How to multiply a single number in a column. Single-digit multiplication by a column

Municipal budgetary educational institution Secondary School No. 27 of Penza

Math lesson in grade 3 on the topic "Single-digit multiplication by a column»

Prepared by:

primary school teacher

Medvedeva S.M.

Penza, 2017

Math lesson in grade 3.

Educational system: Promising primary school

Lesson topic: Multiplication by a single number in 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 multi-digit numbers;

practice oral computation 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 towards the meaningful moments of school life 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 a learning task;

take into account the reference points of action identified by the teacher in the new teaching material in cooperation with the teacher;

plan your 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 way and the result of the action;

Cognitive:

use symbolic means and schemes to solve problems;

build messages in oral and written form;

establish analogies;

control and evaluate the process and the result of the activity;

pose, formulate and solve problems;

Communicative:

adequately use communicative, primarily speech, means for solving various communication tasks, build a monologue statement

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

formulate your own opinion and position;

negotiate and come to a common solution in joint activities, including in a situation of conflict of interests;

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

to ask questions;

control the actions of the partner;

use speech to regulate your actions;

Equipment:

Slide presentation of the lesson;

Quest cards;

Assistant cards;

Algorithm - handouts;

Textbook, notebook.

The simplest case of multiplication on abacus is multiplication by a single-digit number. Since multiplication is an action by which the sum of several identical terms is found, the problem of multiplying by a single-valued factor can be reduced to addition, that is, to repeat a given multiplication by the term as many times as there are units in the factor. Many counting workers use this method of multiplication when multiplying by single-digit numbers even now. However, when performing actions with large numbers, starting with approximately four-digit numbers, the addition method turns out to be too cumbersome. It is much easier and faster to arrive at the same result using the multiplication table.

The technique used in this case is that each bit of the multiplier, starting with the highest, is sequentially multiplied by the given factor using the multiplication table.

Let's look at a few examples.

Example 1. Multiply 23 by 3.

We will always start multiplication on accounts with units of the highest digits.

Let's put this multiplier 23 in the accounts and multiply in this way: we shift the bones of tens to the right and at the same time 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 dropped two.

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

Now the desired result is on the accounts - the number € 9. The multiplication is over.

Example 2. Multiply 13 by 6.

We put aside the multiplier 13 in the accounts and, like the previous one, we multiply according to the multiplication table, starting with the highest bit:

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 ones: shift it to the right and simultaneously multiply in our mind by the given factor (6); we get a two-digit number 18 in the product. This number contains 1 dozen and 8 units, which means that the first digit - 1 (ten) - should be put in the row of tens, adding 6 to the number standing here, and 8 units in place of the shifted number.

The number 78 is now on the accounts, that is, the result of multiplying 13 by 6.

Example 3. Multiply 37 by 5.

1. We proceed as before: putting this multiplier (37) on the accounts, we shift the number of tens to the right (and at the same time in our mind we multiply it by this factor, it holds one hundred and five tens, therefore, the first digit - one - must be put in the place of hundreds, i.e. in the third digit, and the second - five - in place of the Painted number of tens.
2. In the same way, we multiply the number of units in the multiplication 35. We add three tens to the number of tens (5) already on the accounts and we get here 8 (tens), and put five units in place of the shifted number. The desired result is now on the accounts - a number
3. We shift to the right the number of hundreds (1) of the multiplier, at the same time we multiply it in our mind by 5 and the result of the multiplication - five hundred - is put aside in the place of the discarded hundred. The accounts now have the number 535.
4. In the same way, we multiply the number of tens (3) of the multiplier: dropping the number of tens, multiply it in our mind by a 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 the 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 dozen products to the 5 (tens) already on the accounts, and put the number of units (5) in place of the shifted number of units (5). The desired result is now on the accounts - the number 675.

We draw the reader's attention to the fact that the multiplication of each digit of the multiplier is preceded by the discarding of this digit. This is done in order to avoid possible errors when postponing products on the accounts. As we will see later, once a certain skill has been 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 techniques, before moving on to the study of more complex cases of multiplication. For the same purpose, it is recommended to do the following examples, strictly observing all the previous instructions:

Exercise 11. Find works: 32 X 3 71 X 5 27 X 6 24 X 8 84 X 6 13 X 7 24 X 4 55 X 3 75 x 5 48 X8 16 X 6 34 X 4 47 X 6 69 X 3 88 X9

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

Now let's move on to multiplying numbers with a large number of signs by a single-digit factor.

Example 4. Multiply 135 by 5.

We put aside in the accounts "the multiplication 135 and, (using the multiplication table, we multiply according to the" method described above, starting with the units of the highest category.

If, when multiplying any digit of the multiplier by a given factor, a two-digit number is obtained, the first digit of which, together with the digit already on the accounts, unites the highest category exceeds 10, then in this case, as it is easy to figure out, the ten is passed on to the next digit. Let us 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 factor (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) on the accounts, and there are only four free tiles on the left, we have to use the method of transferring tens to the next category, namely: in the row of hundreds we put one a hundred, and in the row of dozens we drop five dozen. We put the number of units (4) in their place. The number 1614 now standing on the accounts is the desired result.

In the examples we have considered for multiplication, two- and three-digit numbers appeared as the multiplier. Multiplication of four-, five-, six-digit and larger numbers is done using the same techniques.

Example 6. Multiply 345 239 by 7. We put aside the multiplier in the accounts and start multiplying with ones, the highest order:

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

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

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

1st reception. Reset 2 (3rd digit) and postpone AND (4th and 3rd digits).

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

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

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

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

To multiply any multi-digit number by a single-digit one, it is necessary to postpone the multiplication in the accounts, then, using the multiplication table, sequentially multiply each digit of the multiplier by the given factor, starting with the units of the highest category; in this case, discard the multiplied digit, and put the result of the multiplication in its place. If, when multiplying any digit of the multiplier by a given factor, a two-digit number is obtained in the product, then its first digit should be placed in a higher position, and the second in the place of the multiplied one.

Exercise 12. Find works:

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

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Slide captions:

Mathematical dictation. ACCOUNT 6 multiply by 8. 7 multiply 4 times. The first factor is 9, the second is 5. Find the product. 2 will increase by 6 times. Take 9 three times. 8 times 9. The first factor is 5, the second is 10. Find the product. Find the product of the numbers 23 and 3. Increase 48 by 2 times.

Swap notebooks. Mathematical dictation. 48 28 45 12 27 72 50 69 96 ACCOUNT

1800 60 5 0 4 0: +: + 3 0 3 00 33 0 2 80 7 807 800 Who is faster?

VALID ACCOUNT Joke tasks. 100

VALID ACCOUNT Joke tasks. nine

VALID ACCOUNT Joke tasks.

Distribution property Recall what we know (a + b + c) d = a d + b d + c d 274 5 = (200 + 70 + 4) 5 = 200 5 + 70 5 + 4 5 = 1000 + 350 + 20 = 1370 What mathematical properties do you know?

ALGORITHM I write a single-digit number under the units of a three-digit number. I multiply units, write under units, and memorize tens (if any). I multiply tens and add tens that I remember. I am writing under tens. I remember hundreds. I multiply hundreds. I am writing under the hundreds. I read the answer. 2 7 4 5 274 5 = 0 2 7 3 1 3 1370

Work according to the textbook p.3 We apply knowledge. We develop skills.

Thanks for your work!

On the subject: methodological developments, presentations and notes

Math lesson Topic: Subtracting a single-digit number from a two-digit number with a transition through the digit.

A lesson with a presentation in the 2nd grade on the program "Harmony" Compiled by the primary school teacher Fedorova O.Yu. KhMAO, g. Surgut Topic: Subtraction unambiguous ...

Topic: SINGLE NUMBERS Lesson objectives: - to introduce the concept of "single-digit numbers"; to consolidate knowledge of the composition of the studied numbers; -to improve counting skills and addition skills of the form  + 1,  + ...

Math lesson in grade 3.

Primary school teacherbudgetary educational institution

"Kirillovskaya secondary school

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

Educational system: Promising primary school

Lesson topic: Multiplication by a single number in 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 multi-digit numbers;

practice oral computation 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 towards the meaningful moments of school life 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 a learning task;

take into account the reference points of action identified by the teacher in the new teaching material in cooperation with the teacher;

plan your 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 way and the result of the action;

Cognitive:

use symbolic means and schemes to solve problems;

build messages in oral and written form;

establish analogies;

control and evaluate the process and the result of the activity;

pose, formulate and solve problems;

Communicative:

adequately use communicative, primarily speech, means for solving various communication tasks, build a monologue statement

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

formulate your own opinion and position;

negotiate and come to a common solution in joint activities, including in a situation of conflict of interests;

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

to ask questions;

control the actions of the partner;

use speech to regulate your actions;

Equipment:

Slide presentation of the lesson;

Quest cards;

Assistant cards;

Algorithm - handouts;

Textbook, notebook.

2. Actualization of knowledge and fixation of difficulties in activities

Let's start our lesson by all means with a smile.

Please, give smiles to me, the deskmate, and the other guys. Thanks.

Well, check it out, my friend,

Ready to start your lesson?

Is everything in place, is everything all right?

A book, pen and notebooks?

Then go ahead!

Let's start our lesson with an oral account.

Why do we carry out oral counting in the lesson?

Exercise 1.

Find the extra number:

10, 20, 30, 40, 55, 60

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

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

Task 2.

Solve the rule by which the numbers are written and fill in the empty windows:

Task 3.

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

Graphic dictation:

I read expressions, if the answer is correct, then put a line _, if it is 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

Verification in pairs (slide).

Stand up those who have no mistakes.

Stand up those who made 1-2 mistakes.

Complete the task, explain their choice

3. Statement of the educational problem

4. Building a project for getting out of difficulty, discovering new knowledge

5.Primary reinforcement in external speech

6.Individual work of students with mutual examination according to the standard

7.Reflection of activity (lesson summary)

Consider the diagrams on the board:

What do these diagrams mean?

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

Work on cards: calculated

– What difficulties have you encountered?

What topic do you think we will be working on today?

So, the topic of the lesson:Single-digit multiplication by a column.

What task will we set ourselves?

How and where can we apply the knowledge gained?

Speak out the plan of our work in the lesson:

Exercise 2.

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

– What number is obtained by multiplying in the ones place?(9.) Is it possible to immediately write it down in the category of result units?(Can.)

– What number is obtained by multiplying in the tens place?(21.) How many dozens contain hundreds and how many dozens more?(2 hundred 1 dozen.)

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

– What number is obtained by multiplying in the hundreds place?(6.) How many hundreds went into this category when performing multiplication in the previous bit?(2 hundred.)

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

– In which case, during bitwise multiplication, there was no transition through the digit: 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 on top in the tens place mean?(The number of tens, which was remembered.)

Physical minute.

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

What is an Algorithm?

Now you will try to compose it yourself.

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

Algorithm:

I write down the multiplication in a column.

I multiply units.

I write the units of the answer under the units.

I remember dozens.

I multiply tens.

To the number of dozens I add dozens from memory.

I write tens under tens, hundreds under hundreds.

I multiply hundreds.

To the number of hundreds I add hundreds from memory.

How to multiply a multi-digit number

on a single-digit column? What rules should you follow? Why be careful? (Slide)

Follow # 2 on page 7 of the tutorial

TVET problem on page 4 # 4 in the notebook.

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

2) Perform crosscheckaccording to the standard.

Lesson summary:

Name the topic of the lesson

What learning problem did you solve?

Did you manage to solve it?

How do you multiply such numbers?

What are the difficulties, and have you managed to overcome them?

Self-esteem.

Self-assessment sheet

Primary school teacher: A.A. Kopachan MBOU SOSH №9 Noyabrsk Educational complex "Primary school of the 21st century" Theme. Multiplication by one-digit number in a column.

Target:

building a model of a new way of multiplying by a single number;

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

practice oral computation 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 towards the meaningful moments of school life and acceptance of the model of a “good student”;

the ability to self-esteem based on the criteria for the success of educational activities; setting for a healthy lifestyle;

Regulatory:

accept and save a learning task;

take into account the reference points of action identified by the teacher in the new teaching material in cooperation with the teacher;

plan your 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;

distinguish between the way and the result of the action;

Cognitive:

build messages in oral and written form;

carry out the analysis of objects with the allocation of essential and insignificant features;

establish analogies;

control and evaluate the process and the result of the activity;

pose, formulate and solve problems;

Communicative:

adequately use communicative, primarily speech, means for solving various communication tasks, build a monologue statement

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

formulate your own opinion and position;

negotiate and come to a common solution in joint activities, including in a situation of conflict of interests;

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

to ask questions;

control the actions of the partner;

use speech to regulate your actions;

Equipment:

Slide presentation of the lesson (Appendix 1);

Math simulator (Appendix 2)

Quest cards;

Assistant cards;

Algorithm - handouts;

Textbook, notebook.

During the classes

Teacher activity

(Children: Yes!)

Checking d / s (mutual check)

What helped you solve the examples correctly? (i.e. and algorithm)

Slide 3.

Then go ahead! Verbal counting ahead!
Well, pencils aside.
No knuckles, no pens, no chalk.
Verbal counting! We do this business
Only by the power of the mind and soul.

2) Repetition of the multiplication table

(8 people work with cards, 4 cards (attach1), mutual check; or

math simulator - electronic version, work with netbooks)

3) Arithmetic dictation:

(one student works at the blackboard) children write in notebooks.

Two hundred forty five (245);
Thirty nine tens (390);
Eight hundred, eight tens, one unit (881);
Eighty five (85);
Four hundred sixty five (465);
Seven hundred forty two (742)

3units

(mutual check in pairs according to the standard -

Slide 4.)

245, 390, 881, 85, 465, 742, 3

4) Creation of difficulty in activity.

What groups can the numbers be divided into?

How does each group differ?

Compose products with the given numbers:

245 x 3 85 x 3

390 x 3 465 x 3

881 x 3 742 x 3

Homework.

I write down the multiplication in a column. I multiply units. I write the units of the answer under the units. I remember dozens. I multiply tens. To the number of dozens I add dozens from memory. I write tens under tens, hundreds under hundreds. I multiply hundreds. To the number of hundreds I add hundreds from memory. I multiply by thousands, etc.

I read the answer.