Municipal budgetary educational institution secondary school No. 27 of Penza

Mathematics 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.

Lesson stages	Teacher activity	Student activities
1. Self-determination for activity (org. moment) 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. (Five minutes of reading) And let's start our lesson with an oral account. Why do we use oral counting in class? SLIDE 1 Exercise 1."SILENT" - marker board SLIDE 2, 3 Mathematical dictation. SLIDE 4 Checking in pairs (according to the slide). Stand up those who have no mistakes. Stand up those who made 1-2 mistakes. - What needs to be done to avoid 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.Reflection of activity (the result of the lesson)	SLIDE 5 Consider the expressions on the board: 7024-483 837+582 274*5 Complete tasks. Work in groups GROUP WORK SLIDE 6 (Vika and Maxim together) Presentation of results. - 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? So how are we going to solve such examples. Someone knows how to solve such examples. (Example of a child's decision) 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. (WORK IN PAIRS) Fizminutka. Algorithm: I write a one-digit number under the units of a three-digit number. I multiply units, write under units, and remember tens (if any). I multiply the tens and add the tens that I remember. I write in tens. I remember hundreds. Multiply hundreds. I write hundreds. I read the answer. SLIDE 7 How to multiply a multi-digit number on unambiguous in a column? What rules must be followed? Why should you be careful? SLIDE 8 We perform according to the algorithm. Textbook p. 82 No. 269 - collectively on the board RESERVE: with. 81 No. 268 - independently "column" 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? How and where can we apply the acquired knowledge? I'm giving you a memo with the algorithm. Evaluation ruler for self-assessment SLIDE 9 Homework: learn the algorithm; optional: make 3 examples for multiplication by a "column".

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 conformity 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 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)

What 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 units of the answer. 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…

It is convenient to multiply multi-digit or multi-digit numbers in writing in a column, successively multiplying each digit. Let's see how to do it. Let's start by multiplying a multi-digit number by a single-digit number and gradually increase the capacity of the second multiplier.

To multiply two numbers in a column, place them one below the other, ones under ones, tens under tens, and so on. Compare two factors and place the smaller one under the larger one. Then start multiplying each bit of the second multiplier by all the bits of the first multiplier.

Multiplication of a multi-digit number by a single-digit number

We write a one-digit number under the units of a multi-digit number.

Multiply 2 sequentially to all digits of the first multiplier:

Multiply by units:

8 x 2 = 16

6 write under units, and 1 remember ten. In order not to forget, we write 1 over dozens.

Multiply by tens:

3 tens × 2 = 6 tens + 1 tens (remembered) = 7 tens. We write the answer under tens.

Multiply by hundreds:

4 hundreds × 2 = 8 hundreds . We write the answer under hundreds. As a result, we get:

438 x 2 = 876

Multiplication of a multi-digit number by a multi-digit number

Multiply a three-digit number by a two-digit number:

924×35

We write a two-digit number under a three-digit one, units under units, tens under tens.

Stage 1: find the first incomplete product, multiplying 924 on the 5 .

Multiply 5 sequentially to all digits of the first multiplier.

Multiply by units:

4 x 5 = 20 0 we write under the units of the second multiplier, 2 remember ten.

Multiply by tens:

2 tens × 5 = 10 tens + 2 tens (remembered) = 12 tens , we write 2 under the tens of the second multiplier, 1 remember.

Multiply by hundreds:

9 hundreds × 5 = 45 hundreds + 1 hundred (remembered) = 46 hundreds, we write 6 under the hundreds digit, and 4 under the thousands place of the second multiplier.

924 × 5 = 4620

Stage 2: find the second incomplete product, multiplying 924 on the 3 .

Multiply 3 sequentially to all digits of the first multiplier. We write the answer under the answer of the first stage, shifting it one place to the left.

Multiply by units:

4 x 3 = 12 2 write under the tens place, 1 remember.

Multiply by tens:

2 tens × 3 = 6 tens + 1 tens (remembered) = 7 tens, we write 7 under the hundreds digit.

Multiply by hundreds:

9 hundreds × 3 = 27 hundreds , 7 write in the thousands place, and 2 into the tens of thousands.

Stage 3: add both incomplete products.

We add bit by bit, taking into account the shift.

As a result, we get:

924 × 35 = 32340

Multiply a three-digit number by a three-digit number:

Let's take the first factor from the previous example, and the second factor from the previous one, but 8 hundred more:

924×835

So, the first two steps are the same as in the previous example.

Stage 3: find the third incomplete product, multiplying 924 on the 8

Multiply 8 sequentially to all digits of the first multiplier. We write the result under the second incomplete product shifted to the left, to the hundreds place.

4 x 8 = 32, we write 2 into the hundreds 3 remember

2 x 8 = 16 + 3(remembered) = 19 , we write 9 in the ranks of thousands 1 remember

9 x 8 = 72 + 1(remembered) = 73 , we write 73 into the hundreds and tens of thousands, respectively.

Stage 4: add three incomplete products.

As a result, we get:

924 × 835 = 771540

So, how many digits are in the second factor, there will be so many terms in the sum of incomplete products.

Let's take two multipliers with the same bit depth:

3420×2700

When multiplying two numbers ending in zeros, we write one number under the other so that the zeros of both factors are left out.

Now we multiply two numbers, ignoring the zeros:

342 × 27 = 9234

We attribute the total number of zeros to the resulting product.

As a result, we get:

3420 × 2700 = 9234000

Summarize. In order to multiply two numbers in a column in writing, you need to :

1. Compare two numbers and write the smaller one under the larger one, units under units, tens under tens, and so on. If there are numbers with zeros, then we write one number under the other so that the zeros of both factors are left out.

2. We multiply successively each bit of the second factor, starting from units, by all the bits of the first multiplier. We don't pay attention to zeros.

3. We write incomplete works one under the other, shifting each incomplete work one digit to the left. How many significant digits (not 0) are in the second multiplier, so many incomplete products will be.

4 . We add up all the incomplete works.

5. We assign zeros from both factors to the result obtained.

That's all, thanks for being with us!

Multiplication by a single digit by a column

You can multiply a multi-digit number by a single-digit number using the rule for multiplying a sum by a number, while decomposing a multi-digit number into bit terms. But this method is not always convenient.

When multiplying a multi-digit number by a single-digit number, you can record in a column, as with addition and subtraction. This method is very helpful when multiplying multi-digit numbers. In this lesson, we will learn how to find the value of the product of multi-digit and single-digit numbers by writing in a column.

Find the value of the product: 32 ∙ 2.

Let's write the work in a column.

The first multiplier 32 has two digits: 3 tens, 2 ones.

The second multiplier 2 has one bit - 2 units.

When writing in a column, we write the multipliers bit by bit: units under units.

When multiplying by a column, we write the multiplication sign with a cross "x".

Instead of an equal sign, we draw a line under the second factor.

Note that when multiplying a multi-digit number by a single-digit number, we multiply the number of each digit of the first multiplier by the second multiplier.

We start multiplying with units: 2 times 2 is equal to 4.

4 units are written under the units.

Then we multiply the tens of the first factor, 3 tens times 2 - equal to 6 tens.

We write 6 under tens.

We read the result 64.

Similarly, you can multiply any multi-digit number by a single-digit number.

For example, 4211 times 2.

We start with units:

1 multiplied by 2 is equal to 2, 2 units are written under the units.

1 ten multiplied by 2 is equal to 2 tens, 2 is written under the tens.

2 hundreds multiplied by 2 is equal to 4 hundreds, 4 is written under hundreds.

4 units of thousands multiplied by 2 is equal to 8 units of thousands, 8 is written under the units of thousands.

We read the result: 8422.

Now consider the products in which, when multiplying the numbers of digits, a two-digit number is obtained.

For example, 547 times 4.

We start multiplying from units:

7 times 4 equals 28.

28 is a two-digit number, it has 2 tens and 8 ones.

We write 8 units under the units, remember 2 tens and add to the tens.

We multiply 4 tens of the first factor by 4 - equal to 16, add 2 tens obtained by multiplying units, we get 18 tens.

We write 8 under tens, and remember 1 and add to hundreds.

Multiply 5 hundreds by 4 - equal to 20 hundreds, add 1 hundred by multiplying tens, you get 21.

1 is written under hundreds, 2 are units of thousands.

We read the result: 2 188.

Let's summarize.

1. When multiplying by a column, we write the factors under each other bit by bit: we write units under units.

2. We start multiplying from the units digit.

3. If, when multiplying a single-digit number by the value of the digit of a multi-digit number, a two-digit number is obtained, the number of units of this two-digit number is written to the digit that was multiplied, and the number of tens is added to the result of multiplying the single-digit number by the value of the next digit of the multi-digit number.

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Slides captions:

Mathematical dictation. ORAL COUNT 6 x 8. 7 x 4. 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 ORAL ACCOUNT

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

ORAL ACCOUNT Joke tasks. 100

ORAL ACCOUNT Joke tasks. 9

ORAL ACCOUNT Joke tasks.

Distributive 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 one-digit number under the units of a three-digit number. I multiply units, write under units, and remember tens (if any). I multiply the tens and add the tens that I remember. I write in tens. I remember hundreds. Multiply hundreds. I write 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.

Thank you for your work!

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