- Find the pattern and continue the series:
- 1, 2, 4, 7, 11 …
- 1002, 2004, 3008, 4016, …
2. Determine the procedure:
(a + b) c – m: k + n z
3. Solve chains of examples:
780 + 250 + 240 + 210 – 650
335 + 408 – 109 + 607
621 + 204 – 505 + 70 - 100
How many rectangles are there in the picture?
16 rectangles
Arithmetic dictation. Write down your answers.
- Find the sum of the numbers 5499 and 8000.
- Increase the number 270 by 1000 times.
- Write down the smallest five-digit number.
- How many digits are there in the number 775775?
- Find the difference between the numbers 99000 and 88000.
- Find the fourth part of the number 960.
- Find three quarters of 1000.
- Express 540 minutes in hours
- Express 5 m 20 cm in millimeters.
Check the answers:
13499, 270000, 10000, 2, 11000, 240,750, 9 hours, 5200 mm.
We will find out what we will do in class if we complete the task correctly.
Arrange the answers in ascending order
a h a d a z
TASK
Entertaining tasks
1. Two diggers dig a 2 m ditch in 2 hours. How many diggers will dig 5 m of a ditch in 5 hours?
2. The cranes flew in a wedge. 4 cranes on one side of the wedge and 4 cranes on the other side of the wedge. How many cranes were there?
3. Dima washes 4 plates in the same time as 6 cups. What does he wash faster - a plate or a cup?
4. How many three-digit numbers are there?
Solve problems:
1. A polar bear swam 200 km at a speed of 5 km/h. How many hours did the polar bear swim?
2. Petya read a book at a speed of 20 pages a day. How many days did it take him to read the entire book if it had 200 pages?
3. A swordfish has a speed of 30 m/s. How many seconds will it take the fish to swim a distance of 1 km 500 m?
4. The wind blows at a speed of 25 m/s. How many seconds will it take him to pull the balloon 200 m?
MATERIALS USED:
- Dmitrieva O.I. “Lesson-based developments in mathematics. 4th grade", Moscow "VAKO", 2006.
- Samsonova L.Yu. “Oral counting. Collection of exercises for the textbook by M.I. Moro, S.I. Volkova, S.V. Stepanova" Moscow "Exam", 2009.
3. M.I. Moro Mathematics 3rd grade, Part 2. Textbook, Prosveshchenie Publishing House, 2009.
4. Background for presentation - http://www.pomochnik-vsem.ru
Math test
Compiled by: Khlebinskaya O.V.
primary school teacher
MBOU "Secondary School No. 4" Angarsk
1. Specify the number entry three hundred six thousand eighteen in numbers: a) 360018; b) 30618; c) 306018; d) 306081.
2. Choose a number that is 7 less than 7035. a) 7028; b) 1005; c) 105; d) 7042.
3. Write the number 8563 as a sum of digit terms. a) 8000 + 563; b) 8000 + 500 + 63; c) 8000 + 600 + 50 + 3; d) 8000 + 500 + 60 + 3.
4. Indicate the value of the sum of the numbers 438750 and 234567. a) 663317; b) 672317; c) 673317; d) 204183.
5. Indicate the value of the product of the numbers 70 and 800. a) 560; b) 600; c) 56000; d) 5600.
6. State the meaning of the quotient of the numbers 1962 and 18. a) 19; b) 109; c) 1009; d) 1980.
7. Which action is performed last in the expression: 500 – 81: 3 × (9 + 1) a) subtraction; b) division; c) multiplication; d) addition.
8. Specify the perimeter of the rectangle with sides 3 cm and 5 cm. a) 8 cm; b) 16 cm; c) 15cm; d) 16 cm 2.
9. Indicate the side length of a square whose area is 16 cm 2 . a) 8cm; b) 4cm; c) 2cm; d) 32 cm.
10. We paid 90 rubles for 5 identical magazines. How much do two of these magazines cost? a) 18 rubles; b) 36 rubles; c) 180 rub.; d) 32 rub.
11. Express in minutes 3h 40 min. a) 160 min; b) 340 min; c) 220 min; d) 280 min.
12. What is the largest remainder that can be obtained when dividing a number by 16? a) 16; b) 15; c) 17; d) 10.
13. Solve the equation (25 – a) 7 = 63 a) 17; b) 16; c) 34; d) 416.
14. Which of the following entries is correct: a) 3 kg 55g = 355g; b) 3kg 55g = 3550g; c) 3kg 55g = 3055g; d) 3kg 55g = 30055g.
Mental counting, like everything else, has its tricks, and in order to learn to count faster you need to know these tricks and be able to apply them in practice.
Today we will do just that!
1. How to quickly add and subtract numbers
Let's look at three random examples:
- 25 – 7 =
- 34 – 8 =
- 77 – 9 =
Like 25 – 7 = (20 + 5) – (5- 2) = 20 – 2 = (10 + 10) – 2 = 10 + 8 = 18
Agree that such operations are difficult to carry out in your head.
But there is an easier way:
25 – 7 = 25 – 10 + 3, since -7 = -10 + 3
It is much easier to subtract 10 from a number and add 3 than to make complicated calculations.
Let's return to our examples:
- 25 – 7 =
- 34 – 8 =
- 77 – 9 =
Let's optimize the subtracted numbers:
- Subtract 7 = subtract 10 add 3
- Subtract 8 = subtract 10 add 2
- Subtract 9 = subtract 10 add 1
In total we get:
- 25 – 10 + 3 =
- 34 – 10 + 2 =
- 77 – 10 + 1 =
Now it’s much more interesting and easier!
Now calculate the examples below in this way:
- 91 – 7 =
- 23 – 6 =
- 24 – 5 =
- 46 – 8 =
- 13 – 7 =
- 64 – 6 =
- 72 – 19 =
- 83 – 56 =
- 47 – 29 =
2. How to quickly multiply by 4, 8 and 16
In the case of multiplication, we also break numbers into simpler ones, for example:
If you remember the multiplication table, then everything is simple. What if not?
Then you need to simplify the operation:
We put the largest number first, and decompose the second into simpler ones:
8 * 4 = 8 * 2 * 2 = ?
Doubling numbers is much easier than quadrupling or octupling them.
We get:
8 * 4 = 8 * 2 * 2 = 16 * 2 = 32
Examples of decomposing numbers into simpler ones:
- 4 = 2*2
- 8 = 2*2 *2
- 16 = 22 * 2 2
Practice this method using the following examples:
- 3 * 8 =
- 6 * 4 =
- 5 * 16 =
- 7 * 8 =
- 9 * 4 =
- 8 * 16 =
3. Dividing a number by 5
Let's take the following examples:
- 780 / 5 = ?
- 565 / 5 = ?
- 235 / 5 = ?
Dividing and multiplying with the number 5 is always very simple and enjoyable, because five is half of ten.
And how to solve them quickly?
- 780 / 10 * 2 = 78 * 2 = 156
- 565 /10 * 2 = 56,5 * 2 = 113
- 235 / 10 * 2 = 23,5 *2 = 47
To work through this method, solve the following examples:
- 300 / 5 =
- 120 / 5 =
- 495 / 5 =
- 145 / 5 =
- 990 / 5 =
- 555 / 5 =
- 350 / 5 =
- 760 / 5 =
- 865 / 5 =
- 1270 / 5 =
- 2425 / 5 =
- 9425 / 5 =
4. Multiplying by single digits
Multiplication is a little more difficult, but not much, how would you solve the following examples?
- 56 * 3 = ?
- 122 * 7 = ?
- 523 * 6 = ?
Without special counters, solving them is not very pleasant, but thanks to the “Divide and Conquer” method we can count them much faster:
- 56 * 3 = (50 + 6)3 = 50 3 + 6*3 = ?
- 122 * 7 = (100 + 20 + 2)7 = 100 7 + 207 + 2 7 = ?
- 523 * 6 = (500 + 20 + 3)6 = 500 6 + 206 + 3 6 =?
All we have to do is multiply single-digit numbers, some of which have zeros, and add the results.
To work through this technique, solve the following examples:
- 123 * 4 =
- 236 * 3 =
- 154 * 4 =
- 490 * 2 =
- 145 * 5 =
- 990 * 3 =
- 555 * 5 =
- 433 * 7 =
- 132 * 9 =
- 766 * 2 =
- 865 * 5 =
- 1270 * 4 =
- 2425 * 3 =
Divisibility of a number by 2, 3, 4, 5, 6 and 9
Check the numbers: 523, 221, 232
A number is divisible by 3 if the sum of its digits is divisible by 3.
For example, take the number 732, represent it as 7 + 3 + 2 = 12. 12 is divisible by 3, which means the number 372 is divisible by 3.
Check which of the following numbers are divisible by 3:
12, 24, 71, 63, 234, 124, 123, 444, 2422, 4243, 53253, 4234, 657, 9754
A number is divisible by 4 if the number consisting of its last two digits is divisible by 4.
For example, 1729. The last two digits form 20, which is divisible by 4.
Check which of the following numbers are divisible by 4:
20, 24, 16, 34, 54, 45, 64, 124, 2024, 3056, 5432, 6872, 9865, 1242, 2354
A number is divisible by 5 if its last digit is 0 or 5.
Check which of the following numbers are divisible by 5 (the easiest exercise):
3, 5, 10, 15, 21, 23, 56, 25, 40, 655, 720, 4032, 14340, 42343, 2340, 243240
A number is divisible by 6 if it is divisible by both 2 and 3.
Check which of the following numbers are divisible by 6:
22, 36, 72, 12, 34, 24, 16, 26, 122, 76, 86, 56, 46, 126, 124
A number is divisible by 9 if the sum of its digits is divisible by 9.
For example, take the number 6732, represent it as 6 + 7 + 3 + 2 = 18. 18 is divisible by 9, which means the number 6732 is divisible by 9.
Check which of the following numbers are divisible by 9:
9, 16, 18, 21, 26, 29, 81, 63, 45, 27, 127, 99, 399, 699, 299, 49
Game "Quick addition"
- Speeds up mental counting
- Trains attention
- Develops creative thinking
An excellent simulator for developing fast counting. A 4x4 table is given on the screen, and numbers are shown above it. The largest number must be collected in the table. To do this, click on two numbers whose sum is equal to this number. For example, 15+10 = 25.
Game "Quick Count"
The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer “yes” or “no” to the question “are there 5 identical fruits?” Follow your goal, and this game will help you with this.
Game "Guess the operation"
The game “Guess the Operation” develops thinking and memory. The main point of the game is to choose a mathematical sign for the equality to be true. Examples are given on the screen, look carefully and put the required “+” or “-” sign so that the equality is true. The “+” and “-” signs are located at the bottom of the picture, select the desired sign and click on the desired button. If you answered correctly, you score points and continue playing.
Game "Simplification"
The game “Simplification” develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical operation is given; the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need using the mouse. If you answered correctly, you score points and continue playing.
Today's task
Solve all examples and practice for at least 10 minutes in the game Quick Addition.
It is very important to work through all the tasks in this lesson. The better you complete the tasks, the more benefits you will receive. If you feel that you don’t have enough tasks, you can create examples for yourself and solve them and practice mathematical educational games.
Lesson taken from the course "Mal Calculus in 30 Days"
Learn to quickly and correctly add, subtract, multiply, divide, square numbers, and even take roots. I will teach you how to use easy techniques to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.
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