Routing lesson

Item:mathematics
Class: 2
Name of the educational and methodical kit (EMC): “ Promising Primary School»

Lesson topic:"Permutation of factors"

Lesson type: discovery of new knowledge

The place of the lesson in the system of lessons 1

Target:

introduce students to the commutative property of multiplication; to form the ability to apply it in practice; reinforce the meaning of multiplication;

Tasks:Educational:
Developing:
Educational:

to form the ability to apply it in practice; reinforce the meaning of multiplication;

develop computational skills, mental operations of comparison, classification;

education of interest in the study of the subject, the ability to work in groups.

Subject UUD:

Regulatory UUD:

Communicative UUD:

Cognitive UUD:

Personal UUD:

the ability to determine and formulate the objectives of the lesson with the help of a teacher; pronounce the sequence in the lesson; work according to a collective plan; evaluate the correctness of the performance of an action at the level of an adequate assessment;

plan your action in accordance with the task; make the necessary adjustments to the action after its completion, based on its assessment and taking into account the nature of the errors made; make one's guess

skill listen and understand the speech of others; jointly agree on the rules of behavior and communication at school and follow them

ability to navigate in your knowledge system: to distinguish the new from the already known with the help of a teacher; acquire new knowledge: find answers to questions using a textbook, your life experience and information received in the lesson.

Planned results:

Subject Results:

Subject Results in ICT:

Metasubject results:

Personal results:

understand what the “commutative property of multiplication” is. Fix the meaning of multiplication . Be able to solve word problems. be able to decide combinatorial problems to establish the number of pairs made up of elements of two sets. Finding the whole or parts, read mathematical expressions, inequality, equality.

be able to determine and formulate the goal in the lesson with the help of a teacher; pronounce the sequence of actions in the lesson; work according to a collective plan; evaluate the correctness of the performance of an action at the level of an adequate assessment; plan your action in accordance with the task; make the necessary adjustments to the action after its completion, based on its assessment and taking into account the nature of the errors made; make one's guess Regulatory UUD); be able to formulate your thoughts orally; listen and understand the speech of others; jointly agree on the rules of behavior and communication at school and follow them ( Communicative UUD); be able to navigate in your knowledge system: to distinguish the new from the already known with the help of a teacher; acquire new knowledge: find answers to questions using a textbook, your own life experience and information received in the lesson (Cognitive UUD).

be able to self-assess based on success criteria learning activities.

Basic concepts:

Concepts:

Introduction to the commutative property of multiplication

Interdisciplinary connections:

Mathematics

Resources:

main

additional

EMC "Perspective Primary School" "Mathematics" Grade 2 A.L. Chekin, interactive environment PeroLogo, dzor, handout.

Didactic
structure
lesson

(lesson stages)

Planned results

Tasks for students, the implementation of which will lead to the achievement of planned results

Activity
students

Activity
teachers

Stage 1. Organizing time.

Target: student activation

Creating conditions for inclusion in educational activities (motivation)

Stage 1. Organizing time.

Be able to jointly agree on the rules of conduct for communication at school and follow them. (Communicative UUD)

Be able to verbally express your thoughts. (Communicative UUD)

To be able to find the difference between the new and the already known with the help of a teacher .(Cognitive UUD)

Be able to listen and understand the speech of others. (Communicative UUD)

Has the bell rung already? (Yes)

Are we having a math lesson? (Yes)

Are you ready for the lesson? (Yes)

Will you listen carefully to the lesson? (Yes)

Do you want to know something new? (Yes)

So everyone can sit down!

Let's start our lesson. Let's remember the rules of conduct in the classroom.

Why these rules must be followed by each of us.

We have mathematics

So with new theme meet the whole class.

Today we will open without a doubt.

A very important property of multiplication for us.

Everyone, be careful, active and diligent.

Do you want to know a new topic?

Formulate And argue rules of conduct in the classroom.

Listen and watch.

Conducts instruction, prepares students for work. Creates conditions of the internal need for inclusion in educational activities.

Motivates

2.Updating knowledge.

Target: organize the actualization of the skills of finding the whole or parts;

Organize trial activities for students; arrange by students.individual difficulty.

2.Updating knowledge

(Communicative UUD)

.(Regulatory UUD)

Be able to verbally formulate your thoughts. (Communicative UUD)

Be able to pronounce the sequence of actions in the lesson to express your assumption . (Regulatory UUD)

(Personal UUD)

Front work

1. Write down today's date.

What can you say about the number 12? (natural, two-digit, odd, consists of 1 dec. and 2 units, neighbors 11 and 13)

How to get the number 12 using two single-valued terms?

Can you replace addition with multiplication? Why7

Read the expression different ways.

1. What does each factor in the number entry mean?

2. Read the words: term, multiplier, product value, sum value, term, multiplier.

What two groups can these words be divided into? (Group 1 - components of the addition action, group 2 - components of the multiplication action)

3. Let's count orally.

The kitten has 4 paws. How many paws does 2 kittens have? (8)

How many ears do 4 dogs have?(8)

How many times does 5 go into 15? (3)

What term must be taken 3 times to get the number to get the number 12? (4)

The goose has 2 wings. How many wings does 7 geese have?

4. Review the notes. How can you name them? (sums)

12+12+12+12+12 22+22+22

Is it possible to replace the operation of addition with multiplication? Why? (Yes, in expressions all terms are the same)

Individual work.

Replace addition with multiplication and calculate the result.

Work with information

Participate in discussion problematic issues.

own opinion.

Work on one's own

Organizes frontal work, offers tasks for practicing oral calculations

Includes students to discuss problematic issues.

Organize and provide control over the execution of the task.

Organizes individual work

Stage 3. Formulation of the problem. Target- make the initial assumption that the value of the product does not depend on the permutation of factors.

Stage 3. Formulation of the problem.

Be able to verbally formulate your thoughts. (Communicative UUD)

Be able to navigate your system of knowledge: to distinguish the new from the already known. (Cognitive UUD)

Cognitive UUD

Regulatory UUD

Cognitive UUD

Regulatory UUD

Open the textbook and read the topic of the lesson. ("Permutation of factors")

What is the purpose of the lesson? (To get acquainted with the permutation property of the factor)

1. Learn the property of multiplication

2. Be able to apply the commutative law of multiplication

3. Practice math

What will help us achieve our goal of the lesson.

I can tell you;

Or will you work in pairs and bring out yourself? (themselves)

Let's compare and find the result of two tasks?

Well, a physical education lesson, the boys lined up in two lines of 4 people each. How many boys lined up in two lines?

2. The girls lined up for a tennis lesson in 2 columns of 4 people each. How many girls lined up?

Do you think these tasks are different or the same? Can we answer the question of the problem?

What will help us answer the question?

(It will help us to create an illustration for the problem.) Where can we create an illustration? (In the program Pervologo) What should we remember? (Remember the rules of working with a computer.)

Rules for working with a computer

1) Start work strictly,

With the permission of the teacher,

And remember: you are the answer,

For order in the office.

2) If it sparkles somewhere,

Or something smokes.

Don't waste time -

You need to call the teacher.

3) The mouse loves to be

Hands are clean and dry.

It's better not to drink here, not to eat,

So as not to disturb the order.

4) Do not enter in wet clothes,

Don't get your hands wet either.

5) Cords, sockets, wires

You should never touch.

6) Keep your back straight

At a distance of 60 cm

From the screen you sit.

7) You sit at the computer,

You are watching the display.

No extra items

It can't be on the table.

8) Worked, read,

Everything you need is written down.

You turn off your computer

Take everything off the table.

Turn on your computer.

Find the Pervologo folder on your desktop .

Open it.

1.Select the drawing tool in the tools.

2. Then select backgrounds.

3. Select the Newborn Turtle from the toolbox and place it on the sheet.

4. Select the turtle costume tab from the command tabs:

5. Click on the desired suit. (we need boys and girls) The turtle on the sheet will turn into a boy, then into a girl

6. Copy as many items as you need to solve these problems. while choosing the stamp command

7.Select in tools new text(letter A)

8. Write down the desired expression.

9.Italicize the expression and select the desired font (20)

10.Select the desired color (blue)

11.Click on the letter A in the lower right corner.

12.Check the work.

And now independently depict in the upper left corner first the boys who stand in two lines of 4 people, and in the upper right corner depict the girls.

Work in pairs.

Compare illustrations.

Write down the result by multiplying. 2*4=8(m) and 4*2=8(d)

What conclusion can be drawn? (permutation of the factors does not change the value of the product)

Participate in research and practical work

Fulfill work according to the algorithm proposed by the teacher

Work in pairs

Implement and provide mutual control in cooperation, the necessary mutual assistance

Organize research work

Conducts student instruction.

Learn work in the program Pervologo

Estimate the correctness of the task

Stage 4.Fizkultminutka.

Communicative UUD

Let's leave the desks. Watch and repeat the movements (music sounds)

Perform movements, mobilize strength and energy

Organizes physical education minute.

Stage 5 Discovery of new knowledge Purpose: carry out their assumptions that the product does not depend on the order of the factors.

Regulatory UUD

Cognitive UUD

Regulatory UUD

Be able to pronounce the sequence of actions in the lesson. (Regulatory UUD)

Working with the textbook on p.108

Open the textbook on p.108.

Read the dialogue between Masha and Misha.

- How did Misha build the soldiers?

What did Masha say?

- Which of them is right, prove it.

On the board: 5 2 2 5

Can it be argued that the values ​​of these products are equal? Why?

Open your notebooks and write down the corresponding equality of the two expressions.

5 2 = 2 5

Check the validity of this equality by calculating the value of each of the products using addition.

5 2 = 5 + 5 = 10

2 5 = 2 + 2 + 2 + 2 + 2 = 10

Who is right: Masha or Misha? Why? (both are right. The values ​​of the product are equal)

What conclusion did you draw?

(The value of the product does not change from the rearrangement of factors)

Work with information presented in the form of a drawing.

Realize mutual control

Render in cooperation mutual assistance

Formulate and justify own opinion

Organizes individual presentation, exchange of opinions

Stage 5 Primary fastening.

Find the value of expressions, first based on the formulated property, and then calculations (replacing products with sums)

Develop math skills and logical thinking, building chains of inference

Be able to formulate your thoughts orally and in writing: listen and understand the speech of others ( Communicative UUD), (Regulatory UUD)

Let's once again be convinced of our assumptions (discoveries).

#2, p109 in writing (we make 2-3 columns).

Calculate the values ​​of the products in the column.

1 row-2 column

2 row-3 column

What conclusion can be drawn?

- Let's check our assumptions with the rule in the textbook on p.109.

Were our discoveries confirmed?

Fulfill tasks

Organizes students learning a new mode of action

Stage 7. Systematization and repetition of previously studied.

Ability for self-assessment based on the criterion of success of educational activities (Personal UUD)

Working with a computer (TB)

task 2.

Group work (3 people)()

Fulfill tasks

Independent application information. Perform self-test

Recall group work rules

Organizes doing self-work, self-checking

Stage 8. Reflection of activity

Target: fix the new content of the lesson; Summarize the work done in class.

Be able to pronounce the sequence of actions in the lesson (Regulatory UUD)

Ability for self-assessment based on the criterion of success of educational activities (Personal UUD)

What new did you learn in the lesson?

Have you completed all the tasks?

Where will we use the new property of multiplication?

Thank you for the lesson.

Formulate end result of your work

Organizes reflection

Project training session mathematics

Subject and teaching materials: mathematics grade 1, teaching materials "Perspective elementary school".

Topic of the lesson: Addition with the number 10.

Place of the lesson in the topic: 1 lesson

Type of lesson: discovery of new knowledge.

Purpose and expected result: Discover a new addition technique and use it in assignments different kind.

Lesson objectives (teacher activities):

1. Create a problem situation for the discovery of new knowledge.

2. Contribute to the discovery of students of a new method of addition.

3. Promote the conscious assimilation and application of new knowledge when adding to the number 10.

4. Organize self-assessment of the work of students in the lesson.

Equipment for the lesson: mathematics textbook grade 1 (A.L. Chekin), workbook"Mathematics in questions and assignments" No. 2 (O.A. Zakharova, E.P. Yudina), cards

Stages of the lesson, tasks and activities of students

Teacher activity

Student activities

Studying

problematic situation.

Learn to see the problem and find ways out of it.

Expressions are written on the board.

Guys, Misha got confused in solving expressions, he was able to solve only one expression. Which?

And with what expressions he could not cope.

Let's help him.

How are these expressions similar?

How are they different?

Find an extra expression? Why do you think it's redundant?

Close with a card the expression that you think is superfluous.

He had already solved such expressions with Masha.

Children answer:

they are similar in that all expressions involve addition.

They differ in that not all expressions have the same second term.

The second expression is superfluous, because the first term is a single-digit number.

Communicative

(children's statements)

2. Goal setting.

Determine the topic of the lesson, set a goal, learning objectives.

The teacher removes this expression and a note remains on the board:

Open the textbook and read the topic of the lesson. (the topic is posted on the board)

What should be done to find the meaning of these expressions?

I propose to discuss the following course of action in the lesson:

(the plan is posted on the board)

Tasks: 1) 10+2

Fizminutka.

Children read the topic of the lesson.

Addition with the number 10.

Discover a new method of addition and learn how to write down its result.

Open the addition trick with the number 10.

Learn how to correctly write the result of addition with the number 10

Practice solving these examples.

Rate your work.

Search and extraction of information)

Regulatory (goal acceptance and lesson setting)

Regulatory (action planning)

3. Discovery of new knowledge

Learn how to add single digit numbers with the number 10.

Develop the ability to generalize observations, draw conclusions.

What is the first task of the lesson?

Working with the tutorial on page 32

The teacher reads the task:

Once Misha said: “Masha, I noticed that if you add the number 10 with the single-digit number 2, you get the number 12, in which there is 1 ten and 2 more units.”

Can you tell me how to solve this example using the model?

What can be said?

How many tens and how many units in the number 1

Who wants to run the second model and tell how the expression 10 + 5 is solved

What did you notice as a result of the addition action?

How are these examples similar and different, and why?

Compare your rule with what is in the textbook.

Write down the rest of the addition steps in your notebook.

Can you complete the new scheme by adding any one-digit number to the number 10?

Finish the output:

When you add 10 to any single digit, you get two-digit number, which one…

Check our conclusion with the conclusion in the textbook.

Let's summarize the work. Read 1 problem.

Are we up to the task? (put v opposite the completed task)

Well done boys.

Open the addition trick with the number 10.

Children lay out mugs on the board and in notebooks. (10 green and 2 red)

1 term - 10 denote in green, the second term - 2 is denoted in red

There are 12 circles in total.

In the number 12 = 1 ten and 2 units.

Children do the same.

The result is two-digit numbers.

They are similar in that in the answer the number 1 is in the place of tens, but they differ in that in the place of units in the first example there is the number 2, and in the second -5, because in the first example they added a single-digit number 2, and in the second example they added 5.

in the tens place is the number 1, and in the units place is the digit of this single-digit number.

Children read:

When adding the number 10 to a single-digit number, a two-digit number is obtained, in which the digit 1 is in the tens place, and the digit of this single-digit number is in the ones place.

Regulatory (holding the goal of the lesson)

Communicative (monologic statements of children)

cognitive

(logical observations, comparisons, inferences)

Cognitive (informational)

cognitive

(modeling)

Cognitive (informational)

4. Shaping

primary skills based on self-control

Learn how to add 10.

Learn to do difficult tasks.

Let's move on to lesson 2.

Task number 2.

Work in pairs.

Read the task.

Take the chips and close the correct amounts.

Write down the amounts in your notebook. What task still needs to be completed?

Have you solved all the addition examples with the number 10?

Run the simulation.

Make a conclusion.

Read lesson 2.

Did we get it right on task 2? (put v opposite the completed task)

Tell us why you value yourself so much?

What task have we not completed yet?

Task number 2 in the notebook on page 31

Read the task.

1 option-1 column (1-4 examples)

Option 2 1 column (5-8 examples)

We do the task ourselves.

Look carefully at the examples of the second column. What needs to be done to make the records correct?

Tell us how to control yourself when writing missing terms?

Option 1 - 2 columns (1-4 examples)

Option 2 - 2 column (5-8 examples)

Can we say that we coped with the 3rd task.

(put v opposite the completed task)

Examples are written on a hidden blackboard. After finishing the work, the children independently check their work.

1 criterion: I know the output when adding to the number 10

Criterion 2: I can write missing terms

Who will tell you how you value yourself?

Write down in a notebook all the sums in which the first term is -10, and the second is a single-digit number.

Children discuss and complete the task in pairs.

Find the value of the sum.

10+1=11, 10+7=17, 10+9=19, 10+4=14

No, there are 2 examples left:

Children draw 2 red circles and 10 green ones.

Children conclude that with this addition, the same result is obtained.

Yes. (Children hold hands)

Several children talk about their work results.

Practice solving these examples.

Fill in the blanks so that the entries are correct.

Mutual check

Write either the first term or the second.

Based on the value of the sum, based on the rule, determine which term is the number 10, and which term is a single-valued term.

Children evaluate themselves according to criteria.

Communicative (statements of children)

Communicative (communication)

cognitive

(modeling)

Regulatory (control)

Cognitive (sign-symbolic and literal)

Regulatory (control)

5. Reflection

Learn to evaluate your work in class.

What was our goal at the beginning of the lesson?

Did they cope with all the tasks (clearly visible)

1. I can teach another student a new addition trick.

2. I know and can add with the number 10.

3. I know, but I doubt the solution of these examples.

Children are talking.

Self-assessment of students with the help of statements.

Regulatory

(target hold)

Personal

(ability for self-assessment based on the criterion of success in educational activities)

Demonstration lesson of mathematics in the 2nd grade

Technological map of the lesson of mathematics

in grade 2 on the topic "Permutation of factors"

Item: mathematics Class: 2-a

Lesson topic : Permutation of multipliers.

Target: creating conditions for students to achieve educational outcomes:

- personal: 1) have a positive attitude towards school, teaching; show cognitive needs and learning motives; maintain orderliness and discipline in the classroom.

2) show attention and patience to the interlocutor, the ability to carry out self-assessment of their activities.

- metasubject:

Cognitive UUD:acquire new knowledge find the necessary information, process information (analysis, comparison,) presented in different forms.

Regulatory UUD:together with the teacher to discover and formulate a learning problem,determine the purpose of your work, evaluate your own result and the result of your comrades, distinguish a correctly completed task from an incorrect one.

Communicative UUD:listen and engage in dialoguedefend one's positionparticipate in a group discussion,collaborate in pairs, speak in front of the class,

- subject: to understand what the “displacement property of multiplication” is, to be able to apply it, to consolidate the meaning of the action of multiplication, to form computational skills in mental counting.

Lesson objectives:

familiarization of students with the commutative property of multiplication using specific examples;

to form the ability to apply it in practice; reinforce the meaning of multiplication;

development of mathematical speech based on the use of the studied pattern; develop computational skills, mental operations of comparison, classification;

Methods and forms of education : Explanatory and illustrative; individual, frontal, steam room.

Methods for organizing the educational activities of students: search for new knowledge through interviews and pair work; independent work with pedagogical support for those students who need it

During the classes:

Didactic structure lesson

(Lesson steps

Teacher activity

Activity
students

Planned results

1. Motivation for learning activities .

Reception: expressing good wishes to students

The bell brought us all to class,

We have a math lesson.

Let's think and discuss.

It's time for us to start the lesson.

Do you want to know something new? (Yes)

So everyone can sit down!

Let's start our lesson.

Everyone, be careful, active and diligent.

Open your notebooks and write down the date and classwork.

express good wishes each other.

Write down the date, type of work.

Organizing time.

Be able to jointly agree on the rules of conduct for communication at school and follow them.

Knowledge update.

Look at numeric expressions

(Slide)

2 + 2 + 2 + 2

5 + 5 + 55 + 5

6 + 6 + 6

Find the extra expression.

Why did you choose the third expression?

What do all expressions have in common?

What action can replace the sum of the same terms?

Express the sums as a product and find the values.

Check from a slide(slide)

What does the work consist of?

What is the result of multiplication?

What action are we working on?

Find an extra expression.

- terms are not the same

-multiplication

2*4=8

6*3=18

-From multipliers.

- the meaning of the work

-With multiplication action

(Communicative UUD)

Be able to pronounce the sequence of actions,

speculate.(Regulatory UUD)

Be able to verbally formulate your thoughts.(Communicative UUD)

Formulation of the problem. Lesson topic.

goal setting

You have envelopes on your desks. (Envelope No. 1)

Analyze the contents of the envelope, which of these do you already know?

Whatfor you is unknown, new.

What we learned, we know, put it back in the envelope.

And what is new to you, leave in front of you.

What topic are we working on?

And what will help us to check the topic of the lesson?

Let's check and compare if we are right.

Let's define the objectives of our lesson.

- What will we need to know?

- What are we going to learn then?

Let's try to evaluate our knowledge on the topic at the beginning of the lesson. And then compare the result at the end of the lesson at the end of the lesson.

Complete the task in envelope No. 1

Check on the slide

- textbook content

What is multiplier permutation?

Learn to apply the rule when performing various tasks

Be able to verbally formulate your thoughts.(Communicative UUD)

Be able to navigate your system of knowledge: to distinguish the new from the already known.(Cognitive UUD)

Primary assessment of knowledge on the topic

Let's try to evaluate our knowledge on the topic at the beginning of the lesson. And then compare the result at the end of the lesson at the end of the lesson.

Assess knowledge at the beginning of the lesson.

(traffic signals)

(Personal UUD)

Discovery of new knowledge.

Now we will play a little toy soldiers. We will work in pairs.

Soldiers are lying on your tables in envelopes. (envelope №2)

Try (in pairs) to arrange all the soldiers in a column of 2

What did you do7 Who will be able to demonstrate at the blackboard using the sailors as an example?

(Option 2: If children find it difficult, open textbooks)

Consider the illustration where Masha and Misha are playing with soldiers and arguing.

Misha tells his sister that he arranged the soldiers in 2 lines, each with 5 soldiers. But Masha believes that the soldiers are built in 5 rows. Each row has 2 soldiers. Which child is right?

write down total number soldiers in the form of a worktwo ways.

- Is it possible to assert that the values ​​of the products will be equal?

What sign shall we put between the works? Why?

5*2=2*5

How can you check that this equality is true?

What surprised you?

We are explorers! Let's check if this statement is true for other expressions?

Working in pairs with soldiers

Give time to complete the task

Explanation on the board.

Children explaining new material at the blackboard

We listen to the opinion of the children and offer to arrange the chips in the same way as the soldiers stand

Two children write two options at the blackboard

Check verbally and write on the board: 5 2 And 2 5

-Yes, because it's the same number of soldiers.

- The multipliers are the same, only they have been swapped,

Replace the multiplication with the sum of the same terms.

You can call two students to the board, offering one to calculate the value of the product 5 2, and the other - 2 5 (5 2 = 5 + 5 = 10, 2 5 = 2 + 2 + 2 + 2 + 2 = 10).

The multipliers are reversed, and the value of the products is the same

Be able to pronounce the sequence of actions in the lesson.(Regulatory UUD)

Primary fastening.

Application of knowledge

Let's once again verify our assumptions (discoveries)

Let's complete task number 2

3 art. - 1 row

4 st. - 2 row.

5 st. - 3 row

What rule did you use to complete this task?

- Were our discoveries confirmed?

What conclusion can be drawn?

- Let's compare our assumptions with the rule in the textbook on p.109.

Do you know what a permutation of factors is called in mathematics? The commutative property of multiplication or the commutative law of multiplication.

Task number 3 (oral)

2 8 = 8 2

9 4 = 4 9

5 3 = 3 5

8 4 = 4 8

5 9 = 9 5

3 7 = 7 3

Perform columns 1 and 2 - together at the board.

Swap notebooks with a neighbor and evaluate his work (mutual check).

multiplier permutation rule

They conclude: From the permutation of factors, the value of the product does not change.

Read the rule

Be able to formulate your thoughts orally and in writing: listen and understand the speech of others ( Communicative UUD), (Regulatory UUD)

Be able to verbally formulate your thoughts. (Communicative UUD

self control

Evaluation of results

their actions

Task No. 4 (U-1, p. 109)

Using the knowledge gained. Complete the task on your own.

- Read the wording of the assignment. (Find the values ​​of the first product) How will we perform?(

We illustrate on the board a sample of written execution of an oral answer.

self check(answers on the slide)

Who made two mistakes - 4

Who made 3 mistakes - 3

Independent work.

You can work in pairs

If the children find it difficult to ask a neighbor!

-To find the value of the product 5 4 used

equality 4 5 = 20.)

5 4 = 4 5 = 20.

Students independently find the rest of the meanings of the works and make notes

Assess the completed task

Be able to pronounce the sequence of actions in the lesson to express your assumption. (Regulatory UUD)

Be able to evaluate your actions, your assumption. (Regulatory UUD)

Reflection of activity. Lesson summary

What was the task in the lesson?

Were you able to achieve your goal?

Where will we use the new property of multiplication?

Who has changed results? Complete the sentences….

Thank you for the lesson!

Evaluation with traffic lights.

Ability for self-assessment based on the criterion of success of educational activities (Personal UUD)

How funny it is to watch the seething of shit in the minds of people who are far from mathematics, physics, natural sciences in general and on the methods of their teaching in secondary schools.

This is me about the widespread discussion of the "unfair" assessment by the teacher of such a solution to a simple problem:

When people see such an assessment in their heads, as a rule, there is a cognitive dissonance associated with the fact that the majority, albeit intuitively, remember that the multiplication operation is communicative, i.e. from the permutation of the places of the factors, the product does not change, i.e. a*b = b*a.

But here you need to understand that the problem under discussion belongs to the category of the most elementary, when the child not only does not know the properties of multiplication, but has just met for the first time the concept of multiplication, introduced as the addition of identical terms.

So from a mathematical point of view, the solution to the problem should look like this:

2l + 2l + 2l + 2l + 2l + 2l + 2l + 2l + 2l = 2l * 9 = 18l

And the order of the factors is really important for understanding the operation of multiplication. And this is not a whim of contemporary Russian Methodists. This is what they wrote in mathematics textbooks 130 years ago: § 42. What is multiplication. Multiplication is the addition of like terms. In this case, the number that is repeated as a term is called a multiplier (it is multiplied), and the number showing how many such identical terms are taken is called a multiplier.(Kiselev, first edition 1884).

The same was written about in the communist textbooks of the beginning of the last century (State pedagogical institute them. Herzen, I.N. Kavun, N.S. Popova, "Methods of teaching arithmetic. For teachers elementary school and students of pedagogical colleges". Approved by the People's Commissariat for Education of the RSFSR, 1934):

It is obvious that the solution proposed by the student shows that he did not understand the essence of the multiplication operation, which was appropriately assessed by the teacher.

Even assuming that the genius student himself guessed (or even knew) about the communicativeness of the multiplication operation, his decision is still wrong. The point is that if he wrote in the solution:

then the answer would be correct. However, liters, as a dimension, are missing on the left side of the equation and appear out of nowhere on the right side. Record same

moreover, is correct, despite the lack of dimension (n) in the left part, because this dimension is omitted, based on the initial conditions of the problem, implying that the dimension of the answer will be the same as the dimension of the multiplicand, which always comes first.

By the way, a misunderstanding of dimensions leads to sad consequences in adult life. Read an angry opus biglebowsky who, with a smug smile, writes frank nonsense, calculating the distance that the car traveled in 2 hours at a speed of 60 kilometers per hour: S = 60km/h * 2h = 120km/h. Next, we remember physical meaning problem and discard the tail of the solution "/h".

And such illiterate people, who are not versed in elementary mathematics and physics, consider it possible and acceptable to scold the one and a half century methods of teaching children the basics of mathematics.

Moreover, they themselves (yes, all of you too) studied multiplication at school in due time. In the USSR, there was one textbook for all schools, and in it the order of factors in the study of the multiplication operation was important. And in the same way, they lowered the marks for rearranging the factors, since this showed the student's misunderstanding of the essence of the multiplication operation and testified to a simple selection of factors, without understanding the essence of the phenomena.

Another thing is that later, after studying the laws of multiplication and consolidating knowledge about the communicativeness of the multiplication operation, the skill of correctly writing multipliers becomes unnecessary and is forgotten about. But at the same time, one should not forget about the correct dimension. In the end, all further study of physics is based on this.

In general, I wanted to convey a simple idea. If a person does not understand what the teacher tells him, then, as a rule, it is not the teacher's fault, but the person has problems.

Definition. Multiplication is an operation that results in finding the sum of identical terms. Multiply number A per number b means to find the sum b terms, each of which is equal to a.

The numbers that are multiplied are called factors (or multipliers), and the result of multiplication is called a product.

At multiplication natural numbers product is always a positive number. If one of the factors is 0 (zero), then the product is 0. If the product is zero, then at least one of the factors is 0.

If one of the two factors is equal to 1 (one), then work equal to the second factor.

• For example:
• 5 * 6 * 8 * 0 = 0
• 132 * 1 = 132

Laws of multiplication

associative law

Rule. To multiply the product of two factors by the third factor, you can multiply the first factor by the product of the second and third factors.

• For example:
• (7 * 6) * 5 = 7 * (6 * 5) = 210
• (a * b) * c = a * (b * c)

displacement law

Rule. By rearranging the factors, the product does not change.

• For example:
• 7 * 6 * 5 = 5 * 6 * 7 = 210
• a * b * c = c * b * a

distributive law

Rule. To multiply a number by a sum, you can multiply this number by each of the terms and add the resulting products.

• For example:
• 7 * (6 + 5) = 7 * 6 + 7 * 5 = 77
• a * (b + c) = ab + ac

The distributive law also applies to subtraction.

• For example:
• 7 * (6 — 5) = 7 * 6 — 7 * 5 = 7

The laws of multiplication apply to any number of factors in numerical or literal terms. The distributive law of multiplication is used to take the common factor out of brackets.

Rule. To convert the sum (difference) into a product, it is enough to bracket the same factor of the terms, and write the remaining factors in brackets as the sum (difference).