Demonstration lesson of mathematics in 2-class

Routing lesson mathematics

in grade 2 on the topic "Rearrangement of multipliers"

Thing: mathematics Class: 2-A.

Theme lesson : Rearrangement of multipliers.

Purpose: creating conditions for the emphasis of educational results:

- personal: 1) positive to school, teaching; show cognitive needs and training motives; Observe the organization, discipline in the lesson.

2) To show attention and patience to the interlocutor, the ability to perform self-esteem.

- MetaPered:

Cognitive Wood:minimize new knowledge, find the necessary information, recycle information (analysis, comparison,) presented in different forms.

Regulatory Wood:together with the teacher to detect and formulate the study problem,determine the purpose of your work, evaluate your result and result of comrades, distinguish the correct task from the wrong.

Communicative Wood: listen and join dialogue defend your position to express your assumption, participate in a collective discussion,cooperate in a pair, to perform in front of the class,

- subject: Understand what "Motive Multiplication Property" is, to be able to apply it, consolidate the meaning of the multiplication action, form computational oral account skills.

Tasks lesson:

acquaintance of students with a moving property of multiplication on specific examples;

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

the development of mathematical speech based on the use of the patterns under study; develop computing skills thinking operations comparison, classification;

Methods and forms of training : Explanatory-illustrative; Individual, frontal, steam room.

Acceptance of the organization of educational activities of students: search for new knowledge through interview and steam work; independent work from pedagogical accompaniment those students who need it

During the classes:

Didactic structure lesson

(Stages of the lesson

Teacher's activities

Activity
pupils

Planned results

1.Motion to learning activities .

Reception: Saying good wishes to students

We called us a call to all in the classroom,

Mathematics lesson with us.

We will think to reason.

We have time to start a lesson.

Want to know new? (Yes)

You can all sit down!

We start our lesson.

Be all, carefully active and diligent.

Open the notebook and write down the number and class work.

Express good wishes to each other.

Record the date, type of work.

Organizing time.

To be able to jointly agree on the rules of behavior of communication at school and follow them.

Actualization of knowledge.

Look at numeric expressions

(Slide)

2 + 2 + 2 + 2

5 + 5 + 55 + 5

6 + 6 + 6

Find an extra expression.

Why did you choose exactly the third expression?

What is common in all expressions?

What action can be replaced by the amount of the same terms?

Imagine the sum of the work and find the values.

Check from Slide(slide)

What is the work?

What happens as a result of multiplication?

What action continue to work?

Find an extra expression.

- the components are not the same

-Motion

2*4=8

6*3=18

- Multiplers.

-Notion of the work

- with the action of multiplication

(Communicative Wood)

Be able to prove the sequence of actions

to express your assumption. (Regulatory Wood)

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

Formulation of the problem. Theme lesson.

Goaling

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

Analyze the contents of the envelope, what do you already know from this?

whatfor you is not known, new.

What we studied, know, put back to the envelope.

And the fact that for you is new, leave before yourself.

What topic will we work on?

And what will it help us check the subject of the lesson?

Let's check and compare if we are right.

Let's determine our goals of our lesson.

- What do we need to know?

- What will we learn with you 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.

Perform a task in Envelope No. 1

Check on the slide

- content textbook

What is the permutation of multipliers?

Learn to apply the rule when performing various tasks

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

Be able to navigate in your knowledge system: to distinguish a new one from the already known.(Cognitive Wood)

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 lights)

(Personal Wood)

Opening of new knowledge.

We will play a little now in the soldiers. We will work in pairs.

You are on the tables in envelopes lie soldiers. (Envelope №2)

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

What did you do7 who can demonstrate at the board on the example of sailors?

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

Consider the illustration where Masha and Misha are playing soldiers and argue.

Misha speaks sister that he settled the soldiers in 2 ranks, in each of which 5 soldiers. But Masha believes that the soldiers are built in 5 rows. In each row 2 soldiers. Who among children rights?

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

- Is it possible to argue that the values \u200b\u200bof the works will be equal?

What sign do you put between works? Why?

5*2=2*5

How can you check that this equality is right?

What surprised you?

We researchers! Check whether this statement is true for other expressions?

Work in pairs with soldiers

I give time to perform the task

Explanation at the board.

Explanation of the new material at the board of children

Listen to the opinion of children and offer to arrange chips just like the soldiers

Two children write two options at the board

We check orally and write on the board: 5 · 2. and 2 · 5.

Yes, as this is the same number of soldiers.

- The factors are the same, only they changed them,

Replace multiplication of the sum of the same terms.

You can call two students to the board, offering one calculation of the value of the work of 5 · 2, and the other - 2 · 5 (5 · 2 \u003d 5 + 5 \u003d 10, 2 · 5 \u003d 2 + 2 + 2 + 2 + 2 \u003d 10).

Multiplers have changed in places, and the value of works is the same

Be able to prove the sequence of actions in the lesson. (Regulatory Wood)

Primary consolidation.

Application of knowledge

Let's make sure of our assumptions (discoveries)

Perform Task number 2

3 tbsp. - 1 rows

4 st. - 2 row.

5 st. - 3rd row

What rule did you use when performing this task?

- Reaffirmed our discoveries?

What conclusion can be done?

- Compare our assumptions with the rules in the textbook on C.109.

Do you know how to rearrange multipliers called in mathematics? Motive multiplication property or multiplication Movement.

Task number 3 (orally)

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 1 and 2 columns - together at the board.

Change notebooks with a neighbor and appreciate his work. (mutual test).

rule of rearrangement of multipliers

Conclusion: From the permutation of multipliers, the product does not change.

Read the rule

To be able to draw up your thoughts in oral and writing: to listen and understand the speech of others ( Communicative Wood), (regulatory Wood)

Be able to verbally to formulate your thoughts. (Communicative Woods

Self Control

Assessment of results

his action

Task number 4 (U-1, p. 109)

Taking advantage of the knowledge gained. Perform the task yourself.

- Read the wording of the task. (Find the first work values) How will we perform?(

Illustrate on the board a sample of a written interpretation of an oral response.

Self-brand(Slide answers)

Who made two mistakes - 4

Who allowed 3 errors - 3

Independent work.

You can organize a pair job,

Elutes, children find it difficult to ask the neighbor!

-The finding value of the work of 5 · 4 took advantage

equality 4 · 5 \u003d 20.)

5 · 4 \u003d 4 · 5 \u003d 20.

Students independently find the remaining values \u200b\u200bof the works and draw up records

Assess the task performed

Be able to pronounce a sequence of actions in the lesson to express their assumption. (Regulatory Wood)

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

Reflection. Total lesson

What kind of task was set in the lesson?

Managed to achieve the goal?

Where will we use a new multiplication property?

Who changed the results? Complete the sentences….

Thank you for the lesson!

Evaluation using traffic lights.

Self-esteem ability based on the criterion of successful learning activities (Personal Wood)

3 · 4 \u003d 12

COMPOSITION

The layering of the same terms can be replaced by multiplication.

Multiplication sign - point (·).

2 · 3 \u003d 6

3 · 2 \u003d 6

2 · 3 \u003d 3 · 2

Component names

Actions multiplication

Deli divider private

6: 3 = 2

Private

To find unknown Delimi, you need to multiply

On the divider.

2 · 3 \u003d 6

To find unknown

Divider, you need to divide into private.

6: 2 = 3

1. Content division

12 apples laid out on plates, 3 apples for each plate. How many plates needed?

In order to solve the task, you need to answer the question - How many times in 12 contains 3.

12: 3 = 4

2. Division

12 apples laid down on 4 plates equally. How many apples on each plate?

We argue:

We take 4 apples, lay out one apple for each plate. Then take another 4 apples, we launch another apple to the plate. And we take another 4 apples, lay out again one apple in a plate. Thus, in order to solve the task, you need to answer the question - How many times in 12 contains 4.

Communication

Between I.

Components of multiplication

4 · 2 \u003d 8

8: 4 = 2

8: 2 = 4

If the product of two multipliers is divided into one of them, then another multiplier will be.

C and d and and and and x in and d s

Class

1. Task analysis occurs according to plan:

Nastya gathered a bouquet of daisies and cornflowers. In the bouquet of 6 chamomile, and 3 more cornflowers. How many in the bouquet of cornflowers?

1. Who is the saying about the task? What is said in the task?
2. Repeat the condition of the task.
3. Question problem.
4. What colors did a bouquet Nastya?
5. How many daisies were?
6. Did we know how many cornflowers were there? / How many cornflowers were. What do we know about cornflowers?
7. What do you need to know?

At the end of the pars, a brief record is recorded, a diagram or pattern is made.

2. The task always writes an explanation in all actions other than the latter.

3. In the task with more than 1 action, the expression is written.

4. The answer is written strictly on the problem.

Tasks for finding the amount

There were 7 blue machines and 10 red machines on the shelf. How many machines all stood on the shelf?

The method of dating children with this rule (law) was due to the previously entered meaning of multiplication. Using subject models of sets, children pass the results of grouping their elements different waysBy making sure that the results do not change from changing ways to group.

The count of the elements of the pattern (set) pairs horizontally coincides with the score of the elements three vertical. Consideration of several options for such cases gives the teacher the foundation to produce inductive generalization (i.e., a generalization of several special cases in a generalized rule) that the rearrangement of multipliers does not change the value of the work.

Based on this rule used as an invoice, a multiplication table is compiled by 2.

For example: Using the multiplication table of Numbers 2, calculated and remember the multiplication table by 2:

Based on the same reception, a 3D multiplication table is drawn up:

The preparation of the two first tables is distributed into two lessons, which, accordingly, increases the time allotted by their memorization. Each of the last two tables is drawn up in one lesson, since children, knowing the source table, should not separately memorize the results of the tables obtained by rearrangement of multipliers. In fact, many children teach each table separately, since the insufficient level of development of thinking flexibility does not allow them to easily rebuild the model of the scared scheme of the table occasion in reverse order. When calculating cases of the form 9 2 or 8 3, children are again returned to the reception of consistent addition, which naturally requires time to obtain the result. This situation is likely to be generated by the fact that for a significant number of children, such separation of interconnected cases of multiplication (those that are linked to the rules for rearrangement of multipliers) does not allow associative chainfocused precisely on the relationship.

In compiling the multiplication table of the number 5 in grade 3, only the first product is obtained by adding the same terms: 5 5 \u003d 5 + 5 + 5 + 5 + 5 \u003d 25. The remaining cases receive the addition of grade five to the previous result:

5 6 = 5 5+ 5 = 30 5 7 = 5 6+ 5 = 35 5 8 = 5 7 + 5 = 40 5 9 = 5 8 + 5 = 45

Simultaneously with this table, the interconnected multiplication table by 5: 6 5 is also compiled; 7 5; 8 5; 9 5.

The multiplication table of the number 6 contains four cases: 6 6; 6 7; 6 8; 6 9.

The multiplication table on 6 contains three cases: 7 6; 8 6; 9 6.

A theoretical approach to such a construction of the study system of table multiplication assumes that it is in such a correspondence that the child will remember the cases of table multiplication.

The greatest number of cases contains the easiest to memorize the multiplication table of the number 2, and the most difficult to memorize the multiplication table of the number 9 contains only one case. Really, considering every new "portion" of multiplication tables, the teacher usually restores the entire volume of each table (all cases). Even with the condition that the teacher draws the attention of children to the fact that a new case in this lesson is, for example, only the case 9 9, and 9 8, 9,900. P. studied at previous lessons, most of the children perceives the entire suggested volume as a material for a new learning. Thus, in fact, for many children, the multiplication table of the number 9 is the largest and complex (and this is true, referring to the list of all cases that relates to it).

A large amount of material requiring memorization by heart, the complexity in the formation of associative connections when memorizing interrelated cases, the need to achieve all children of lasting memorization of all table cases by heart in the time-established timeline - all of this makes the topic of studying table multiplication in primary grades One of the most methodically complex. In this regard, issues related to memorization of multiplication tables are important.

Feature on a sheet into a cell a rectangle with 5 cm sides and 3 cm. We break it into squares with a side of 1 cm (Fig. 140). How to calculate the number of these squares?

You can, for example, argue so. The rectangle is divided into three rows, in each of which there are five squares. Therefore, the desired number is 5 + 5 + 5 \u003d 15. The left part of the recorded equality is the amount of equal terms. As you know, this amount is recorded using a product 5 * 3. We have: 5 * 3 \u003d 15.

In the equality A * B \u003d C of the number a and b call multipliers, and the number C and record A * B - work.

So, 5 * 3 \u003d 5 + 5 + 5.

Similarly:

3 * 5 = 3 + 3 + 3 + 3 + 3 ;

7 * 4 = 7 + 7 + 7 + 7 ;

1 * 6 = 1 + 1 + 1 + 1 + 1 + 1 ;

0 * 5 = 0 + 0 + 0 + 0 + 0 .

In letterproof, write it like this:

$$ A * B \u003d \\ Underbrace (A + A + A + ... + A) _ (B-component) $$

By the number A on natural number B, not equal to 1, call the amount consisting of B terms, each of which is a.

And if b \u003d 1? Then you will have to consider the amount consisting of one terms. And this in mathematics is not accepted. Therefore, we agreed that:

a * 1 \u003d a.

If b \u003d 0, then agree that:

a * 0 \u003d 0.

In particular,

0 * 0 = 0 .

Consider the works 1 * a and 0 * A, where a is a natural number, different from 1.

$$ 1 * a \u003d \\ underbrace (1 + 1 + 1 + ... + 1) _ (A-terms) \u003d a, $$

$$ 0 * a \u003d \\ Underbrace (0 + 0 + 0 + ... + 0) _ (A-terms) \u003d 0. $$

Now you can draw the following conclusions.

If a one of the two factors is 1, then the work is equal to another multiplier:

a * 1 \u003d 1 * a \u003d a

If a one of the two factors is zero, then the work is zero:

a * 0 \u003d 0 * a \u003d 0

The product of two numbers other than zero, can not be null.

If the work is zero, then at least one of the multipliers is zero.

The number of squares in Figure 140 we calculated so:

5 + 5 + 5 \u003d 5 * 3 \u003d 15. However, this half can be done in another way. The rectangle is divided into five columns, each of which has three squares. Therefore, the isomic number of squares is equal

3 + 3 + 3 + 3 + 3 = 3 * 5 = 15 .

Square counts in Figure 140 in two ways illustrates move the multiplication property.

From the permutation of multipliers, the work does not change.

This property is written in this way:

aB \u003d BA.

You know how to multiply in writing (in the column) a multi-valued number on a double-digit. Similarly, multiplying any two multivalued numbers.

For example:

This method is convenient because only unambiguous numbers have to multiply.

Consider the tasks in which the multiplication action is used.

Example 1 . Cherry, apple and pears grew in the garden. Cherries had 24 wood, which is 6 times less than an apple tree, and 18 trees are less than pears. How many trees grew in the garden?

1) 24 * 6 \u003d 144 (wood) - came up an apple tree.

2) 24 + 18 \u003d 42 (wood) - made up pears.

3) 24 + 144 + 42 \u003d 210 (trees) - grew in the garden.

Answer: 210 trees.

Example 2 . From one city at the same time in one direction, a truck was left at a speed of 48 km / h and a passenger car at a speed of 64 km / h. What distance will be between them after 3 hours after the start of movement?

1) 64 - 48 \u003d 16 (km) - the distance between cars each hour increases so much.

2) 16 * 3 \u003d 48 (km) - the distance between cars after 3 h.

Answer: 48 km.

Example 3 . From one village in opposite directions, a rider at the same time was departed at a speed of 14 km / h and a pedestrian at a speed of 4 km / h. What distance will be between them 4 hours after the start of movement?

1) 14 + 4 \u003d 18 (km) - so much the distance between the rider and the pedestrian every hour increases.

2) 18 * 4 \u003d 72 (km) - the distance between the rider and pedestrian after 4 hours.

Answer: 72 km.

Example 4 . From the two stares at the same time, two boats came to each other, who met 5 hours after the start of the movement. One of the boats was moving with a leaning of 28 km / h, and the second is 36 km / h. Find the distance between the pins.

1) 28 + 36 \u003d 64 (km) - the boats every hour came closer.

2) 64 * 5 \u003d 320 (km) - the distance between the marins.

Answer 320 km.