Multiplication and division of three-digit numbers assignments. Multiplication and division
Zaostrovye
2014
annotation
Lesson summary accompanied by a presentation on the topic Multiplication and division of three-digit numbers (Lesson of transferring existing knowledge to a new number concentration) for grade 3 in the school 2100 system. An 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 multiplying and dividing three-digit numbers, test on the card, textbook, (part 2).
Lesson 87 (§ 2.32).
Subject: Multiplying and dividing three-digit numbers (Lesson of transferring existing knowledge to a new number concentration)
Goals: introduce algorithms for oral techniques for multiplying and dividing three-digit numbers, similar to the same techniques for multiplying and dividing two-digit numbers
Tasks:
Educational:
Get acquainted with algorithms for oral techniques for multiplying and dividing three-digit numbers, similar to the same techniques for multiplying and dividing two-digit numbers.
Solve text problems of the studied type using a new numerical concentration.
Solve inequalities by selecting variable values.
Systematically repeat and consolidate what you have previously learned.
Educational: develop mental calculation skills, improve mental operations, the ability to argue one’s opinion, and mathematical abilities.
Educational: cultivate interest in the subject, curiosity, independence, accuracy, and the ability to listen to the teacher and his friends.
Form UUD:
Personal UUD: Independently determine and express the simplest rules of behavior common to all people in communication and cooperation. In independently created situations of communication and cooperation, based on simple rules of behavior common to everyone, make a choice about what action to take.
Regulatory learning activities: independently formulate lesson goals after preliminary discussion. Learn together with the teacher to discover and formulate an educational problem. Make a plan to solve the problem together with the teacher. Working according to the plan, check your actions with the goal and, if necessary, correct mistakes with the help of the teacher. In dialogue with the teacher, learn to develop evaluation criteria and determine the degree of success in performing your own work and the work of everyone, based on the existing criteria.
Communicative UUD: Convey your position to others: express your point of view and try to substantiate it by giving arguments. Listen to others, try to accept another point of view, be willing to change your point of view.
Cognitive UUD: Independently assume what information is needed to solve a learning task. Solve problems by analogy.
Symbols:
Lesson type: introducing 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 or shortcomings?
– Did you decide everything yourself or with someone’s help?
What level of difficulty was the task?
Do the guys have any additions or comments? Do you agree with this self-assessment?
Conclusion? Students: consolidated the ability to solve a text problem, in which they repeated multiplication and division, the order of actions, learned to compose and solve expressions, etc.
Test.
Well done! Here we end our journey. To get us back, try solving the test in groups. If you do it correctly, you should have a word. But first, let's remember the rules for working in groups. Do it.
1. How can you represent it as a product of two
multipliers 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 needs to be substituted for equality to be
63 * = 9 l) 7 b) 6 c) 8
4. What numbers have the quotient equal to 4?
a) 36 and 6 o) 24 and 6 c) 2 and 2
5. Find the numbers whose product is equal to 12?
a) 6 and 3 b) 2 and 7 c) 3 and 5 d) 6 and 2 f) 4 and 3
6. How much should you divide 48 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 b) 6 books c) 3 books
4 – working according to plan, check
your actions to 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 performing one’s own work and the work of everyone, based on the existing criteria.
Communicative UUD
We develop skills:
1.- convey your position to others: formalize your thoughts in oral and written speech (expressing the solution to a learning task in generally accepted forms) taking into account your learning speech situations;
TOUU
2 – convey your position to others: express your point of view and try to justify it by giving arguments;
3 – listen to others, try to accept 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 thing; to make plan;
5 – negotiate with people: performing various roles in a group, cooperate in jointly solving a problem (task).
Personal results:
1 – adhere to ethical standards of communication and cooperation when working together on a learning task;
Target audience: for 3rd grade.
If you want to learn how to multiply and divide round three-digit numbers in your head, then you are in luck, because in this lesson you will be able to 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. How great it is to be able to quickly count, do multiplication and division calculations! While everyone is thinking, you will already know the answer.
In this lesson we will look at two main techniques: representing a number as a sum of place value terms and representing a number as hundreds or tens. Let us also remember how examples are solved using the verification method. You will definitely have a good time. Forward to success and knowledge!
And appreciation and honor -
For everyone who loves mental arithmetic!
Sharpen your skills
In multiplication and division!
Choose the method you need -
Count quickly and have fun!
Multiplying and dividing a round three-digit number by a single-digit number can easily be 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. Let's remember the rule for multiplying a sum by a number.
When multiplying a sum by a number, each term must be multiplied by that number, and the resulting products added.
Let's remember the rule for dividing a sum by a number.
When dividing a sum by a number, you must divide each term by that number and add the resulting quotients.
Solution: 1. We break down the number 240 into its components and carry out the calculations:
2. Replace the first factor in the second example with the sum of the bit terms and find the product:
3. Let's do the same technique, only to find the quotient:
4. Let's repeat the operation in the last example, only here we replace the dividend not with bit terms, but with convenient terms:
You can use another method for multiplying and dividing three-digit numbers by a single-digit number.
Solution: 1. If we multiply the divisor by three, we get the dividend ninety.
2. Let's take two hundred and four times and get eight hundred - the dividend, 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 completely.
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 will use the technique of decomposition into bit terms:
3. In the last pair of examples, we use the selection method to solve:
, examination
Summary of an open lesson in 3rd grade.
Volkova Lyubov Andreevna, primary school teacher.
Lesson type: combined.
Target: - consolidate the ability to divide and multiply three-digit numbers by a single-digit number;
Develop 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 mental counting skills;
Improve the ability to solve problems and examples;
Develop mental processes - memory, thinking, attention;
To foster communicative relationships between students and a sense of teamwork;
Cultivate interest in the subject;
Cultivate a child’s interest in the subject and knowledge of the world.
Equipment: textbook, workbook, colored task cards for differentiated work, computer, presentation, poster (digits of three-digit numbers), picture with a picture of a cat.
During the classes.
Organizing time.
(slide 1)
There are many interesting things in life,
But so far 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 and practice multiplying and dividing them. Our lesson today will begin in an unusual way. Listen to the melody from a well-known cartoon.
An excerpt from the song “There is nothing better in the world…” is played (30 sec., slide 1)
Teacher: Do you recognize the melody? From what cartoon?
Children: Bremen Town Musicians.
Teacher: That's right! Today in the lesson we will solve problems and find the meaning of expressions together with the troubadour and the Bremen musicians.
(slide 2)
Verbal counting.
a) And here is the first task!(slide 3) The Bremen musicians staged a performance in the city square. The first number with the sign is 75:15. Who's speaking next?
Children find the meaning of expressions by reasoning out loud. The answer to the previous example serves as the beginning of each next one.
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 a question, and you will name a number.(The work is carried out on a chalkboard, under a table with the ranks of three-digit numbers and a picture of a cat).
Now a number will appear in which there are 5 hundreds, 6 tens and 2 ones.
…… 30 tens.
… 4 hundreds.
A number that is greater than 289 by 1
A number that is less than 658 by 1.
Fizminutka (game “attention”)
Updating knowledge. Statement of a problematic question.
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 examples here with solutions that we have not yet met.
Teacher: Let's reason and find a solution to the problem.
We open the notebooks, write down the number, cool work, No. 1
Discovery of new knowledge.
One student decides at the board, the rest of the students do the work in their notebooks. When we reach the fourth column, we display a “new” technique for dividing a three-digit number. We divide a three-digit number into round two-digit and three-digit numbers, reasoning 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
Consolidation
Textbook assignments page 56 No. 5 (1, 2 columns)
One student works at the board, reasoning out loud, the rest in their notebooks.
Problem No. 8 p. 56
The teacher, together with the children, makes a short note on the board and analyzes the stages of solving the problem. One student solves the problem from the back of the board. At the end there is a check: students compare their notes with the notes on the board. Compare the answer with the answer on the slide(slide 8)
Physical exercise (eye exercises)
Working with cards.
Solving problems of two levels of complexity. For successful students, the text of the problem coincides with the text of problem No. 9 from the textbook.
Card level 1 (green card)
Bremen musicians gave a concert for city residents. The audience heard 27 songs, which is 8 less than dance tunes. How many pieces of music were performed in the concert?
Card level 2 (red card)
Bremen musicians gave a concert for city residents. The audience heard 27 songs, which is 8 less than dance tunes. These musical works were performed in two parts of the concert, equally divided in each part. How many pieces of music were performed in each department?
Compilation of a short note for both tasks is discussed together with the teacher.(slide 13-14)
Independent work of the guys.
Lesson summary.
Teacher: Every lesson we try to learn more than we knew. Let's go up a step. What new have we learned today?
(Learned to divide three-digit numbers into round two-digit and three-digit numbers)
Homework.
The task is offered to the children at different levels. Written with multi-colored chalk on a blackboard.
In green (for everyone): p. 56 No. 5 (3.4 columns), No. 7.
With red chalk (for those who want something more complicated): p.56 No. 6, No. 10.
Additional task (if there is time left)
Slide 15
Write down the names of all polygons containing angle ABC (No. 11 p. 56)
Slide 16 Well done!
Municipal state educational institution Lyceum No. 7
Summary of an open mathematics lesson.
Multiplying and dividing three-digit numbers by single-digit numbers.
Primary school teacher
Volkova Lyubov Andreevna
Solnechnogorsk
2013
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 as a whole class (25 people) donate money and buy a gift for the teacher, but you don’t spend it all, there will be change left over. So you will need to divide the change among everyone. The division operation comes into play to help you solve this problem.
Division is an interesting operation, as we will see in this article!
Dividing numbers
So, a little theory, and then practice! What is division? Division is breaking something into equal parts. That is, it could be a bag of sweets that needs to be divided into equal parts. For example, there are 9 candies in a bag, and the person who wants to receive them is three. Then you need to divide these 9 candies among 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 three numbers contained in the number 9. The reverse action, a check, will be multiplication. 3*3=9. Right? Absolutely.
So let's look at example 12:6. First, let's name each component of the example. 12 – dividend, that is. a number that can be divided into parts. 6 is a divisor, this is the number of parts into which the dividend is divided. And the result will be a number called “quotient”.
Let's 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 a 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, then the answer will be 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. The answer then 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 would be division by the number 3 and the number 9. If you want to find out 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 is 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 remainder.
For example, the number 63. The sum of the digits is 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 whether it is divisible with the remainder by 3 or 9, or not.
Multiplication and division
Multiplication and division are opposite operations. Multiplication can be used as a test for division, and division can be used as a test for multiplication. You can learn more about multiplication and master the operation in our article about multiplication. Which describes multiplication in detail and how to do 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 the example is 6*4. Answer: 24. Then let's check the answer by division: 24:4=6, 24:6=4. It was decided correctly. In this case, the check is performed by dividing the answer by one of the factors.
Or an example is given for the division 56:8. Answer: 7. Then the test will be 8*7=56. Right? Yes. In this case, the test is performed by multiplying the answer by the divisor.
Division 3 class
In third grade they are just starting to go through division. Therefore, third graders solve the simplest problems:
Problem 1. A factory worker was given the task of putting 56 cakes into 8 packages. How many cakes should be put in each package to make the same amount in each?
Problem 2. On New Year's Eve at school, children in a class of 15 students were given 75 candies. How many candies should each child receive?
Problem 3. Roma, Sasha and Misha picked 27 apples from the apple tree. How many apples will each person get if they need to be divided equally?
Problem 4. Four friends bought 58 cookies. But then they realized that they could not divide them equally. How many additional cookies do the kids need to buy so that each gets 15?
Division 4th grade
The division in the fourth grade is more serious than in the third. All calculations are carried out using the column division method, and the numbers involved in the division are not small. What is long division? You can find the answer below:
Column division
What is long division? This is a method that allows you to find the answer to dividing large numbers. If prime numbers like 16 and 4 can be divided, and the answer is clear - 4. Then 512:8 is not easy for a child in his mind. And it’s our task to talk about the technique for solving such examples.
Let's look at an example, 512:8.
1 step. Let's write the dividend and divisor as follows:
The quotient will ultimately be written under the divisor, and the calculations under the dividend.
Step 2. We start dividing from left to right. First we take the number 5: 
Step 3. The number 5 is less than the number 8, which means it will not be possible to divide. Therefore, we take another digit of the dividend:
Now 51 is greater than 8. This is an incomplete quotient.
Step 4. We put a dot under the divisor.
Step 5. After 51 there is another number 2, which means there will be one more number in the answer, that is. quotient is a two-digit number. Let's put the second point:
Step 6. We begin the division operation. The largest number divisible by 8 without a remainder to 51 is 48. Dividing 48 by 8, we get 6. Write the number 6 instead of the first dot under the divisor:
Step 7. Then write the number exactly below the number 51 and put a “-” sign:
Step 8. Then we subtract 48 from 51 and get the answer 3.
* 9 step*. We take down the number 2 and write it next to the number 3:
Step 10 We divide the resulting number 32 by 8 and get the second digit of the answer – 4.
So the answer is 64, without remainder. If we divided the number 513, then the remainder would be one.
Division of three digits
Dividing three-digit numbers is done using the long division method, which was explained in the example above. An example of just a 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 method of this division is quite simple. 2/3 is the dividend, 1/4 is the divisor. You can replace the division sign (:) with multiplication ( ), but to do 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 better understanding. Consider the fractions (4/7):(2/5):
As in the previous example, we reverse the 2/5 divisor and get 5/2, replacing division with multiplication. We then get (4/7)*(5/2). We make a reduction and answer: 10/7, then take out the whole part: 1 whole and 3/7.
Dividing numbers into classes
Let's imagine the number 148951784296, and divide it into 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 digit. 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 ones, 9 is tens, 2 is hundreds.
Division of natural numbers
Division of natural numbers is the simplest division described in this article. It can be either with or without a remainder. The divisor and dividend can be any non-fractional, integer numbers. 
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Division presentation
Presentation is another way to visualize the topic of division. Below we will find a link to an excellent presentation that does a good job of explaining how to divide, what division is, what dividend, divisor and quotient are. Don’t waste your time, but consolidate your knowledge!
Examples for division
Easy level
Average level
Difficult level
Games for developing mental arithmetic
Special educational games developed with the participation of Russian scientists from Skolkovo will help improve mental arithmetic skills in an interesting game form.
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.
Game "Quick addition"
The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers whose sum is equal to a given number. In this game, a matrix from one to sixteen is given. A given number is written above the matrix; you need to select the numbers in the matrix so that the sum of these digits is equal to the given number. If you answered correctly, you score points and continue playing.
Visual Geometry Game
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, you need to quickly count them, then they close. Below the table there are four numbers written, you need to select one correct number and click on it with the mouse. If you answered correctly, you score points and continue playing.
Game "Piggy Bank"
The Piggy Bank game develops thinking and memory. The main essence of the game is to choose which piggy bank has more money. In this game there are four piggy banks, you need to count which piggy bank has the most money and show this piggy bank with the mouse. If you answered correctly, then you score points and continue playing.
Game "Fast addition reload"
The game “Fast addition reboot” develops thinking, memory and attention. The main point of the game is to choose the correct terms, the sum of which will be equal to the given number. In this game, three numbers are given on the screen and a task is given, add the number, the screen indicates which number needs to be added. You select the desired numbers from three numbers and press them. If you answered correctly, then you score points and continue playing.
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« Oral techniques for multiplying and dividing three-digit numbers."
Goals:
1. Teach how 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 units of measurement.
4. Consolidate knowledge of the multiplication tables.
5. Build computational skills and develop logical thinking.
6. Develop students’ cognitive activity when studying mathematics.
Tasks: develop the ability to search for information and work with it;
develop the ability to substantiate and defend the expressed judgment;
develop motivation for learning activities and interest in acquiring knowledge and methods of action;
cultivate interest in the subject and activity.
Org. moment
Children, today is a wonderful day. Look, I smile at you and you will smile at me. Turn to each other and smile. Well done, sit down at your desks. You can feel how warm and bright our class has become from the smiles.
Rook offers you a game called “Tangram”. Take envelopes with geometric shapes and make a silhouette drawing of a rook from them. (work in pairs).
- Look what a rook I made. Compare.
— Tell me, what figures did you use?
— How many triangles?
- What other geometric figures do you know?
Rook asks you to remember what you learned in previous lessons, so how will this knowledge 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 hundred, 11 des.
3. Increase the numbers by 10 times: 42, 27, 91, 65, 73, 58.
2. Blitz survey
1.Volodya stayed with his grandmother for two weeks and another 4 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 are there than old ones? (for 19 apple trees)
- Well done! Well done. Let `s have some rest.
3. Physical exercise
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 and find the value.
— What groups did you divide these expressions into?
— Which tasks are more difficult for you to cope with? (Why do you think?)
- What was the difficulty?
(In that one column contains three-digit numbers)
— Try to set a learning task for today’s lesson yourself.
(Learn to multiply and divide three-digit numbers orally)
5. Report the topic of the lesson. Setting educational objectives.
The topic of today's lesson: “Techniques for mental calculations within 1000”
— 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. Getting to know new material.
Let's try to solve the expression: 120*4. To orally multiply a number by a single-digit factor, perform the action, starting the multiplication not with units, as in written multiplication, but differently: first multiply hundreds, 100 * 4 = 400, then tens 20 * 4 = 80, after one, but we will study this later As a result, we add the resulting numbers 400+80=480
Let's try to solve the division expression: 820:2. To verbally divide a number into 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 a tractor plow, is capable of destroying 420 plant pests in a day. How many worms will a rook eat in 2 days?
— What does the problem statement say?
- What question needs to be answered?
— How many actions do you need to perform to do this?
— How can you find out how many worms a rook will eat in two days?
— Write down the solution to the problem in your notebook.
- What answer did you get?
- Who agrees with... show me.
- How did you think?
— Guys, you coped very well with the tasks that the birds offered you.
Lesson summary. Reflection.
— Guys, have we completed our tasks?
