Math textbook for third grade. Basic Level
How much do each of these items cost in hundreds of rubles?
Read the number names.
| Number of hundreds | Written in digits | Name |
| 2 hundreds | 200 | two hundred |
| 3 hundreds | 300 | three hundred |
| 4 hundreds | 400 | four hundred |
| 5 hundreds | 500 | five hundred |
| 6 hundreds | 600 | six hundred |
| 7 hundreds | 700 | seven hundred |
| 8 hundreds | 800 | eight hundred |
| 9 hundreds | 900 | nine hundred |
One thousand is the word used to name ten hundreds, and it is written as: 1,000.
Count in hundreds:
from one hundred to one thousand; from three hundred to eight hundred;
from one thousand to one hundred; from seven hundred to two hundred;
from one hundred to five hundred; from six hundred to nine hundred.
Read the numbers:
1) 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000;
2) 800, 300, 500, 200, 700, 400.
Write the numbers in words: 200, 500, 400, 700, 1,000, 900, 600.
Enter the following numbers into the calculator: four hundred, forty, eighty, eight hundred, thirty-six, three hundred, seventy, seven hundred.
Follow the plan:
1. Turn on the calculator (press the button ).
2. Enter the number four hundred (press the keys , , ).
3. Press the reset button
Enter the remaining numbers as the number four hundred.
When counting after the number 100, the number 101 (one hundred and one) is called, after the number 101 – the number 102 (one hundred and two), and so on; after the number 199 – the number 200 (two hundred), after the number 200 – the number 201 (two hundred and one), and so on; after the number 999 (nine hundred and ninety-nine) – the number 1,000 (one thousand).
What number is called when counting after the number: one hundred and seven, three hundred and five, two hundred and eighteen, one hundred and ninety-nine, four hundred, seven hundred and two, nine hundred and ninety-nine, seven hundred and twenty?
In the number 625, the digits 6, 2, 5 form three digits: hundreds, tens, units.
|
Digit |
||
| Hundreds | Tens | Units |
| 6 | 2 | 5 |
What does each of the digits in the notation of this number mean?
To read the number 625, you need to name the units of each place value, starting with the hundreds place, and the name of that place value: six hundred, twenty, five (the name of the units place is not pronounced). Therefore, it is: six hundred twenty-five.
What does each digit in the notation of the numbers 546, 404, 578, 700, 777 mean?
Read the numbers:
1) 134, 198, 111, 103, 118, 181, 177, 101, 149;
2) 263, 259, 290, 207, 222, 288, 260, 201, 299;
3) 888, 880, 808, 800, 899, 801, 810, 804, 833;
4) 360, 307, 452, 681, 555, 909, 999, 666, 795.
Count in order:
1) from 100 to 119;
2) from 810 to 820;
3) from 396 to 415.
Consider three groups of numbers:
1) 0, 5, 9, 1;
2) 10, 23, 64, 11;
3) 100, 330, 999, 507.
Read the numbers in each group.
Compare these groups. How many digits are in the representation of each group’s numbers? What are the names of the numbers in the first group; in the second group?
Make a hypothesis about the names of the numbers in the third group.
Name two more numbers that can be included in each group.
In the representation of a three-digit number, the same digit can have different values depending on which place value it occupies.
What does the digit 3 mean in each of the place values of the number 333? By how much does the value of the digit 3 increase from the units place to the hundreds place?
Ten units make up the next place value – a ten; ten tens make up the next place value – a hundred; ten hundreds make up the next place value – a thousand.
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двести тридцать три; четыреста семьдесят;
триста двадцать три; девятьсот; четыреста
семнадцать; тысяча.
Вырази в сантиметрах: 1 м, 5 м, 7 м, 9 м.
ВСПОМИНАЕМ ПРОЙДЕННОЕ
Дети собирали в лесу землянику. Шестеро детей набрали по 9 стаканов ягод, и столько же детей набрали по 5 стаканов. Сколько всего стаканов ягод набрали дети?
Напиши двузначное число, в котором:
1) число десятков больше числа единиц в 9 раз;
2) число единиц на 9 меньше числа десятков.
Вычисли устно.
40 + 30 60 – 10 60 +4
60 + 20 90 – 80 90 -20
70 + 3 78 – 8 68 -60
Выполни действия, записывая числа столбиком.
43 + 19 35 + 35 100 – 6 9 + 28
60 – 28 81 – 29 52 – 7 7 + 93
Record the results of the operations.
5-8 1-7 35 : 7 27 :3
7-9 9-4 64 : 8 18 :9
6-3 7-7 36 : 6 72 :9
5-5 3-4 56 : 7 45 :5
Check your answers using the multiplication table.
A book costs 27 p., a notebook costs 9 p. How many rubles are four notebooks more expensive than a book?
In the morning, children were playing in the yard. During the day, six of them went home, and there were 9 children left in the yard. How many children were playing in the yard in the morning?
Natasha made 17 flags for a garland. This is 9 flags less than her brother made. How many flags did the children make in total?
Choose and explain the correct solution to the problem:
1) 17 – 9 = 8 1) 17 + 9 = 26
2) 17 + 8 = 25 2) + 17
Answer: 25 flags. 26
43
Answer: 43 flags.
There are 7 apples on the table. This is three times less than in the basket. How many apples are in the basket?
The train consists of 9 cars. Two friends decided to travel together in the fifth car. One boy sat in the fifth car from the beginning of the train, and the other in the fifth car from the end. Did the friends sit in the same car?
Find:
1) the fifth part of each of the numbers: 45, 15, 5;
2) the fourth part of each of the numbers: 12, 20, 36.
There are 30 plants – eggplants and tomatoes – in the greenhouse. Tomatoes account for one-sixth of all plants. How many eggplants are there in the greenhouse?
Sasha had 32 badges in her collection. Over two months, the number of badges in her collection increased by a quarter. How many badges does Sasha have now? Is there any unnecessary information in the problem? If so, name it.
Copy the rectangle onto a grid sheet of paper and cut it out. Cut the rectangle into two parts so that a square can be formed from them.
Draw a ray and label it with letters. Write down and read the notation of the ray.
Draw segment AB. Extend this segment along the ruler from point B, without marking the end. What figures were obtained on the drawing?
Construct a segment that is longer than 7 cm, but shorter than 8 cm. How many segments like this do you think can be constructed?
Try to read what the great German mathematician Carl Friedrich Gauss said about arithmetic.
Answer the questions.
What is greater: the sum of 56 and 24 or the difference between 36 and 9?
What is smaller: the product of 8 and 7 or
the product of 7 and 6?
What is greater: the product of 1 and 9 or
the quotient of 72 and 9?
What is smaller: the quotient of 24 and 8 or the
quotient of 20 and 5?
The width of a rectangle is 14 cm, and its length is 6 cm greater than the width. Calculate the perimeter of the rectangle.
The area of a rectangle is 40 cm2, and its width is 5 cm. Calculate the length of the rectangle.
Find:
the sum of 4 m and one-fourth of 12 dm;
one-third of the sum of 1 m and 8 dm.
What is the name of the figure shown in the picture?
Are the following statements true?
The figure is a polygon.
The figure is a quadrilateral.
The figure is a rectangle.
The figure is a square.
It is incorrect that the figure is a hexagon.
Draw a square in your notebook with a side length of 3 centimeters. Draw its axes of symmetry. How many axes of symmetry does a square have?
Choose the correct answer: 2, 4, 6.
Check by making the necessary measurements that the diagonals of square ABCD intersect at the midpoint.
■ШШаШШ^^
In the distant past, people did not know numbers. When a person wanted to say that they had, for example, five fish, they would say, “As many as fingers on one hand.”
Gradually, people came to the idea that different groups of objects – five fingers, five fish, five apples – have a common property that can be expressed with the word “five.” That’s how numbers appeared.
But it took a long time before people learned to write numbers and perform arithmetic operations.
The numerals that we use to write numbers were invented in India. The Arabs adopted them, and the Europeans adopted them from the Arabs. That’s why Europeans call these numerals Arabic.
Arithmetic – the mathematical science of numbers and operations on them – appeared as a result of the long development of mankind. The name of this science comes from the Greek word “arithmetic,” which means number.
Comparing Numbers. > and < Signs
Compare prices. Whose purchase is more expensive? Explain your answer, compare it to the text.
The number 560 is called out later than the number 450 when counting. Therefore, the number 560 is greater than the number 450.
Which number is called out earlier? Which one is smaller?
682 or 21 1 890 or 980
307 or 37 0 568 or 561
Which number is called out later? Which one is greater?
328 or 529 983 or 987
647 or 651 400 or 800
Three-digit numbers are easily compared by the number of units in the digits.
First, compare the units in the hundreds place.
If the hundreds are equal, compare the units in the tens place.
If the tens are equal, compare the units in the ones place.
The two three-digit numbers, the one with more units in the highest place is bigger.
Compare the numbers using the method of comparing the number of units in the digits.
500 and 499 1000 and 999
85 and 805 301 and 311
In mathematical notation, the sign > is used instead of the word “greater”, and the sign < is used instead of the word “less”.
| Expression in Russian |
Expression in mathematical language |
|
| Eighteen is greater than nine | 18 : | > 9 |
| Forty is less than one hundred | 40 < | 100 |
Read the expressions written in mathematical language.
300 > 299 425 > 0 1 000 > 989
807 <817 0 < 100 106 < 109
Write the sentences in mathematical language using the signs > and <.
1) The sum of 35 and 5 is greater than 10.
2) The quotient of 10 and 2 is less than the product of 4 and 3.
3) The number 1 000 is greater than the difference of 43 and 26.
4) The difference between 48 and 40 is greater than 5.
Check yourself: perform calculations.
Which digits can be placed instead of the asterisk (*), so that the statement is true? Justify your answer.
5* > 56 91 > 9*
*6 < 72 64 < *3
REVIEWING WHAT WE LEARNED
Write down all the numbers in digits.
Option 1 Option 2
From 495 to 503. From 896 to 904.
From 299 to 307. From 699 to 706.
Exchange notebooks and check each OTHER’S work.
Write the numbers in digits: six hundred forty-two, seven hundred, eight hundred ninety-three, three hundred five.
In which number: 3 hundreds 5 tens, 3 hundreds 5 tens 2 units, 3 hundreds 2 units?
What does the digit 5 mean in the number representation: 500, 405, 158, 555?
Compare pairs of expressions. What are their similarities and differences?
1) (3 • 8) – (20 : 4) and ((3 • 8) – 20) : 4
2) 30 – (9 : 3) and (30 – 9) : 3
Make a conjecture about whether the values of the expressions in each pair are equal.
Check your conjecture: perform the calculations.
Find the values of the expressions and write them in ascending order.
56 – (16 + 29) (51 – 16) + (35 – 13)
(38 + 49) – 18 (48 + 50) – (63 + 17)
Calculate mentally.
700 + 70 960 – 60 128 – 8
700 + 7 804-4 128 – 20
700 + 70 = 7 c. + 7 d. = 7 c. 7 d. = 770
Around the school, students planted 24 shrubs of rose hip, 4 times less hawthorn than rose hip, and as much lilac as rose hip and hawthorn combined. How many shrubs did the students plant in total?
Express in kopecks: 2 rubles 54 kopecks; 7 rubles 5 kopecks; 7 rubles; 2 rubles 90 kopecks.
In the two youngest swimming groups, there are 10 students, and in the two middle groups, there are 5 more students than in the two youngest groups. How many students are studying in these four groups?
Sergey solved this problem like this:
1) 10 ÷ 5 = 15
2) 10 + 15 = 25
Answer: 25 people.
What mistakes did Sergey make? Write down the correct solution to the problem.
The garden has a rectangular shape. One of its sides is 32 m long, and the other side is 5 m shorter. What is the length of the border of this garden?
The length of the red stripe is 42 cm. It is longer than the blue stripe by 17 cm, and the blue one is shorter than the green one by 29 cm. What is the length of the green stripe?
The book has 32 pages. Dasha read one-fourth of the entire book. How many pages did Dasha read?
Come up with another question for the problem. Solve a new problem.
What numbers should be written in the boxes for the equations to be true?
Answer: 5. Answer: 9.
Kolya, Tolya, and Yuri decided to ride on a two-seat swing. Who can ride with whom? Consider all the options.
Each of the items – a jacket, a coat, and a fur coat – has 3, 4, and 6 buttons respectively. The coat has 4 buttons. The jacket has more buttons than the coat. How many buttons are on the jacket and how many on the fur coat?
Olya is younger than Katya. Each of the girls is younger than Lida. Who is older than everyone? Who is younger than everyone?
What figures have an axis of symmetry? Choose one of such figures, draw it in your notebook, and draw its axis of symmetry.
Draw a ray with its starting point at point O. Using a compass and a ruler, mark on this ray four segments of 2 cm each starting from point O.
Create a plan for completing the task: where will you start and what will you do next? Perform the construction according to the plan.
Sveta wrote numbers on six cards:
What is the largest and the smallest three-digit number she can make from these cards?
Create an expression and calculate its value.
Subtract the difference between 23 and 7 from the number 42.
Subtract the product of 4 and 8 from the number 50.
Add the quotient of 36 and 9 to the number 63.
Add the product of 8 and 7 to the number 16.
Which of the formulated expressions are additions and which are subtractions?
Name all the segments and rays depicted in the picture.
Check your answer: 1) 2 segments and 4 rays; 2) 3 segments and 6 rays.
Call three three-digit numbers that are written with the same digits. Name and write down all such numbers in increasing order. Which of these numbers is the largest and which is the smallest?
Check yourself: there should be a total of 9 numbers.
Consider the picture.
How many on the picture: triangles; quadrilaterals; pentagons?
Are there rectangles among the quadrilaterals; squares? Name them.
Choose one of the polygons in the picture and characterize it (name its main features).
What is segment AK for square ABCD, for square KLEM?
Name the common part: triangle ABC and square KLEM; triangle ABC and square ABCD.
The cinema hall can accommodate 500 spectators. Calculate how many tickets the cashier has, the numbers of which end in 15.
Choose the correct answer: 4; 5; 10; 15 tickets.
What number is composed of:
seven hundreds and nine tens; four hundreds and four units; five hundreds, two tens, and three units; three hundreds, two tens, and five units?
Kilometer.
Millimeter
Large distances are often measured in kilometers. In the word kilometer, kilo means thousand. A kilometer is a thousand meters.
Remember! 1 km = 1,000 m.
Wolf and Hare are going to the country house. They need to travel 100 km. Help Hare answer Wolf’s question.
The driver drove on the highway from the post with a mark of 35 km to the post with a mark of 126 km. How many kilometers did the driver drive?
Lengths that are less than 1 cm are usually measured in millimeters. In the word millimeter, milli means thousandth. A millimeter is one thousandth of a meter. There are 10 millimeters in one centimeter.
Remember! 10 mm = 1 cm.
Find several segments on the ruler that are 1 cm long, 1 mm long.
What is the length of a ladybug in millimeters?
Read the values of the quantities: 12 km; 4 km 325 m; 27 mm; 9 cm 8 mm.
Choose appropriate units of length.
The height of the house is 15 … .
The skier ran a distance of 10 … .
The height of a person is 1 … 70 … .
Ant’s length is 12 … .
Estimate by eye:
1) the height of uppercase and lowercase letters in your math textbook;
2) the length and width of a notebook cell;
3) the length, width, and height of an eraser.
Check your answers: measure these objects in millimeters.
Construct line segments with the following lengths: 8 mm; 1 cm 5 mm; 5 cm 1 mm; 1 dm 2 cm 3 mm.
Express in millimeters.
2 cm 8 cm 2 cm 4 mm
3 cm 15 cm 10 cm 6 mm
2 cm 5 mm = 20 mm + 5 mm = 25 mm
2 cm = 10 • 2 (mm) = 20 mm
Solve orally.
508 km + 20 km 408 km — 8 km
910 km — 10 km 810 km + 5 km
Dima rides the bus to school. First, he walks 50 m from home to the bus stop, and then he rides the bus 6 km to school. The bus stops right at the school gate. Calculate Dima’s round trip distance from home to school and back.
MιifιTflTiΓi∣IT^
In books about sea voyages, distances are often given in miles. In many countries, one nautical mile is considered to be approximately 1 km 852 m.
In Russia, large distances on land used to be measured not in kilometers, but in versts. One verst is approximately equal to 1 km 67 m.
Solve old problems.
Problem 1. The distance from the village to the forest is 8 versts, and to the mill it is twice as close. How many versts is it from the village to the mill?
Problem 2. A peasant went from his village to the fair. After traveling 30 versts,
he stopped at an inn to feed the horse. From here, it is another 19 versts to the city. How many versts does the peasant have to travel in total to reach the city for the fair?
Problem 3. The schooner left the pier and traveled 12 miles to the east, and then 18 miles to the north. Calculate the length of the schooner’s route.
REMEMBERING WHAT’S BEEN COVERED
Which of the statements are true and which are false?
Explain your answers.
Calculate mentally the difference between the numbers: 7 42 and 7 00; 8 5 6 and 50; 907 and 7.
Find the sum of the numbers: 202 and 20; 6 and 300; 80 and 400.
Compare the lengths.
5 m 2 cm and 5 m 2 dm
4 dm 3 cm and 3 dm 4 cm
6 cm 2 mm and 2 cm 6 mm
87 dm and 9 m
721 cm and 7 m 21 cm 9 m and 90 cm
They bought a book, an album, and a notebook. They paid 75 rubles for the whole purchase without the notebook. The book costs 40 rubles. How much does the album cost? Is there enough information to find the price of the notebook?
They bought milk, cottage cheese, and sour cream for 72 rubles. If they didn’t buy milk, they would have paid 55 rubles, and if they didn’t buy sour cream, they would have paid 47 rubles. How much does each of the products cost?
Using three fives, any arithmetic signs, and parentheses, write any numerical expression that has a value of 5; 0.
In a store, there were 52 cans of canned food on three shelves. When they took 16 cans from one shelf and 9 cans from another, there were an equal number of cans on all three shelves. How many cans are left on each shelf?
Vitya and Dima were collecting acorns. Vitya collected 18 more acorns. He gave Dima 9 acorns. Who had more acorns and by how many?
Check your answer if Dima collected 20 acorns; 42 acorns.
In the village, they first built 19 houses, and then 5 more houses. A third of all the houses are still unoccupied. How many houses are occupied in the village?
Assess (true, false) the solution of the problem.
1) 19 ÷ 5 = 24
2) 3 – 1 = 2
3) 24 : 3 = 8
4) 8 • 2 = 16 Answer: 16 houses.
Explain your reasoning.
From a rope 27 meters long, they cut off a third part. How many meters of rope did they cut off? How many meters of rope are left?
Resolve the problem in two ways.
How many axes of symmetry does each figure have?
Draw a ray with the starting point at point O. Mark points B, C, and M on the ray. Mark points K, X, and E outside the ray.
Exchange notebooks and check each other’s work.
Draw a rectangle on grid paper. Draw the diagonals. Mark the point where the diagonals intersect. Use measurements to verify that the diagonals of the rectangle are equal and intersect at the midpoint.
What number will you get if you increase:
8 by 7; 8 by 7 times; 6 by 6; 6 by 6 times?
What number will you get if you decrease:
35 by 5; 35 by 5 times; 49 by 7; 49 by 7 times?
Draw the same quadrilaterals on grid paper, cut them out, and assemble them to form a square.
Write down the expressions that are sums in one column and differences in the other. 27 + (54 : 9) (48 : 6) – 8 (15 + 8) – 11 43 + (87 – 59)
Find the values of these numerical expressions.
Write down all the single-digit numbers that each of the numbers 18, 27, 36, 45 is divisible by.
Which numbers are divisible by all of them?
The length of a rectangle is 9 cm. Its area is 27 cm2. Calculate the width of the rectangle.
Polygonal
The Wolf and the Hare are making a picture from colored straws.
What shape is the red straw?
How many times did the Wolf break the yellow straw to make the roof?
How many times did the Hare break the blue straw? How many segments are in the yellow and blue straws?
The figures depicted in the illustration are called broken lines or simply broken lines.
How many segments are in the broken line? Show each segment and its endpoints.
AMVO – broken line.
Segments AM, MV, and VO are called links of the broken line, and points A, M, V, O are called vertices of the broken line.
Show and name the vertices and links of each broken line.
Compare the broken lines in the illustration. What are their similarities and differences?
A broken line ABCD is called open, and a broken line MCR is called closed.
Why did these broken lines get such names?
Consider the broken lines in the drawing.
Divide the set of broken lines into two groups (classify): closed and open. Name the numbers of figures in each group. Compare the number of links and vertices in each broken line in both groups. How many vertices will an open broken line with six links have?
How many links will a closed broken line with six vertices have?
What conclusion can be made?
The links of a broken line can intersect.
Name the links of each broken line.
Draw a broken line with two links in blue pencil, and a broken line with four links in red pencil.
Before performing the task, make a plan: what will you start with, what will you do next.
Draw a broken line with three links, where the length of each link is 4 cm.
First, make a construction plan. Compare this plan with the construction plan of the broken lines in the previous task. What are their similarities and differences? Complete the construction.
The length of one link of the broken line is 3 cm, the other is 5 cm, and the third is 4 cm 5 mm. Draw this broken line.
Label the broken line with letters. Name the length of the longest link and the shortest link.
RECALLING WHAT WE LEARNED
Express in millimeters:
5 dm 7 cm; 5 dm 8 mm; 6 cm 4 mm.
Express in centimeters:
4 m 35 cm; 6 m 9 cm; 8 m; 42 dm.
Express in meters:
600 cm; 30 dm; 400 cm; 1,000 mm.
Express in meters and decimeters:
41 dm; 76 dm; 50 dm; 68 dm.
Name the units of length you know, starting with the largest.
In which larger units of length can you express 500 mm?
What numbers need to be written in the boxes for the records to be correct?
Answer: 2. Answer: 18.
By how much is the sum of 500 and 2 greater than the number: 500; 2?
By how much is the difference between 824 and 20 greater than the number: 4; 800?
Answer the questions.
How many times is 1 m greater than 1 cm?
How many times is 1 m greater than 1 dm?
What part of a meter is 1 cm?
What part of a meter is 1 dm?
Check if the calculations are correct.
(9 • 7) – 48 = 15
(6 • 6) + (8 • 8) = 100
100 – (35 + 44) = 31
(41 – 36) • (72 : 8) = 45
What is the largest two-digit number that can be written with two different digits?
What is the smallest three-digit number that can be written with three different digits?
Which number is bigger: the smallest three-digit number or the largest two-digit number?
Kolya was watering the garden. He has already completed three-fifths of all the work. What part of the work does Kolya still have to do? How many beds does Kolya have left to water if there are 20 beds in the garden?
Solve the problem in two ways.
Increase the numbers by 5 times: 8, 6, 9, 7, 3, 1.
Decrease the numbers by 7 times: 14, 28, 35, 49, 56.
Katya and her mom were picking mushrooms. Katya found 8 mushrooms. When mom gave her 2 of her mushrooms, Katya had twice as many mushrooms as her mom. How many mushrooms did mom find?
Petya, Vasya, and Kolya caught fish and started dividing their catch. Petya took half of all the fish, Vasya took 4 perches, and Kolya took 5 breams. How many fish did the boys catch in total?
8 boys are going fishing: four of them have fishing rods and six have buckets. Is there at least one boy with both a fishing rod and a bucket?
A rectangle’s width is 3 times smaller than its length. The width of this rectangle is 4 cm. Find the perimeter and area of the rectangle.
Determine the area of a rectangle without measuring.
Lena, Katya and Ira found 30 white mushrooms: Lena – 5, Katya – 10, and Ira – 15. For this, their grandmother gave the girls 18 candies and offered to divide these candies fairly. How many candies did each girl get?
Katya answered the question about her age like this: “In 3 months, I will be 9 years old.” Calculate Katya’s age. How old will Katya be in a year?
Determine by sight which segment is shorter than the other one.
Check your answer: measure it.
Determine how many millimeters one of the segments is shorter than the other.
Perform the operations.
(42 : 7) + (36 : 6) (97 – 47) – (16 -6)
(9 • 8) – (6 • 7) (64 ÷ 36) – (6 •9)
(56 – 18) + (28 : 7) (32 : 4) • (27 :3)
(64 : 8) – (24 : 3) (72 : 8) : (12 :4)
Identify the expressions that have: value less than or equal to 30; value greater than or equal to 40.
Which expressions are: sums; differences?
Which of the statements about the polygon shown in the picture are true?
It is a quadrilateral.
It is a square.
It is not a square.
It is not a rectangle.
It is a rectangle.
It is not a rectangle.
It is a square.
It is a polygon.
Which buses stop at the “Mars Cinema” bus stop?
Examine the table. It shows the number of buses for each route passing the stop from 6 am to 12 midnight.
| Bus Number | 53 | 637 | 803 |
| Number of Trips | 72 | 108 | 54 |
Which bus route passes most frequently and least frequently? By how many trips does bus No. 637 exceed bus No. 803? Name the bus route numbers in order of increasing number of trips.
Polygon Length
The Wolf and the Hare are making football goals.
How many meters of timber do they need for one goal? How did the Hare calculate it?
Measure the length of each segment of the broken line.
Explain how to find the length of this broken line. Perform calculations.
To find the length of a broken line, you need to add up the lengths of all its segments.
Perform the necessary measurements and calculate the length of the broken line.
Draw a broken line with two segments. The length of one segment is 5 cm 4 mm, and the other is 1 cm 8 mm shorter.
The broken line ABCD has three segments: AB = 42 mm, BC = 38 mm, CD = 19 mm. Calculate the length of the broken line.
The length of a broken line consisting of two segments is 50 dm. The length of one segment is 36 dm. What is the length of the other segment?
The broken line consists of eight segments of equal length. The length of each segment is 6 m. What is the length of the broken line?
The broken line consists of two segments. One segment is twice as long as the other. Draw the broken line and calculate its length.
| REMEMBERING WHAT WE’VE LEARNED
How, without measuring tools, can you cut a piece of wire from a spool that is 1 m 60 cm long, of lengths: 80 cm; 40 cm?
Using the digits 7 and 4, write down all two-digit numbers so that the digits in each number: 1) are repeated; 2) are not repeated. How many numbers did you get in each case?
Masha wrote down a two-digit number. Then she reversed the digits and wrote down another number. The difference between the first and second numbers is 0. Name the number that Masha could have written down first. What is its peculiarity?
How many such numbers are there? Explain how to choose solution options without missing any.
Calculate the values of the expressions.
Variant 1 Variant 2
(48 + 24) : 8 7 – (96 – 87)
100 – 6-9 36 : 4 + 81
Check each other’s work.
A glass, a cup, and a mug were filled with different drinks: tea, coffee, and milk. The glass is to the right of the coffee drink, the tea drink is to the right of the glass, and the cup is to the right of the glass. What drinks were poured into the glass, cup, and mug?
Sasha bought a pencil and an eraser. The pencil costs 7 rubles, and the eraser is 2 rubles cheaper. Sasha paid for the entire purchase with six identical coins. What coins were they?
72 kg of marshmallows were delivered to the store, 8 kg in each box, and 49 kg of candies, 7 kg in each box. How many boxes of sweets were delivered to the store in total?
The gardener had 8 sacks of potatoes. He used 5 sacks during the winter, and planted the remaining potatoes in the spring. In the fall, he harvested 5 sacks from each planted sack. How many sacks of potatoes did he harvest in the fall?
The Yak-40 aircraft accommodates 27 passengers. This is 3 passengers less than the An-24 aircraft accommodates. How many passengers does the An-24 aircraft accommodate? Change the question so that the problem can be solved in two steps. Solve the new problem.
18 boxes with cargo were transported by car in 3 trips. How many trips are needed to transport 48 such boxes if the load capacity of the car is the same for each trip?
Yura solved this problem as follows:
1) 18 : 3 = 6
2) 48 – 18 = 30
3) 30 : 6 = 5
4) 3 + 5 = 8
Answer: 8 trips.
Explain Yura’s reasoning.
Solve the problem in a different way. Which method of solving is better? Explain your answer.
Which numbers should be written in the boxes to make the equations correct?
Answer: 3. Answer: 3.
In the cages, there are 5 tits, 6 parrots, and 7 canaries. There are more tits than canaries or parrots. There are more parrots than canaries. How many canaries are there?
The rectangle has sides of length 1 meter and 1 centimeter, and the square has a side length of 1 decimeter. Compare the areas of both figures.
Before drawing a conclusion, think in which units it is most convenient to compare the areas of these figures.
Misha folded four-sided figure ABCM from three identical triangles. The figure ABCK is a square with a side length of 2 centimeters. Calculate the area of the quadrilateral ABCM.
Try to read a famous Russian proverb.
Describe the broken line in the picture. Answer the following questions.
How many vertices and edges does this broken line have?
Is it closed or open? Do its edges intersect? How many pairs of intersecting edges are there in total?
Mass. Kilogram. Gram
Why are the scales not in balance?
The scales are not in balance because the weight of the bag of flour is greater than the weight of the weight (the weight of the weight is less than the weight of the bag of flour).
The mass of objects is often measured in kilograms.
The word “kilogram” is abbreviated as “kg”.
What is the mass of the Wolf in kilograms?
Numbers
from 100 to 1,000
How much do each of these items cost in hundreds of rubles?
Read the number names.
| Number of hundreds | Written in digits | Name |
| 2 hundreds | 200 | two hundred |
| 3 hundreds | 300 | three hundred |
| 4 hundreds | 400 | four hundred |
| 5 hundreds | 500 | five hundred |
| 6 hundreds | 600 | six hundred |
| 7 hundreds | 700 | seven hundred |
| 8 hundreds | 800 | eight hundred |
| 9 hundreds | 900 | nine hundred |
One thousand is the word used to name ten hundreds, and it is written as: 1,000.
Count in hundreds:
from one hundred to one thousand; from three hundred to eight hundred;
from one thousand to one hundred; from seven hundred to two hundred;
from one hundred to five hundred; from six hundred to nine hundred.
Read the numbers:
1) 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000;
2) 800, 300, 500, 200, 700, 400.
Write the numbers in words: 200, 500, 400, 700, 1,000, 900, 600.
Enter the following numbers into the calculator: four hundred, forty, eighty, eight hundred, thirty-six, three hundred, seventy, seven hundred.
Follow the plan:
1. Turn on the calculator (press the button ).
2. Enter the number four hundred (press the keys , , ).
3. Press the reset button
Enter the remaining numbers as the number four hundred.
When counting after the number 100, the number 101 (one hundred and one) is called, after the number 101 – the number 102 (one hundred and two), and so on; after the number 199 – the number 200 (two hundred), after the number 200 – the number 201 (two hundred and one), and so on; after the number 999 (nine hundred and ninety-nine) – the number 1,000 (one thousand).
What number is called when counting after the number: one hundred and seven, three hundred and five, two hundred and eighteen, one hundred and ninety-nine, four hundred, seven hundred and two, nine hundred and ninety-nine, seven hundred and twenty?
In the number 625, the digits 6, 2, 5 form three digits: hundreds, tens, units.
|
Digit |
||
| Hundreds | Tens | Units |
| 6 | 2 | 5 |
What does each of the digits in the notation of this number mean?
To read the number 625, you need to name the units of each place value, starting with the hundreds place, and the name of that place value: six hundred, twenty, five (the name of the units place is not pronounced). Therefore, it is: six hundred twenty-five.
What does each digit in the notation of the numbers 546, 404, 578, 700, 777 mean?
Read the numbers:
1) 134, 198, 111, 103, 118, 181, 177, 101, 149;
2) 263, 259, 290, 207, 222, 288, 260, 201, 299;
3) 888, 880, 808, 800, 899, 801, 810, 804, 833;
4) 360, 307, 452, 681, 555, 909, 999, 666, 795.
Count in order:
1) from 100 to 119;
2) from 810 to 820;
3) from 396 to 415.
Consider three groups of numbers:
1) 0, 5, 9, 1;
2) 10, 23, 64, 11;
3) 100, 330, 999, 507.
Read the numbers in each group.
Compare these groups. How many digits are in the representation of each group’s numbers? What are the names of the numbers in the first group; in the second group?
Make a hypothesis about the names of the numbers in the third group.
Name two more numbers that can be included in each group.
In the representation of a three-digit number, the same digit can have different values depending on which place value it occupies.
What does the digit 3 mean in each of the place values of the number 333? By how much does the value of the digit 3 increase from the units place to the hundreds place?
Ten units make up the next place value – a ten; ten tens make up the next place value – a hundred; ten hundreds make up the next place value – a thousand.
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двести тридцать три; четыреста семьдесят;
триста двадцать три; девятьсот; четыреста
семнадцать; тысяча.
Вырази в сантиметрах: 1 м, 5 м, 7 м, 9 м.
ВСПОМИНАЕМ ПРОЙДЕННОЕ
Дети собирали в лесу землянику. Шестеро детей набрали по 9 стаканов ягод, и столько же детей набрали по 5 стаканов. Сколько всего стаканов ягод набрали дети?
Напиши двузначное число, в котором:
1) число десятков больше числа единиц в 9 раз;
2) число единиц на 9 меньше числа десятков.
Вычисли устно.
40 + 30 60 – 10 60 +4
60 + 20 90 – 80 90 -20
70 + 3 78 – 8 68 -60
Выполни действия, записывая числа столбиком.
43 + 19 35 + 35 100 – 6 9 + 28
60 – 28 81 – 29 52 – 7 7 + 93
Record the results of the operations.
5-8 1-7 35 : 7 27 :3
7-9 9-4 64 : 8 18 :9
6-3 7-7 36 : 6 72 :9
5-5 3-4 56 : 7 45 :5
Check your answers using the multiplication table.
A book costs 27 p., a notebook costs 9 p. How many rubles are four notebooks more expensive than a book?
In the morning, children were playing in the yard. During the day, six of them went home, and there were 9 children left in the yard. How many children were playing in the yard in the morning?
Natasha made 17 flags for a garland. This is 9 flags less than her brother made. How many flags did the children make in total?
Choose and explain the correct solution to the problem:
1) 17 – 9 = 8 1) 17 + 9 = 26
2) 17 + 8 = 25 2) + 17
Answer: 25 flags. 26
43
Answer: 43 flags.
There are 7 apples on the table. This is three times less than in the basket. How many apples are in the basket?
The train consists of 9 cars. Two friends decided to travel together in the fifth car. One boy sat in the fifth car from the beginning of the train, and the other in the fifth car from the end. Did the friends sit in the same car?
Find:
1) the fifth part of each of the numbers: 45, 15, 5;
2) the fourth part of each of the numbers: 12, 20, 36.
There are 30 plants – eggplants and tomatoes – in the greenhouse. Tomatoes account for one-sixth of all plants. How many eggplants are there in the greenhouse?
Sasha had 32 badges in her collection. Over two months, the number of badges in her collection increased by a quarter. How many badges does Sasha have now? Is there any unnecessary information in the problem? If so, name it.
Copy the rectangle onto a grid sheet of paper and cut it out. Cut the rectangle into two parts so that a square can be formed from them.
Draw a ray and label it with letters. Write down and read the notation of the ray.
Draw segment AB. Extend this segment along the ruler from point B, without marking the end. What figures were obtained on the drawing?
Construct a segment that is longer than 7 cm, but shorter than 8 cm. How many segments like this do you think can be constructed?
Try to read what the great German mathematician Carl Friedrich Gauss said about arithmetic.
Answer the questions.
What is greater: the sum of 56 and 24 or the difference between 36 and 9?
What is smaller: the product of 8 and 7 or
the product of 7 and 6?
What is greater: the product of 1 and 9 or
the quotient of 72 and 9?
What is smaller: the quotient of 24 and 8 or the
quotient of 20 and 5?
The width of a rectangle is 14 cm, and its length is 6 cm greater than the width. Calculate the perimeter of the rectangle.
The area of a rectangle is 40 cm2, and its width is 5 cm. Calculate the length of the rectangle.
Find:
the sum of 4 m and one-fourth of 12 dm;
one-third of the sum of 1 m and 8 dm.
What is the name of the figure shown in the picture?
Are the following statements true?
The figure is a polygon.
The figure is a quadrilateral.
The figure is a rectangle.
The figure is a square.
It is incorrect that the figure is a hexagon.
Draw a square in your notebook with a side length of 3 centimeters. Draw its axes of symmetry. How many axes of symmetry does a square have?
Choose the correct answer: 2, 4, 6.
Check by making the necessary measurements that the diagonals of square ABCD intersect at the midpoint.
■ШШаШШ^^
In the distant past, people did not know numbers. When a person wanted to say that they had, for example, five fish, they would say, “As many as fingers on one hand.”
Gradually, people came to the idea that different groups of objects – five fingers, five fish, five apples – have a common property that can be expressed with the word “five.” That’s how numbers appeared.
But it took a long time before people learned to write numbers and perform arithmetic operations.
The numerals that we use to write numbers were invented in India. The Arabs adopted them, and the Europeans adopted them from the Arabs. That’s why Europeans call these numerals Arabic.
Arithmetic – the mathematical science of numbers and operations on them – appeared as a result of the long development of mankind. The name of this science comes from the Greek word “arithmetic,” which means number.
Comparing Numbers. > and < Signs
Compare prices. Whose purchase is more expensive? Explain your answer, compare it to the text.
The number 560 is called out later than the number 450 when counting. Therefore, the number 560 is greater than the number 450.
Which number is called out earlier? Which one is smaller?
682 or 21 1 890 or 980
307 or 37 0 568 or 561
Which number is called out later? Which one is greater?
328 or 529 983 or 987
647 or 651 400 or 800
Three-digit numbers are easily compared by the number of units in the digits.
First, compare the units in the hundreds place.
If the hundreds are equal, compare the units in the tens place.
If the tens are equal, compare the units in the ones place.
The two three-digit numbers, the one with more units in the highest place is bigger.
Compare the numbers using the method of comparing the number of units in the digits.
500 and 499 1000 and 999
85 and 805 301 and 311
In mathematical notation, the sign > is used instead of the word “greater”, and the sign < is used instead of the word “less”.
| Expression in Russian |
Expression in mathematical language |
|
| Eighteen is greater than nine | 18 : | > 9 |
| Forty is less than one hundred | 40 < | 100 |
Read the expressions written in mathematical language.
300 > 299 425 > 0 1 000 > 989
807 <817 0 < 100 106 < 109
Write the sentences in mathematical language using the signs > and <.
1) The sum of 35 and 5 is greater than 10.
2) The quotient of 10 and 2 is less than the product of 4 and 3.
3) The number 1 000 is greater than the difference of 43 and 26.
4) The difference between 48 and 40 is greater than 5.
Check yourself: perform calculations.
Which digits can be placed instead of the asterisk (*), so that the statement is true? Justify your answer.
5* > 56 91 > 9*
*6 < 72 64 < *3
REVIEWING WHAT WE LEARNED
Write down all the numbers in digits.
Option 1 Option 2
From 495 to 503. From 896 to 904.
From 299 to 307. From 699 to 706.
Exchange notebooks and check each OTHER’S work.
Write the numbers in digits: six hundred forty-two, seven hundred, eight hundred ninety-three, three hundred five.
In which number: 3 hundreds 5 tens, 3 hundreds 5 tens 2 units, 3 hundreds 2 units?
What does the digit 5 mean in the number representation: 500, 405, 158, 555?
Compare pairs of expressions. What are their similarities and differences?
1) (3 • 8) – (20 : 4) and ((3 • 8) – 20) : 4
2) 30 – (9 : 3) and (30 – 9) : 3
Make a conjecture about whether the values of the expressions in each pair are equal.
Check your conjecture: perform the calculations.
Find the values of the expressions and write them in ascending order.
56 – (16 + 29) (51 – 16) + (35 – 13)
(38 + 49) – 18 (48 + 50) – (63 + 17)
Calculate mentally.
700 + 70 960 – 60 128 – 8
700 + 7 804-4 128 – 20
700 + 70 = 7 c. + 7 d. = 7 c. 7 d. = 770
Around the school, students planted 24 shrubs of rose hip, 4 times less hawthorn than rose hip, and as much lilac as rose hip and hawthorn combined. How many shrubs did the students plant in total?
Express in kopecks: 2 rubles 54 kopecks; 7 rubles 5 kopecks; 7 rubles; 2 rubles 90 kopecks.
In the two youngest swimming groups, there are 10 students, and in the two middle groups, there are 5 more students than in the two youngest groups. How many students are studying in these four groups?
Sergey solved this problem like this:
1) 10 ÷ 5 = 15
2) 10 + 15 = 25
Answer: 25 people.
What mistakes did Sergey make? Write down the correct solution to the problem.
The garden has a rectangular shape. One of its sides is 32 m long, and the other side is 5 m shorter. What is the length of the border of this garden?
The length of the red stripe is 42 cm. It is longer than the blue stripe by 17 cm, and the blue one is shorter than the green one by 29 cm. What is the length of the green stripe?
The book has 32 pages. Dasha read one-fourth of the entire book. How many pages did Dasha read?
Come up with another question for the problem. Solve a new problem.
What numbers should be written in the boxes for the equations to be true?
Answer: 5. Answer: 9.
Kolya, Tolya, and Yuri decided to ride on a two-seat swing. Who can ride with whom? Consider all the options.
Each of the items – a jacket, a coat, and a fur coat – has 3, 4, and 6 buttons respectively. The coat has 4 buttons. The jacket has more buttons than the coat. How many buttons are on the jacket and how many on the fur coat?
Olya is younger than Katya. Each of the girls is younger than Lida. Who is older than everyone? Who is younger than everyone?
What figures have an axis of symmetry? Choose one of such figures, draw it in your notebook, and draw its axis of symmetry.
Draw a ray with its starting point at point O. Using a compass and a ruler, mark on this ray four segments of 2 cm each starting from point O.
Create a plan for completing the task: where will you start and what will you do next? Perform the construction according to the plan.
Sveta wrote numbers on six cards:
What is the largest and the smallest three-digit number she can make from these cards?
Create an expression and calculate its value.
Subtract the difference between 23 and 7 from the number 42.
Subtract the product of 4 and 8 from the number 50.
Add the quotient of 36 and 9 to the number 63.
Add the product of 8 and 7 to the number 16.
Which of the formulated expressions are additions and which are subtractions?
Name all the segments and rays depicted in the picture.
Check your answer: 1) 2 segments and 4 rays; 2) 3 segments and 6 rays.
Call three three-digit numbers that are written with the same digits. Name and write down all such numbers in increasing order. Which of these numbers is the largest and which is the smallest?
Check yourself: there should be a total of 9 numbers.
Consider the picture.
How many on the picture: triangles; quadrilaterals; pentagons?
Are there rectangles among the quadrilaterals; squares? Name them.
Choose one of the polygons in the picture and characterize it (name its main features).
What is segment AK for square ABCD, for square KLEM?
Name the common part: triangle ABC and square KLEM; triangle ABC and square ABCD.
The cinema hall can accommodate 500 spectators. Calculate how many tickets the cashier has, the numbers of which end in 15.
Choose the correct answer: 4; 5; 10; 15 tickets.
What number is composed of:
seven hundreds and nine tens; four hundreds and four units; five hundreds, two tens, and three units; three hundreds, two tens, and five units?
Kilometer.
Millimeter
Large distances are often measured in kilometers. In the word kilometer, kilo means thousand. A kilometer is a thousand meters.
Remember! 1 km = 1,000 m.
Wolf and Hare are going to the country house. They need to travel 100 km. Help Hare answer Wolf’s question.
The driver drove on the highway from the post with a mark of 35 km to the post with a mark of 126 km. How many kilometers did the driver drive?
Lengths that are less than 1 cm are usually measured in millimeters. In the word millimeter, milli means thousandth. A millimeter is one thousandth of a meter. There are 10 millimeters in one centimeter.
Remember! 10 mm = 1 cm.
Find several segments on the ruler that are 1 cm long, 1 mm long.
What is the length of a ladybug in millimeters?
Read the values of the quantities: 12 km; 4 km 325 m; 27 mm; 9 cm 8 mm.
Choose appropriate units of length.
The height of the house is 15 … .
The skier ran a distance of 10 … .
The height of a person is 1 … 70 … .
Ant’s length is 12 … .
Estimate by eye:
1) the height of uppercase and lowercase letters in your math textbook;
2) the length and width of a notebook cell;
3) the length, width, and height of an eraser.
Check your answers: measure these objects in millimeters.
Construct line segments with the following lengths: 8 mm; 1 cm 5 mm; 5 cm 1 mm; 1 dm 2 cm 3 mm.
Express in millimeters.
2 cm 8 cm 2 cm 4 mm
3 cm 15 cm 10 cm 6 mm
2 cm 5 mm = 20 mm + 5 mm = 25 mm
2 cm = 10 • 2 (mm) = 20 mm
Solve orally.
508 km + 20 km 408 km — 8 km
910 km — 10 km 810 km + 5 km
Dima rides the bus to school. First, he walks 50 m from home to the bus stop, and then he rides the bus 6 km to school. The bus stops right at the school gate. Calculate Dima’s round trip distance from home to school and back.
MιifιTflTiΓi∣IT^
In books about sea voyages, distances are often given in miles. In many countries, one nautical mile is considered to be approximately 1 km 852 m.
In Russia, large distances on land used to be measured not in kilometers, but in versts. One verst is approximately equal to 1 km 67 m.
Solve old problems.
Problem 1. The distance from the village to the forest is 8 versts, and to the mill it is twice as close. How many versts is it from the village to the mill?
Problem 2. A peasant went from his village to the fair. After traveling 30 versts,
he stopped at an inn to feed the horse. From here, it is another 19 versts to the city. How many versts does the peasant have to travel in total to reach the city for the fair?
Problem 3. The schooner left the pier and traveled 12 miles to the east, and then 18 miles to the north. Calculate the length of the schooner’s route.
REMEMBERING WHAT’S BEEN COVERED
Which of the statements are true and which are false?
Explain your answers.
Calculate mentally the difference between the numbers: 7 42 and 7 00; 8 5 6 and 50; 907 and 7.
Find the sum of the numbers: 202 and 20; 6 and 300; 80 and 400.
Compare the lengths.
5 m 2 cm and 5 m 2 dm
4 dm 3 cm and 3 dm 4 cm
6 cm 2 mm and 2 cm 6 mm
87 dm and 9 m
721 cm and 7 m 21 cm 9 m and 90 cm
They bought a book, an album, and a notebook. They paid 75 rubles for the whole purchase without the notebook. The book costs 40 rubles. How much does the album cost? Is there enough information to find the price of the notebook?
They bought milk, cottage cheese, and sour cream for 72 rubles. If they didn’t buy milk, they would have paid 55 rubles, and if they didn’t buy sour cream, they would have paid 47 rubles. How much does each of the products cost?
Using three fives, any arithmetic signs, and parentheses, write any numerical expression that has a value of 5; 0.
In a store, there were 52 cans of canned food on three shelves. When they took 16 cans from one shelf and 9 cans from another, there were an equal number of cans on all three shelves. How many cans are left on each shelf?
Vitya and Dima were collecting acorns. Vitya collected 18 more acorns. He gave Dima 9 acorns. Who had more acorns and by how many?
Check your answer if Dima collected 20 acorns; 42 acorns.
In the village, they first built 19 houses, and then 5 more houses. A third of all the houses are still unoccupied. How many houses are occupied in the village?
Assess (true, false) the solution of the problem.
1) 19 ÷ 5 = 24
2) 3 – 1 = 2
3) 24 : 3 = 8
4) 8 • 2 = 16 Answer: 16 houses.
Explain your reasoning.
From a rope 27 meters long, they cut off a third part. How many meters of rope did they cut off? How many meters of rope are left?
Resolve the problem in two ways.
How many axes of symmetry does each figure have?
Draw a ray with the starting point at point O. Mark points B, C, and M on the ray. Mark points K, X, and E outside the ray.
Exchange notebooks and check each other’s work.
Draw a rectangle on grid paper. Draw the diagonals. Mark the point where the diagonals intersect. Use measurements to verify that the diagonals of the rectangle are equal and intersect at the midpoint.
What number will you get if you increase:
8 by 7; 8 by 7 times; 6 by 6; 6 by 6 times?
What number will you get if you decrease:
35 by 5; 35 by 5 times; 49 by 7; 49 by 7 times?
Draw the same quadrilaterals on grid paper, cut them out, and assemble them to form a square.
Write down the expressions that are sums in one column and differences in the other. 27 + (54 : 9) (48 : 6) – 8 (15 + 8) – 11 43 + (87 – 59)
Find the values of these numerical expressions.
Write down all the single-digit numbers that each of the numbers 18, 27, 36, 45 is divisible by.
Which numbers are divisible by all of them?
The length of a rectangle is 9 cm. Its area is 27 cm2. Calculate the width of the rectangle.
Polygonal
The Wolf and the Hare are making a picture from colored straws.
What shape is the red straw?
How many times did the Wolf break the yellow straw to make the roof?
How many times did the Hare break the blue straw? How many segments are in the yellow and blue straws?
The figures depicted in the illustration are called broken lines or simply broken lines.
How many segments are in the broken line? Show each segment and its endpoints.
AMVO – broken line.
Segments AM, MV, and VO are called links of the broken line, and points A, M, V, O are called vertices of the broken line.
Show and name the vertices and links of each broken line.
Compare the broken lines in the illustration. What are their similarities and differences?
A broken line ABCD is called open, and a broken line MCR is called closed.
Why did these broken lines get such names?
Consider the broken lines in the drawing.
Divide the set of broken lines into two groups (classify): closed and open. Name the numbers of figures in each group. Compare the number of links and vertices in each broken line in both groups. How many vertices will an open broken line with six links have?
How many links will a closed broken line with six vertices have?
What conclusion can be made?
The links of a broken line can intersect.
Name the links of each broken line.
Draw a broken line with two links in blue pencil, and a broken line with four links in red pencil.
Before performing the task, make a plan: what will you start with, what will you do next.
Draw a broken line with three links, where the length of each link is 4 cm.
First, make a construction plan. Compare this plan with the construction plan of the broken lines in the previous task. What are their similarities and differences? Complete the construction.
The length of one link of the broken line is 3 cm, the other is 5 cm, and the third is 4 cm 5 mm. Draw this broken line.
Label the broken line with letters. Name the length of the longest link and the shortest link.
RECALLING WHAT WE LEARNED
Express in millimeters:
5 dm 7 cm; 5 dm 8 mm; 6 cm 4 mm.
Express in centimeters:
4 m 35 cm; 6 m 9 cm; 8 m; 42 dm.
Express in meters:
600 cm; 30 dm; 400 cm; 1,000 mm.
Express in meters and decimeters:
41 dm; 76 dm; 50 dm; 68 dm.
Name the units of length you know, starting with the largest.
In which larger units of length can you express 500 mm?
What numbers need to be written in the boxes for the records to be correct?
Answer: 2. Answer: 18.
By how much is the sum of 500 and 2 greater than the number: 500; 2?
By how much is the difference between 824 and 20 greater than the number: 4; 800?
Answer the questions.
How many times is 1 m greater than 1 cm?
How many times is 1 m greater than 1 dm?
What part of a meter is 1 cm?
What part of a meter is 1 dm?
Check if the calculations are correct.
(9 • 7) – 48 = 15
(6 • 6) + (8 • 8) = 100
100 – (35 + 44) = 31
(41 – 36) • (72 : 8) = 45
What is the largest two-digit number that can be written with two different digits?
What is the smallest three-digit number that can be written with three different digits?
Which number is bigger: the smallest three-digit number or the largest two-digit number?
Kolya was watering the garden. He has already completed three-fifths of all the work. What part of the work does Kolya still have to do? How many beds does Kolya have left to water if there are 20 beds in the garden?
Solve the problem in two ways.
Increase the numbers by 5 times: 8, 6, 9, 7, 3, 1.
Decrease the numbers by 7 times: 14, 28, 35, 49, 56.
Katya and her mom were picking mushrooms. Katya found 8 mushrooms. When mom gave her 2 of her mushrooms, Katya had twice as many mushrooms as her mom. How many mushrooms did mom find?
Petya, Vasya, and Kolya caught fish and started dividing their catch. Petya took half of all the fish, Vasya took 4 perches, and Kolya took 5 breams. How many fish did the boys catch in total?
8 boys are going fishing: four of them have fishing rods and six have buckets. Is there at least one boy with both a fishing rod and a bucket?
A rectangle’s width is 3 times smaller than its length. The width of this rectangle is 4 cm. Find the perimeter and area of the rectangle.
Determine the area of a rectangle without measuring.
Lena, Katya and Ira found 30 white mushrooms: Lena – 5, Katya – 10, and Ira – 15. For this, their grandmother gave the girls 18 candies and offered to divide these candies fairly. How many candies did each girl get?
Katya answered the question about her age like this: “In 3 months, I will be 9 years old.” Calculate Katya’s age. How old will Katya be in a year?
Determine by sight which segment is shorter than the other one.
Check your answer: measure it.
Determine how many millimeters one of the segments is shorter than the other.
Perform the operations.
(42 : 7) + (36 : 6) (97 – 47) – (16 -6)
(9 • 8) – (6 • 7) (64 ÷ 36) – (6 •9)
(56 – 18) + (28 : 7) (32 : 4) • (27 :3)
(64 : 8) – (24 : 3) (72 : 8) : (12 :4)
Identify the expressions that have: value less than or equal to 30; value greater than or equal to 40.
Which expressions are: sums; differences?
Which of the statements about the polygon shown in the picture are true?
It is a quadrilateral.
It is a square.
It is not a square.
It is not a rectangle.
It is a rectangle.
It is not a rectangle.
It is a square.
It is a polygon.
Which buses stop at the “Mars Cinema” bus stop?
Examine the table. It shows the number of buses for each route passing the stop from 6 am to 12 midnight.
| Bus Number | 53 | 637 | 803 |
| Number of Trips | 72 | 108 | 54 |
Which bus route passes most frequently and least frequently? By how many trips does bus No. 637 exceed bus No. 803? Name the bus route numbers in order of increasing number of trips.
Polygon Length
The Wolf and the Hare are making football goals.
How many meters of timber do they need for one goal? How did the Hare calculate it?
Measure the length of each segment of the broken line.
Explain how to find the length of this broken line. Perform calculations.
To find the length of a broken line, you need to add up the lengths of all its segments.
Perform the necessary measurements and calculate the length of the broken line.
Draw a broken line with two segments. The length of one segment is 5 cm 4 mm, and the other is 1 cm 8 mm shorter.
The broken line ABCD has three segments: AB = 42 mm, BC = 38 mm, CD = 19 mm. Calculate the length of the broken line.
The length of a broken line consisting of two segments is 50 dm. The length of one segment is 36 dm. What is the length of the other segment?
The broken line consists of eight segments of equal length. The length of each segment is 6 m. What is the length of the broken line?
The broken line consists of two segments. One segment is twice as long as the other. Draw the broken line and calculate its length.
| REMEMBERING WHAT WE’VE LEARNED
How, without measuring tools, can you cut a piece of wire from a spool that is 1 m 60 cm long, of lengths: 80 cm; 40 cm?
Using the digits 7 and 4, write down all two-digit numbers so that the digits in each number: 1) are repeated; 2) are not repeated. How many numbers did you get in each case?
Masha wrote down a two-digit number. Then she reversed the digits and wrote down another number. The difference between the first and second numbers is 0. Name the number that Masha could have written down first. What is its peculiarity?
How many such numbers are there? Explain how to choose solution options without missing any.
Calculate the values of the expressions.
Variant 1 Variant 2
(48 + 24) : 8 7 – (96 – 87)
100 – 6-9 36 : 4 + 81
Check each other’s work.
A glass, a cup, and a mug were filled with different drinks: tea, coffee, and milk. The glass is to the right of the coffee drink, the tea drink is to the right of the glass, and the cup is to the right of the glass. What drinks were poured into the glass, cup, and mug?
Sasha bought a pencil and an eraser. The pencil costs 7 rubles, and the eraser is 2 rubles cheaper. Sasha paid for the entire purchase with six identical coins. What coins were they?
72 kg of marshmallows were delivered to the store, 8 kg in each box, and 49 kg of candies, 7 kg in each box. How many boxes of sweets were delivered to the store in total?
The gardener had 8 sacks of potatoes. He used 5 sacks during the winter, and planted the remaining potatoes in the spring. In the fall, he harvested 5 sacks from each planted sack. How many sacks of potatoes did he harvest in the fall?
The Yak-40 aircraft accommodates 27 passengers. This is 3 passengers less than the An-24 aircraft accommodates. How many passengers does the An-24 aircraft accommodate? Change the question so that the problem can be solved in two steps. Solve the new problem.
18 boxes with cargo were transported by car in 3 trips. How many trips are needed to transport 48 such boxes if the load capacity of the car is the same for each trip?
Yura solved this problem as follows:
1) 18 : 3 = 6
2) 48 – 18 = 30
3) 30 : 6 = 5
4) 3 + 5 = 8
Answer: 8 trips.
Explain Yura’s reasoning.
Solve the problem in a different way. Which method of solving is better? Explain your answer.
Which numbers should be written in the boxes to make the equations correct?
Answer: 3. Answer: 3.
In the cages, there are 5 tits, 6 parrots, and 7 canaries. There are more tits than canaries or parrots. There are more parrots than canaries. How many canaries are there?
The rectangle has sides of length 1 meter and 1 centimeter, and the square has a side length of 1 decimeter. Compare the areas of both figures.
Before drawing a conclusion, think in which units it is most convenient to compare the areas of these figures.
Misha folded four-sided figure ABCM from three identical triangles. The figure ABCK is a square with a side length of 2 centimeters. Calculate the area of the quadrilateral ABCM.
Try to read a famous Russian proverb.
Describe the broken line in the picture. Answer the following questions.
How many vertices and edges does this broken line have?
Is it closed or open? Do its edges intersect? How many pairs of intersecting edges are there in total?
Mass. Kilogram. Gram
Why are the scales not in balance?
The scales are not in balance because the weight of the bag of flour is greater than the weight of the weight (the weight of the weight is less than the weight of the bag of flour).
The mass of objects is often measured in kilograms.
The word “kilogram” is abbreviated as “kg”.
What is the mass of the Wolf in kilograms?
The weight of small objects or a small amount of liquid is usually measured in grams.
The word “gram” is abbreviated as “g”.
The wolf asked the Hare to give him a vitamin injection.* Look at the picture. How many milligrams of vitamin are in the ampoule?
In a large ampoule, there are 5 grams of iodine, while in a small one, there are 3 grams of iodine. The iodine was poured from both ampoules into an empty vial. How many grams of iodine are in the vial?
The weight of the beetle is 6 grams, and the weight of the caterpillar is twice as much. What is the weight of the caterpillar?
Remember! 1 kg = 1,000 g
There are one thousand grams in one kilogram.
The weight of objects is determined using various scales.
Read the records in ascending order of weight.
26 kilograms 1,000 g
125 grams 16 kg 80 g
4 kilograms 300 grams 30 kg 130 g
Using scales, determine the weight of: a math textbook; a pen; an apple; an orange.
Calculate mentally.
370 kg ÷ 9 kg 683 kg – 80 kg
46 g + 800 g 400 kg + 16 kg
504 g – 500 g 736 kg – 36 kg
The Russian Language
In the past, in Russia, units such as the “pood” and the “pound” were used for measuring weight.
1 pood is approximately equal to 16 kg.
1 pound is approximately equal to 400 g.
How do you understand the proverb?
A pound is inferior to a pood.
Solve the old problems.
Problem 1. Two pounds of kerosene were burned in the house every evening. How much kerosene was burned in a week?
Problem 2. The shepherd first wove 8 pairs of sandals, then 4 more pairs. Three pounds of bark are needed for a pair of sandals. How much bark was used for all the sandals?
Task 3. The peasant brought 3 poods of wheat and 2 poods of rye to the mill. What is the weight of the grain in kilograms?
What is the weight of the pumpkin?
There are 3 identical bags of flour on the scales. How many kilograms of flour are in one bag?
Misha is known for his strength in class. Once he wanted to lift a basket that weighed 12 kg of potatoes, but he couldn’t do it. Then he poured out a third of the potatoes from the basket, but still couldn’t lift the weight. Therefore, he poured out half of the remaining potatoes and then lifted a record weight for himself. What is Misha’s record weight if the weight of the basket is 450 g?
Let’s recap what we have learned.
Draw a broken line consisting of three segments so that the length of the first segment is 9 cm and each subsequent segment is three times shorter than the previous one. Calculate the length of the broken line.
The price of potatoes is 9 rubles per kilogram. What is the cost of two bags of potatoes if each bag contains 3 kg of potatoes?
For salting, we bought 6 kg of cabbage for 8 rubles per kilogram and cranberries. We paid 12 rubles less for cranberries than for cabbage. What is the total cost of the purchase?
> Compete with your neighbor at your desk to see who can write down the results faster.
3-4 6-6 42 : 7 28 :4
5-7 7-8 64 : 8 35 :7
8-9 9-3 15 : 5 81 :9
Exchange notebooks and check each other’s work.
Calculate.
16 + 5 22 – 823 -8
9 + 9 18 + 815-9
Check yourself: add up the values of all the expressions, the sum should be equal to the number 100.
Compare the expressions. Put the signs >, < or = so that the statements are correct.
69 + 15 and 14 + 70 44 – 25 and 53 – 36
28 + 39 and 46 + 37 86 – 28 and 64 – 15
The climbers walked 4 km from their camp to the foot of the mountain. Then they climbed to the summit, covering a distance twice as short. What is the length of the climbers’ route: from the camp to the mountain peak; from the camp to the mountain peak and back?
The weight of a watermelon is 12 kg 500 g. A melon is 3 kg lighter than a watermelon, and a pumpkin is 5 kg heavier than a melon. What is the weight of the pumpkin?
From a spool of ribbon, they first cut off 5 m 5 dm, and then another 1 m 5 dm. There were 15 m of ribbon left on the spool. What was the length of the spool of ribbon?
5 m 5 dm = 50 dm
1 m 5 dm = 15 dm
15 m = dm
From a piece of fabric, you can sew 6 dresses, using 3 m for each. How many shirts can be made from this piece of fabric if 2 m are used for each?
In the store, pens are sold for 5 r. and 9 r. Anya, Vanya, and Tanya each bought one pen. How much money could they have paid for the entire purchase?
Continue the following reasoning. Perform calculations.
1) If all the children bought pens for 5 r., they paid: 5 r. * 3 = G r.
2) If two bought pens for 5 r.,
and one bought a pen for 9 r., they paid: (5 r. * 2) + 9 r. = ∏p. • • •
How many solutions does this problem have?
Cut a square out of paper with side length 6 cm. Prove by folding that each of its diagonals is an axis of symmetry of the square.
Cut a rectangle out of paper with the given side lengths. Fold it along the diagonal. Is the diagonal of this rectangle an axis of symmetry?
Variant 1 Variant 2
5 cm and 3 cm 4 cm and 6 cm
At the factory, parts are machined from blanks. One part is obtained from one blank. The chips obtained when making six parts can be melted down and used to make one more blank. How many parts can be made in this way from 36 blanks?
What measurements need to be made to construct the same circles? Develop and explain a plan of action. Perform the construction.
Non-adjacent vertices of a polygon are connected by line segments. Name a few of these line segments. Invent a method for counting them. How many such line segments are there in total?
Select the correct answer for each figure: 4, 5, 9, 10.
The length of a square side is 6 cm. Its area is equal to the area of a rectangle with a length of 9 cm. What is the width of this rectangle?
Calculate the length of the rectangle if its width is 7 dm and the perimeter is 30 dm.
By how many times is a notebook more expensive than a pen?
How many rubles do 3 notebooks and 2 pens cost?
How many pens can you buy for 24 r.?
How many notebooks can you buy if you only have 18 r.?
Capacity.
Litre
Fill the jar and the bottle with water to the brim. Determine by eye which container contains more water. Take some measure, for example, a glass, and check yourself.
The unit of capacity often used for measuring is the litre.
The word “litre” is abbreviated as “l”.
The weight of 1 liter of pure water is 1 kg.
The weight of 1 liter of another liquid can be greater or less than 1 kg.
For example, the weight of 1 liter of oil is 760 g, and 1 liter of seawater has a weight of 1 kg 25 g.
How many liters of milk can be poured into the canister up to the top mark?
Using a liter jar, pour 12 liters of water into the bucket, 5 liters of water. Explain the sequence of actions.
Calculate mentally.
56 liters + 100 liters 200 liters + 12 liters
207 liters + 80 liters 418 liters – 18 liters
126 liters – 120 liters 909 liters + 60 liters
There are 40 liters of kvass in the barrel. One-eighth
of all the kvass was sold in an hour, and after one more hour there were 25 liters of kvass left in the barrel. How much kvass was sold in 2 hours?
Is there any unnecessary information in the problem? Formulate the problem without this information and solve it.
иввзшиав
Barrel and bucket are vessels for bulk materials and liquids. But in ancient Russia, these words also referred to units of capacity.
1 bucket holds approximately 12 liters.
1 barrel holds approximately 40 buckets.
Solve the ancient problem.
A peasant used one-fifth of the barrel of water for irrigation. How many buckets of water were used approximately for irrigation? How many liters of water were used approximately for irrigation?
How can you pour 4 liters of water into a bucket using a three-liter and a five-liter jar? Explain the sequence of actions.
| RECALLING WHAT WE HAVE LEARNED
On one side of the scales is a box and two weights of 1 kg, and on the other side are two weights of 10 kg and 5 kg. The scales are in balance. What is the mass of the box?
What numbers should be written in the boxes to make the equations correct?
Answer: 3. Answer: 3.
Increase the numbers by 4: 3, 7, 5, 8, 2.
Decrease the numbers by 6: 18, 36, 48, 12, 54.
Compare the links of the broken line using a compass. Perform the necessary measurements and calculate the length of this broken line.
How much change should you receive from 50 rubles if you buy 3 stamps for 7 rubles and
4 stamps for 5 rubles?
There were 60 kg of flour in the bag. After taking out several kilograms of flour evenly into 5 bags, there were 45 kg of flour left in it. How many kilograms of flour are in each bag?
Mom gave Masha a piece of fabric and asked her to cut a square piece. After cutting a quadrilateral piece by eye, Masha decided to check her work. She folded the piece of fabric diagonally and saw that the edges coincided. “If the edges coincide, then the cut piece must be square,” Masha decided. Is Masha right? Explain your answer.
In the school greenhouse, the children grew cucumbers. After distributing the cucumbers into 4 baskets, with 6 kg in each, there were 39 kg of cucumbers left. How many kilograms of cucumbers did the children grow?
Lunch in the cafeteria consists of two courses – the first and the second. What lunches can you choose if there is borscht, fish soup, and kharcho for the first course, and cutlet and fish for the second one? Write the solution options in the table.
| First course | Second course |
| b | k |
| b | F |
| • • • | ♦️ • • |
b – borscht u – fish soup h – kharcho k – cutlet F – fish
Explain the order in which you can proceed when selecting solution options. How many lunch options are there?
There are three cartoons shown in the movie theater: “Hedgehog in the Fog,” “Who Said “Meow”?,” and “Twelve Months”. In what order can these cartoons be shown? Consider all the options.
Petya says that a square is a rectangle, so the diagonal of a square is not its axis of symmetry. Is Petya right? Explain your answer.
Yura claims that the number 18 can be divided not only by 2 and 3, but also by the product of these numbers. Check Yura’s statement.
Which two triangles have something in common: side AK; side AB; vertex A; vertex C?
How many triangles are there in total in each of the pictures?
A men’s suit consists of a jacket, a waistcoat, and trousers. The tailor sewed 4 black and 5 blue suits. How many items were sewn in total at the tailor’s? Solve the problem using different methods.
It takes the seamstress 6 minutes to sew on a zipper in a dress, and 2 minutes to sew on a pocket. How much time will she spend processing eight dresses if each dress must have one zipper and one pocket? Solve the problem using different methods.
The sum of two numbers is greater than the first addend by 36. What is the value of the second addend? Give an example and write it down.
Read the numbers.
320, 7, 28, 46, 1, 504, 0, 700, 60.
Divide these numbers into three groups (classify them): single-digit numbers, two-digit numbers, and three-digit numbers.
Name the numbers in each group.
Write all the numbers in a table in ascending order: in the top row – single-digit numbers, in the middle row – two-digit numbers, and in the bottom row – three-digit numbers.
Check the results of your work: there should be a number 0 in the top row and left column; there should be a number 46 in the middle row and middle column; there should be a number 700 in the bottom row and right column.
Calculate the values of the expressions.
(4 • 7) – 19 38 – (5 • 7)
42 + (54 : 6) 53 + (4 •9)
(27 : 9) : 3 (42 : 7) :1
8 • (40 : 5) 16 : (48 :6)
(32 : 8) • 5 (3 • 4) : 6
0 : (56 – 18) 54 : (9 +0)
Докажи, что верно утверждение: «
, у которого все углы прямые, а каждая сторона равна 2 дм, является 
».
Действуй по плану:
1) сформулируй определение 
;
2) выдели из определения признаки ;
3) проверь выполнение каждого признака для данного ;
4) сделай вывод.
По какому признаку отобраны слова:
КОТ СОК ОСА МЕЛ ЛЕС
Выбери верный ответ.
1) В каждом слове есть буква О.
2) Каждое слово начинается с согласной буквы.
3) В каждом слове 3 буквы.
Туристов разместили поровну в шестиместных лодках. Сколько лодок заняли 24 туриста? Как это можно узнать? Выбери правильный ответ.
1) Сложить 24 и 6. 3) Умножить 24 на 6.
2) Из 24 вычесть 6. 4) Разделить 24 на 6.
Все музыкальные инструменты, изображённые на рисунке, кроме одного, обладают общим признаком. Один из них не обладает этим признаком. Какой это инструмент? Ответ поясни.
Гитара Скрипка Саксофон Балалайка
Addition
Explain how each student solved the addition. Who solved the most difficult problem and who solved the easiest one? Explain your answer.
Find the sum.
84 + 48 17 + 89 624 + 9
7 5 + 8 7 28 + 82 7 +136
94 + 39 49 + 67 5 +375
60 + 45 34 + 66 999 +1
Find the sum.
162 + 32 7 347 + 214 528 +191
200 + 196 434 + 256 375 +163
305 + 104 57 + 128 48 +361
453 + 41 805 + 79 714 +95
From Olya’s house to Masha’s house is 590 m. From Olya’s house to Katya’s house is 250 m farther than to Masha’s house. How many meters will Masha walk if she goes to Katya’s house but first visits Olya?
Mama spent 183 rubles in the store. She has 209 rubles left. How much money did Mama take to the store?
Over the week, the tourist swam 56 km, walked 41 km, and drove 473 km. What distance did the tourist cover during the week?
Three friends – Vasya, Vitya, and Kolya – decided to buy a soccer ball that costs 150 rubles. Vasya has 63 rubles, Vitya has 55 rubles, and Kolya has 19 rubles less than Vitya. Can the friends buy this ball?
In Saturday, zoologists traveled 126 km across the steppe, and on Sunday – 18 km more. How many kilometers did the zoologists travel in 2 days?
Perform the actions.
327 kg + 268 kg
45 l + 126 l
848 g + 95 g
364 m + 86 m
435 cm2 + 193 cm2
5 kg 325 g + 1 kg 468 g
What is the length of the fence?
Mentally calculate.
500 + 300 120 +40
100 + 900 120 +400
20 + 300 240 +10
450 + 7 356 +3
Find the values of the expressions.
(365 + 124) + 108 73 + (418 + 418)
(91 – 63) + 396 277 + (100 – 19)
Check the results using a calculator.
Find the sum of two addends if:
1) one of the addends is 532 and the other is 368;
2) both addends are equal to 346;
3) the first addend is 178 and the second one is 12 more;
4) the second addend is 97 and the first one is 8 less.
Calculate orally.
274 + 99 209 +599
305 + 198 97 +686
444 + 297 299 +401
128 + 98 = (128 + 100) – 2 = 226
128 + 100 = 228
228 – 2 = 226
REMEMBER WHAT HAS BEEN PASSED
Read the records: 13 liters, 15 cm, 450 grams, 518 kilograms, 38 dm, 42 cm2, 50 m, 100 mm, 32.5 cm, 48.8 cm, 2.5 kg, 150 m2, 15 mm2, 7 liters. What does each of these values mean?
Classify: divide the given values of the quantities into 4 groups. Make records. Name the largest and smallest values of the quantity in each group.
How many axes of symmetry does a circle have? Explain your answer.
After pouring out 8 liters of milk from a canister, there was 24 liters more left than poured out. How many liters of milk were in the canister?
Choose the correct solution to the problem. Explain your choice.
1) 24 – 8 = 16 (l) 1) 24 + 8 = 32 (l)
2) 24 + 16 = 40 (l) 2) 32 + 8 = 40 (l)
Answer: 40 liters. Answer: 40 liters.
When 5 liters of milk were taken from the first container and 3 liters from the second container, there was an equal amount of milk left in these containers. In which container was there more milk and how many liters?
Calculate orally.
50 + 70 48 – 18 42 + 4 58 +2
70 – 40 52 – 2 60 – 9 36 +64
20 + 18 6 7 – 60 90 + 7 45 +45
The area of each square is 1 cm2. Calculate the areas of the figures in different ways.
When Pete was 7 years old, his father was 32 years old. Now, his father is twice as old as Pete. How old is Pete now and how old is his father?
Last year there were 3 rows of carrots in the garden and the number of cabbage rows was 5 times greater. This year, there are 6 fewer rows of cabbage than last year. How many times greater is the number of cabbage rows than the number of carrot rows this year, if the number of carrot rows has not changed?
The area of the playground is 36 m2. Calculate the length of the playground.
Are all the necessary data for solving the problem given in the text? Formulate the problem in such a way that it can be solved without using the picture.
Choose a sequence of numbers according to the rule: “Each subsequent number is 12 more than the previous one”.
The flight attendant offered the passenger a choice of three drinks: mineral water, juice, and lemonade. He took two drinks. What drinks could the passenger take? Consider all the options. How many are there?
Copy the triangle on square grid paper and draw its axis of symmetry.
Option 1 Option 2
Exchange notebooks and check each other’s work.
What segments can be drawn to divide the figure into 4 triangles?
Check your answer: copy the figure on a sheet of graph paper. Draw the segments. Cut the figure into 4 triangles. Put the triangles together to form a new polygon and describe it.
Two bugs are sitting on a straw that is 19 cm long. One of them is located 5 cm from the left end of the straw, and the other one is located at a distance of 7 cm from the right end of the straw. Make a drawing, marking the bugs with dots. Measure the distance between the dots.
63 : 9 24 : 4 4-8 9-9
Postman delivered 40 newspapers and 12 magazines to the apartments. He brought something to each apartment. How many apartments received a newspaper or a magazine?
Each child received a doll or a bunny as a gift. A total of 30 gifts were given. All 16 girls received a doll each. How many boys were there?
The length of a pen is 15 cm. What is the length of a pencil if it is 3 cm shorter than the pen? How many solutions does the problem have? Explain your answer.
Yesterday Yura read a book from page 45 to page 56. How many pages of the book did he read yesterday?
Choose the correct answer: 11, 12, 13.
Subtraction
Tell how each student performed the subtraction.
Who solved the easiest problem and who solved the most difficult one? Explain your answer.
In which examples is the difference a two-digit number?
500 – 300 418 – 18 5 7 0 -60
800 – 400 275 – 5 630 -600
400 – 40 300 – 7 355 -300
Check your answer: perform the calculations.
Find the difference between the numbers.
346 and 217 275 and 259 162 and 44
524 and 303 627 and 19 321 and 8
Perform the subtraction.
364 – 191 627 – 266 429 -87
243 – 162 938 – 52 813 -20
Calculate the difference between the numbers.
524 and 368 817 and 649 920 and 350
333 and 222 540 and 534 325 and 115
In which example is the difference equal to the subtrahend?
700 – 231 900 – 308 401 -86
252 – 126 200 – 63 605 -197
Calculate.
837 – 254 629 + 95 100 -36
276 + 98 500 – 55 67 +584
600 – 322 900 – 265 75 +87
301 – 159 196 + 74 297 +558
Find the values of the expressions.
(9 + 347) – (600 – 308)
(925 – 154) – (530 – 215)
(678 – 87) + (47 + 94)
(504 – 386) + (208 – 169)
Check your answers using a calculator.
Mentally calculate.
600 – 14 1 000 – 19 1 000 – 25
480 – 23 750 – 33 580 – 42
800 – 51 200 – 28 200 – 18
300 – 26 = (300 – 20) – 6 = 274
300 – 20 = 280
280 – 6 = 274
The master received a daily order to repair four alarm clocks and 13 wristwatches. During the day, he repaired all the alarm clocks, and the number of wristwatches repaired was three times more than the number of alarm clocks. Did the master complete the daily order?
The master planned to make 150 toys, but he made 212. How many toys did the master exceed the plan by?
On Monday, 540 glass items were sent from the warehouse, and on Tuesday, 920 glass items were delivered to the warehouse. How did the glass inventory on the warehouse change?
Luba can take two different paths from home to school. On the first path, she walks 120 m from home to the clinic and then 180 m from the clinic to school. On the second path, she walks 150 m from home to the store, and then 130 m from the store to school. Which path is longer and by how many meters?
The first tank has 285 liters less kerosene than the second tank* 620 liters of kerosene were poured out of the second tank. In which tank is there more kerosene, and by how many liters?
A worker was supposed to make 220 parts according to the plan, but he fell short by 35 parts. How many parts did the worker make?
In the canteen, 530 first-course dishes, 287 meat second-course dishes, and 418 vegetable second-course dishes were prepared. How many more second-course dishes were prepared than first-course dishes?
What numbers should be written in the boxes to make the equations correct?
Perform the operations.
406 kg – 202 kg 126 kg 258 g – 96 kg 168 g — 76 g 5 m 16 cm — 38 cm
500 m2 – 120 m2 1 km – 825 m
Calculate mentally.
900 – 99 321 -299
480 – 199 1000 -98
540 – 298 745 -197
730 – 198 = (730 – 200) + 2 = 532
730 – 200 = 530
530 + 2 = 532
The height of Sergey is 164 cm, Katya is 8 cm shorter than Sergey, but 12 cm taller than Dima. Calculate the height of Katya and the height of Dima. Name the children in order of their height.
REMEMBERING WHAT WE HAVE LEARNED
How much does a lunch consisting of borscht, fried meat, juice, and two pieces of bread cost?
Menu
Borscht 25 rubles
Fried meat 60 rubles
Squash 8 rubles
Bread 1 ruble
Juice 12 rubles
Coffee 10 rubles
What is the similarity and difference of these sums: 646 + 300, 646 + 30, 646 + 3? Calculate mentally.
When the mother was 29 years old, the son turned 7. Now the son is 11. How old is the mother?
1) Multiply 9 by 4.
2) How many times is 72 bigger than 8?
3) Write three examples of division with the answer of 7. 4) Write two examples of multiplication with the answer of 24.
There are two barrels next to each other. When 7 buckets of water were taken from one barrel and 3 buckets of water were poured into the other, the water in both barrels became equal. How many buckets of water were there in one of the barrels more than in the other?
Choose the correct answer: 4 buckets; 10 buckets.
Think of a number that is divisible by 6. Find its half, third, and sixth part.
Check your answers: add these three numbers and you will get the intended number.
Brother is 24 years old. Sister is 12 years old. How many times was the brother older than the sister 9 years ago?
The total age of a mother and daughter is 48 years. The mother is 24 years older than the daughter. How old is each of them?
There are apples, pears, and oranges in a vase. There are 2 more apples than pears. How many fruits of each kind are in the vase, if there are 5 in total?
Solve the problem by trial and error. How many solutions does the problem have?
Solve the problems.
1) Grandfather allowed to cut no more than four roses from the bush. How many roses can be cut?
2) There are at least three and no more than six people in a boat. How many people can be in the boat?
State all possible solution options for each problem. Explain your answers.
Draw a circle with a radius of 2 cm 5 mm. Draw a line segment through the center of the circle so that its ends are on this circle. Measure the length of the line segment. Compare your result with your desk mate’s result. Why should you get the same answer?
Approximately estimate the length of a teaspoon; the height of a cup.
Check your answer: measure it.
Count the number of squares in Figures A and B. Can Figure A be divided into such parts as Figure B?
Check your answer: copy Figure A and divide it into parts that are equal to Figure B.
Draw a rectangle with side lengths of 3 cm and 2 cm on the cells and draw all its axes of symmetry. How many axes of symmetry does this rectangle have?
Draw a line segment with a length of 4 cm, mark its midpoint, and draw the axis of symmetry of the line segment.
How many line segments are there in each of the figures? How do you count all the line segments in the figures without missing any and without counting them twice? Think of a convenient counting method.
Without performing the specified calculations, answer whether the sum will be greater or less than the number 100.
64 + 56; 15 + 69; 49 ÷ 72; 96 + 5
What is the area of the shaded figure?
Vitya collected information about the residents of his house. He found out that there are 47 men, 52 women, 7 boys, and 4 girls in the first entrance. In the second entrance there are 36 men, 48 women, and 5 boys. And in the third entrance there are 28 men, 56 women, 6 boys, and 5 girls. Fill in the table with the data that Vitya collected.
|
Entrance number |
Number of residents |
|||
| Men | Women | Boys | Girls | |
| 1 | ||||
| 2 | ||||
| 3 | ||||
Using the data from the table, answer the following questions. How many men and women live in the building? How many adults and how many children?
In which entrance do the most men live? The most women?
How many times fewer girls live in the building compared to boys?
How many more women live in the building compared to men?
How many residents are there in total?
All expressions, except one, have the same values. Identify that expression.
30 + 18, 8-6, 50 – 2, 0 : 48
Additive property of addition
Express your speculation about the results that the Wolf and the Hare will obtain. Check yourself by performing the calculations on a calculator.
Check if the values of the expressions are equal.
(5 + 3) + 6 and 5 + (3 + 6) (20 + 40) + 10 and 20 + (40 + 10) (300 + 100) + 600 and 30 0 + (100 + 600) Draw a conclusion.
To add a third number to the sum of two numbers, you can add the sum of the second and third numbers to the first number.
This property of addition is called the additive property of addition.
Find the values of the expressions using the additive property of addition.
(48 + 27) + 3 (57 + 692) + 8
(254 + 86) + 14 (399 + 299) + 1
Calculate the values of the expressions and verify using the additive property of addition.
(624 + 158) + 42 (396 + 121) + 439
Solve each problem using two methods.
1) One box contains 36 red and 25 yellow apples, while another box contains 75 green apples. How many apples are there in total in the two boxes?
2) One cage has 13 white and 8 gray rabbits, while another cage has 22 black rabbits. How many rabbits are there in total in the two cages?
Which method gave the result faster?
REVIEWING WHAT WE HAVE LEARNED
How are the expressions 274 – (96 + 158) and (274 – 96) + 158 similar and different?
Without performing the specified calculations, prove that the first expression has a smaller value.
Compare the expressions. Without performing the specified calculations, determine which expression has a greater value. Explain your answer.
605 + (216 – 97) and 605 – (216 – 97)
Which numbers are twenty more than each of the following numbers: 225; 600; 308; 471; 708; 780?
Which numbers are three hundred less than each of the following numbers: 630; 904; 321; 1,000; 333; 803?
1) Calculate the sum of the numbers if the first addend is 426 and the second addend is 289.
2) The first addend is 384, and the second addend is 95 less. What is the sum?
3) The sum of two numbers is 704, one of them is 569. Find the other number.
Find the solutions for each of the following numbers: 7, 26, 34, 48, 64, and 68.
(9 • 6) – 28 (45 – 39) • 8
74 – (48 : 8) (19 + 23) : 6
(54 : 9) + 58 82 – (6 • 8)
Find two-thirds of the number 24 and three-fourths of the number 36.
Find the number whose one-third is equal to: 6; 9.
There are 56 birds in the zoo. Pelicans make up one-seventh of all birds. In addition to them, there are 12 flamingos, and the rest of the birds are swans. How many swans are there in the zoo?
The fabric was cut into three pieces of different sizes. The second piece has 5 meters more fabric than the first. The third piece has 5 meters more than the second. How many more meters of fabric are in the third piece compared to the first?
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