If you want to mentally learn how to multiply and divide round three-digit numbers, then you are in luck, because it is in this lesson that you can do it. If you do not know or know, but poorly, how to multiply and divide round three-digit numbers, then this lesson is designed specifically for you. It's great to be able to quickly count, do calculations for multiplication and division! While everyone is thinking, you will already know the answer.
In this lesson, we will look at two basic techniques: representing a number as a sum of place terms and representing a number as hundreds or tens. Let us also recall how the examples are solved by the verification method. You will definitely make good use of your time. Forward to success and knowledge!
And appreciation, and honor -
Anyone who loves mental counting!
Sharpen your skills
In multiplication and division!
Choose the method you need -
Count fast, have fun!
Multiplication and division of a round three-digit number by a single-digit number can be easily replaced by hundreds and tens.
Solution: 1. Replace the number 180 with tens:
2. In the second example, we replace the number 900 with hundreds:
Let's get acquainted with another method of mental calculations and solve examples. Remember the rule for multiplying a sum by a number.
When multiplying a sum by a number, it is necessary to multiply each term by this number, and add the resulting products.
Remember the rule for dividing a sum by a number.
When dividing a sum by a number, each term must be divided by this number, and the resulting quotients must be added.
Solution: 1. We decompose the number 240 into components and carry out calculations:
2. Let's replace the first factor in the second example with the sum of bit terms and find the product:
3. Let's do the same technique, only to find the quotient:
4. Repeat the operation on last example, only here we replace the dividend not with bit terms, but with convenient terms:
You can use another method of multiplying and dividing three-digit numbers by a single-digit number.
Solution: 1. If we multiply the divisor by three, we get the divisible ninety.
2. Let's take two hundred and four times and get eight hundred - divisible, therefore, the selection was made correctly.
.
If you cannot find the correct answer the first time, you must continue to select numbers until the results match.
Solve the examples in figure 1.
Rice. 1. Examples
Solution: 1. In the first and second examples, replace the first numbers with hundreds:
2. In the third and fourth examples, we use the decomposition into bit terms:
3. In the last couple of examples, we use the selection method to solve:
, examination
Division is one of the four basic mathematical operations (addition, subtraction, multiplication). Division, like other operations, is important not only in mathematics, but also in Everyday life. For example, you will hand over the money with a whole class (25 people) and buy a gift for the teacher, but you will not spend everything, there will be change. So you will have to share the change among all. The division operation comes into play to help you solve this problem.
Division is an interesting operation, as we will see with you in this article!
Number division
So, a little theory, and then practice! What is division? Division is breaking something into equal parts. That is, it can be a package of sweets that needs to be divided into equal parts. For example, there are 9 sweets in a bag, and the person who wants to receive them has three. Then you need to divide these 9 sweets into three people.
It is written like this: 9:3, the answer will be the number 3. That is, dividing the number 9 by the number 3 shows the number of numbers three contained in the number 9. The reverse action, the test, will be multiplication. 3*3=9. Right? Absolutely.
So, consider the example of 12:6. First, let's name each component of the example. 12 - divisible, that is. number that is divisible. 6 - divisor, this is the number of parts into which the dividend is divided. And the result will be a number called "private".
Divide 12 by 6, the answer will be the number 2. You can check the solution by multiplying: 2*6=12. It turns out that the number 6 is contained 2 times in the number 12.
Division with remainder
What is division with remainder? This is the same division, only the result is not an even number, as shown above.
For example, let's divide 17 by 5. Since the largest number divisible by 5 to 17 is 15, the answer is 3 and the remainder is 2, and is written like this: 17:5=3(2).
For example, 22:7. In the same way, we determine the maximum number divisible by 7 to 22. This number is 21. Then the answer will be: 3 and the remainder 1. And it is written: 22:7=3(1).
Division by 3 and 9
A special case of division will be division by the number 3 and the number 9. If you want to know whether a number is divisible by 3 or 9 without a remainder, then you will need:
Find the sum of the digits of the dividend.
Divide by 3 or 9 (depending on what you need).
If the answer is obtained without a remainder, then the number will be divided without a remainder.
For example, the number 18. The sum of the digits 1+8 = 9. The sum of the digits is divisible by both 3 and 9. The number 18:9=2, 18:3=6. Divided without a trace.
For example, the number 63. The sum of the digits 6+3 = 9. Divisible by both 9 and 3. 63:9=7, and 63:3=21. Such operations are carried out with any number to find out if it is divisible with the remainder 3 or 9 or not.
Multiplication and division
Multiplication and division are opposite operations. Multiplication can be used as a division test, and division as a multiplication test. You can learn more about multiplication and master the operation in our article about multiplication. In which multiplication is described in detail and how to perform it correctly. There you will also find the multiplication table and examples for training.
Here is an example of checking division and multiplication. Let's say an example is 6*4. Answer: 24. Then let's check the answer by division: 24:4=6, 24:6=4. Decided right. In this case, the check is made by dividing the answer by one of the factors.
Or an example is given for dividing 56:8. Answer: 7. Then the test will be 8*7=56. Right? Yes. In this case, the check is made by multiplying the answer by the divisor.
Division 3 class
In the third grade, division is just beginning to pass. Therefore, third-graders solve the simplest problems:
Task 1. A factory worker was given the task of putting 56 cakes into 8 packages. How many cakes must be put in each package to get the same amount in each?
Task 2. On New Year's Eve, the school gave out 75 sweets to children in a class of 15 students. How many candies should each child get?
Task 3. Roma, Sasha and Misha picked 27 apples from the apple tree. How many apples will each get if they need to be divided equally?
Task 4. Four friends bought 58 cookies. But then they realized that they could not divide them equally. How many cookies do you need to buy for each child to get 15 cookies?
Division 4 class
Division in the fourth grade is more serious than in the third. All calculations are carried out by dividing into a column, and the numbers that participate in the division are not small. What is division into a column? You can find the answer below:
Long division
What is division into a column? This is a method that allows you to find the answer to the division of large numbers. If prime numbers like 16 and 4, can be divided, and the answer is clear - 4. That 512:8 in the mind is not easy for a child. And to tell about the technique for solving such examples is our task.
Consider the example, 512:8.
1 step. We write the dividend and the divisor as follows:
The quotient will be written as a result under the divisor, and the calculations under the dividend.
2 step. The division starts from left to right. Let's take number 5 first. 
3 step. The number 5 is less than the number 8, which means that it will not be possible to divide. Therefore, we take one more digit of the dividend:
Now 51 is greater than 8. This is an incomplete quotient.
4 step. We put a dot under the divider.
5 step. After 51 there is another number 2, which means that the answer will have one more number, that is. quotient is a two-digit number. We put the second point:
6 step. We begin the division operation. The largest number divisible without a remainder by 8 to 51 is 48. Dividing 48 by 8, we get 6. We write the number 6 instead of the first point under the divisor:
7 step. Then we write the number exactly under the number 51 and put the "-" sign:
8 step. Then subtract 48 from 51 and get the answer 3.
* 9 step*. We demolish the number 2 and write next to the number 3:
10 step The resulting number 32 is divided by 8 and we get the second digit of the answer - 4.
So, the answer is 64, without a trace. If we divided the number 513, then the remainder would be one.
Three-digit division
The division of three-digit numbers is performed using the long division method, which was explained using the example above. An example of just the same three-digit number.
Division of fractions
Dividing fractions is not as difficult as it seems at first glance. For example, (2/3):(1/4). The division method is quite simple. 2/3 is the dividend, 1/4 is the divisor. You can replace the division sign (:) with multiplication ( ), but for this you need to swap the numerator and denominator of the divisor. That is, we get: (2/3)(4/1), (2/3) * 4, this is equal to - 8/3 or 2 integers and 2/3. Let's give another example, with an illustration for a better understanding. Consider fractions (4/7):(2/5):
As in the previous example, we flip the divisor 2/5 and get 5/2, replacing division with multiplication. We get then (4/7)*(5/2). We make a reduction and answer: 10/7, then we take out the whole part: 1 whole and 3/7.
Dividing a Number into Classes
Let's imagine the number 148951784296, and divide it by three digits: 148 951 784 296. So, from right to left: 296 is the class of units, 784 is the class of thousands, 951 is the class of millions, 148 is the class of billions. In turn, in each class 3 digits have their own category. From right to left: the first digit is units, the second digit is tens, the third is hundreds. For example, the class of units is 296, 6 is units, 9 is tens, 2 is hundreds.
Division of natural numbers
Division natural numbers- this is the simplest division described in this article. It can be both with a remainder and without a remainder. The divisor and dividend can be any non-fractional, whole numbers. 
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division presentation
The presentation is another way to visually show the topic of division. Below we will find a link to an excellent presentation that explains well how to divide, what division is, what is dividend, divisor and quotient. Don't waste your time and consolidate your knowledge!
Division examples
Easy level
Average level
Difficult level
Games for the development of mental counting
Special educational games developed with the participation of Russian scientists from Skolkovo will help improve oral counting skills in an interesting game form.
Game "Guess the operation"
The game "Guess the operation" develops thinking and memory. Main essence game, you need to choose a mathematical sign for the equality to be true. Examples are given on the screen, look carefully and put the desired “+” or “-” sign so that the equality is true. The sign "+" and "-" are located at the bottom of the picture, select the desired sign and click on the desired button. If you answer correctly, you score points and continue playing.
Game "Simplify"
The game "Simplify" 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 action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and continue playing.
Game "Fast Addition"
The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers, the sum of which is equal to a given number. This game is given a matrix from one to sixteen. A given number is written above the matrix, you must select the numbers in the matrix so that the sum of these numbers is equal to the given number. If you answer correctly, you score points and continue playing.
Game "Visual Geometry"
The game "Visual Geometry" develops thinking and memory. The main essence of the game is to quickly count the number of shaded objects and select it from the list of answers. In this game, blue squares are shown on the screen for a few seconds, they must be quickly counted, then they close. Four numbers are written below the table, you must select one correct number and click on it with the mouse. If you answer correctly, you score points and continue playing.
Piggy bank game
The game "Piggy bank" develops thinking and memory. The main essence of the game is to choose which piggy bank has more money. In this game, four piggy banks are given, you need to count which piggy bank has more money and show this piggy bank with the mouse. If you answer correctly, then you score points and continue to play further.
Game "Fast addition reload"
The game "Fast Addition Reboot" develops thinking, memory and attention. The main essence of the game is to choose the correct terms, the sum of which will be equal to given number. In this game, three numbers are given on the screen and the task is given, add the number, the screen indicates which number to add. You choose from three numbers the right numbers and press them. If you answer correctly, then you score points and continue to play further.
Development of phenomenal mental arithmetic
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« Oral techniques for multiplying and dividing three-digit numbers.
Goals:
1. Learn to multiply and divide multi-digit numbers;
2. Repeat the commutative property of multiplication and the property of multiplying a sum by a number;
3. Repeat the units of measure.
4. Consolidate knowledge of the multiplication table.
5. Form computational skills and develop logical thinking.
6. To develop the cognitive activity of students in the study of mathematics.
Tasks: to form the ability to search for information and work with it;
develop the ability to reasonably substantiate and defend the stated judgment;
develop motivation learning activities and interest in acquiring knowledge and ways of doing things;
educate interest in the subject, activity.
Org. moment
Children, today is a wonderful day. Look, I smile at you and you smile at me. Turn to each other and smile. Well done, take a seat. Feel how warm and bright it became in our class from smiles.
Rook offers you a game called Tangram. Take envelopes with geometric shapes and make a silhouette drawing of a rook out of them. (work in pairs).
- Look what a rook I got. Compare.
- Tell me, what figures did you use?
- How many triangles?
- And what else geometric figures You know?
The rook asks you to remember what you learned in the past lessons, since this knowledge will be useful to us today?
1. Read the numbers: 540, 700, 210, 900, 650, 380,400, 820
- Indicate the number of hundreds and tens in each of them.
2. Name the number in which: 87dec., 5hundred., 64dec., 3hundred., 25dec., 49dec.,
7 cells, 11des.
3. Increase 10 times the numbers: 42, 27, 91, 65, 73, 58.
2. Blitz Poll
1. Volodya stayed with his grandmother for two weeks and 4 more days. How many days did Volodya stay with his grandmother? (18 days)
2. Vitya swam 26 meters. He swam 4 meters less than Seryozha. How many meters did Seryozha swim? (30 meters)
3. There are 38 old apple trees and 19 young ones in the garden. How many fewer young apple trees than old ones? (for 19 apple trees)
- Well done! Well done. Let `s have some rest.
3. Physical Minute
4. Introduction to the topic.
What groups can the following expressions be divided into:
15 ∙ 4 200 ∙ 4
320 ∙ 2 25 ∙ 3
Write them down in 2 columns, find the value.
What groups did you divide these expressions into?
What tasks are more difficult for you to handle? (Why do you think?)
- What was the problem?
(In that one column - with three-digit numbers)
- Try to set a learning task for today's lesson.
(Learn to multiply and divide three-digit numbers verbally)
5. Post the topic of the lesson. Statement of educational tasks.
The topic of today's lesson: "Receptions of oral calculations within 1000"
- And what do we need to do to make it easier to solve such examples? ( Listen to the teacher's explanation, read the information in the textbook, listen to classmates, remember the multiplication and division tables, practice solving such examples, etc.)
6. Acquaintance with new material.
Let's try to solve the expression: 120*4. In order to verbally multiply a number by a single-digit factor, an action is performed, starting multiplication not from units, as in written multiplication, but otherwise: hundreds are multiplied first, 100 * 4 = 400, then tens 20 * 4 = 80, after one, but we will study this later as a result, add up the resulting numbers 400 + 80 = 480
Let's try to solve the division expression: 820:2. To verbally divide a number by a single-digit factor, perform the same action as in the multiplication method. First we divide the hundreds 800:2=400, then the tens 20:2=10, then we add the results 400+10=410 Let's try to do it together:
230 * 4 = 200 * 4 + 30 * 4=920; 360: 4 =300:4(75)+60:4(15)=90
150 * 4 =100*4+50*4=600; 680: 4 =600:4(150)+80:4(20)=170
TASK. One rook, following the plow of a tractor, is capable of destroying 420 plant pest worms in a day. How many worms will a rook eat in 2 days?
What does the condition of the problem say?
What question should be answered?
How many steps do you need to take to get it done?
- How to find out how many worms a rook will eat in two days?
- Write the solution to the problem in your notebook.
- What answer did you get?
- Who agrees with ... show.
- How did you think?
- Guys, you did a very good job with the tasks that the birds offered you.
Summary of the lesson. Reflection.
- Guys, did we cope with the tasks?
Zaostrovie
2014
annotation
Lesson summary accompanied by a presentation on the topic Multiplication and division of three-digit numbers (Lesson transferring existing knowledge to a new numerical concentrator) for grade 3 according to the school 2100 system. Entertaining selection of material, various forms of work increase students' interest in the material being studied .. The lesson was developed within the framework of the Federal State Educational Standard .
Equipment: presentation, cards with examples A and B for multiplication and division of three-digit numbers, test on the card, textbook, (part 2).
Lesson 87 (§ 2.32).
Subject: Multiplication and division of three-digit numbers (Lesson of transferring existing knowledge to a new numerical concentration)
Goals: introduce algorithms for oral methods of multiplying and dividing three-digit numbers, similar to the same methods for multiplying and dividing two-digit numbers
Tasks:
Educational:
To get acquainted with the algorithms of oral methods for multiplying and dividing three-digit numbers, similar to the same methods for multiplying and dividing two-digit numbers.
Solve text problems of the studied type on a new numerical concentrator.
Solve inequalities by selecting variable values.
Systematically repeat and reinforce previously learned.
Developing: develop oral numeracy skills mental operations, the ability to argue one's opinion, mathematical abilities.
Educational: to cultivate interest in the subject, curiosity, independence, accuracy, the ability to listen to the teacher and his comrades.
Form UUD:
Personal UUD: Independently determine and express the simplest rules of conduct common to all people in communication and cooperation. In self-created situations of communication and cooperation, relying on simple rules of behavior common to all, make a choice of what action to take.
Regulatory UUD: independently formulate the objectives of the lesson after a preliminary discussion. Learn to identify and formulate a learning problem together with the teacher. Make a plan to solve the problem together with the teacher. Working according to the plan, compare your actions with the goal and, if necessary, correct mistakes with the help of a teacher. In dialogue with the teacher, learn to develop evaluation criteria and determine the degree of success in the performance of one's work and the work of everyone, based on the existing criteria.
Communicative UUD: Communicate your position to others: express your point of view and try to justify it, giving arguments. Listen to others, try to take a different point of view, be ready to change your point of view.
Cognitive ECM: Independently guess what information is needed to solve learning task. Solve problems by analogy.
Symbols:
Lesson type: introduction of new knowledge
Teaching methods: visual, verbal, problem-search.
What did you have to do in the task?
- Did you manage to solve the assigned tasks correctly?
- Did you do everything right or were there mistakes, shortcomings?
Did you decide everything on your own or with someone else's help?
What was the difficulty level of the task?
Do the guys have any additions, comments? Do you agree with this self-assessment?
Conclusion? Pupils: consolidated the ability to solve a text problem, in which they repeated multiplication and division, the procedure, learned to compose and solve expressions, etc.
Test.
Well done! Here we end our journey. In order for us to go back, try to solve the test in groups. If you do it right, you should have a word. But first, let's remember the rules of working in groups. Do it.
1. As can be represented as a product of two
multiplier number 24 ?
a) 8 * 2 b) 7 * 3 m) 8 * 3 d) 3 * 6
2. What number is divisible by 6?
a) 46 o) 42 c) 28
3. What number should be substituted for equality to be
63 * = 9 l) 7 b) 6 c) 8
4. What private numbers is 4?
a) 36 and 6 o) 24 and 6 c) 2 and 2
5. Find the numbers whose product is 12?
a) 6 and 3 b) 2 and 7 c) 3 and 5 e) 6 and 2 f) 4 and 3
6. By how much should 48 be divided to get 6?
c) by 8 b) by 7 c) by 6
7. There were 18 books on the top shelf, and on the bottom - 3 times less than on the top. How many books were on the bottom shelf?
a) 9 books s) 6 books c) 3 books
4 - working according to plan, check
their actions with the goal and, if necessary, correct errors using the class;
5 - in dialogue with the teacher and other students, learn to develop evaluation criteria and determine the degree of success in the performance of their work and the work of everyone, based on the existing criteria.
Communicative UUD
We develop skills:
1.- convey your position to others: formulate your thoughts orally and writing(expression of the solution of the educational problem in generally accepted forms), taking into account their educational speech situations;
TOUU
2 - communicate your position to others: express your point of view and try to justify it, giving arguments;
3 - listen to others, try to take a different point of view, be ready to change
questions to the text and look for answers; check yourself;
separate the new from the known;
highlight the main to make plan;
5 - negotiate with people: performing various roles in a group, cooperate in a joint solution of a problem (task).
Personal results:
1 - adhere to ethical standards of communication and cooperation when working together on a learning task;
Target Audience: 3rd grade.
Abstract of an open lesson in grade 3.
Volkova Lyubov Andreevna, primary school teacher.
Lesson type: combined.
Target: - to consolidate the ability to divide and multiply three-digit numbers by a single-digit number;
To form the ability to perform calculations of the form 800: 200; 630:90 (dividing three-digit numbers into round three-digit and two-digit numbers);
Tasks:
Continue to develop oral counting skills;
Improve the ability to solve problems and examples;
Develop mental processes - memory, thinking, attention;
To cultivate communicative relations between students, a sense of collectivism;
Raise interest in the subject;
To educate the child's interest in the subject, knowledge of the world.
Equipment: textbook, workbook, colored task cards for differentiated work, a computer, a presentation, a poster (digits of three-digit numbers), a picture of a cat.
During the classes.
Organizing time.
(slide 1)
There are many interesting things in life
But while unknown to us,
And learn a lot.
Teacher: Guys, I see that you are all ready for the lesson. Sit down. We continue to study three-digit numbers, we train to multiply and divide them. Today's lesson will start unusually. Listen to the melody from the famous cartoon.
An excerpt from the song “There is nothing better in the world ...” sounds (30 sec., slide 1)
Teacher: Did you recognize the tune? From what cartoon?
Children: Bremen town musicians.
Teacher: Right! Today in the lesson we will solve problems and find the meanings of expressions together with the troubadour and the Bremen town musicians.
(slide 2)
Verbal counting.
a) And here is the first task!(slide 3) The Bremen Town Musicians staged a performance on the town square. The first room with a sign 75:15. Who's next?
Children find the meaning of expressions by reasoning aloud. The answer to the previous example serves as the beginning of each following.
b)slide 4
Teacher: Let's imagine that the Cat from the Bremen Town Musicians decided to show tricks with three-digit numbers. I will ask the question, and you will name the number.(Work in progress on chalkboard, below the table with digits of three-digit numbers and the image of a cat).
Now a number will appear in which 5 hundreds 6 tens and 2 units.
…… 30 tens.
… 4 hundreds.
The number that more number 289 for 1
A number that is less than 658 by 1.
Fizminutka (game "attention")
Knowledge update. Problem statement.
Teacher: Let's check how we learned to multiply and divide three-digit numbers. The rooster prepared examples.(Slide 5)
Look, have we already solved all kinds of examples? The rooster hid here examples with methods for solving which we have not yet met.
Teacher: Let's talk and find a solution to the problem.
Open notebooks, write down the number, class work, No. 1
Discovery of new knowledge.
At the blackboard, one student decides, the rest of the students in the notebook. When we reach the fourth column, we display the “new” method of dividing a three-digit number. We divide a three-digit number into round two-digit and three-digit ones, arguing as follows (by analogy with dividing round two-digit numbers):
800: 200 = 4 since 4*200 = 800 (slide 6)
We confirm the validity of our conclusion with the rule in the textbook on page 55
Anchoring
Textbook tasks p. 56 No. 5 (1, 2 columns)
One student works at the blackboard, thinks aloud, the rest in notebooks.
Task number 8 p. 56
The teacher, together with the children, makes a short note on the board, analyzes the stages of solving the problem. One student solves the problem on the back of the board. At the end of the check: students check their record with the record on the board. The answer is compared with the answer on the slide(slide 8)
Fizminutka (exercises for the eyes)
Working with cards.
Solving problems of two levels of complexity. For successful students, the text of the task is the same as the text of task No. 9 from the textbook.
Card level 1 (green card)
The Bremen Town Musicians gave a concert for the inhabitants of the city. The audience heard 27 songs, which is 8 less than dance melodies. How many pieces of music were performed in the concert?
Card level 2 (red card)
The Bremen Town Musicians gave a concert for the inhabitants of the city. The audience heard 27 songs, which is 8 less than dance melodies. These pieces of music were performed in two parts of the concert, equally in each part. How many pieces of music were performed in each section?
The preparation of a short note for both tasks is analyzed together with the teacher.(slide 13-14)
Children's independent work.
Lesson results.
Teacher: Every lesson we try to learn more than we knew. Let's go up a step. What new did we learn today?
(We learned to divide three-digit numbers into round two-digit and three-digit ones)
Homework.
The task is offered to the children at different levels. Written with colored chalk on a blackboard.
In green (for all): p. 56 No. 5 (3.4 columns), No. 7.
With red chalk (for those who want it more difficult): p.56 No. 6, No. 10.
Additional task (if there is time)
slide 15
Write down the names of all polygons containing the angle ABC (No. 11 p. 56)
slide 16 Well done!
Municipal State Educational Institution Lyceum No. 7
Abstract of an open lesson in mathematics.
Multiplication and division of three-digit numbers by single-digit numbers.
Primary school teacher
Volkova Lyubov Andreevna
Solnechnogorsk
2013
