Multiplication by a single number in a column 3. Stage I - Multiplication by a single number

Abstract of a mathematics lesson, grade 3, Federal State Educational Standard OS "Perspective".

Lesson topic. Multiplication by a single-digit number by a column.

Lesson type: lesson learning new material

Target: building a model of a new way of multiplication by a single-digit number.

Tasks:

+ educational

Build a model of a new way of multiplying by a single-digit number (column);

Repeat and generalize the multiplication rules, extending them to a wider area;

Develop the ability to solve problems and write a brief condition for it

+ developing

Develop thinking, competent mathematical speech, interest in mathematics lessons;

*regulatory

Awareness by students of what has already been learned and what still needs to be learned;

Develop control and self-control when checking tasks;

Plan your actions in accordance with the task and the conditions for its implementation, including in the internal plan;

Evaluate the correctness of the performance of an action at the level of an adequate assessment of the compliance of the results with the requirements of a given task and task area.

*cognitive

Improve computing skills;

Develop the ability to extract information;

Process the received information: compare and group mathematical facts;

+ communicative

adequately use communicative, primarily speech, means to solve various communicative tasks, build a monologue statement

take into account different opinions and strive to coordinate various positions in cooperation;

to formulate own opinion and position;

to ask questions;

use speech to regulate their actions;

+ educational

Cultivating accuracy in notebooks

Equipment:

Textbook;

Notebook;

Presentation

Algorithm (handout)

During the classes

1. Organizational moment

Now we have a math lesson.

2.Updating knowledge

What numbers can we already multiply? (Round numbers, single digit to single digit, double digit to single digit)

- Let's solve examples (Slide 1):

What do we use when solving an example? (Multiplication table)

What do we use when solving an example? (Performing multiplication by a column, we also use the multiplication table, not forgetting to demolish zero.)

What do we use when solving an example? (We perform multiplication by a column, we also use the multiplication table, remembering to remember the tens if the product is more than ten.)

Exercise (Slide 2)

Guess the rule by which the numbers are written and fill in the empty boxes:

(The first number is the sum of 10 and 2(12), the second 2 numbers are the terms (10, 1) and the factors 1, the third number (4) is the factor 2, the fourth 2 numbers are the products of 10 and 4, 2 and 4 and the terms, the fifth number (48) is the sum of 40 and 8.)

3.Checking homework

Check your homework, open the textbook on page 111 No. 6.

Name the answer of the example under the letter "a".

a) 2047639 - 459086 = 1588553;

Name the answer of the example under the letter "b".

b) 305296 + 72058 = 233238;

And what is the answer in the example under the letter "c".

c) 1800 * 70 = 126000

How did you solve this example? (You need to perform the multiplication, despite the zeros (126), and assign as many zeros to the right in response as there were in both factors (i.e. 000).)

Let's move on to № 7.

We listen to the answers of the first three examples.

What answer did you get in the 4th? (632 kg)

Which rule helped you in translating from c. in kg. ? (1 q = 100 kg)

What answer did you get in the 5th? (3054 kg)

What rule helped you in converting from t. to kg.? (1 t = 1000 kg)

What answer did you get in the 6th? (21 kg)

Let's move on to № 9.

What action did you get the answer 60? (4th)

What action did you get the answer 5? (7th)

What is the final answer? (12)

4. Statement of the problem

Solve examples (on the board):

73 * 3 = 219 (column)

273 * 3 = 819 (column)

Did you have difficulty making a decision?

Have you solved all such examples? (No. The solution of the 4th example is not familiar to us.)

Do you have any suggestions how to solve the fourth example? (Student statements.)

What do you think, what topic will we work on today? (Multiplication by a single-digit number in a column.)

What about multiplying numbers? (Three-valued and multi-valued, because we know the multiplication of two-digit ones.)

What is the task before us? (Learn to multiply three-digit, multi-digit numbers by a single-digit number in a column.)

5.Messaging new material

Algorithm:

I write the multiplication in a column.

Multiply units.

I write the units of the answer under the units.

I remember dozens.

I multiply tens.

To the number of tens I add tens from memory.

I write tens under tens, hundreds under hundreds.

Multiply hundreds.

To the number of hundreds I add hundreds from memory.

How to multiply a multi-digit number by a single-digit number in a column? What rules must be followed? Why should you be careful?

(Adhering to the same rules as multiplying a three-digit number by a one-digit number, but remember that there are more digits in multi-digit numbers.)

5. Physical education minute

Get up quickly, smile
Pull up higher, pull up.
Come on, straighten your shoulders
Raise, lower
Turned left, turned right
They touched their hands with their knees.
Sit down, get up, sit down, get up
And they ran on the spot.

6. Consolidation of the studied material

Now let's turn our attention to No. 1 on page 1 of the second part of the textbook.

What is shown in the picture? (Rectangle.)

What can you say about a rectangle? (One side is divided into parts a, b, c, and the other d)

How do you find the area of ​​a rectangle? (a*d+b*d+с*d=(a+b+с)*d – multiplying a sum by a number also applies to the sum of three terms)

- Now let's solve an example p.1 No. 2(a)(we divide the number 576 into bit terms and solve according to the rule (576=500+70+6)*9=500*9+70*9+6*9=4500+630+54=5184 (write down in the book)

Is this record convenient or not? (It is more convenient to write in a column.)

Let's look at №2(b) p.1

First counted the number of units, tens, hundreds. Compare: it is more convenient to write 3 columns.

- Guess how the record turned out from the previous one? (Ones were multiplied. And tens were remembered by writing over tens, etc.)

Let's solve an example with which we had difficulties:

What number is obtained when multiplied in the units place? (9.) Can it be immediately written to the category of units of the result? (Can.)

What number is obtained when multiplied in the tens place? (21.) How many hundreds are there in 21 tens, and how many more tens? (2 hundreds 1 tens.)

What number do we put in the tens place of the result? (2.) In what category do 2 hundreds go? (To the hundreds place.)

What number is obtained when multiplied in the hundreds place? (6.) How many hundreds went into this place when multiplying in the previous place? (2 hundreds.)

- How many hundreds did you get, taking into account the transition? (8 hundreds.) What number should be placed in the hundreds place of the result? (8.)

- In what case did the transition through the digit not occur during bitwise multiplication: when the result was a single-digit number or two-digit? (Unambiguous.)

let's move on to No. 3 (work in the book)

Let's solve the first example under "a" on our own.

What answer did you get? (196)

Let's solve the second example under "a", pronouncing it according to the algorithm.

(I multiply 329 by 5. I multiply units 9 * 5, I get 45, because the answer is more than 10, I remember 4, and write 5 in the category of answer units. I multiply tens 2 * 5, I get 10 and add 4 from memory to this number , I get 14, because the answer is more than 10, I remember 1, and write down the digit of tens of the answer 4. I multiply hundreds of 3 * 5, I get 15 and add 1 to this number from memory, I get 16, the answer is 1645.)

Let's solve the third example under "a" at the board (wishing)

Let's solve the fourth example under "a" at the board (wishing)

Let's move on to № 4.

Read the problem and write a short condition.

1 computer - 9356 rubles.

3 computers - ? rub.

9356 * 3 = 28068 (rubles)

Answer: 28068 rubles cost 3 computers.

7.Homework(Slide 4)

Page 1 No. 3(b), p. 2 No. 5, 8(a)

Are there any homework questions?

8. Summary of the lesson

What did we learn in class today?

What was difficult for you?

Did you like the lesson?

Marking up…

The simplest case of multiplication on abacus is multiplication by a single digit. Since multiplication is an action by which the sum of several identical terms is found, the problem of multiplication by a single-valued factor can be reduced to addition, i.e., repeat this multiplicand by the term as many times as there are units in the factor. Many counting workers, when multiplying by single digits, use this method of multiplication even now. However, when performing operations with large numbers, starting from about four digits, the addition method turns out to be too cumbersome. Much easier and faster you can come to the same result using the multiplication table.

The technique used in this case is that each digit of the multiplicand, starting from the highest, is successively multiplied by the given factor using the multiplication table.

Let's look at a few examples.

Example 1. Multiply 23 by 3.

Multiplication on the accounts will always start with units of higher digits.

Let's set aside this multiplier 23 on the accounts and we will multiply in this way: we shift the bones of tens to the right and at the same time we multiply in our mind the shifted number of tens (2) by a given factor (3), mentally saying: "three times two - six." The resulting product (6) is put in place of the discarded deuce.

We repeat the same technique with the second digit of the multiplier: we shift the bones of units to the right and at the same time multiply in our mind the shifted number (3) by the factor (3), mentally saying: "three times three - nine." We put the result (9) in place of the removed units.

Now the accounts have the desired result - the number €9. Multiplication completed.

Example 2. Multiply 13 by 6.

We set aside the multiplier 13 on the accounts and, like the previous one, we multiply according to the multiplication table, starting from the highest digit:

1. We shift one ten to the right and at the same time multiply it in our mind by a factor (6); the result (six tens) is put in place of the removed number.
2. We repeat the same technique with the number of units: we shift it to the right and at the same time multiply in our mind by this factor (6); we get a two-digit number 18 in the product. This number contains 1 ten and 8 units, which means that the first digit - 1 (ten) - should be placed in the row of tens, adding 6 to the number standing here, and 8 units - in place of the shifted number.

The abacus now has the number 78, i.e. the result of multiplying 13 by 6.

Example 3. Multiply 37 by 5.

1. We act according to the previous one: putting aside the given multiplier (37) on the accounts, we shift the number of tens to the right (and at the same time multiply it in the mind by the given multiplier holds one hundred and five tens, therefore, the first digit - one - must be put in place of hundreds, i.e. in the third digit, and the second - five - in place of the Brightened number of tens.
2. In the same way, we multiply the number of units of the multiplier product 35. We add three tens to the number of tens (5) already on the accounts and we get 8 (tens) here, and we place five units in place of the shifted number. The desired result is now on the accounts - the number
3. We shift the number of hundreds (1) of the multiplicand to the right, simultaneously multiply it in our mind by 5 and put the result of the multiplication - five hundred - into the place of the dropped hundred. The abacus now has the number 535.
4. In the same way, we multiply the number of tens (3) of the multiplicand: dropping the number of tens, we multiply it in our mind by the factor and we get 15 tens, that is, one hundred and five tens. We add the received hundred to the five hundred already on the accounts, and put the number of tens (5) in place of the discarded number of tens. On the accounts we get the number 655.
5. We multiply the number of units 5 by a factor of 5, we get 25 in the product, that is, two tens and five units. As before, we add two tens of the product to the 5 (tens) already on the accounts, and put the number of ones (5) in place of the shifted number of ones (5). On the accounts, the desired result is now the number 675.

We draw the reader's attention to the fact that the multiplication of each digit of the multiplicand is preceded by dropping this digit. This is done in order to avoid possible errors when postponing products on the accounts. As we will see later, when a certain skill is achieved, this technique can be dispensed with.

It is necessary to repeat the above examples several times in a row in order to better master the technique and their simplest tricks before moving on to studying more complex cases of multiplication. For the same purpose, it is recommended to do the following examples, strictly following all the previous instructions:

Exercise 11

Above, we considered the multiplication of two-digit numbers by single-digit ones. If the described techniques are learned well enough, then the further will not cause difficulties.

We now turn to multiplication by a single-digit factor of numbers with a large number of signs.

Example 4. Multiply 135 by 5.

We set aside on the accounts “the multiplier 135 and, (using the multiplication table, we multiply according to the method described above, starting with units of the highest category.

If, when multiplying any digit of the multiplier by a given multiplier, a two-digit number is obtained, the first digit of which, together with the digit already on the accounts, unites the highest rank exceeds 10, then in this case, as it is easy to figure out, ten is transferred further to the next digit. Let's explain this with the following example:

Example 5. Multiply 269 by 6.

After multiplying the first digit, we have 1269 on the accounts. After multiplying the second digit, we have 1569. When multiplying the third digit of the multiplier (9) by the multiplier (6), it is required to put the number 54 on the accounts, that is, five tens and four units. Since, according to the above rule, the number of tens (5) must be added to the number 6 (tens) standing on the accounts, and only four free bones remain on the left, we have to use the technique of transferring tens to the next digit, namely: in the series of hundreds we put one a hundred, and in a row of tens we drop five tens. The number of units (4) is put in its place. The number 1614 now on the accounts is the desired result.

In the examples we have considered for multiplication, two- and three-digit numbers appeared as a multiplicand. Multiplication of four-, five-, six-digit and larger numbers is performed using the same tricks.

Example 6. Multiply 345,239 by 7. Set aside the multiplicand on the accounts and start multiplication from units, the highest digit:

1st reception. Drop 3 (6th digit) and set aside 21 (7th and 6th digits).

2nd reception. Drop 4 (5th digit) and set aside, to (6th and 5th digits).

3rd reception. We discard 5 (4th digit) and set aside L, for which we set aside the unit of the 6th digit and discard seven units of the 5th digit, then add Shm "b units of the 4th digit.

1st reception. Drop 2 (3rd digit) and set aside AND (4th and 3rd digits).

:>-th reception. Drop 3 (2nd digit) and set aside 21 (3rd and 2nd digits).

(i-th reception. Reset 9 (1st digit) and set aside 03 (2nd and 1st digits).

The desired result is now on the accounts - 2,416,673.

The general rule of multiplication by a single-valued factor can be formulated as follows:

To multiply any multi-digit number by a single-digit one, you need to put the multiplicand on the accounts, then, using the multiplication table, successively multiply each digit of the multiplier by the given multiplier, starting from units of the highest digit; at the same time, the multiplied figure is discounted, and the result of multiplication is put in its place. If, when multiplying any digit of the multiplicand by a given factor in the product, a two-digit number is obtained, then its first digit should be placed a higher digit, and the second - in place of the multiplied.

Exercise 12

a) 167 X 5 b) 1234 X 4 c) 18 208 X 4 228 X 3 2316 X 4 27 556 X5

234 X 4 2713 X 7 48 954 X6

328 X 6 2827 X 5 66 877 X 7

456 X 4 4728 X 5 75 218 X7

782 X 6 5672 X 7 81 579 X 8

827 X 7 7723 X 8 94 578 X 9

Math lesson in 3rd grade.

Primary school teacherbudget educational institution

"Kirillovskaya secondary school

named after the Hero of the Soviet Union A.G. Obukhova" Shorokhova Vera Nikolaevna.

Educational system: Promising Primary School

Lesson topic: Multiplication by a single digit by a column

The purpose of the lesson: building a model of a new way of multiplying by a single digit.

Lesson objectives:

repeat and generalize the rules of multiplication, extending them to a wider area;

to consolidate knowledge and skills in the field of numbering of multi-digit numbers;

practice oral arithmetic skills;

develop thinking, competent mathematical speech, interest in mathematics lessons;

education of partnership, mutual assistance.

UUD:

Personal:

the internal position of the student at the level of a positive attitude towards school, orientation to the meaningful moments of school reality and acceptance of the model of a “good student”;

sustainable educational and cognitive interest in new general ways of solving problems;

Regulatory:

accept and save the learning task;

take into account the guidelines for action identified by the teacher in the new educational material in cooperation with the teacher;

plan their actions in accordance with the task and the conditions for its implementation, including in the internal plan;

evaluate the correctness of the action at the level of an adequate assessment of the compliance of the results with the requirements of a given task and task area;

distinguish between the method and the result of an action;

Cognitive:

use sign-symbolic means and schemes to solve problems;

build messages in oral and written form;

establish analogies;

control and evaluate the process and results of activities;

pose, formulate and solve problems;

Communicative:

adequately use communicative, primarily speech, means to solve various communicative tasks, build a monologue statement

take into account different opinions and strive to coordinate various positions in cooperation;

to formulate own opinion and position;

negotiate and come to a common decision in joint activities, including in situations of conflict of interest;

build statements that are understandable for the partner, taking into account what the partner knows and sees, and what is not;

to ask questions;

control the actions of the partner;

use speech to regulate their actions;

Equipment:

Slide presentation of the lesson;

Task cards;

Cards are helpers;

Algorithm - handouts;

Textbook, notebook.

2. Actualization of knowledge and fixation of difficulties in activities

Let's start our lesson with a smile.

Please give smiles to me, to my desk mate, to other guys. Thank you.

Well, check it out, my friend

What, ready to start the lesson?

Is everything in place, is everything in order?

Book, pen and notebooks?

Then go ahead!

And let's start our lesson with an oral account.

Why do we use oral counting in class?

Exercise 1.

Find the odd number:

10, 20, 30, 40, 55, 60

1,2,31,4,5,6,7

24, 11, 13, 15, 17, 19,12

Task 2.

Guess the rule by which the numbers are written and fill in the empty boxes:

Task 3.

How many breaks do you need to make to divide a chocolate bar into 6 identical pieces:

Graphic dictation:

I read the expressions, if the answer is correct, then put the line _, if incorrect, then ^.

9*9=81 8*3=32 4*3=12

6*7=42 8*6=48 8*8=72

7*9=56 6*9=36 5*9=45

Checking in pairs (according to the slide).

Stand up those who have no mistakes.

Stand up those who made 1-2 mistakes.

Complete the task and explain your choice

3. Statement of the educational task

4. Building a project to get out of a difficulty, discovering new knowledge

5. Primary consolidation in external speech

6. Independent work of students with mutual verification according to the standard

7.Reflection of activity (the result of the lesson)

Look at the charts on the board:

What do these diagrams mean?

What action do you think we have to work with today?

Card work: calculate

– What difficulties did you have?

What do you think, what topic will we work on today?

So, the topic of the lesson:Multiplication by a single-digit number by a column.

What is the task before us?

How and where can we apply the acquired knowledge?

Speak the plan of our work in the lesson:

Exercise 2.

– Multiply the number 273 by 3 by a column, answering these questions.

– What number is obtained when multiplied in the units place?(9.) Can it be immediately written to the category of units of the result?(Can.)

– What number is obtained when multiplied in the tens place?(21.) How many hundreds are there in 21 tens, and how many more tens?(2 hundreds 1 tens.)

– What number do we write in the tens place of the result?(2.) In what category do 2 hundreds go?(To the hundreds place.)

– What number is obtained when multiplied in the hundreds place?(6.) How many hundreds went into this place when multiplying in the previous place?(2 hundreds.)

– How many hundreds did it turn out, taking into account the transition?(8 hundreds.) What number should be placed in the hundreds place of the result?(8.)

– In which case did the bitwise multiplication not go through the bit: when the result was a single-digit number or two-digit?(Unambiguous.)

Exercise 3.

– Masha multiplied the number 218 by the number 4 in a column.

– What does the number 3 inscribed at the top in the tens place mean?(The number of tens that you remember.)

Fizminutka.

To correctly solve such examples, you need to know the solution algorithm.

What is an algorithm?

Now you can try to compose it yourself.

You have cards on your desks on which the actions of the algorithm are printed. Working and discussing in pairs, you will arrange the cards in the correct order.

Algorithm:

I write the multiplication in a column.

Multiply units.

I write the units of the answer under the units.

I remember dozens.

I multiply tens.

To the number of tens I add tens from memory.

I write tens under tens, hundreds under hundreds.

Multiply hundreds.

To the number of hundreds I add hundreds from memory.

How to multiply a multi-digit number

on unambiguous in a column? What rules must be followed? Why should you be careful? (Slide)

Complete #2 on page 7 of the tutorial

TPO task on page 4 No. 4 in a notebook.

1) Solve typical tasks for a new mode of action;

2) Perform cross-checkingaccording to the standard.

Lesson Summary:

Name the topic of the lesson

What learning problem did you solve?

Did you manage to solve it?

How to multiply such numbers?

What were the challenges and were they overcome?

Self-esteem.

Self-assessment sheet

Municipal budgetary educational institution secondary school No. 27 of Penza

Math lesson in grade 3 on the topic "Multiplication by a single digit by a column»

Prepared by:

primary school teacher

Medvedeva S. M.

Penza, 2017

Math lesson in 3rd grade.

Educational system: Promising elementary school

Lesson topic: Multiplication by a single digit by a column

The purpose of the lesson: building a model of a new way of multiplying by a single digit.

Lesson objectives:

repeat and generalize the rules of multiplication, extending them to a wider area;

to consolidate knowledge and skills in the field of numbering of multi-digit numbers;

practice oral arithmetic skills;

develop thinking, competent mathematical speech, interest in mathematics lessons;

education of partnership, mutual assistance.

UUD:

Personal:

the internal position of the student at the level of a positive attitude towards school, orientation to the meaningful moments of school reality and acceptance of the model of a “good student”;

sustainable educational and cognitive interest in new general ways of solving problems;

Regulatory:

accept and save the learning task;

take into account the guidelines for action identified by the teacher in the new educational material in cooperation with the teacher;

plan their actions in accordance with the task and the conditions for its implementation, including in the internal plan;

evaluate the correctness of the action at the level of an adequate assessment of the compliance of the results with the requirements of a given task and task area;

distinguish between the method and the result of an action;

Cognitive:

use sign-symbolic means and schemes to solve problems;

build messages in oral and written form;

establish analogies;

control and evaluate the process and results of activities;

pose, formulate and solve problems;

Communicative:

adequately use communicative, primarily speech, means to solve various communicative tasks, build a monologue statement

take into account different opinions and strive to coordinate various positions in cooperation;

to formulate own opinion and position;

negotiate and come to a common decision in joint activities, including in situations of conflict of interest;

build statements that are understandable for the partner, taking into account what the partner knows and sees, and what is not;

to ask questions;

control the actions of the partner;

use speech to regulate their actions;

Equipment:

Slide presentation of the lesson;

Task cards;

Cards are helpers;

Algorithm - handouts;

Textbook, notebook.

In this lesson, you can learn how to multiply three-digit and two-digit numbers in a column. First, we will recall what tricks are used to multiply three-digit numbers verbally. When multiplying by a column, we will develop an algorithm by which we can further solve examples, make calculations in tasks and various tasks. After this lesson, you will be able to apply the acquired skills in practice in real life.

What is multiplication?

This is smart addition.

After all, it’s smarter to multiply times,

Than to add up everything for an hour.

multiplication table,

We all need it in life.

And not without reason named

By multiplying it!

A. Usachev

Find the meaning of expressions.

Solution: 1. Let's decompose the number 34 into the sum of bit terms. We multiply each term by the number 2. We add the resulting products:

2. We replace the first multiplier with the sum of the bit terms and proceed similarly to the first example:

3. Each time to perform multiplication in this way is inconvenient, and sometimes difficult. In such cases, they use a written technique, namely multiplication in a column. Therefore, we solve the second example in a column. First, we write down the first factor, and under it the second. Be sure to write the corresponding digits under each other. So we write the deuce under the four in the one place. Then we sequentially multiply each number in the first factor by the second factor, starting with units and moving up to tens and hundreds. The answer is written under the line.

Multiplications by a column should be performed in the order shown in diagram 1.

Scheme 1. The order of multiplication in a column

Solve the examples by doing column calculations.

Solution: 1. When multiplying units in the first example, we get a number greater than nine. In this case, the units value is written under the bar, and the tens value is added to the tens after the multiplication is performed.

2. We act according to the algorithm.

3. We write down the numbers correctly and multiply sequentially.

4. Solve the last example using the algorithm

Find out which is bigger and by how much: the product of the numbers 151 and 6 or the product of the numbers 161 and 5.

Solution: 1. First, find the product of the first pair of numbers:

2. Calculate the product of the second pair of numbers:

3. Find out how much more the first number is than the second.

Find the mistakes and write down the correct answers (Table 1).

Table 1. Task number 3

Solution: 1. To find out where the error is, you need to solve the examples (Table 2).

Table 2. Task number 3

Find the area of ​​the given rectangle (Scheme 2).

Scheme 2. Rectangle

Solution: 1 way

1. This rectangle (diagram 2) is divided into three parts. In each of these rectangles, the width is the same, but the length is different. You can find the area of ​​each rectangle, and add the results.

(m 2)