fact that a number containing a greater number of characters will always be greater than a number containing a smaller number of characters.
When comparing numbers of the form:
99 999 ... 100 000 989 000 ... 989 001
567 999 ... 568 000 599 999 ... 600 000
you should refer to the order of numbers when counting: the next number is always greater than the previous one.
7) on the decimal composition of multi-digit numbers:
Write down the numbers: 376, 6 517, 85 742, 375 264. How many tens are there in each of them? Emphasize them.
To determine the number of tens in a multi-digit number, you can cover the last digit (first from the right) with your hand. The remaining digits will show the number of tens.
To determine the number of hundreds in a number, you can cover two last digits in the number record (first and second from the right). The remaining digits will show the number of hundreds in the number.
For example, in the number 2,846 there are 284 tens, 28 hundreds. In the number 375,264 there are 37,526 tens, 3,752 in hundreds.
Look at the numbers: 3849. 56018. 370843. Which of the underlined numbers shows how many tens there are in the number? Hundreds? Thousands?
How many hundreds are there in 6,800?
Write down 5 numbers, each containing 370 tens.
8) on the relationships between the categories:
Write down, filling in the blanks:
1 thousand = ...hundreds. 1 cell = ... dec. 1 thousand = ... des.
How will the numbers 3,000, 8,000, 17,000 change if we remove one zero from their notation on the right? Two zeros? Three zeros?
Compare the numbers in each column. How many times does a number increase when one zero is added to its right side? Two zeros? Three zeros?
17 170 1 700 17000
Increase the numbers 57, 90, 300 10 times, 1,000 times.
Reduce the numbers 3,000, 60,000, 152,000 by 10 times, 100 times, 1,000 times.
When performing the last two tasks, they refer to the fact that increasing a number by 10 times transfers it to the adjacent digit on the left (tens to hundreds, hundreds to thousands, etc.), and decreasing the number to. 10 times transfers it to the adjacent digit on the right (tens to units, hundreds to tens).
When increasing a number by 10 times (100.1 000), in this way you can simply assign a zero (two zeros, three zeros) to the right. When decreasing a number by 10 times (100, 1,000), you can discard one zero on the right in the notation of the number (two zeros, three zeros).
The study of the class of thousands ends with an introduction to the number 1,000,000 (million).
Ten hundred thousand is a million. A thousand thousand is a million.
A million is written like this: 1,000,000.
The number 1,000,000 completes the study of numbers in the thousands class.
Million (1000,000) is a unit of a new class - the class of millions.
Million (1,000,000) is the first seven-digit number in the series of natural numbers.
A million is the smallest seven-digit number.
Million is a new unit of account in the decimal number system.
In writing the number 1,000,000, the digit 1 means that in the VII digit (millions digit) there is one unit, and in the digits of hundreds of thousands, tens of thousands, units of thousands, etc., zeros mean that there are no significant digits in these digits.
The millions class contains three digits of units of millions, tens of millions and hundreds of millions (VII, VIII and IX digits).
The class of millions is completed by the number billion.
A billion is 1000 million.
1000 billion is a trillion.
1000 trillion is a quadrillion.
1000 quadrillion is a quintillion.
It is impossible to imagine such a quantity of something. AND I. Depman in “The History of Arithmetic” gives the following example to illustrate large numbers: “A heavy-duty railway car can hold 50 million rubles in ten-ruble tickets (bills). To transport a trillion rubles, 20 thousand cars would be needed.”
A visual model of a class table:
The number is read like this: 412 million 163 thousand 539
Write it like this: 412 163 539
For numbers in the million class, the reading rule, the writing rule, and the comparison rule for multi-digit numbers apply (see above).
In a stable mathematics textbook for primary grades, numbers over a million are not discussed.
84. How many units of each digit are in the number 176? 176 thousand? 420? 420 thousand? 809? 809 thousand? 300 thousand? 80 thousand?
The number 176 contains 1 units in the hundreds place, 7 units in the tens place and 6 units in the ones place.
The number 176 thousand contains 1 unit of the hundreds of thousands place, 7 units of the tens of thousands place, 6 units of the thousand place and 0 units of the first class.
The number 420 contains 4 hundreds places, 2 tens places and 0 ones places. The number 420 thousand contains 4 hundreds of thousands units, 2 tens of thousands units, 0 thousands units and 0 first class units.
The number 809 contains 8 hundreds places, 0 tens places and 9 ones places.
The number 809 thousand contains 8 hundreds of thousands units, 0 tens of thousands units, 9 thousands units and 0 first class units.
The number 300 thousand contains 3 units of the hundreds thousand place and 0 units of each of the remaining places of the thousand class and the units class.
The number 80 thousand contains 0 hundreds of thousands units, 8 tens of thousands units, 0 thousand units and 0 first class units.
85. Read the numbers of each pair. What do the same digits in each pair of numbers mean?
In the number 9, the number 9 denotes the number of ones, and in the number 9000 the number of units of thousands.
In the number 15, the digit 1 denotes the number of tens, 5 - the number of units, and in the number 15000, the digit 1 denotes the number of tens of thousands, and 5 - the number of units of thousands.
In the number 90, the digit 9 denotes the number of tens, and in the number 90000 denotes the number of tens of thousands.
In the number 608, the digit 6 denotes the number of hundreds, and 8 - the number of units, and in the number 608000, the digit 6 denotes the number of hundreds of thousands, and 8 - the number of units of thousands.
86. The game “Constructor” has 130 parts. The boy used 28 parts to assemble the car, but 16 fewer parts to assemble the trailer.
1) Explain what the expressions mean.
28 — 16, 28 + (28 — 16), 130 — 28
2) Find out how many parts are not used.
1)
28 - 16 - number of parts for trailer assembly.
28 + (28 - 16) - the number of parts for assembling the car and trailer.
130 - 28 - the number of parts remaining after assembling the machine.
2)
1) 28 - 16 = 12 parts used to assemble the trailer.
2) 28 + 12 = 40 parts used to assemble the car and trailer.
3) 130 - 40 = 90 parts not used.
Answer: 90 parts.
87. Complete the condition of the problem and solve it. 120 seedlings were brought for landscaping the streets. Of these, 40 are linden, 20 are maple, the rest are oak. How many oak trees did you bring?
1) 40 + 20 = 60 linden and maple seedlings were brought.
2) 120 - 60 = 60 oak seedlings were brought.
Answer: 60 oaks.
88. 30 apple trees, 10 plums and several cherries were planted in the school garden. How many cherries were planted if 48 trees were planted in total? 60 trees?
1) 30 + 10 = 40 apple and plum trees were planted in the garden.
2) 48 - 40 = 8 cherries were planted (if 48 trees were planted in total).
2) 60 - 40 = 20 cherries were planted (if 60 trees were planted in total).
Answer: 8 cherries, 20 cherries.
89.
400 — 208 = 192
504 — 397 = 107
109 * 6 = 654
205 * 4 = 820
168 * 4 = 672
90. Find the values of the expressions 16 * d, 16: d, if d = 2, d = 4, d = 8, d = 1.
91.
40: 8 + 2 * 100 = 5 + 200 = 205
40: (8 + 2) * 100 = 40: 10 * 100 = 4 * 100 = 400
(40: 8 + 2) * 100 = (5 + 2) * 100 = 7 * 100 = 700
100 — (40 + 36) : 4 = 100 — 76: 4 = 100 — 19 = 81
(100 — 40 + 36) : 4 = (60 + 36) : 4 = 96: 4 = 24
100 — (40 + 36: 4) = 100 — (40 + 9) = 100 — 49 = 51
900: 9 — 6 * 10 = 100 — 60 = 40
600: 100 + 50 * 10 = 6 + 500 = 506
70 * 5 + 3 * 100 = 350 + 300 = 650
In the formation of many qualities necessary for successful to modern man, can play a big role school discipline– mathematics. In mathematics lessons, schoolchildren learn to reason, prove, find rational ways to complete tasks, and draw appropriate conclusions. It is generally accepted that “mathematics is the shortest path to independent thinking,” “mathematics puts the mind in order,” as M.V. noted. Lomonosov.
The activity approach was developed in the works of Alexei Nikolaevich Leontyev, Daniil Borisovich Elkonin, Pyotr Yakovlevich Galperin, Alexander Vladimirovich Zaporozhets in the mid-20th century.
Pedagogical practice shows that the formation of universal educational activities, that is, actions that ensure the ability to learn, independently search, find and assimilate knowledge - the most progressive way of organizing learning.
The basis of the concept of the activity-based approach to learning is the following: the mastery of the content of learning and the development of the student occurs in the process of his own activity.
Any assimilation of knowledge is based on the student’s assimilation of educational actions, having mastered which, the student would be able to assimilate knowledge independently, using various sources information. Teaching to learn (assimilate information) is the main thesis of the activity approach.
Target: introduce the concept of " numeric expression", learn to speak mathematical language.
Tasks:
- learn to recognize numerical expressions, read them correctly, find their meanings;
- develop logical thinking, ability to analyze, draw conclusions, develop children’s speech;
- cultivate independence and perseverance in achieving goals.
PROGRESS OF THE LESSON
I. Organizational moment
- Today we are not quite regular lesson. Guests are present at the lesson. Turn around and say hello to our guests.
- Turn to me.
WITH good morning the day has begun.
First of all, we drive away laziness.
Don't yawn in class
And work and count!
- Guys, what do you already know how to do? (Children's answers) What do you already know?
(On the board there are cards with the names of the topics: “How many times more or less?” “Multiplication and division. Part of a number.” “Solving problems involving decreasing and increasing by several times” “Finding a number using several fractions” “Finding several fractions of a number” "Name of numbers in action records")
- Let's start the math lesson.
II. Updating knowledge
– In your last math lesson you learned to read. different examples, using the names of the components and the result of the action.
– Read the examples on the board in different ways: 8 + 2 (a card appears: “addend + addend = sum”)
8 – 2 (minuend – subtrahend = difference)
8 * 2 (first factor second factor = product)
8:2 (dividend: divisor = quotient)
III. Statement of the problem
On the board:
25 + 4 33 + a c – 7 6 8 c 5 (15 – 7) + 4 18: 3 6 – 3
– Divide the notes on the cards into two groups. (The student at the board divides the notes into groups) (Several grouping options are being considered)
– Which entry turned out to be superfluous?
- Why?
- Give common name group. What else can you call these records? (Expressions))
– I suggest playing the game “What do you think?” I need two pairs.
Each pair receives a sheet - a playing field and a set of cards. (Play on the board)
4 > 40
7 = 7
x + 5 > 8
13 – 9
(16 – 9) 2
63: 9
– Place the cards on which, in your opinion, numerical expressions are written, on the “numeric expressions” sector. If you are sure that the card contains non-numeric expressions - the “no” sector, if you are in doubt - the “?” sector.
(perform)
– Do you think the guys completed the task correctly or incorrectly?
– How would you determine the topic of our lesson?
– What will we learn in class?
– Open your textbook to page 68.
– Read the topic of the lesson at the top of the page.
– Look at the textbook page and think about what you would like to ask me about this topic?
(On the board there are help cards: What...? Why...? Why...?)
(If there are no questions: “You’ll probably have questions later”)
IV. "Discovery" of new knowledge
– What do you see on page 68? (Table)
– Read the names of the columns in the table.
– These are four questions that we need to understand.
– What do all the entries in column 1 have in common?
– What does the 1st entry consist of? (Composed of two digits, and a “+” sign between the numbers)
– What do they mean? (Numbers)
(Records 2, 3 and 4 are considered similarly)
- What do you have in common? What is very important in numerical terms? (Consist of numbers)
On the board: 1. Numbers
– What are the numbers in the first entry? (in the 2nd, 3rd, 4th)
On the board: 1. Numbers 5;4
6;7
15;8
48;6
–
What else is in the record besides numbers? (Action Signs)
On the board: 1. Numbers 5;4
6;7
15;8
48;6
2. action signs
– What is the sign in the first entry? (second, third, fourth)
On the board: 1. Numbers 5;4
6;7
15;8
48;6
2. action signs +
–
:
–
Work in pairs: create new number expressions using the same numbers and action signs. Prove it.
(Work in pairs. Examination.)
– What is the name of the second column? (Expression name)
– Every expression has a name. Who guessed how to determine the name of the expression?
– Work in pairs: discuss what expression we will call the sum? A work? Difference? Private? (Discussion)
– What expression will we call the sum? ( An expression in which numbers are connected by a “+” sign) (Similar to the rest)
On the board: 1. Numbers 5; 4
6;
7
15; 8
48; 6
2. action signs + – sum
- work
– – difference
: – quotient
– Read the expressions.
– What is the name of the 3rd column? (Calculation)
– What does this column tell about? (That you can perform actions with an expression (calculate, find the answer, count, solve)
– You can perform actions and calculations with any expression.
– Have you looked at the entire table?
– What is the name of the fourth column? ( Expression value)
– Who guessed what the meaning of the expression is? How would you explain what the meaning of an expression is? (This is the number)
- What number?
– How do you understand the task “calculate the value of an expression”? (Perform calculations, find result, number)
On the board: 1. Numbers 5; 4
6; 7
15; 8
48; 6
2. action signs + – sum
- work
– – difference
: – quotient
there is a meaning of the expression (it can be found)
– What can you tell us about the expression?
Fizminutka
We'll rest a little.
Let's stand up and take a deep breath.
Hands to the sides, forward.
Children walked through the forest
Nature was observed.
We looked up at the sun -
And the rays warmed them all.
Miracles in our world:
The children became dwarfs.
And then everyone stood up together,
We have become giants.
Let's clap together
Let's stomp our feet!
Well we had a walk
And a little tired!
– The numbers in the expression have their own name, but the meaning of the expression does not?
– Is this fair?
– Look at page 68 of the textbook. What were the Wolf and the Hare talking about?
– It turns out that the name of the expression and its meaning are called the same.
– What did you study?
V. Commenting on the decision typical tasks
– Let’s practice applying our knowledge.
– Open the notebook on page 41 No. 129.
– How can we judge whether this recording is an expression?
(Operational control card:
- Read the first entry. We work on the operational control card and draw a conclusion.
(Work on each entry using a card)
– Who understood what a numerical expression is?
– What did you study?
– Open page 42 No. 131 (1st table).
– Let’s fill out the first table together.
– What do you see in the table?
– What should we do?
(Comment on filling out the 1st table)
– What did you study?
– It seems to me that you understand everything well. What do you think, can this entry – (15 – 7) + 4 – be called a numerical expression?
- Why?
– We will become more familiar with such expressions in mathematics lessons.
VI. Independent work with self-test in class
– Open your textbook to page 69. Find No. 3.
– Read what needs to be done.
– Who doesn’t understand what needs to be done, raise your hands.
(If you don’t understand, return to the table on page 68, third column, find out again that to calculate is to count, solve, and the value of an expression is a number, which means to calculate the value of an expression means to solve an expression, to find a number)
1 var. – calculate the values of the sum and product,
2 var. – difference and quotient ( writing the task on the board)
(A self-control card appears on the board:
1st option: 36 + 20 = 56 6 8 = 48
2 options: 60 – 3 = 57 21: 7 = 3)
VII. Formation of a knowledge system
– What is a numerical expression?
– We still have a lot to learn ( if you have time, you can consider No. 1, 2 in the textbook)
- Let's learn how to evaluate expressions.
(Game for repeating the multiplication table “Sprint Lottery”)
– Listen carefully to the task, do mental calculations and cross out the answer in the blank table.
Recruitment tasks:
1. 5: 5 5. 21: 7 9. 4 3
2. 49: 7 6. 27: 3 10. 3 5
3. 3 6 7. 32: 8 11. 18: 9
4. 4 4 8. 48: 6 12. 8 2 + 1
(Answer: as a result, the crossed out numbers in the table result in “5”:)
– If you got a grade of “5” from the crossed out answers, then you coped with the task perfectly, but if not, then you made a mistake somewhere, which means you need to repeat the multiplication and division tables.
- Solve the problem. Write the solution to the problem as an expression.
Balloons –
So naughty!
There were seven of them in total.
Nine flew into the sky.
How many of them there are - figure it out.
(Solution: 7 8 – 9 = 47 (sh.))
– Write the solution to the problem on the board.
VIII. Reflection
– Our lesson is coming to an end. Was he interesting? Useful?
– Did you learn anything new?
– What is a numerical expression?
-What did they repeat?
– At what level of knowledge on our ladder are you now? Paint over the sun on this step.
I want to know more
Okay, but I can do better
I'm still experiencing difficulties
IX. Homework
– Come up with tables with numerical expressions, as in No. 131 in your notebook. And those who want, try to think about task No. 4 on page 69 in the textbook.
Task 127.
Name: the number that follows the number 1999; numbers from two thousand to two thousand and twelve; numbers from two thousand thirteen to two thousand twenty.
Solution:
1) 2000; 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 1011, 2012; 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020.Task 128.
Solution:
- 1) Two thousand, two thousand six hundred fifty-two, four thousand thirty, seven thousand eight hundred, three thousand three hundred thirty-three,
- 2) Two thousand seven hundred fifty-three, four thousand five hundred, four thousand fifty, three thousand three, four thousand nine hundred ninety-nine.
Task 129.
Break down the numbers into bit terms: 1587; 2579; 3650; 5005; 6800.
Solution:
- 1587=1000+500+80+7 ;
- 2579=2000+500+70+9 ;
- 3650=3000+600+50 ;
- 5005=5000+5 .
- 6800=6000+800 ;
Task 130.
Write each amount as one number.
Solution:
- 57: 3 = 19 how many calves are in the herd;
- 57: 3 + 57 = 76 how many calves and cows are in the herd;
- 57 − 57: 3 = 38 There are 38 more cows than calves.
Task 132.
Name the figures shown in the picture. Measure the sides and find the perimeter of each polygon. 
Task 133.
Read the explanation about the angle. An angle is a figure formed by two rays (half-line) emanating from one point. General beginning The rays are called the vertex of the angle, and the rays themselves are called the sides of the angle. The angle is indicated by the sign “∠” and three in capital letters Latin alphabet. Sometimes an angle is denoted by one letter. In the figure, the extreme angles are indicated by three letters - angle ABC and angle KDM, and the middle angles are indicated by one letter - angle O and angle E. In the figure, ∠ ABC and ∠ E are right angles, the remaining angles are not right angles. An angle less than a right angle is called acute, and an angle greater than a right angle is called obtuse. In the figure, ZO is sharp, and ∠ KDM is obtuse. 
Using a ruler, draw acute and obtuse angles in your notebook.
Task 134.
- 1) Write each amount as one number.
2)- 2384 = 2000 + 300 + 80 + 4;
- 2205 = 2000 + 200 + 5;
- 7070 = 7000 + 70;
- 7007 = 7000 + 7.
Task 135.
The sewing workshop was supplied with 60 m of calico, 24 m of cloth, and k times less silk than calico and cloth together. How much silk did you bring? Write an expression to solve the problem and calculate its value if k = 12.
Solution:
- (60 + 24) : k, k = 12
- (60 + 24) : 12 = 7 (m)
- Answer: 7 meters of silk were delivered to the workshop.
Task 136.
Read the numbers of each pair: 5 and 5000; 7 and 7000; 9 and 9000. What do they have in common and what is different?
Solution:
Five, five thousand; seven, seven thousand; nine, nine thousand. Total quantity units in the first coincides with the number of thousands in the second. They differ in numerical value.
Task 137.
- 1) Write down a number containing: 3 thousand, 7 hundreds, 5 tens and 8 units; 7 thousand and 9 units; 7 thousand and 9 tens.
- 2) Write down the numbers: five thousand seven hundred forty-three; four thousand three hundred; three thousand sixty one; two thousand eight.
Solution:
- 1) 3758, 7009, 7090;
- 2) 5743, 4300, 3061, 2008.
Task 138.
Task 139.
- 1) Find 1/4 of: 2 UAH; 3 UAH 20 k.; 10 UAH
- 2) Write in hryvnias and kopecks: 520 kopecks; 7050 k. 40009 k.; 80080 k.
Solution:
- 1) 2 UAH: 4 = 200 k: 4 = 50 k.
3 UAH 20 k: 4 = 320 k: 4 = 80 k.
10 UAH: 4 = 1000 k: 4 = 250 k. - 2) 520 k = 5 UAH 20 k.
7050 k. = 70 UAH 50 k.
40009 k. = 400 UAH 9 k.
80080 k. = 800 UAH 80 k.
Task 140.
There were 48 birch and 56 pine logs in the warehouse. A quarter of the pine logs were sawn into boards. How many logs are left in the warehouse?
Solution:
- 1) 48 + 56 = 104 (there were all the logs);
- 2) 56: 4 = 14 (logs were cut into boards);
- 3) 104 − 14 = 90 (logs left in the warehouse)
- Viraz: 48 + 56 − 56: 4 = 90 (logs).
- Update: There are 90 logs left in the warehouse.
Task 141.
Solve the problem in two ways: in two and in three steps. To repair one classroom, 4 kg of white paint and 3 kg of brown paint were used. How many kilograms of paint will be needed to repair 12 of these classrooms?
Solution:
- 1) method
- 1) 4 + 3 = 7 (kg) - white and brown paint;
- 2) 7 * 12 = 84 (kg) - for apartment renovation.
- Expression: (4 + 3) * 12 = 84 (kg).
- 2) method
- 1) 4 * 12 = 48 (kg) - white paint;
- 2) 3 * 12 = 36 (kg) - brown paint;
- 3) 48 + 36 = 84 (kg) - together.
- Expression: 4 * 12 + 3 * 12 = 84 (kg).
- Answer: 84 kg of paint is needed to renovate 12 apartments.
Task 142.
Write down: the largest and smallest four-digit numbers; five consecutive numbers starting from 6997.
Solution:
- 1) The largest four-digit number is 9999, the smallest four-digit number is 1000.
- 2) 6997, 6998, 6999, 7000, 7001.
Task 143.
Write down a number containing: 2 thousand, 4 hundreds, 5 tens and 7 units; 5 thousand, 4 tens and 5 ones; 1 thousand, 3 hundreds and 6 tens; 9 thousand and 9 hundreds.
84. How many units of each digit are in the number 176? 176 thousand? 420? 420 thousand? 809? 809 thousand? 300 thousand? 80 thousand?
The number 176 contains 1 units in the hundreds place, 7 units in the tens place and 6 units in the ones place. The number 176 thousand contains 1 unit of the hundreds of thousands place, 7 units of the tens of thousands place, 6 units of the thousand place and 0 units of the first class.
The number 420 contains 4 hundreds places, 2 tens places and 0 ones places. The number 420 thousand contains 4 hundreds of thousands units, 2 tens of thousands units, 0 thousands units and 0 first class units.
The number 809 contains 8 hundreds places, 0 tens places and 9 ones places.
The number 809 thousand contains 8 hundreds of thousands units, 0 tens of thousands units, 9 thousands units and 0 first class units.
The number 300 thousand contains 3 units of the hundreds thousand place and but 0 units of each of the remaining places of the thousand class and the units class.
The number 80 thousand contains 0 hundreds of thousands units, 8 tens of thousands units, 0 thousand units and 0 first class units.
85. Read the numbers of each pair. What do the same digits in each pair of numbers mean?
9 000 15 000 90 000 608 000
In the number 9, the number 9 denotes the number of ones, and in the number 9000 the number of units of thousands.
In the number 15, the digit 1 denotes the number of tens, 5 - the number of units, and in the number 15000, the digit 1 denotes the number of tens of thousands, and 5 - the number of units of a thousand.
In the number 90, the digit 9 denotes the number of tens, and in the number 90000 denotes the number of tens of thousands.
In the number 608, the digit 6 denotes the number of hundreds, and 8 - the number of units, and in the number 608000, the digit 6 denotes the number of hundreds of thousands, and 8 - the number of units of thousands.
86. The game “Constructor” has 130 parts. The boy used 28 parts to assemble the car, but 16 fewer parts to assemble the trailer.
1) Explain what the expressions mean.
28 — 16
28 + (28 — 16)
130 — 28
2) Find out how many parts are not used.
1) 28-16 - number of parts for trailer assembly.
28 + (28 - 16) - the number of parts for assembling the car and trailer.
130 - 28 - the number of parts remaining after assembling the machine.
2) 28 - 16 = 12 parts used to assemble the trailer.
28+12 = 40 parts used to assemble the car and trailer.
130 - 40 = 90 parts not used.
Answer: 90 parts.
87. Complete the condition of the problem and solve it.
120 seedlings were brought for landscaping the streets. Of these, 40 are linden, □ maples, the rest are oaks. How many oak trees did you bring?
Let there be 30 maples. 120 - (40 + 30) = 40 oaks.
Answer: 20 oaks.
88. 30 apple trees, 10 plums and several cherries were planted in the school garden. How many cherries were planted if 48 trees were planted in total? 60 trees?
1) 48 - (30 + 10) = 8 cherries were planted if 48 trees were planted.
2) 60 - (30 + 10) = 20 cherries were planted if 60 trees were planted.
Answer: 8 cherries, 20 cherries.
89. Decide:
90. Find the meaning of expressions
91. Decide:
92. Draw a square ABCD, the side length of which is 7 cm. Find the area and perimeter of this square.
The area of the square is 7 7 = 49 sq. cm.
The perimeter of the square is 4 7 = 28 sq. cm.
93. When asked how old he was, grandfather answered: “If I live another half of what I lived, and 1 more year, then it will be exactly 100.” How old is grandpa?
1) 100 - 1 = 99 years.
2) 99: 3 = 33 years - half of what he lived.
3) 33 2 = 66 years - the age of the grandfather.
Answer: 66 years old.
Name the numbers that contain:
Field task
