Volumetric figure and geometric body – lesson. Geometry, 10th grade.

Working with three-dimensional geometric shapes as a means of developing spatial thinking in elementary school students.

Working with three-dimensional geometric shapes as a means of developing spatial thinking in elementary school students.

The content of geometric material in primary school constitutes the preparatory part of the geometry course and is included step by step in the mathematics course. From the second grade under the “Harmony” program and from the fourth grade under the “21st Century School” program, children begin to work with the image of three-dimensional figures.

For the first time, a beginning student consciously studies the geometry of the world around him. The most important property of any object is its shape, and therefore the child must be taught, first of all, to correctly perceive the shape of the object, and this means learning to highlight the contour of the object, learning to highlight its individual properties, the relative position of the lines. However, until now the question of the organized perception of form by primary schoolchildren remains practically unresolved.

The low level of spatial thinking of students requires greater clarity when solving geometric problems. At the same time, the question often arises about the ease of operating with spatial images of figures and the teacher himself. The most effective means of developing students’ spatial concepts, as is known, are, according to L. L. Burkova: demonstrating figures, comparing the positions of geometric figures relative to each other, modeling, competent depiction of figures, reading a drawing. These remedies lead to the best results if they are used systematically and in combination. The creation of graphic images or graphic modeling is necessary not only for successful teaching of the basics of science, but is also of considerable importance in visual, design, and technical activities, and is implemented in everyday life.

When studying the basics of geometry by primary schoolchildren, relying only on direct contemplation is not enough. Mobility and the associated muscular feeling play a fundamental role in the development of the intellect of the psyche and personality; the visual and practical teaching of geometry should allow the work of the subject model to determine geometric facts. This means that any new knowledge that will be gained during the child’s active operations, but not limited to observing the actions of others.

Cognitive activity organized on such a basis allows one to practically transform the subject of study in accordance with the set goal. Thus, the formation of a geometric image is very important for the activity of tactile and visual analyzers. Tactile analyzers are also one of the most important sources of knowledge about the space and mechanical properties of objects.

Research by psychologists of the last decade on the theory of sensory perception of schoolchildren was aimed, along with other questions, at clarifying the role of the contour in the perception of the shape of an object in various types of practical activities of children of different age groups.

So V.P. Sokhina studied the formation of visual analysis in the process of constructing an object from planar elements. To do this, when teaching children, she used the technique of superimposing parts of a sample onto a whole sample.

G. A. Uruntaeva considered the question of how children become familiar with the shape and size of an object during play activities.

The main objectives of the study, according to G. A. Uruntaeva, were: “the ability to form a complete, dissected perception of the properties of objects, to teach the forms of methods of analysis and the value of things, in order to understand relatively complex connections and relationships between objects.”

Research by G. A. Uruntaeva, Yu. A. Afonkina shows that errors in the perception of children are formed not due to their age or natural characteristics, but “the very nature of preparation, which often does not provide the opportunity to see and analyze what The child’s eyes look and he touches them with his fingers.”

The works of a group of psychologists – M.V. Matyukhina, T.S. Mikhalchik and K.T. Patrina – show the following: “The process of perception is often limited only to the recognition of an object and the subsequent name of the object. At first, students do not make the subject the object of careful and lengthy examination. The perceptions of first grade students are poorly differentiated.”

First-graders depict the shape of an object by its name, without analyzing this shape, as a result of which the images of the same shape turn out to be very diverse. In order to organize the correct perception of geometric information by younger schoolchildren, the question of the need to decide what should be the object of perception and how it should continue the process of perception. It should be noted that when studying volumetric geometric forms provided for in a number of primary mathematics course programs – for example, “School of the 21st Century”, “Harmony”, “Perspective”, etc. At the same time, the volume, content, and methodological aspects of studying this material are different .

Consideration of objects in the surrounding world and contrasting them with each other makes it possible to distinguish shape among other properties of objects (color, size, quality of material, etc.). Compare and contrast objects of the same shape, facilitates the transition to geometric shapes in the form of a bulk material model of a geometric figure.

The experience of foreign teachers and the research of our domestic teachers and psychologists show that the process of perception becomes more complete and deeper if not only the eyes, but also the hands of a person are included in cognition. So, the initial acquaintance with three-dimensional figures in their objective meaning is carried out by turning to the objects of reality and their materialized norms.

Analysis of the shape model, drawing on the child’s sensory experience, allows one to select the elements of the main body of a geometric figure by obtaining a graphic trace to place them in the line of a flat figure. Comparing flat figures, three-dimensional figures, and flat and three-dimensional figures with each other helps form an idea of ​​their properties.

Appeal to objects of reality proves the existence of geometric forms; the use of models and ready-made drawings contributes to their detailed perception. The fact that the ability to feel (hold) his hands of geometric shapes and arrange them in different ways increases the motivation of design and research activities.

A. M. Astryab, considering the two stages of cognition of geometric forms (perception and formation of geometric images in the child’s mind), emphasizes that in order for the perception to be as bright as possible and complete, it is necessary that the perception is accompanied by muscle and tactile sensations [1].

Therefore, he attaches particular importance to such types of child activities as modeling, cutting, gluing, drawing. The child learns to know well if they are acquired from the material, requiring from him the ability to do something with his own hands. The starting point for an initial introduction to the concept and its properties is practical activities. Their goal is to determine the meaning of a new term. Thus, the subject of action creates the basis for the development of cognitive processes.

Analysis of scientific and methodological literature allows us to highlight methodological provisions for teaching the elements of geometry to junior schoolchildren:

1. Students obtain a geometric representation through abstraction from objects of reality. The basis of academic knowledge is the child’s personal sensory experience and observations.

2. The success of all geometric propaedeutics significantly depends on the correct organization of the phase of clarifying and expanding the sensory experience of preschool children.

3. In the elementary grades, flat geometric figures and their individual properties should be studied.

Using the model of flat figures, it makes it possible to show how the process of abstraction is carried out, as the identification of the general properties of figures – form and its generalization in a word, the meaning of which is now clear to schoolchildren.

4. In the process of studying the elements of geometry by first familiarizing children with the figure, first become familiar with the existing quality of their understanding of the properties of the figures, and then with their quantitative characteristics.

5. Conscious perception of geometric facts, memorizing them, as well as the formation of skills to identify and generalize the properties of geometric figures, the ability to justify their observations and produced actions associated with the development of mathematical language, using scientific terminology available for this age.

Knowledge of these features, as well as knowledge of the patterns of development of mental operations, is necessary for the effective formation of geometric ideas and concepts.

When carrying out the formation and development of spatial ideas about geometric volumetric figures during training, it is necessary to take into account the age and individual characteristics of the students.

There are pronounced age-related differences in the spatial representations of students, which manifest themselves, according to S.D. Kamilova as follows:

– With age, with the accumulation of geometric knowledge and skills, there is a reserve for processing spatial representations, and their qualitative change, expressed in dynamic and rich content;

– Teaching young children works with those visual aids that were used or given by teachers in the textbook; with age, they begin to make independent choices of visual material;

– Teaching and raising young children, when performing almost any task in geometry, they try to make drawings, sketches, older students use their visual support much less;

– For students of primary school age, the general geometric situation arises as a generalization based on experience, for older students this often occurs on the basis of logical and theoretical considerations;

– Teaching and raising young children often cannot tell us about the difficulties they encounter when working with images of geometric objects and solving problems;

– The ability to transfer images of operational methods of geometric objects to new challenges increases with age;

– Training and education of young children in solving problems mainly focused on the final result of operation; older students are most interested in the process of achieving results, trying to master the most rational methods of working with images of geometric objects.

Age-related characteristics are taken into account when selecting exercises available to a particular age group of students, when using certain visual aids in the learning process, when relying on their existing knowledge, on already formed spatial representations.

The practical part of the development of spatial thinking in mathematics lessons in primary school is based on construction and modeling from materials known to children: sticks, plasticine, wire, which allows students to consolidate a stable image of a figure in their memory. At the same time, there is an acquaintance with the details of the designer, simple connections of parts with each other. Familiarity with the origami technique allows students to develop the ability to pose questions about the world and look for answers to them, develop curiosity and creativity, and teach basic skills in reading drawings and technological maps.

Concept formation occurs in the following stages:

I. Preparatory stage. I I. Introduction to the concept. I II. Consolidation.

IV. Generalization.

Introducing three-dimensional bodies in mathematics lessons can occur in the following sequence:

I. Introduction to the ball and its properties.

II. Introduction to the cylinder and its properties.

III. Introduction to the cone and its properties.

IV. Generalization on the topics “Ball”, “Cylinder”, “Cone”.

V. Introduction to the prism and its properties; acquaintance with parallelepiped and cube.

VI. Introduction to the pyramid and its properties.

VII. Generalization on the topics “Prism”, “Pyramid”; introduction of the concept of “Polyhedron”.

VIII. Generalization and consolidation of knowledge on the topics “Ball”, “Cylinder”, “Cone” and “Polyhedron”.

Using an example, we will present a system of tasks for the formation of the concept “Ball”.

I. Purpose: to introduce the ball. Introduce the concept of “form”.

Equipment: spherical objects, a set of photographs and drawings of spherical objects, a cylinder, a cone, a circle. Additionally, you can prepare a presentation and show pictures of the balls on a projector or monitor.

Examination of a group of objects. What is this? (Globe, tennis ball, inflatable ball, ball, beads, peas. See how all these objects differ from each other?

– by color, by size; according to the material from which they are made; made by man or created by nature; by appointment; by severity; on transparency, etc.

What techniques do artists use to depict three-dimensional bodies? What about mathematicians?

What unites, how are they similar? (If “round”, then show a circle. A circle is round, but what about these objects?) These are balls. So what do all these items have in common? (Form)

What else do these items have in common? Look, they don’t want to lie on the table. They all ride. Is the ball rolling? So he’s a ball. Is the pea rolling? This is also a ball. Show cylinder and cone. Are they skating? So they are also balls?

Try it, ride it. How do these figures roll, and how does the ball roll? (The ball rolls in all directions.)

Draw a conclusion. What do all these items have in common? (Ball-shaped, three-dimensional, ability to roll in different directions.) How can you call all these objects in one word? (Ball).

Look around you. Are there any balloons in the classroom? Remember where you saw spherical objects at home or on the street? (Christmas tree decorations in the shape of a ball, lampshades, berries, balls, etc.) Look at the photographs and drawings.

Do you know why a ball is called a ball? The word “ball” comes from the Greek word [fatra], which means “ball”.

Homework is to write down in your notebooks the names of spherical objects that we didn’t remember in class.

II. Goal: to consolidate the concept of “ball” and its properties.

Equipment: a set of objects of different shapes for playing “Black Box”; geometric bodies and flat figures made of colored paper, balls, plasticine.

Let’s play the game “Silence”. You must silently show me, draw a ball with your hands, show all its properties. Who has it better?

Take plasticine and mold each of your own balls. What is the difference? (Color, size.) What’s in common?

Place the largest ball on the right and the smallest on the left. Place a green ball, followed by a red one, and a blue one in front of it.

At the board there are objects of various shapes, figures cut out of colored paper. Show only balls.

The board has two spherical objects, a cone, a cylinder and a circle made of paper. Children close their eyes, the teacher removes one object. Children open their eyes, if the ball has disappeared, clap their hands.

Game “Black Box”. There are many different items in the box. Your task is to get the ball, determining that it is a ball by touch.

When forming concepts, various creative tasks and exercises can be used. This could be writing fairy tales, poems, various crafts, drawings, mathematical newspapers and wall newspapers, etc.

One type of creative task when working with concepts is the compilation of a “Geometric Dictionary” by children. When compiling a dictionary, he defines children (in their own words, as they understand), will highlight essential properties, select interesting material, draw up a dictionary, come up with stories, poems, riddles, and make drawings.

Children also become familiar with various techniques for depicting three-dimensional objects on a plane, creating the illusion of volume. Through a system of tasks, children independently come to the conclusion that artists, graphic artists, and draftsmen are used for this purpose. For this purpose, painters use the play of chiaroscuro or perspective, graphic artists use the curvature of lines, draftsmen use orthogonal projection.

In addition to these techniques, children become familiar with the image of three views of an object (front, top, side). This method is especially important for the development of spatial thinking.

Comparison of models of different names can be used as an effective method for developing spatial imagination. All this material is studied at an introductory level. For example, when comparing models of a ball, cylinder, cone, children note that what they have in common is the ability to roll (roll). The difference is that the ball rolls arbitrarily, the cylinder rolls in a straight line, the cone rolls in a circle, in the center of which its vertex is located. The differences between these bodies are also that a ball has neither vertices nor bases, a cylinder has two bases but no vertices, a cone has one base and one vertex. Similarly, a prism and a pyramid, a cylinder and a prism, a pyramid and a cone, etc. are considered and compared.

A variant of this work is to compare three-dimensional figures of the same name. For example, children are asked to compare several different prisms. When completing a task, signs of similarities and differences are revealed.

Signs of similarity: all prisms have two polygonal bases, edges and vertices, their side faces are rectangles (in elementary school we consider only straight prisms).

Signs of difference: the bases are different polygons, the number of vertices and edges is different, the lengths of the edges are different.

You can have students find prisms that have only one or another number of differentiating features and discuss why this is so.

In addition, when forming and developing spatial concepts, including when working with three-dimensional figures, it is also necessary to take into account the individual characteristics of students, which are associated with the level of development of cognitive capabilities and abilities. As research shows, persistent individual differences are observed in solving problems involving spatial transformations, that is, in the levels of development of spatial thinking.

In the conditions of specially organized training, it is possible to both expand age-related opportunities and level out individual differences. Taking into account individual characteristics presupposes a differentiated approach to training, which can be implemented in the methodology of conducting classes and developing a system of exercises.

Thus, in the methodology for the formation and development of spatial representations, special methodological techniques can be used to stimulate and guide this process. These include, for example, the creation of situations that contribute to the creation of holistic, generalized spatial representations; creating situations that promote active manipulation of images of geometric objects, creative construction of images of geometric configurations, etc.

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Development of cognitive interest in mathematics lessons

/from the experience of primary school teacher L. N. Alekhina

Municipal educational institution “Secondary school No. 64”, Novokuznetsk /

Cognitive interest is a selective focus of the individual on objects and phenomena surrounding reality.

This orientation is characterized by children’s constant desire for knowledge, for new, more complete and profound knowledge. Systematically strengthening and developing cognitive interest becomes the basis of a positive attitude towards learning; under his influence, even weak students’ academic work is more productive.

Cognitive interest is a powerful means of communication. Classical pedagogy of the past stated: “The deadly sin of a teacher is to be boring.” When a child studies under pressure, he causes the teacher a lot of trouble and grief. When children engage in hunting, things go completely differently.

Activating a student’s cognitive activity without developing cognitive interest is not only difficult, but practically impossible. That is why, in the learning process, it is necessary to systematically develop and strengthen cognitive interest in students, both as an important motive for learning, and as a persistent personality trait, and as a powerful means of educational learning.

Every person has a desire to be smarter, better and more resourceful. It is this desire of the student that affirms self-esteem, brings him satisfaction and a good mood during successful activities, in which he works faster, more successfully and more productively.

The first thing that is a subject of cognitive interest for schoolchildren is new knowledge about the world. Showing the wealth contained in scientific knowledge is the most important element in developing interest in learning. Interest is aroused by educational material that is new, unknown, and surprising for students. Surprise is a strong stimulus for cognition. Being surprised, a person seems to strive to look ahead. He is in a state of anticipation of something new. Students are surprised when, while solving a problem, they learn that one owl destroys a thousand mice in a year, which can destroy a ton of grain in a year, and that an owl, living on average 50 years, saves us 50 tons of bread. Interest in knowledge is also promoted by displaying the latest achievements of science. In the educational process, it is necessary to expand the scope of programs, to acquaint students with different areas of scientific research and discoveries.

But not everything in the educational material can be interesting for students. And then another, no less important source of cognitive interest appears – the process of activity itself.

To make children want to learn, I use different types of activities in my lessons. First of all, a variety of independent work, organized in accordance with the specific interests of the class. I teach children to independently look for different ways to solve a problem.

Independent work

for schoolchildren – this is a form of organizing educational activities and the most difficult moment of the lesson. Therefore, in my work I use preparatory exercises, cards with differentiated tasks, think through the sequence of tasks, use variation, commenting, and clarity. Children learn to work independently in pairs, in groups and find different ways to solve tasks. Finding a way is a learning action – it is a unit of knowledge.

Works related to imagination especially develop interest. For this purpose I use

Support diagrams

For example, using this diagram-drawing we study the order of actions

In expressions, first we count what is in parentheses, then multiplication and division in order from left to right, then addition and subtraction in order.

I also use it in my work

Problem-based learning

Problem-based learning, rather than presenting ready-made facts and conclusions suitable only for memorization, always arouses the unflagging interest of students. Such training forces us to seek the truth and find it as a whole team. Problem-based learning is the basis of new educational curricula. In problem-based learning, a question-problem is raised for general discussion, sometimes containing an element of contradiction, sometimes of surprise.

Children discuss the problem posed; The lesson creates an atmosphere of excitement, reflection, and search. For example, a lesson in 2nd grade:

Lesson topic:
Solving examples of the form 30-6

Before explaining the topic, I used preliminary preparation for the perception of new things – this creates a situation of success.

– Populate the house with numbers.

Repeat the composition of the number 10.

– Insert the numbers into the boxes according to the given pattern.

40=30 1080= 10

60=50 1050=

Select 1 ten in round tens.

– Solve the expression in a convenient way

(40 10 ) – 7 (60 10 ) – 4

When writing the solution on the board, I give the children the task:

– Find how the amounts in these examples are similar? And having received the answer:

– The second terms are the same – this is the number 10, children circle the terms in red. Then I record it visually by connecting the number 10 and the number that is being subtracted with an arc. After this work, children independently draw conclusions as from 30-6; They establish a pattern themselves, using previously acquired knowledge. Using

Entertaining material

The element of entertainment is a game that arouses keen interest in children and helps them learn any educational material. The game puts the student in search conditions and awakens interest in winning. Children strive to be fast, dexterous, and resourceful.

In my work I use different games: “Ladder”, “Milchanka”, “Train” and others. Let me give you an example of two games.

1.
Free the birdie
.

The birds are in a cage. I invite the children to let them out into the wild. Students take the bird from the cage and read the task from the back. If the student answers correctly, the bird flies to the tree; if not, it returns to the cage.

“Riddle.”

I make a riddle: “A silver saw in the sky forked a thread. Who was brave enough to sew the sky with a white thread, but hastened and fluffed up the tail of the thread?”

– To solve the riddle, replace the number with tens and ones and find the letters in the table.

5 units.

6 units.

8 units.

L

3 dec.

K

D

H

76

98

75

38

95

35

7dec.

T

L

M

9 dec.

AND

Yu

Ё

Answer: pilot.

– Answer: pilot. Whoever guessed the riddle is taken on board by the pilot and we set off on a flight-journey on a new topic.

I also conduct relay races in lessons: “A very long example”, “Assemble a robot”, “An example to each”.

I use it in lessons

Geometric material.

I’m giving away a drawing of a cat made up of geometric shapes. I ask:

– What figures does the drawing consist of?

– What figure represents the torso?

– Measure and find the area and perimeter of this figure.

Or, on the contrary, I distribute geometric figures to the children with the task:

– Make a house, a Christmas tree, a boat from these figures.

Problem solving

At every lesson, I ensure that students engage in mathematics with interest, I teach them to solve problems. To develop interest in solving problems, I use a system of exercises that develop mathematical memory. I teach how to highlight numbers in problems and memorize them, since mathematics is the world of numbers, and mathematical abilities are the manipulation of numbers.

When a child reads the statement of a problem, he cannot immediately remember all the numbers that appear there, he is confused and cannot build an internal strategy for solving the problem. To develop mathematical memory, I suggest children listen to the text and remember only the numbers, and then write them down in a notebook. At the beginning of the exercises, the texts have no more than three numbers, then I increase the number of numbers. Here are two texts for grade 4:

1.“What is the Milky Way? This galaxy is just one of 10 billion observable galaxies. It has the shape of a giant rotating disk with spiral “sleeves”. Our tiny planet is quite far away, at a distance of two-thirds of the radius from the center of the galaxy. And our Universe was born 15-20 billion years ago. years ago as a result of the Big Bang.”

2. “The ship “Erasmus” tilted from a sudden squall. The rigging groaned. The vessel, displacing 260 tons, had three masts and was a twenty-gun merchant warship that survived the first expedition to open the Straits of Magellan. 496 Dutch were following orders: to discover new islands in the Pacific Ocean.”

Such texts develop an understanding of the world and broaden one’s horizons.

In the process of a schoolchild’s educational activities, a major role, as psychologists note, is played by the level of development

Cognitive processes:

attention, perception, thinking, memory.

To develop attention I use the following tasks:

Finding moves in number mazes.

Find who is hiding.

Read the scattered words.

To develop perception (and it is the basis of thinking in practical activities), I use the following exercises:

Collect the broken jug and vase.

Exercises with geometric figures.

Match the patch to the boot.

To develop logical thinking and mathematical logic I use:

Challenges for ingenuity.

Joke problems.

Crosswords and puzzles.

Logical exercises.

To develop memory, I teach to memorize numbers, chains of words, mathematical terms, and draw patterns from memory.

Already in the elementary grades, interest in academic subjects is formed. However, this process does not occur automatically; it is associated with the activation of students’ cognitive activity during the learning process.

Anton Semenovich Makarenko believed that the life and work of a child should be imbued with interest.

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SPECIFICATIONS

test work

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 1. “Tabular Multiplication and Division”

Purpose: to test knowledge of table multiplication and division, ability to solve problems, build a rectangle and find its perimeter.

Job No.

Verified ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems to find the sum

B

RO

See grading system

2

ability to solve problems involving dividing a whole number into parts

B

RO

3

knowledge of table multiplication and division,

B

KO

4

the ability to construct a rectangle and find its perimeter

B

KO

5

students’ readiness to solve non-standard educational problems

P

RO

6

students’ readiness to solve non-standard educational problems

P

RO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”
– 1 rude and 1-2 black mistakes, with rude
there should be no mistakes
be on task.

“3” – 2-3 blunders and 3-4 non-blunders, with
In this case, the solution to problem must be correct.

“2”
– 4 serious mistakes.

Blunders:


computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,
extra
actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:


irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

Option 1.

1. Solve the problem.

26 baskets of plums were collected in the garden, and 7 baskets more apples than pears. How many baskets of fruit did you collect in the garden?

2. Solve the problem.

The guys took 21 cans of canned food on a hike and divided them equally into 3 backpacks. How many cans did each person carry?

3. Calculate:

6 ∙ 3 : 2 15 81 – (52 – 9)

6 ∙10 – 18 80 : (49 – 39)

21 : 7 ∙ 9 – 5 (76 14) : 9

4
. Draw a rectangle with sides 4 cm and 3 cm. Find the perimeter of this rectangle.

5.
*
Dima bought a set of colored paper for 30 rubles. and glue. He gave 50 rubles to the cashier. and received change of 11 rubles. How much did the glue cost?

6
*

.
How much greater is the product of the numbers 9 and 2 than the difference of these numbers?

Option 2.

1. Solve the problem.

The teacher checked 35 squared notebooks, and 6 less lined notebooks. How many notebooks did the teacher check?

2. Solve the problem.

12 liters of milk were poured into jars, 2 liters each. How many cans did you need?

3. Calculate:

2∙ 3 ∙10 – 60 (17 43) : 10

2 ∙ 4 ∙ 3 – 20 90 : (69 – 60)

12 : 6 ∙ 8 (12 – 8) ∙ 3

4.
Draw a rectangle with sides 5 cm and 2 cm. Find the perimeter of this rectangle.

5.
*
Dima bought a set of colored paper for 30 rubles. and glue. He gave 50 rubles to the cashier. and received change of 11 rubles. How much did the glue cost?

6
*

.
How much greater is the product of the numbers 9 and 2 than the difference of these numbers?

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 2 (Final for 1 quarter.)

Purpose: to test computational skills, problem solving ability, and find the perimeter of a rectangle.

Job No.

Verifiable records

Difficulty level

Answer type

Number of points

1

ability to solve multiplication problems

B

RO

See grading system

2

ability to solve multiple comparison problems

B

RO

3

knowledge of table multiplication and division

B

KO

4

ability to find the perimeter of a rectangle

B

KO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –

no mistakes.

“4”

– 1 rude and 1-2 black mistakes, with rude

there should be no errors

be on task.


“3” – 2-3 blunders and 3-4

non-blunders, with

In this case, the solution to the problem

must be correct.

“2”

– 4 serious mistakes.

Blunders:

computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,

extra

actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:

irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

Option 1.

1. Solve the problem.

Kolya has 6 postcards, and there are 3 times more stamps than postcards. How many stamps does Kolya have?

2. Solve the problem.

The children found 16 russula and 4 boletus. How many times fewer children found boletus than russula?

3. Find the meaning of the expressions.

24 – 18 : 6 7 ∙ (2 3) 19 24 : 6
25 : 5 9 (13 7) : 5 (4 2) ∙ 4

4.
Find the perimeter of a rectangle with sides 5cm and 4cm.
Option 2.

1. Solve the problem.

32 boys took part in the chess tournament, and 4 times less girls. How many girls participated in the tournament?
2. Solve the problem.


There are 16 chairs and 2 tables in the hall. How many times are there fewer tables than chairs?
3. Find the meaning of the expressions.

6 7 ∙ 4 15 : (1 4) 41 – 24 : 3
36 : 4 : 3 8 ∙ (6 – 2) 49 : (10 – 3)

4.

Find the perimeter of a rectangle with sides 7cm and 3cm.

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 3

Purpose: testing computing skills, knowledge of the procedure, ability to solve problems.

ability to construct a square and find its perimeter

B

5


students’ readiness to solve non-standard educational problems

P

RO


Task No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied type

B

RO

See grading system

2

knowledge of table multiplication and division

B

KO

3

knowledge of the procedure

B

KO

4

RO


Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”

– 1 rude and 1-2 black

mistakes, with rude

there should be no errors

be on task.

“3” – 2-3 blunders and 3-4

non-blunders, with
In this case, the solution to problem must be correct.

“2”
– 4 serious mistakes.

Blunders:


computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,

extra

actions); not completing the solution to a problem or example; unfinished task.

irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

1. Solve the problem:

The piece contained 54 m of fabric. 9 jackets were sewn from this fabric, using 3 meters for each. How many meters of fabric are left in the piece?

2. Solve the examples:

Non-blunders:

Option 1

63 : 7 ∙4= 15 :3∙9=

24 : 4 ∙7= 54 : 9 ∙8=
79 :7 ∙ 5= 14 : 2 ∙ 4=
3. Indicate the procedure and perform the calculations:

90-6∙6 29= 5∙ (62-53)=

4. Insert x or : so that the entries are correct:

8 * 4 * 9 = 18 4 * 4 * 1 = 16

5. Draw a square with a side of 4 cm. Find its perimeter.

6. *

The product of two numbers is 81. How will the product change if one of the factors is reduced by 3 times?

Option 2

1. Solve the problem:

The guys prepared 50 sheets of paper to make folders. They made 8 folders, using 4 sheets of paper for each. How many sheets of paper do the guys have left?

2. Solve the examples, writing them in a column:

21 : 3 ∙ 8= 45 : 5 ∙ 6=

28 : 4 ∙9= 32 : 8 ∙ 4=

54 : 6 ∙7= 27 : 3 ∙ 5=

3. Indicate the procedure and perform the calculations:

90 – 7 ∙ 5 26= 6 ∙ (54 – 47)=

4. Insert x or : so that the entries are correct:

6 * 3 * 9 = 18 3 * 3 * 1 = 9

5. Draw a square with a side of 3 cm. Find its perimeter.

6 *
.

The product of two numbers is 64. How will the product change if one of the factors is reduced by 2 times?

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 4 (final for the 2nd quarter)

Tse
Purpose: testing computing skills, the ability to solve problems on finding area, proportional division.

5

knowledge of table multiplication and division

B

Task No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied types

B

RO

See grading system

2

knowledge of table multiplication and division

B

KO

3

ability to form equalities and inequalities

B

KO

4

ability to find the area of ​​a rectangle and square

B

RO


KO

6

students’ readiness to solve non-standard educational problems

P

RO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”

– 1 rude and 1-2 black

mistakes, with rude

there should be no errors

be on task.

“3” – 2-3 blunders and 3-4

non-blunders, with

In this case, the solution to problem must be correct.

“2”

– 4 serious mistakes.

Blunders:


computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,
extra

actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:


irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

Option 1

1. Solve the problem:

Three identical boxes contain 27 kg of lemons. How many kg of lemons are in 6 such boxes?

2. Solve the examples:

72-64 : 8= 36 (50-13)=
(37 5) : 7= 25 : 5 ∙9=

63 : 9 ∙ 8= 72 : 9 ∙4=
3. Make up two inequalities and equalities using the expressions:

8 ∙4; 40-5; 4∙8; 40-8.

4. Find the area of ​​a rectangular vegetable garden if the length is 8 meters and the width is 5 meters.
5. Fill in the numbers so that the entries are correct.

36 : 4 = *∙3 4 ∙ * = 6 ∙ 6

8 ∙ 3 = 4 ∙ * * : 9 = 10 : 5

6. * Dad divided 12 firecrackers equally between his son and his three friends. How many crackers did each boy receive?

Option 2

1. Solve the problem:

8 identical suits were sewn from 32 m of fabric. How many meters of fabric will be needed for 9 such suits?

2. Solve the examples:

75-32:8= 81:9∙5=

8∙ (92-84)= 42:7∙3=

(56 7) :9= 64:8∙7=

3. Make up two inequalities and equalities using the expressions:

3∙7; 30-9; 7∙3; 30-3.

4. Find the area of ​​a square flower bed if its side is 4 m.

5. Insert the numbers so that the entries are correct:

30 :5 = 24 : * 6 ∙ 4 = * ∙ 3

* : 8 = 12 : 2 * ∙ 3 = 9 ∙ 2

6. * ∙Katya divided 18 dumplings equally between her brother Tolya and his two friends. How many dumplings were on each plate?

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 5

Purpose: testing computational skills, the ability to solve equations, problems, build a square and find its perimeter and area.

Text of the work.

Job No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied types

B

RO

See grading system

2

knowledge of table multiplication and division

B

KO

3

ability to solve equations

B

KO

4

the ability to compare expressions using knowledge of the property of multiplying a sum by a number

B

KO

5

the ability to construct a square and find its perimeter and area

B

RO


Difficulty level: B – basic, P – advanced, V – high.

Option 1

1. Solve the problem:

35 paintings were brought to the exhibition and hung in the halls, 7 paintings in each hall. The guide has already given a tour of 3 halls. How many more halls are there left for the guide to show?

2. Find the meaning of the expressions:
26 18∙4= 80:16∙13= 72-96:8=

31∙3-17= 57:19∙32= 36 42:3=

3. Solve the equations:
72 : x = 4 x : 5 = 16
4. Compare the expressions:
6∙3 8 ∙ 3 … (6 8) ∙3

5 ∙ 12 …5 ∙ (10 2)

5. Draw a square with a side of 5 cm. Find the perimeter and area.

Option 2

1. Solve the problem:

72 candies were divided into New Year’s gifts, each gift containing 9 candies. 6 gifts have already been given to children. How many gifts are left?

2. Find the meaning of the expressions:

11∙7 23= 56:14∙19= 72:18 78=

23 27∙2= 60:15∙13= 86-78:13=

3. Solve the equations:

x : 6 = 11 x : 6= 14

4. Compare the expressions:

(20 8) x 2 … 28 x 3

(7 4) x 4 … 7 x 4 4 x 4

5. Draw a square with a side of 3 cm. Find the area and perimeter.

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 6

Purpose: testing the ability to divide with a remainder, solve problems, perform extra-table multiplication and division

Task No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied types

B

RO

See grading system

2

ability to divide with a remainder and check division with a remainder

B

KO

3

skill
perform out-of-table multiplication and division

B

KO

4

the ability, by comparing the remainder and the divisor, to determine whether the equality is correct

B

VO

5

students’ readiness to solve non-standard educational problems

P

RO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”
– 1 rude and 1-2 black mistakes, with rude
there should be no mistakes
be on task.

“3” – 2-3 blunders and 3-4 non-blunders, with
In this case, the solution to the problem must be correct.

“2”
– 4 serious mistakes.

Blunders:


computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,
extra
actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:


irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

1. Solve the problem
The people on duty in the dining room have 48 deep plates and the same number of small ones. The attendants must place all plates on 12 tables, equally distributed on each table. How many plates should they put on each table?
2. Divide with remainder and check:

64:7= 50:15= 100:30=
3. Find the meaning of the expressions

Option 1

57:3= 44:22= 8×12=
66:6= 72:12= 26×3=
4. Without filling in the “boxes” with numbers, write down the incorrect equations:
52:4=[ ](rest.4) 7:6=[ ](rest.3) 83:7=[ ](rest.9)
5 * Write down at least three two-digit numbers that, when divided by 7, leave a remainder of 5 Option 2

1. Solve the problem

Sasha has 49 rubles, and Petya has the same amount. With all the money they can buy 14 identical notebooks. How much does one notebook cost?

2. Divide with remainder and check:

40:9= 80:12= 90:20=

3. Find the meaning of the expressions.

55:5= 75:25= 6×14=

87:3= 52:13= 32×2=

4. Without filling in the “boxes” with numbers, write down the incorrect equalities

43:8=[ ](rest.8) 31:7=[ ](rest.3) 62:5=[ ](rest.8)

6. * Write down at least three two-digit numbers that, when divided by 8, leave a remainder of 6

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 7 (final for the 3rd quarter)

Purpose: testing knowledge of the order of operations, knowledge of the multiplication table, ability to divide with a remainder, and solve problems on finding area and perimeter.

Task No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

knowledge of the procedure

B

KO

See grading system

2

ability to divide with remainder

B

KO

3

ability to solve problems of the studied types

B

RO

4

ability to convert length units

B

KO

5

the ability to find the perimeter and area of ​​a rectangle, first finding its width

B

RO

6

students’ readiness to solve non-standard educational problems

P

RO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”
– 1 rude and 1-2 black mistakes, with rude
there should be no mistakes
be on task.

“3” – 2-3 blunders and 3-4 non-blunders, with
In this case, the solution to problem must be correct.

“2”
– 4 serious mistakes.

Blunders:


computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,
extra
actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:


irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

Option 1

1. Specify the order of actions and find the meaning of the expressions:

85 35:5= 96-72:12 15= 8×8-9×4= (92-87)x9= 7x(63: 9-7)= 45:15=

2. Find the quotient and remainder:

17:6 20:3 48:9

57:6 43:8 39:5
3. Solve the problem.
The bouquet contains 20 red roses, and there are 4 times fewer white roses than red ones. How many fewer white roses are there than red ones?

4. Insert numbers into the “boxes” so that the equations become true:

[ ] m 14 cm = 714 cm 8 m 5 cm = [ ] cm
250 cm = [ ]m [ ]cm 400 cm = [ ] dm

5. The length of the rectangle is 20 cm, and the width is 4 times less. Find the perimeter and area of ​​this rectangle.

6* Mukha Tsokotukha bought a samovar and invited guests. She baked 60 pretzels for tea. Each guest got a whole pretzel and a half, with 3 more pretzels left. How many guests were there?

Option 2

1. Specify the order of actions and find the meaning of the expressions:

78 42 :7= 78-19×2 34= 9×8-6×7=

(65-58)x8= 5x(81:9-8)= 96:24=

2. Find the quotient and remainder:

47:5 39:6 71:9

19:6 63:8 49:5

3. Solve the problem.

They put 6 turnips in the bag, and 3 times more in the bag than in the bag. How many more turnips were put in the bag than in the bag?

4. Insert numbers into the “boxes” so that the equations become true:

[ ] m16 cm = 916 cm 4 m 3 cm = [ ] cm

370 cm = [ ]m [ ]cm 700 cm = [ ] dm

5. The length of the rectangle is 40 cm, and the width is 20 times less.

Find the perimeter and area of ​​this rectangle.

6 *The Three Fat Men were afraid that they had lost weight. The three of us stepped on the scales – everything was fine, 750 kg. The first Fat Man and the second Fat Man stood on the scales – 450 kg. Second and third Fat Men – 550 kg. Find the weight of each Fat Man.

Item

Mathematics

Class

3

Topic (purpose of work)

Test 8

Purpose: Test the ability to perform written addition and subtraction of multi-digit numbers, compare named numbers and solve problems.

Task No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied types

B

RO

See grading system

2

ability to write multi-digit numbers

B

KO

3

ability to perform written addition and subtraction of multi-digit numbers

B

KO

4

skill
perform table multiplication and division

B

KO

5

skill
compare named numbers

B

KO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”
– 1 rude and 1-2 black mistakes, with rude
there should be no mistakes
be on task.

“3” – 2-3 blunders and 3-4 non-blunders, with
In this case, the solution to problem must be correct.

“2”
– 4 serious mistakes.

Blunders:


computational errors in examples and problems; order of actions, incorrect solution to a problem (omission of an action, incorrect choice of actions,
extra
actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:


irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade is not reduced.

Text of work

Option 1

1. Solve the problem:

In the morning there were 813 rubles in the class. During the day, 508 rubles were given out of it, and 280 rubles were accepted. How much money was in the cash register at the end of the day?

2. Write down the number consisting of:

– from 6 hundred. 2 dec. 4 units

– from 8 hundred. and 3 des.

– out of 5 units. first category, 2 units. second category and 4 units. third category.

3. Find the meanings of the expressions by writing them in a column:

354 228= 505 337=

867-349= 650-370=

4. Insert the appropriate action sign into the “boxes”:

27 * 3 * 7 = 17

27 * 3 * 7 = 16

27 * 3 * 7 = 23

5. Compare and put comparison marks.

5h … 400 min 91 x 3 … 19 x 3

4m 5dm … 5m 4dm 687 1 … 687 x 1

Option 2

1. Solve the problem:

There are 385 residents in three houses. There are 134 residents in the first house, 117 in the second. How many residents are there in the third house?

2. Write down the number consisting of:

– from 3 hundred. 1dec. 8 units

– out of 6 hundred. and 2 des.

– out of 7 units. first category, 1 unit. second category and 5 units. third category.

3. . Find the meanings of the expressions by writing them in the column:

744 180= 623 79=

925-307= 136-98=

4. Insert the appropriate action sign into the “boxes”:

27 * 3 * 7 =16

27 * 3 * 7 = 37

27 * 3 * 7 = 2

5. Compare and put comparison marks.

6h … 600 min 78 x 4 … 87 x 4

7m 8dm … 8m 7dm 259 – 1 … 259 : 1

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 9.

Purpose: to test the ability to perform written multiplication by a single-digit number, compare quantities, and solve problems.

Job No.

Verifiable records

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied types

B

RO

See grading system

2

ability to perform written multiplication by a single-digit number

B

KO

3

ability to compare quantities

B

KO

4

the ability to find the length of the side of a square based on its perimeter

B

RO

Difficulty level: B – basic, P – advanced, V – high.

Answer type: VO – choice of answer, KO – short answer, RO – extended answer.

Grading system

“5” –
no mistakes.

“4”
– 1 gross and 1-2 non-blank errors, while there should be no gross errors in the problem.

“3” – 2-3 blunders and 3-4 non-blunders, while the course of solving the problem must be correct.

“2”
– 4 serious mistakes.

Blunders:

computational errors in examples and problems; order of actions, incorrect solution of the problem (omission of an action, incorrect choice of actions, unnecessary actions); not completing the solution to a problem or example; unfinished task.

Non-blunders:

irrational calculation methods; incorrect formulation of the question for action when solving a problem; incorrectly formatted answer to the task; incorrect data write-off; failure to complete the transformation.

For grammatical errors made in mathematics work, the grade will not be reduced.

Text of work

Option 1

1. Solve the problem.

The children were sent to camp. They were placed in 10 buses of 43 people each. Among the children there were 184 boys and the rest were girls. How many girls went to the camp?

2. Find the meanings of the expressions by writing them in a column.

424 ∙ 2,286 ∙ 3,265 ∙ 3

174 ∙ 5 157 ∙ 4 356 ∙ 2

3. Compare

1kg….980g 606g….660g 1kg70g….1000g

4. The perimeter of the square is 16cm. What is the length of its side? Draw this square.

Option 2.

1. Solve the problem.

The student needs to read a book of 132 pages. He read for 7 days, 15 pages a day. How many pages does he have left to read?

2. Find the meanings of the expressions by writing them in a column

327 ∙ 2,332 ∙ 3,235 ∙ 4

176 ∙ 4 257 ∙ 3 168 ∙ 3

3. Compare.

2kg….2000g 707g….770g 1kg 370g……1000g

4. The perimeter of the square is 20 cm. What is the length of its side? Draw this square.

Item

Mathematics

Class

3

Topic (purpose of work)

Test No. 10 (final for the year)

Job No.

Verifiable ZUN

Difficulty level

Answer type

Number of points

1

ability to solve problems of the studied types

B

RO

See grading system

2

knowledge of table multiplication and division

B

KO

3

ability to determine the order of actions,
skill
perform table multiplication and division

B

KO

4

ability to write numbers in ascending order

B

KO

5

skill
calculate rectangle perimeter and area with initial determination of length

B

RO

Test No. 10 (final for the year)

Purpose: test of knowledge.

Option 1

1. Solve the problem:

The flower seller made a large bouquet of 9 roses and several small bouquets, 3 roses in each bouquet. How many small bouquets did the seller make if he had 30 roses in total?

2. Compare the expressions:

7×8 … 6×9 4×6 … 9×3

36:9 … 42:7 27:3 … 56:8

3. Do the calculations:

70:14×13= 92: (46:2)x2= 170 320-200=

54: (90:5)= (610 20):7:90= 480:6 780=

4. Write the numbers in ascending order:

276, 720, 627, 270, 762, 267, 726, 672, 260, 706.

5. Geometric problem:

The width of the rectangle is 7 cm, and the length is 2 times the width. Calculate the perimeter of this rectangle and the area.

6. * The doctor prescribed seven gnomes to take 3 tablets each a day for a week and gave them 9 packages of medicine, 20 tablets each. Will the dwarves have enough pills?

Option 2

1. Solve the problem:

The sellers decorated a large store window with 15 blue balls, and the rest of the windows were decorated with red balls, 6 balls in each window. How many shop windows were decorated with red balls, if a total of 39 balls were prepared to decorate the shop windows?

2. Compare expressions:

6×7. 9×4 3×8. 2×9

48:6 … 54:9 24:3 … 36:6 ​​

3. Do the calculations:

80:16×2= 84:(42:2)x3= 250 430-300=

57:(76:4)= (530 10):9:60= 420:7 590=

4. Write down the numbers in descending order:

513, 310, 315, 531, 301, 503, 351, 350, 530, 305.

5. Geometric problem:

The length of the rectangle is 1 dm 2 cm, and the width is 2 times less than the length. Calculate the perimeter of this rectangle and the area.

6. * Winnie the Pooh, Brer Rabbit and Piglet ate 7 cans of condensed milk together. Piglet ate half as much as Brother Rabbit, and Brother Rabbit ate half as much as Winnie the Pooh. Who ate how much condensed milk?

Note
.
The tests were compiled according to the manual by S.I. Volkova Mathematics. Test work. M., “Enlightenment”, 2021

Publication address: https://www.obumage.net/metodicheskie-razrabotki/209434-kontrol-predmetnyh-umenij-po-matematike-v-z-k

§

§

§

Municipal state educational institution “Krasnopolyansk secondary school named after twice Hero of the Soviet Union, Colonel General A. I. Rodimtsev” Cheremisinovsky district, Kursk region

Adopted at the PS meeting I approve

Minutes No. __ dated ____ 2021 School director ______ Pikalov V.I.

Order No.___ dated ______2021.

Work program

in Mathematics for grade 3a

Dremova Natalya Nikolaevna

primary school teacher

1st qualification category

2021

Explanatory note

The work program in mathematics for the 3rd general education class was developed on the basis of the Federal Law of the Russian Federation of December 29, 2021 No. 273-FZ “On Education in the Russian Federation”, the Federal State Educational Standard for Primary General Education, the Concept of Spiritual and Moral Development and Personal Education citizen of Russia, the basic educational program of primary general education, the planned results of primary general education, an approximate program of primary general education in mathematics, the curriculum for the 2021 – 2021 academic year, the Federal list of textbooks recommended (approved) for use in the educational process, in educational institutions, implementing general education programs for the 2021 – 2021 academic year, the author’s program of M. I. Moro, M. A. Bantova, G. V. Beltyukova, S. I. Volkova, S. V. Stepanova (Moro, M. I. [ etc.]) Mathematics.

The work program is focused on working on the educational and methodological set “School of Russia”:

1. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 1. M., “Enlightenment”, 2021.

2. M.I. Moreau, M.A. Bantova and others. Mathematics: Textbook. 3rd grade: in 2 parts, part 2. M., “Enlightenment”, 2021.

3. Moro M.I., Volkova S.I. Notebook on mathematics. 3rd grade. In 2 parts – M,; Enlightenment, 2021

Place of the subject in the curriculum

5 hours a week are allocated for studying mathematics in the 3rd grade. The course lasts 170 hours

General characteristics of the item

The leading principles of teaching mathematics in the elementary grades are an organic combination of teaching and upbringing, the assimilation of knowledge and the development of children’s cognitive abilities, the practical orientation of learning, and the development of the skills necessary for this. Due to the specific nature of mathematical material, great importance is attached to taking into account the age and individual characteristics of children and implementing a differentiated approach to teaching.

The study of mathematics at the level of primary general education is aimed at achieving the following goals:

development
figurative and logical thinking, imagination; formation of subject skills necessary for successfully solving educational and practical problems, continuing education;

mastering the basics of mathematical knowledge, forming initial ideas about mathematics;

nurturing an interest in mathematics and the desire to use the acquired knowledge in everyday life.

The objectives of teaching mathematics include:

mastery of the system of mathematical knowledge and skills necessary for application in practical activities; learning the ability to solve problems, equations, numerical and alphabetic expressions; studying related disciplines, continuing education;

mastering deductive reasoning skills;

intellectual development, the formation of personality qualities necessary for a person to live a full life in modern society: clarity and accuracy of thought, critical thinking, intuition, logical thinking; formation of ideas about the ideas and methods of mathematics as a universal language of science and technology, a means of modeling phenomena and processes;

fostering personal culture, attitudes towards mathematics as part of universal human culture, understanding the importance of mathematics for scientific and technical progress;

development of ideas about the complete picture of the world, about the relationship of mathematics with other subjects.

 The initial mathematics course is an integrated course: it combines arithmetic, algebraic and geometric material. At the same time, the basis of the initial course is the understanding of the natural number and zero, the four arithmetic operations with non-negative integer numbers and their most important properties, as well as the conscious and solid assimilation of oral and written calculation techniques based on this knowledge.
Along with this, familiarization with quantities and their measurement plays an important role in the course.
The course also involves the formation of spatial concepts in children, familiarization of students with various geometric figures and some of their properties, with the simplest drawing and measuring instruments.
The inclusion of elements of algebraic propaedeutics in the program makes it possible to increase the level of generalizations being formed and contributes to the development of abstract thinking of students.
Studying an initial course in mathematics creates a solid foundation for further study in this subject. To do this, it is important not only to equip students with the range of knowledge, skills and abilities provided for by the program, but also to ensure the necessary level of their general and mathematical development, as well as to develop general educational skills (setting an educational task; performing actions in accordance with the plan; checking and evaluating work; ability work with a textbook, reference material, etc.).
The concentric structure of the course, associated with the consistent expansion of the field of numbers, allows one to observe the necessary gradualness in increasing the difficulty of the educational material and creates good conditions for improving the knowledge, skills and abilities being formed.
The course ensures accessibility of learning, helps awaken students’ interest in mathematics, and accumulate experience in modeling (objects, connections, relationships) – the most important method of mathematics. The course is the beginning and an organic part of school mathematics education.

       When teaching mathematics, an individual approach to students is important.

Value guidelines for the content of the academic subject

The educational process is based on the following values ​​of mathematics:

• understanding mathematical relationships is a means of understanding the laws of existence of the surrounding world, facts, processes and phenomena occurring in nature and in society (chronology of events, length of time, formation of a whole from parts, changes in shape, size, etc. );

mathematical ideas about numbers, quantities, geometric figures are a condition for a holistic perception of the creations of nature and man (architectural monuments, treasures of art and culture, objects of nature);

mastery of mathematical language, algorithms, and elements of mathematical logic allows the student to improve communicative activities (argue his point of view, build logical chains of reasoning; refute or confirm the truth of an assumption).

Content of the subject.

NUMBERS FROM 1 TO 100. ADDING AND SUBTRACTING (continued) 11 hours

Repetition of what has been learned.
Oral and written addition and subtraction techniques.

Solving equations with an unknown term based on the relationship between numbers during addition

Solving equations with an unknown minuend and an unknown subtrahend based on the relationship between numbers when subtracting. Designation of geometric figures with letters .
“Pages for the curious”
— creative and exploratory tasks: collecting, systematizing and presenting information in tabular form; determination of the pattern according to which number series and series of geometric figures are compiled .
Repetition of what has been covered “What we learned. What we learned”

Table multiplication and division (continued) 4 hours.

Repetition.
Relationship between multiplication and division; multiplication and division tables with numbers 2 and 3; even and odd numbers; dependencies between quantities: price, quantity, cost. The order of operations in expressions with and without parentheses

Relationships between proportional quantities. 10 hours

Dependencies between proportional quantities: the mass of one object, the number of objects, the mass of all objects; fabric consumption per item, number of items, fabric consumption for all items. Word problems for increasing (decreasing) a number several times, for multiple comparison of numbers. Problems on finding the fourth proportional. “Pages for the curious”
— creative and exploratory tasks: collecting, systematizing and presenting information in tabular form; work on a computer;
combinatorial tasks Repetition of what has been covered “What we learned. What we learned”

Test work “Let’s test ourselves and evaluate our achievements”
(test form). Analysis of results

Multiplication and division tables with numbers 4, 5, 6, 7. 26 hours

Multiplication and division table with numbers 4, 5, 6, 7

“Pages for the curious”
— tasks of a creative and exploratory nature: mathematical games “Guess the number”, “Eleven sticks” . Project:
“Mathematical Tales”. Repetition of what has been covered “What we learned. What we learned”
.

Control and recording of knowledge .

Multiplication and division table with numbers 8 and 9 14 hours

Multiplication and division table with numbers 8 and 9. Summary multiplication table .
Square. Ways to compare figures by area. Units of area: square centimeter, square decimeter, square meter. Area of ​​a rectangle .
Multiplication by 1 and 0. Division of the form and

:

a,

0 : a

at а≠

0 .
Word problems in three steps .

Drawing up an action plan and determining the most effective ways to solve problems. Circle. Circle (center, radius, diameter). Drawing circles using a compass. Shares 11 hours

Shares (half, third, quarter, tenth, hundredth). Formation and comparison of shares. Problems on finding the fraction of a number and a number from its fraction.

Time units: year, month, day. “Pages for the curious”
— tasks of a creative and exploratory nature: calculation tasks; image of objects on the room plan according to a description of their location; work on a complicated computer;
tasks containing statements with logical connectives “if not . then .”, “if then not .”; dividing geometric shapes into parts. Review of what has been covered “What we learned. What we learned”
.
Test work “Let’s test ourselves and evaluate our achievements”
(test form). Analysis of results. Control and accounting of knowledge .

Out-of-table multiplication and division 9 hours

Multiplication techniques for cases of the form
23-4,

4-23

Multiplying a sum by a number. Multiplication techniques for cases of the form 23 • 4,

4 • 23. Methods of multiplication and division for cases of the form 20 • 3, 3 • 20, 60: 3, 80: 20.

Division techniques for cases of the form 78: 2, 69: 3 12 hours

Dividing a sum by a number. The connection between numbers when dividing. Checking division Division techniques for cases of the form

87 : 29, 66 : 22. Checking multiplication by division. Expressions with two variables of the form a b

,
a


b

, a ∙b,
with

:

d


(

d


≠0),

calculating their values ​​for given letter values ​​(1h)

Solving equations based on the relationship between the components and the results of multiplication and division.

Division with remainder 11 hours

Techniques for finding the quotient and remainder. Checking division with remainder

Solving problems to find the fourth proportional. “Pages for the curious”
— tasks of a creative and exploratory nature: logical tasks; work on a complicated computer;
tasks containing statements with logical connectives “if not then not.” Project:
“Tasks-calculations.” Repetition of what has been covered “What we learned. What we learned”
Test work “Let’s test ourselves and evaluate our achievements”
(test form). Analysis of results

NUMBERS FROM
1 TO
1000
. Numbering 16 hours

Numbering

Oral and written numbering. Digits of counting units.

Natural sequence of three-digit numbers. Increase and decrease in number by 10 times, 100 times. Replacing a three-digit number with a sum of digit terms. Comparison of three-digit numbers. Determination of the total number of units (tens, hundreds) in the number .
Units of mass: kilogram, gram .

“Pages for the curious” —
creative and exploratory tasks: calculation tasks; designation of numbers using Roman numerals. Repetition of what has been covered “What we learned. What have we learned?

Test work “Let’s test ourselves and evaluate our achievements”
(test form). Analysis of results.

Addition and subtraction

Techniques for oral addition and subtraction within 1000 13 hours

Methods of oral calculations, in cases that can be reduced to actions within 100 (900 20, 500 – 80, 120 x 7, 300 : 6, etc.)

Algorithms for written addition and subtraction within 1,000

Techniques for written calculations: written addition algorithm, written subtraction algorithm .

Types of triangles: scalene, isosceles, equilateral .

“Pages for the curious”
— tasks of a creative and exploratory nature: logical tasks and tasks of an increased level of complexity .

Review of what has been covered “What we learned. What we learned”
Mutual knowledge testing: “We help each other take a step towards success.”
Pair work on the test “Right? Wrong?”
Multiplication and division

Multiplication and division. 18 hours

Methods of mental calculations

Techniques for oral multiplication and division.

Types of triangles: right, obtuse, acute.

Reception of written multiplication and division by a single-digit number.

Method of written multiplication by a single-digit number. Acceptance of written division by a single-digit number. Repetition of what has been covered “What we learned. What we learned”

Final repetition “What we learned, what we learned in 3rd grade.” 8 hours

Knowledge test

Planned results of studying the subject

Personal results

The student will have formed:

skills in self-monitoring and self-assessment of the results of one’s educational activities;

the basics of motivation for learning activities and the personal meaning of studying mathematics, interest in expanding knowledge, in the use of search and creative approaches when completing tasks, etc., proposed in the textbook or by the teacher;

positive attitude towards mathematics lessons, studies, school;

understanding the importance of mathematical knowledge in one’s own life;

understanding the importance of mathematics in human life and activity;

perception of criteria for assessing educational activities and understanding of teacher assessments of the success of educational activities;

the ability to independently perform types of work (activities) determined by the teacher and an understanding of personal responsibility for the result;

knowledge and application of communication rules, cooperation skills in educational activities;

initial ideas about the basics of civic identity (through a system of specific tasks and exercises) 1
;

respect and acceptance of family values, understanding of the need to take care of nature, one’s health and the health of other people.

The student will have the opportunity to form:

initial ideas about the universality of mathematical methods of knowing the world around us:

awareness of the importance of mathematical knowledge in human life, when studying other school disciplines;

conscious self-control and adequate self-assessment of the results of one’s educational activities;

interest in studying the academic subject “Mathematics”: quantitative and spatial relationships, dependencies between objects, processes and phenomena of the surrounding world and ways of describing them in the language of mathematics, in mastering mathematical methods for solving cognitive problems.

Meta-subject results

Regulatory

Student will learn:

understand, accept and maintain various learning tasks, search for means to achieve a learning task;

find a way to solve a learning problem and perform learning activities orally and in writing, use mathematical terms, symbols and signs;

plan your actions in accordance with the assigned educational task to solve it;

carry out step-by-step control under the guidance of a teacher, and in some cases independently;

carry out self-monitoring and self-assessment of the results of their educational activities in the lesson and based on the results of studying individual topics.

The student will have the opportunity to learn:

independently plan and control educational activities in accordance with the set goal, find a way to solve the educational problem;

adequately conduct self-assessment of the results of their educational activities, understand the reasons for failure at one stage or another;

independently draw simple conclusions about mathematical objects and their properties;

control your actions and correlate them with the goals and actions of other participants working in pairs or in a group

Cognitive

Student will learn:

•establish mathematical relationships between objects, relationships in phenomena and processes and present information in symbolic and graphic form, build models reflecting various relationships between objects;

make comparisons based on one or more characteristics and draw conclusions on this basis;*

establish a pattern of objects (chi
villages, numerical expressions, equalities, geometric figures, etc.) and determine the missing elements in it;

carry out classification according to several proposed or independently found grounds;

•draw conclusions by analogy and check these conclusions;

make simple generalizations and use mathematical knowledge in an expanded field of application;

understand basic interdisciplinary subject concepts: number, magnitude, geometric figure;

record mathematical relationships between objects and groups of objects in sign-symbolic form (on models);

strive to make fuller use of your creative potential;

meaningfully read texts of mathematical content in accordance with the goals and objectives;

independently carry out an extensive search for the necessary information in the textbook, reference book and other sources;

carry out an advanced search for information and present information in the proposed form.

The student will have the opportunity to learn:

independently find the necessary information and use sign-symbolic means to represent it, to build models of the objects and processes being studied;

search and highlight the necessary information to complete educational and search-creative tasks.

Communication

The student will learn:

construct a speech utterance orally, use mathematical terminology;

understand different positions in the approach to solving an educational problem, ask questions to clarify them, clearly and reasonably express your assessments and suggestions;

take an active part in work in pairs and in groups, use the ability to conduct dialogue, verbal communication means;

“take part in the discussion of mathematical facts, strategies for a successful mathematical game, express your position;

“apply the learned rules of communication, master cooperation skills in educational activities;

•control your actions when working in a group and realize the importance of timely and high-quality fulfillment of your obligations for the common cause

The student will have the opportunity to learn:

use speech means and means of information and communication technologies when working in pairs, in a group while solving educational and cognitive problems, while participating in project activities;

coordinate your position with the position of the participants on working in a group, in pairs, recognize the possibility of the existence of different points of view, correctly defend your position;

control your actions and correlate them with the goals and actions of other participants working in pairs or in a group;

resolve conflicts constructively, take into account the interests of the parties and cooperate with them.

Subject results

Numbers and quantities

The student will learn:

form, name, read, write numbers from 0 to 1000;

compare three-digit numbers and write down the result of the comparison, order given numbers, replace a three-digit number with the sum of digit terms, small units of counting with large ones and vice versa;

establish a pattern – the rule by which a numerical sequence is compiled (increase/decrease a number by several units, increase/decrease a number several times), continue it or restore missing numbers in it;

group numbers according to a given or independently established one or more characteristics;

read, write and compare area values, using the studied units of this value (square centimeter, square decimeter, square meter) and the ratio between them: 1 dm 2
= 100 cm 2
, 1 m 2
= 100 dm 2
; convert one area unit to another;

read, write and compare mass values, using the studied units of this quantity (kilogram, gram) and the ratio between them: 1 kg = 1,000 g;

read, write and compare time values ​​using the studied units of this value (day, month, year) and the ratio between them: 1 year = 12 months. and 1 day. = 24 hours

The student will have the opportunity to learn:

classify numbers according to several bases (in more complex cases) and explain their actions;

independently choose a unit for measuring quantities such as area, mass, under specific conditions and explain your choice.

Arithmetic operations

The student will learn:

perform table multiplication and division of numbers; multiplication by 1 and 0, division of the form a:

a,

0 : a;

perform extra-table multiplication and division, including division with a remainder, checking arithmetic operations multiplication
and division;

perform written actions addition
and subtraction,
as well as multiplication
and division
to a single digit within 1000;

calculate the value of a numerical expression in two or three steps (with and without parentheses).

The student will have the opportunity to learn:

use the properties of arithmetic operations for ease of calculation;

calculate the value of a literal expression given the values ​​of the letters included in it;

solve equations based on the relationship between components and results of arithmetic operations.

Working with word problems

The student will learn:

analyze the task, make a brief recording of the task in various forms: in a table, in a schematic drawing, in a schematic drawing;

draw up a plan for solving a problem in two or three steps, explain it and follow it when writing down the solution to the problem;

transform a problem into a new one by changing its condition or question;

compose a problem according to a short notation, according to a scheme, according to its solution;

solve problems that consider relationships: price, quantity, cost; material consumption per item, number of items, total material consumption
to

all specified items, etc.,
tasks to increase/decrease a number several times.

The student will have the opportunity to learn:

compare tasks based on the similarities and differences in the relationships between the objects considered in the tasks;

complete the problem with missing data with possible numbers;

find different ways to solve the same problem, compare them and choose the most rational one;

solve problems on finding the fraction of a number and a number from its fraction;

solve practical problems, including calculation problems.

Spatial relations. Geometric shapes

The student will learn:

designate geometric figures with letters;

distinguish between a circle and a circle;

•draw a circle of a given radius using a compass.

The student will have the opportunity to learn:

distinguish triangles by the ratio of side lengths,

by types of angles;

depict geometric figures (segment, rectangle) on a given scale;

read the site plan (room, garden, etc.).

Geometric quantities

The student will learn:

•measure the length of a segment;

calculate the area of ​​a rectangle (square) from the given lengths of its sides;

express the areas of objects in different units of area (square centimeter, square decimeter, square meter), using relationships between them.

The student will have the opportunity to learn:

select the most suitable area units for

specific situation;

calculate the area of ​​a right triangle by completing it to form a rectangle.

Working with information

The student will learn:

analyze ready-made tables, use them to perform given actions, to build a conclusion;

establish the rule by which the table is compiled, fill the table according to the established rule with the missing elements;

independently draw up connections between proportional quantities in a table;

build a chain of logical reasoning, do

conclusions.

The student will have the opportunity to learn:

read simple ready-made tables;

understand statements containing logical connectives (“. and.”, “if., then.”, “each,” “all,” etc.), determine whether the given statement about numbers is true or false , results of actions, geometric shapes.

FORMS OF CONTROL AND EVALUATION OF ACHIEVEMENT OF PLANNED RESULTS

Oral control self-control.

Individual and frontal survey

Individual work on cards

Work in pairs, in groups (mutual and self-esteem)

Dictations (mathematical)

Cutting works (tests)

Combined tests

SYSTEM OF TESTING AND CONTROL MEASUREMENTS ON THE SUBJECT

Timing of control work

Incoming control
– to determine the level of formation of subject UUDs on the studied topics of grade 2 (September)

Intermediate
– to determine the level of formation of subject-specific UUDs on the topics studied (December);

Final
– to compare results and determine the level of mastery of the standard of primary general education (April – May).

Form of control work

Tests are carried out in the form of combined tests in mathematics.

Calendar and thematic planning

No.

lessons

Date

Section of the curriculum, lesson topic

Characteristics of student activities

Number of hours

Plan.

Fact.

Numbers from 1 to 100. Addition and subtraction. Repetition.

(11 hours)

1

Repetition. Numbering of numbers.

Execute
adding and subtracting numbers within 100

Solve
word problems in arithmetic way

1

1

1

2

Oral addition and subtraction techniques.

3

Written addition and subtraction techniques

4

Solving equations with an unknown term based on the relationship of numbers during addition

Solve
equations for finding an unknown summand, an unknown minuend, an unknown subtrahend based on knowledge about the relationship of numbers during addition and subtraction.

Solve
word problems in arithmetic way

Execute
adding and subtracting numbers within 100

1

1

1

5

Solving equations with an unknown minuend based on the relationship of numbers when subtracting

6

Solving equations with an unknown subtrahend based on the relationship of numbers when subtracting

7

Designation of geometric shapes with letters.

Designate
geometric shapes with letters. Solve
word problems in arithmetic way

Execute
adding and subtracting numbers within 100

1

8

Consolidation of what has been learned. Pages for the curious.

Solve
word problems in arithmetic way

Execute
adding and subtracting numbers within 100

1

1

1

9

Reinforcement of what has been covered on the topic “Addition and Subtraction”

10

Repetition of what has been covered on the topic “Addition and subtraction. Repetition”.

11

Entrance test.

1

Table multiplication and division. Repeat (4 hours)

12

Analysis of test work. The specific meaning of multiplication and division

Use
various techniques for checking the correctness of calculating the value of a numerical expression (based on the properties of arithmetic operations, on rules about the order of execution of actions in numerical expressions). Execute
adding and subtracting numbers within 100

1

13

Relationship between multiplication and division

Solve
word problems in arithmetic way Play
from memory the multiplication table and corresponding cases of division with numbers 2 and 3 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

14

Even and odd numbers.

Play
from memory the multiplication table and corresponding cases of division with numbers 2 and 3 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions Solve
word problems in arithmetic way

1

15

Multiplication and division table with number 3

Solve
word problems in arithmetic way Play
from memory the multiplication table and corresponding cases of division with numbers 2 and 3 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

Relationship between proportional quantities

(10 hours)

16

The relationship between the quantities price, quantity, cost

Analyze
text problem and perform
briefly recording the task in various ways, including in tabular form. Model
using schematic drawings of relationships between proportional quantities

1

1

17

Relationship between quantities mass, quantity

18

The order of execution of actions in expressions with brackets.

Apply
rules on the order of performing actions in numeric expressions with and without parentheses when calculating the values ​​of numeric expressions.

Calculate
meanings of numerical expressions in two or three steps with and without parentheses.

Use
mathematical terminology when reading and writing numerical expressions.

1

1

1

19

The order of execution of actions in expressions with and without parentheses.

20

The order of performing arithmetic operations.

Fastening.

21

The relationship between proportional quantities: fabric consumption per item, number of items, fabric consumption for all items.

. Compose
plan for solving the problem.

Act
according to a proposed or independently drawn up plan.

Explain
progress in solving the problem.

Watch
and describe
changes in the solution of a problem when its conditions change and, conversely, make
changes in the condition (question) of the problem when there is a change in its solution. Detect and install
logical errors (during solution) and

of a computational nature, admitted in the solution.

1

1

22

A page for the curious. Problem solving.

23

Repetition of what has been covered on the topic “Dependence between proportional quantities”

Rate
results of mastering the topic, show personal interest in acquiring and expanding knowledge and methods of action. Analyze
your actions and manage them.

Execute
creative and exploratory tasks, apply
knowledge and ways of acting in changed conditions

1

24

Test on the topic “Dependence between proportional quantities”

1

25

Analysis of test work. Consolidation of what has been covered on the topic “Tabular multiplication and division by 2 and 3”

Rate
results of mastering the topic, show personal interest in acquiring and expanding knowledge and methods of action. Analyze
your actions and manage them.

Execute
creative and exploratory tasks, apply
knowledge and methods of action in changed conditions

1

Multiplication and division tables with numbers: 4, 5, 6, 7.

(26 hours)

26

Multiplication and division table with number 4

Play
from memory the multiplication table and the corresponding division cases with the numbers 2,3, 4

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

27

Reinforcing what has been learned

1

28

Problems to increase a number several times

Compare
problems to increase (decrease) a number by several units and to increase (decrease) a number several times, give
explanations. Compose
plan for solving the problem.

Act
according to a proposed or independently drawn up plan.

Explain
progress in solving the problem.

Watch
and describe
changes in the solution of a problem when its conditions change and, conversely, make
changes in the condition (question) of the problem when there is a change in its solution.

1

1

1

29

Solving problems to increase a number several times

30

Consolidation of solutions to problems to increase the number several times

31

Problems involving reducing a number by several times

Compare
problems to increase (decrease) a number by several units and to increase (decrease) a number several times, give
explanations. Make up
plan for solving the problem.

Act
according to a proposed or independently drawn up plan.

Explain
progress in solving the problem.

Watch
and describe
changes in the solution of a problem when its conditions change and, conversely, make
changes in the condition (question) of the problem when there is a change in its solution.

1

1

1

32

Consolidation of solutions to problems involving reducing a number several times

33

Solving problems involving reducing a number by several times

34

Multiplication and division table with number 5

Play
from memory the multiplication table and the corresponding division cases with the numbers 2,3,4,5 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

35

Problems involving multiple comparisons of numbers

Compare
problems to increase (decrease) a number by several units and to increase (decrease) a number several times, give
explanations. Compose
plan for solving the problem.

Act
according to a proposed or independently drawn up plan.

Explain
progress in solving the problem.

Watch
and describe
changes in the solution of a problem when its conditions change and, conversely, make
changes in the condition (question) of the problem when there is a change in its solution.

1

1

1

36

Solving problems involving multiple comparisons of numbers

37

Multiple and difference comparison problems

38

Multiplication and division table with number 6

Play
from memory the multiplication table and the corresponding division cases with the numbers 2,3,4,5,6 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions Solve
word problems in arithmetic way

1

39

Multiplication and division with numbers 5,6

Solve
word problems in arithmetic way

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

40

Problems for finding the fourth proportional

Compose
plan for solving the problem.

Act
according to a proposed or independently drawn up plan.

Explain
progress in solving the problem.

Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

41

Solving problems to find the fourth proportional

42

Multiplication and division table with number 7

Play
from memory the multiplication table and the corresponding division cases with the numbers 2,3,4,5, 6, 7 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

Solve
word problems in arithmetic way

1

43

A page for the curious. Math games.

Find
a number that is several times larger (less) than a given one.

Play
from memory the multiplication table and the corresponding division cases with the numbers 2, 3, 4, 5, 6, 7.

Find
a number that is several times greater (less than) given Work
paired with.

Solve
word problems in arithmetic way

1

1

44

Consolidation of what has been covered on the topic: “Multiplication and division tables with numbers 4,5,6,7

45

Test on the topic “Multiplication and division tables with numbers 4,5,6,7”

1

46

Analysis of test work.

Repetition of what has been covered on the topic Multiplication and division tables with numbers 4,5,6,7

Execute
creative and exploratory tasks. Work
paired with. Compose
plan for a successful game. Solve
word problems in arithmetic way

1

47

Project “Mathematical Tales”

Compose
fairy tales, stories using mathematical concepts, interdependencies, relationships, numbers, geometric shapes, mathematical terms. Analyze
and evaluate
compiled fairy tales from the point of view of the correct use of mathematical elements in them. Collect
and classify information. Work
paired with. Rate
progress and result of work

1

48

Area. Ways to compare figures by area.

. Compare
geometric shapes by area.

Analyze
tasks, install
dependencies between quantities, amount to
plan for solving the problem, solve
word problems of different types.

Model
different arrangement of circles on a plane. Add
problems-calculations with missing data and solve
their. Position
objects on the room plan as described. Work
(but drawing) on ​​ computer,
making the choice to continue working.

Rate
results of mastering the topic, show personal interest in acquiring and expanding knowledge and way of action. Analyze
your actions and manage them.

1

49

Units of area are square centimeter.

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

50

Area of ​​the rectangle.

Calculate
area of ​​a rectangle in different ways Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

51

Solving problems on finding the area of ​​a geometric figure

Multiplication and division table with numbers 8 and 9 (14 hours)

52

Multiplication and division table with number 8.

Play
from memory the multiplication table and the corresponding cases of division. Apply
knowledge of multiplication tables when performing calculations. Solve
word problems in arithmetic way Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

53

Solving examples of multiplication and division with the number 8

Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding cases of division with the numbers 2 and 3,4,5,6 , 7,8 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

54

Solving problems of the studied types

55

Multiplication and division table with number 9.

Play
from memory the multiplication table and the corresponding cases of division. Apply
knowledge of multiplication tables when performing calculations. Solve
word problems in arithmetic way

1

56

Units of area – square decimeter.

Compare
geometric figures by area Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6,7,8,9 Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

57

Multiplication table. Consolidation.

Play
from memory the multiplication table and the corresponding cases of division. Apply
knowledge of multiplication tables when performing calculations.

1

58

Solving multiplication and division examples using the summary multiplication table.

Analyze
tasks, install
dependencies between quantities, amount to
plan for solving the problem, solve
word problems of different types Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

59

Unit of area – square meter

Compare
geometric shapes by area. Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

60

Solving problems with proportional quantities.

Analyze
tasks, install
dependencies between quantities, amount to
plan for solving the problem, solve
word problems of different types Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

61

A page for the curious. Problem solving.

Execute
creative and exploratory tasks. Add
problems-calculations with missing data and solve
their. Classify
geometric shapes according to a given or found classification basis. Execute
creative and exploratory tasks

1

62

Repetition of what has been learned.

Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

63

Repetition of what has been covered on the topic “Multiplication and division tables with numbers 8,9”

64

Test on the topic “Multiplication and division tables with numbers 8,9.

1

1

65

Analysis of test work. Repetition of what has been covered on the topic “Multiplication and division tables.”

Multiplication and division by 1, 0 (7 hours)

66

Multiply by 1

Multiply
numbers with 1 and 0. Execute
dividing 0 by a number not equal to 0. Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

1

1

67

Multiply by 0

68

Division of type a:a.

69

Divide zero by number

70

Word problems in three steps

Analyze
tasks, install
dependencies between quantities, amount to
plan for solving the problem, solve
word problems of different types Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 , 7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

71

A page for the curious.

Execute
creative and exploratory tasks. Add
problems-calculations with missing data and solve
their. Position
objects on the room plan as described

1

1

72

Consolidation of the studied material.

Shares (11 hours)

73

Shares. Formation and comparison of shares.

Solve
word problems in arithmetic way

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 , 7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

74

Circle. Circle.

Draw
circle (circle) using a compass. Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

75

Circle diameter. Problem solving.

76

Problems on finding the fraction of a number and a number from its fraction.

Find
a share of a quantity and a quantity according to its share. Compare
different fractions of the same quantity.

Solve
word problems in arithmetic way

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

77

Time units – year, month, day

Describe
phenomena and events using time values. Translate
some units of time into others: small ones into larger ones and large ones into smaller ones, using the relationships between them Solve
word problems in arithmetic way

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

1

78

A page for the curious. Problems in pictures.

79

Repetition of what has been covered on the topic “Shares”.

Solve
word problems in arithmetic way

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

80

Test on the topic “Shares”

1

81

Analysis of test work. Problem solving.

Execute
creative and exploratory tasks. Add
problems-calculations with missing data and solve
them Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

82

Solving word problems in three steps

Solve
word problems in arithmetic way Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 ,7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

83

A page for the curious. We are preparing for the Olympics.

Rate
results of mastering the topic, show personal interest in acquiring and expanding knowledge and methods of action. Analyze
your actions and manage them.

Execute
creative and exploratory tasks, apply
knowledge and ways of acting in changed conditions

1

Numbers from 1 to 100. Out-of-table multiplication and division.

Multiplication techniques for cases 23∙4, 4∙23 (9 hours)

84

Techniques for multiplication and division of the form 20∙3, 3∙20, 60:3

Execute
extra-table multiplication and division within 100 in different ways.

Solve
word problems in arithmetic way

1

85

Reception of division of the form 80:20.

Solve
word problems in arithmetic way Complete
extra-table multiplication and division within 100 in different ways.

1

86

Multiplying the sum by the number

Solve
word problems in arithmetic way Complete
extra-table multiplication and division within 100 in different ways.

1

87

Solving problems in different ways

Solve
word problems in arithmetic way

Execute
extra-table multiplication and division within 100 types studied

1

88

Multiplication techniques for cases of the form 23 ∙ 4, 4∙ 23

Use
rules for multiplying a sum by a number when performing extra-tabular multiplication and rules for dividing a sum by a number when performing division. Solve
word problems in arithmetic way Complete
extra-table multiplication and division within 100 types studied

1

1

89

Solution of examples of the form 23 ∙ 4, 4∙ 23

90

Solving problems with quantities

Use
different ways to check completed actions multiplication
and division.

Calculate
values ​​

Solve
equations for finding an unknown factor, unknown dividend, unknown divisor Solve
word problems using the arithmetic method.

1

91

Expressions with two variables

expressions with two variables for given values ​​of the letters included in them, using the rules

about the order of performing actions in numerical expressions, properties of addition, estimation of the result.

Execute
tasks of a creative and exploratory nature: tasks that require correlating a picture with statements containing logical connectives: “if not then”, “if not then not.”; execute
transformation of geometric shapes according to specified conditions

1

1

92

A page for the curious. Solving problems on finding the perimeter

Division techniques for cases 78:2, 69:3 (12 hours)

93

Divide the sum by the number

Solve
word problems using the arithmetic method . Execute
extra-table multiplication and division within 100 types studied

1

94

Solving division problems.

Solve
word problems using the arithmetic method . Execute
extra-table multiplication and division within 100 studied types

1

95

Division techniques for cases of the form 69:3, 78:2

Use
rules for dividing a sum by a number when performing division

Solve
word problems using the arithmetic method . Execute
extra-table multiplication and division within 100 types studied

1

96

Relationship between numbers when dividing

Compare
different calculation methods, choose the most convenient one.

Solve
word problems in arithmetic way

1

97

Division check

Solve
word problems using the arithmetic method . Execute
extra-table multiplication and division within 100 types studied

1

98

Division techniques for cases of the form 87:29, 66:22

Solve
word problems in arithmetic way

Execute
extra-table multiplication and division within 100 types studied

1

99

Multiplication check

Solve
word problems in arithmetic way

Execute
extra-table multiplication and division within 100 types studied

1

100

Solving equations based on the connection between numbers in division

Compose
plan for solving the equation. Execute
extra-table multiplication and division within 100 types studied

1

1

101

Solving equations. Consolidation.

102

A page for the curious. Solving logical problems.

Execute
tasks of a creative and exploratory nature: tasks that require correlating a picture with statements containing logical connectives: “if not then”, “if not then not.”; execute
transformation of geometric shapes according to specified conditions.

Compose
and solve
practical tasks with life stories.

Conduct
collection of information to complement
conditions of problems with missing data, and solve them

1

103

Repetition of what has been covered on the topic “Non-tabular multiplication and division”

Solve
word problems in arithmetic way

Execute
extra-table multiplication and division within 100 types studied

1

104

Test on the topic “Non-tabular multiplication and division”

1

Division with remainder (11 hours)

105

Analysis of test work. Techniques for finding the quotient and remainder

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way

Compose
plan for solving the problem. Execute
extra-table multiplication and division within 100 types studied

1

106

Division with remainder

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way

Compose
plan for solving the problem.

Execute
extra-table multiplication and division within 100 studied types

1

107

Division with remainder by selection method

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way

1

1

108

Performing division with remainder in different ways

109

Solving examples of division with remainder.

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way Complete
extra-table multiplication and division within 100 types studied

1

110

Solving division problems with remainder

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way Compose
plan for solving the problem.

1

111

Cases of division with a remainder when the divisor is greater than the dividend

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way Compose
plan for solving the problem.

Execute
extra-table multiplication and division within 100 types studied

1

112

Checking division with remainder

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way Complete
extra-table multiplication and division within 100 types studied

1

113

Repetition of what has been covered on the topic “Division with remainder”

Explain
the meaning of division with a remainder, perform
division with remainder and checking it.

Solve
word problems in arithmetic way

Rate
results of mastering the topic, show interest in acquiring and expanding knowledge and methods of action. Analyze
your actions and manage them. B execute
extra-table multiplication and division within 100 studied types

1

114

Test on the topic “Division with remainder

1

115

Analysis of test work. Project “calculation problems”

Execute
tasks of a creative and exploratory nature: tasks that require correlating a picture with statements containing logical connectives: “if not then”, “if not then not.”; perform
transformation of geometric shapes according to specified conditions.

Compose
and decide
practical tasks with life stories.

Conduct
collecting information to complement
conditions of problems with missing data, and solve them.

1

H starting from 1 about 1000. Numbering (16 hours)

116

Oral numbering. Thousand

Count
hundred.

Analyze
achieved results and shortcomings, show personal interest in expanding knowledge and methods of action Solve
word problems in arithmetic way

1

117

Formation and name of three-digit numbers.

Read
and write down
three-digit numbers.

Compare
three-digit

numbers and write
comparison result.

called
b and form
three-digit numbers Execute
extra-table multiplication and division within 100 types studied

Solve
word problems in arithmetic way

1

118

Counting unit digits

. Arrange
given numbers.

Read
and write down
three-digit numbers replace
a three-digit number by the sum of its digit terms, called
digits of counting units, write three-digit numbers Solve
word problems using arithmetic method

1

119

Relationship between proportional quantities: consumption per day, number of days, total consumption.

Compose
plan for solving the problem.

Act
according to a proposed or independently drawn up plan.

Explain
progress in solving the problem.

Detect and install
logical errors (during solution) and

of a computational nature, made in the solution.

1

120

Natural sequence of three-digit numbers

Arrange
given numbers.

Install
the rule by which the number sequence is composed, continue
it or restore
missing numbers in it.

Group
numbers based on a given or independently established base Solve
word problems in arithmetic way

1

121

Increase and decrease the number by 10 times, 100 times.

Execute
extra-table multiplication and division within 100 types studied

Read
and write down
three-digit numbers

Increase and decrease
numbers 10,100 times Solve
word problems in arithmetic way

1

122

Replacing a three-digit number with a sum of digit terms

Replace
three-digit number by sum of digit terms Increase and decrease
numbers 10,100 times Solve
word problems in arithmetic way

1

123

Representation of numbers as a sum of digit terms.

replace
three-digit number by sum of digit terms Increase and decrease
numbers 10,100 times Solve
word problems in arithmetic way

1

124

Comparison of three-digit numbers.

compare
three-digit numbers z change
three-digit number by sum of digit terms Solve
word problems in arithmetic way

1

125

Determination of the total number of units (tens, hundreds) in the number

Determine
total number of units (tens, hundreds) in number compare
three-digit numbers z change
three-digit number by sum of digit terms Increase and decrease
numbers 10,100 times Solve
word problems in arithmetic way

1

126

A page for the curious. Roman numerals.

Read and Write
numbers in Roman numerals.

Compare
positional decimal number system with the Roman non-positional number system.

Read
entries on watch dials, in the table of contents of books, in the designation of centuries, represented by Roman numerals.

1

127

Units of mass: kilogram, gram

translate
some units of mass into others: small ones into larger ones and large ones into smaller ones, using the relationships between them. Compare
objects by weight, arrange
them Increase and decrease
numbers 10,100 times Solve
word problems in arithmetic way

1

128

A page for the curious. Problem solving.

Execute
creative and exploratory tasks. Add
problems-calculations with missing data and solve
their.

1

129

Repetition of what has been learned on the topic “Numbering”

Arrange
given numbers.

Install
the rule by which the number sequence is composed, continue
it or restore
missing numbers in it.

Group
numbers based on a given or independently established base Solve
word problems in arithmetic way

1

130

Test on the topic “Numbering”

1

131

Analysis of test work. A page for the curious. Solving logic problems

Execute
creative and exploratory tasks:

1

Numbers from 1 to 1000. Addition and subtraction (13 hours)

132

Methods of oral calculations, in cases that can be reduced to actions within 100.

Execute
oral calculations in cases reduced to actions within 100, using various methods of oral calculations. Compare
different methods of calculations, choose a convenient one.

Use
various methods for checking the correctness of calculations.

. Solve
word problems using arithmetic method

1

133

Different methods of calculations.

Execute
oral calculations in cases reduced to actions within 100, using various methods of oral calculations. Compare
different methods of calculations, choose a convenient one Solve
word problems in arithmetic way

1

134

Methods of oral calculations of the form 470 80, 560-90

Execute
oral calculations in cases reduced to actions within 100, using various methods of oral calculations. Compare
different calculation methods, choose a convenient one Use
various techniques for checking the correctness of calculations Solve
word problems in arithmetic way

1

135

Different calculation methods

Execute
oral calculations in cases reduced to actions within 100, using various methods of oral calculations. Compare
different calculation methods, choose a convenient one Use
various techniques for checking the correctness of calculations Solve
word problems in arithmetic way

1

136

Techniques for written calculations

Execute
oral calculations in cases reduced to actions within 100, using various methods of oral calculations. Compare
different methods of calculations, choose a convenient one Solve
word problems in arithmetic way

1

137

Written addition algorithm

Apply
algorithms for written addition and subtraction of numbers and perform
these actions are with numbers within 1,000. Control
step by step correct application of arithmetic algorithms in written calculations. Use
various techniques for checking the correctness of calculations

1

138

Written subtraction algorithm

Apply
algorithms for written addition and subtraction of numbers and perform
these actions with numbers within 1,000. Control
step by step correct application of arithmetic algorithms in written calculations. Solve
word problems in arithmetic way

1

139

Types of triangles.

Discriminate
triangles by type (scalene and isosceles, and among isosceles – equilateral) and call
their.

Apply
algorithms for written addition and subtraction of numbers and perform
these actions with numbers within 1,000. Control
step by step correct application of arithmetic algorithms in written calculations.

1

140

Written addition and subtraction of three-digit numbers.

Apply
algorithms for written addition and subtraction of numbers and perform
these actions with numbers within 1,000. Control
step by step correct application of arithmetic algorithms in written calculations. Solve
word problems in arithmetic way

1

1

141

Exercise in written addition and subtraction of three-digit numbers.

142

Repetition of what has been covered on the topic “Addition and subtraction”.

Execute
creative and exploratory tasks, apply
knowledge and methods of action in changed conditions.

Work
paired with. Find
and correct
incorrect statements. Explain
and defend
your opinion, argue

your point of view, evaluate
classmate’s point of view

1

143

Test on the topic “Addition and subtraction”

1

144

Analysis of test work. A page for the curious. Getting ready for the Olympics

decide
tasks of a creative and exploratory nature. find
and correct incorrect statements. expound and defend
your opinion, argue your point of view, evaluate the point of view of a friend.

1

Multiplication and division (18 hours)

145

Techniques for oral multiplication and division.

Use
various techniques for mental calculations. Compare
different methods of calculations, choose a convenient one.

Solve
word problems in arithmetic way

1

146

Different calculation methods

Solve
word problems in arithmetic way Use
various techniques for mental calculations.

1

147

Oral techniques for multiplying and dividing by round numbers

Solve
word problems in arithmetic way

Use
various techniques for mental calculations.

1

148

Types of triangles

Solve
word problems in arithmetic way

Distinguish
triangles: rectangular, obtuse, acute. Find
them in more complex figures Use
various techniques for mental calculations.

1

149

Method of written multiplication by a single-digit number.

Solve
word problems in arithmetic way

Use
various techniques for mental calculations.

1

150

A page for the curious. Solving logic problems

Execute
creative and exploratory tasks:

1

151

Algorithm for written multiplication of a three-digit number by a single-digit number

Solve
word problems in arithmetic way Apply
algorithms for written multiplication of a multi-digit number by a single-digit number and perform these actions.

Use
various techniques for mental calculations.

1

152

Written multiplication of three-digit numbers by one-digit

Solve
word problems in arithmetic way Apply
algorithms for written multiplication and multi-digit by single-digit number and perform these operations.

Use
various techniques for mental calculations.

1

1

1

153

Exercise in written multiplication of multi-digit numbers by single-digit numbers.

154

Consolidation of written multiplication of multi-digit numbers by single-digit numbers.

155

Reception of written division by a single-digit number

Solve
word problems in arithmetic way Apply
algorithms for written multiplication and multi-digit by single-digit number and perform these operations.

Use
various techniques for mental calculations.

1

156

Algorithm for written division of a three-digit number by a single-digit number.

Solve
word problems in arithmetic way Apply
written algorithms for dividing a multi-digit number by a single-digit number and perform these actions.

Use
various techniques for mental calculations.

1

1

157

Reinforcing the written division of a three-digit number by a single-digit number.

158

Checking division by multiplication.

Solve
word problems in arithmetic way

Apply
written algorithms for dividing a multi-digit number by a single-digit number and perform these actions.

Use
various methods for checking the correctness of calculations, Use
various techniques for mental calculations.

1

1

159

Solving problems of the studied types.

160

Introducing the calculator. Consolidation of what has been learned.

Solve
word problems in arithmetic way

conduct
checking the correctness of calculations using a calculator

1

1

161

Repetition of what has been covered on the topic “Multiplication and Division”.

162

Test on the topic “Multiplication and Division”

1

Final repetition “What we learned, what we learned

in 3rd grade” (8 hours)

163

Analysis of test work. Repetition. Numbering.

Solve
word problems in arithmetic way

Read
and write down
three-digit numbers.

Compare
three-digit

numbers and write
comparison result.

called
b and form
three-digit numbers

1

164

Repetition. Addition and subtraction.

Solve
word problems in arithmetic way

Execute
adding and subtracting numbers within 100

1

165

Repetition. Multiplication and division

Solve
word problems in arithmetic way

Apply
algorithms for written multiplication and division of a multi-digit number by a single-digit number and perform these operations.

Use
various techniques for mental calculations.

1

166

Repetition. Rules on the order of actions

Solve
word problems in arithmetic way

Apply
rules on the order of performing actions in numeric expressions with and without parentheses when calculating the values ​​of numeric expressions.

Calculate
meanings of numerical expressions in two or three steps with and without parentheses.

Use
mathematical terminology when reading and writing numerical expressions.

1

167

Final test

1

168

Analysis of test work. Repetition. Geometric figures and quantities

Solve
word problems in arithmetic way

Calculate
area of ​​a rectangle in different ways Distinguish
triangles by type (scalene and isosceles, and among isosceles – equilateral) and call
their.

1

169

Repetition. Written single-digit multiplication and division

Solve
word problems in arithmetic way

Play
from memory the multiplication table and the corresponding division cases with the numbers 2 and 3,4,5,6 , 7,8,9

Apply
knowledge of multiplication tables when calculating the values ​​of numerical expressions

1

170

Repetition. Units of length, mass, time

Solve
word problems in arithmetic way

translate
some units of mass, length, time into others: small ones into larger ones and large ones into smaller ones, using the relationships between them. Compare
items by weight, arrange
them

1

Material, technical, educational, methodological and information support of the educational process

Moro M. I. et al. Mathematics:

Program: grades 1-4. M: “Enlightenment” 2021

Textbooks

1. Moro M.I., Stepanova S.V., Volkova S.I. Mathematics: Textbook: 3rd grade: At 2 o’clock: Part 1.
M: “Enlightenment” 2021

2. Moro M.I., Stepanova S.V., Volkova S.I. Mathematics: Textbook: 3rd grade: At 2 o’clock: Part 2.
M: “Enlightenment” 2021

Testing and measuring materials in mathematics, grade 3 M: “Wako” 2021

Test work

1. Volkova S. I. Mathematics: Test work: 3rd grade M: “Enlightenment” 2021

Teaching aids for teachers
Bantova M. A., Beltyukova G. V., Stepanova S. V. Mathematics: Methodological manual: 3rd grade. M: “Enlightenment” 2021

T. N. Sitnikova, I. F. Yatsenko Lesson developments in mathematics. 3rd class M: “VAKA”2021

Electronic tutorials:

Electronic supplement to the textbook “Mathematics”, grade 3

(CD-ROM), authors S. I. Volkova, M. K. Antoshin, N. V. Safonova.

Evaluation criteria

Evaluation of written work.

Test.

Work consisting of examples:

Rating “5”
– work without errors.

Rating “4”
–1 blunder and 1–2 minor errors.

Rating “3”
– 2–3 gross and 1–2 minor errors or 3 or more minor errors.

Rating “2”
– 4 or more serious errors.

Work consisting of tasks:

Rating “5”
awarded for work without errors.

Rating “4”
– 1–2 minor mistakes.

Rating “3”
– 1 gross and 3–4 minor errors.

Rating “2”
– 2 or more serious errors.

Combined work (1 task, examples and another type of task)

Rating “5”
assigned: all work was completed without errors and 1-2 corrections;

Rating “4”
placed: admitted
1-2
computational errors
and 1-2 corrections;

Rating “3”
put: mistakes were made while solving the problem when it was correct

completing all other tasks or 3-4 computational errors were made, while the course of solving the problem must be correct and 3-4 corrections;

Score “2” is given: errors were made while solving the problem and at least one computational error
or more than 5 computational errors were made when solving the problem and examples.

Combined work (2 tasks and examples)

Score

“5” is placed:
all work was completed without errors and
1-2 corrections;

Score

“4” is placed:
1-2 computational errors were made
and 1-2 corrections;

Score

“3” is placed:
mistakes were made while solving one of the problems
or

–        3-4 computational errors were made
and 3-4 corrections;

Score

“2” is placed:
mistakes were made while solving 2 problems or

– an error was made while solving one problem and 3-4 calculations
errors
.

Blunders:

1.
Computational errors in examples and problems.

2.
Errors due to ignorance of the order in which arithmetic operations are performed.

3.
Incorrect solution to a problem (omission of an action, incorrect choice of actions, unnecessary actions).

§

Explanatory note

The work program of the training course is compiled taking into account the following regulatory documents:

Law “On Education in the Russian Federation” No.
273-FZ, adopted on December 29, 2021

Order of the Ministry of Education of the Russian Federation dated October 6, 2009 No. 373 “On the approval and implementation of the Federal State Educational Standard for primary general education” (as amended from November 26, 2021 No. 1241 and from September 22, 2021 No. 2357);

A four-year primary school program for teaching literacy and literary reading: the “Primary School of the 21st Century” project. M.: Ventana-Graf, 2021
Curriculum of GBOU “School No. 281” for the 2021/2021 academic year;
Federal list of textbooks recommended (approved) for use in the educational process in

educational institutions implementing general education programs for the 2021/2021 academic year

The subject “Mathematics” implements the main learning objectives:

creating favorable conditions for the full intellectual development of each child at a level corresponding to his age characteristics and capabilities;

ensuring the necessary and sufficient mathematical preparation of the student for further education;

development of interest in mathematics, the desire to use mathematical knowledge in everyday life.

To achieve the set goals, it is necessary to solve the following practical problems:

to form independent thinking in younger schoolchildren when mastering scientific concepts;

develop the creative abilities of schoolchildren (independent transfer of knowledge and skills to a new situation; vision of a new problem in a familiar situation; vision of a new function of an object; independent combination of known methods of activity of a new one; vision of the structure of an object; vision of an alternative solution and its course; construction a fundamentally new method of solution, different from those known to the subject).

to form students’ ideas about natural numbers and zero, to promote their mastery of algorithms for arithmetic operations (addition, subtraction, multiplication, division), the study of the properties of these actions and their application in calculations;

introduce students to the most commonly encountered quantities in practice (length, mass, time, perimeter, area), their units and measurements, the relationships between quantities and their use in simple practical calculations (including household ones: shopping, utilities payments);

prepare primary schoolchildren to master some important concepts of mathematical logic: a statement and its truth; the simplest operations on statements – negation, conjunction, disjunction, logical consequence;

develop students’ geometric and spatial concepts (geometric figures, their image, basic properties, location on a plane).

The program lays the foundation that allows students to master a certain amount of mathematical knowledge and skills that will enable them to successfully study mathematical disciplines in high school.

The uniqueness of the initial stage of education is that it is at this stage that students should begin to form elements of educational activity. On the basis of this activity, the child develops theoretical consciousness and thinking, and develops corresponding abilities (reflection, analysis, mental planning); At this age, children also develop the need and motives for learning.

In this regard, the selection of training content is based on the following most important methodological principles:

analysis of specific educational material from the point of view of its general educational value and the need for study in primary school;

the possibility of widespread application of the studied material in practice;

the relationship of the introduced material with previously studied;

ensuring continuity with preschool mathematical training and the content of the next stage of education in secondary school;

enriching the mathematical experience of younger schoolchildren by including new questions in the course that were not previously studied in elementary school;

development of interests in mathematics.

The formulated principles required the construction of a program that contains information from various mathematical disciplines, forming five interconnected content lines:

elements of arithmetic;

quantities and their measurement;

logical-mathematical concepts;

elements of algebra;

elements of geometry.

For each of these lines, basic concepts are selected, around which the entire content of the training unfolds. The conceptual apparatus includes the following four concepts, introduced without definitions: number, ratio, magnitude, geometric figure.

The logic of presentation and content of the author’s program fully complies with the requirements of the federal state standard of primary general education, therefore no changes have been made to the program

To implement the program, the educational and methodological set “School of the 21st Century” is used:

Rudnitskaya V. N., Yudacheva T. V. Mathematics: 2nd grade textbook for students of general education institutions: in 2 parts – M.: Ventana – Graf, 2021.

Workbook “ Mathematics”,

2nd grade, No. 1, No. 2. Authors: Rudnitskaya V.N., Yudacheva T.V., M.: Publishing house. Ventana-Graf Center, 2021

The program is designed for 140 hours per year (35 working weeks, 4 hours per week). Including 13 hours for carrying out control work.

Requirements for the level of preparation of 2nd grade students

By the end of 2nd grade, students should:

name:

• a number several times larger (smaller) than the given one;

• the figure shown in the picture (angle, circle, polygon);

distinguish:

• right and indirect angles;

• perimeter and area of ​​the figure;

compare:

• any two-digit numbers;

• two numbers, characterizing the result of comparison with the words “more in .”, “less in .”;

play from memory:

• relationships between units of length: 1 m = 100 cm. 1 dm = 10 cm, 1 m = 10 dm;

• definition of a rectangle (square);

give examples:

• numerical expression;

use models (simulate a learning situation):

• compose and solve a problem according to this scheme;

solve educational and practical problems:

• read and write any two-digit numbers;

• make up simple numerical expressions (sum, difference, product, quotient);

• perform simple mental calculations within 100;

• perform written addition and subtraction of numbers when the result of the action does not exceed 100;

• calculate the values ​​of numerical expressions containing 2-3 actions;

• calculate the perimeter of a polygon;

By the end of 2nd grade, students can:

name:

components and results of arithmetic operations: addend, sum, minuend, subtrahend, difference, multiplier, product, dividend, divisor, quotient;

distinguish:

polygon elements: vertex, side, angle;

play from memory:

results of tabular multiplication of single-digit numbers; results of tabular division cases;

solve educational and practical problems:

apply the properties of multiplication and division when performing calculations;

calculate the area of ​​a rectangle (square);

solve compound word problems in two steps, including problems involving increasing and decreasing a number several times;

construct a circle using a compass.

By the end of the 2nd grade, students should have formed the following UUD:

acceptance and mastery of the social role of the student;

development of motives for educational activities and the formation of personal meaning of learning;

development of cooperation skills with adults and peers;

mastering the ability to accept and maintain the goals and objectives of educational activities, searching for means of its implementation;

mastering the initial forms of cognitive and personal reflection;

use of sign-symbolic means of presenting information to create models of studied objects and processes, schemes for solving educational and practical problems;

mastery of the logical actions of comparison, analysis, synthesis, generalization, classification

ensuring the intellectual development of younger schoolchildren: forming the foundations of logical-mathematical thinking, spatial imagination, students’ mastery of mathematical speech to describe mathematical objects and processes of the surrounding world in quantitative and spatial terms, to justify the results obtained in solving educational problems;
providing primary schoolchildren with the basics of basic mathematical knowledge and developing the corresponding skills: solving educational and practical problems; search for information (facts, similarities, differences, patterns, grounds for ordering and classifying mathematical objects); measure the most common quantities in practice;

ability to apply arithmetic algorithms for calculations; recognize familiar geometric shapes in surrounding objects, perform simple geometric constructions;

implementation of the educational aspect of education: nurturing the need to learn new things, expand your knowledge, show interest in mathematics, strive to use mathematical knowledge and skills when studying other school subjects and in everyday life, acquire the habit of completing work begun, and obtain satisfaction from correctly and well-done work, to be able to detect and appreciate the beauty and elegance of mathematical methods, solutions, images.

Learning Objectives:

Main tasks:

– creating favorable conditions for the full mathematical development of each student at a level corresponding to his age characteristics and capabilities;

– providing necessary and sufficient mathematical training for further successful studies in primary school.

Mathematics as an academic subject makes a significant contribution to the implementation of the most important goals and objectives of primary general education of junior schoolchildren. Mastering by primary school students the basics of mathematical language to describe various objects and phenomena of the surrounding world, mastering the general technique of solving problems as a universal action, the ability to build logical chains of reasoning, algorithms for performed actions, the use of measuring and computing skills and abilities create the necessary basis for the successful organization of the learning process students in elementary school.

Place of the subject in the basic curriculum

According to the program, 4 hours a week are allocated for studying program material in grade 2. Based on the school curriculum, 4 hours per week (140 hours) are allocated for studying the “Mathematics” course.

Kochurova E. E., Rudnitskaya V. N., Rydze O. A. Mathematics: 2nd grade: Textbook for students of general education institutions: in 2 hours. Part 1. – M.: Ventana- Count, 2021.

Rudnitskaya V.N. Mathematics: 2nd grade: Textbook for students of general education institutions: in 2 hours. Part 2. – 3rd ed., revised. – M.: Ventana-Graf, 2021.

As a result of training
children in mathematics are expected to achieve the following results:

Planned learning outcomes

name:

– natural numbers from 20 to 100 in forward and reverse order, the next (previous) number when counting;

– a number several times greater or less than a given number;

– units of length, area;

– one or more parts of a given number and a number according to its share;

– components of arithmetic operations (addend, sum, minuend, subtrahend, difference, multiplier, product, dividend, divisor, quotient);

– a geometric figure (polygon, angle, rectangle, square, circle);

compare:

– numbers within 100;

– numbers in multiples (how many times one number is greater or less than another);

— lengths of segments;

distinguish:

– relations “more in” and “more on”, “less in” and “less on”;

– components of arithmetic operations;

– numerical expression and its meaning;

– Russian coins, banknotes of various denominations;

– right and indirect angles;

– perimeter and area of ​​the rectangle;

– circle and circle;

read:

– numbers within 100, written in digits;

– records of the form 5 2 = 10, 1 2 :
4 = 3;

play:

– results of tabular cases of multiplication of single-digit numbers and corresponding cases of division;

– relationships between units of length: 1 m = 100 cm, 1 m = 10 dm;

give examples:

– single-digit and double-digit numbers;

— numerical expressions;

model:

– decimal composition of a two-digit number;

– algorithms for adding and subtracting two-digit numbers;

– a situation presented in the text of an arithmetic problem, in the form of a diagram, drawing;

recognize:

– geometric shapes (polygons, circle, rectangle, angle);

order:

– numbers within 100 in increasing or decreasing order;

characterize:

– numerical expression (name, as composed);

– polygon (name, number of angles, sides, vertices);

analyze:

– the text of a training problem with the aim of finding an algorithm for solving it;

– ready-made solutions to problems in order to choose the right solution, a rational method of solution;

classify:

– angles (straight, indirect);

– numbers within 100 (single-digit, double-digit);

design:

– texts of simple arithmetic problems;

– algorithm for solving a compound arithmetic problem;

control:


— your activities (find and correct errors);
rate:

– a ready-made solution to a learning problem (true, false);

solve educational and practical problems:
– write two-digit numbers in digits; – solve compound arithmetic problems in two steps in various combinations;

– calculate the sum and difference of numbers within 100, using learned oral and written calculation techniques;

— calculate the values ​​of simple and compound numeric expressions;

— calculate the perimeter and area of ​​a rectangle (square);

– construct a circle using a compass; – select from the table the necessary information to solve a learning task;

– fill out tables, having some data bank.

By the end of training in second grade

student can learn
:

formulate:

– properties of multiplication and division;

– definitions of rectangle and square;

— properties of a rectangle (square);

name:

– vertices and sides of the angle, indicated in Latin letters;

– polygon elements (vertices, sides, corners);

– center and radius of the circle;

— coordinates of points marked on the number line;

read:

– designations of ray, angle, polygon;

distinguish:

– ray and segment;

characterize:

– location of numbers on the number line;

– relative position of figures on the plane (intersect, do not intersect, have a common point (common points);

solve educational and practical problems:

— select the unit of length when taking measurements;

– justify the choice of arithmetic operations for solving problems;

– indicate in the figure all the axes of symmetry of the rectangle (square);

– draw a polygon on paper using a ruler or by hand;

– create simple numerical expressions;

– perform simple mental calculations within 100.

Personal, meta-subject and subject results

Personal

Student learning outcomes are:

the ability to establish which educational tasks a student can successfully cope with independently;

readiness and ability for self-development;

the ability to characterize one’s own mathematical knowledge and skills;

interest in expanding and deepening the acquired mathematical knowledge;

readiness to use the mathematical training received in educational activities and in solving practical problems that arise in everyday life;

express your own judgments and give reasons for them;

Metasubject

learning outcomes are:

mastery of basic methods of understanding the world around us (observation, comparison, analysis, synthesis, generalization, modeling);

accepting a learning task, searching and finding ways to solve it;

mastery of planning, control and evaluation of educational activities; determining the most effective way to achieve results;

performing educational activities in various forms (practical work, working with models, etc.);

creating models of studied objects using sign-symbolic means;

understanding the reasons for unsuccessful educational activities and the ability to act constructively in conditions of failure;
active use of mathematical speech to solve various communicative problems;
willingness to listen to the interlocutor, conduct a dialogue;

Subject

student results:

mastery of the basics of mathematical speech;

the ability to apply acquired mathematical knowledge to solve educational, cognitive and educational and practical problems;

mastery of oral and written algorithms for performing arithmetic operations with non-negative integers, the ability to calculate the values ​​of numerical expressions, solve word problems, measure the most common quantities in practice, recognize and depict the simplest geometric figures;

Universal learning activities:

compare objects (figures) according to their shape and size;

distribute a given set of objects into groups according to given characteristics (perform classification);

compare sets of objects according to their numbers (by composing pairs of objects)

Number and counting

count objects; express the result as a natural number;

compare numbers;

order a given set of numbers.

Arithmetic operations with numbers and their properties

simulate a situation illustrating a given arithmetic operation;

reproduce oral and written algorithms for performing four arithmetic operations;

predict the results of calculations;

control your activities: check the correctness of calculations using the studied methods;

evaluate the correctness of the presented calculations;

compare different calculation methods, choose the most convenient one;

analyze the structure of a numerical expression in order to determine the order in which the arithmetic operations contained in it are performed.

Values ​​

compare the values ​​of homogeneous quantities;

arrange given quantities;

establish a relationship between data and desired quantities when solving various educational problems.

Working with word problems

model the dependencies contained in the text of the problem;

plan the progress of solving a problem;

analyze the text of the problem in order to select the necessary arithmetic operations to solve it;

predict the outcome of a decision;

control your activities: detect and eliminate errors of a logical nature (during the solution) and errors of a computational nature;

choose the correct solution to the problem from several presented solutions;

observe how the solution to a problem changes when its conditions change.

Geometric concepts

navigate on a plane and in space (including distinguishing directions of movement);

distinguish geometric shapes;

characterize the relative position of figures on a plane;

construct the indicated figure from parts;

classify triangles;

Logical-mathematical preparation

determine the truth of simple statements;

Working with information

collect the required information from specified sources; record results in different ways;

compare and summarize information presented in tables, graphs and diagrams;

convert information from text form to tabular form.

Federal State Educational Standards requirements

Course content.

Federal State Educational Standards requirements


Planned results


List of program sections

Study material

Number of hours

Universal learning activities



Subject

Know

Be able to

Non-negative integers. Counting in tens within 100. Names, sequence and writing in digits of natural numbers from 20 to 100. Decimal composition of a two-digit number. Number beam. Representation of numbers by dots on a number line. Point coordinate.
Comparison of two-digit numbers.

1. Addition and subtraction within 100

Addition and subtraction

Particular and general oral and written algorithms for addition and subtraction. Using a microcalculator when performing calculations.

Geometric quantities

Unit of length meter and its designation: m. Relationships between units of length:

1 m = 100 cm, 1 dm = 10 cm, 1 m = 10 dm.

Information from the history of mathematics: ancient Russian measures of length: vershok, arshin, span, flywheel and oblique fathom.

42h

1) acceptance and mastery of the social role of the student, 2) development of motives for learning activities and the formation of personal meaning of learning;

3) development of independence and personal responsibility for one’s actions, 4) development of cooperation skills with adults and peers

5) mastering the ability to accept and maintain the goals and objectives of educational activities, searching for means of its implementation;

6) mastering the initial forms of cognitive and personal reflection;

7) use of sign-symbolic means of presenting information to create models of studied objects and processes, schemes for solving educational and practical problems;

8) mastery of the logical actions of comparison, analysis, synthesis, generalization, classification

Number order when counting (forward and reverse)

Name
any next (previous) number within 100 when counting, as well as any segment of the natural series of numbers from 20 to 100 in direct and reverse order, starting from any number; recalculate
objects in tens, express
the number of results obtained.

Characterize
arrangement of numbers on the number line.

Call
coordinate of a given point, indicate (mark) on the ray a point with a given coordinate.

Compare
numbers in different ways: using a number beam, by digits. Model
algorithms for adding and subtracting numbers using colored sticks, followed by recording the calculations in a column.

Execute
actions of self-control and mutual control
: check the accuracy of calculations using a micro calculator

Call
(calculate) one or more parts of a number and a number from its share.
Compare
numbers using division based on the learned rule.

Distinguish
relations “more in” and “more in”, “less in” and “less in”.
Call
a number several times greater or less than a given number

Formulate
learned properties of multiplication and division and
use

2.

Single-digit multiplication table

Multiplication and division

Multiplication table for single digit numbers; corresponding cases of division.

Fraction of a number. Finding one or more fractions of a number; finding a number from its given fraction. Rule for comparing numbers using division. Relationships between numbers “greater than in .” and “less in .”.

Increase and decrease the number several times.

Properties of multiplication and division

Multiplication and division with 0 and 1. Property of multiplication: two numbers can be multiplied in any order. Properties of division: a smaller number cannot be divided by a larger number without a remainder; you cannot divide by zero; the quotient of two identical numbers (except 0) is 1.

54h

Names of numerical expressions, oral and written addition and subtraction algorithms.

Multiplication tables and corresponding cases of division of single-digit numbers. Properties of multiplication and division.

Play

results of tabulated cases of single-digit multiplication and corresponding cases of division.

them in calculations.

Justify

calculation methods based on studied properties

Distinguish

and

call

components of arithmetic operations.

Distinguish

the concepts of “numerical expression” and “value of a numerical expression”.

Distinguish

numerical expression from other mathematical notations.

Calculate

meanings of numeric expressions. Carry out the action of mutual control

correctness of calculations.

Characterize

numerical expression (name, as composed).

Construct
numerical expression containing 1–2 actions


3. Expressions

Perimeter of a polygon.

Methods for calculating the perimeter of a rectangle (square). Area of ​​a geometric figure. Area units: square centimeter, square decimeter, square meter and their designations: cm 2
, dm 2
, m 2
.

Practical ways to calculate the areas of shapes (including using a palette). Rule for calculating the area of ​​a rectangle (square) Numerical expressions

Names of numbers in records of arithmetic operations (addend, sum, multiplier, product, minuend, subtrahend, difference, dividend, divisor, quotient).

The concept of a numerical expression and its meaning. Calculating the values ​​of numeric expressions with brackets containing 2–3 arithmetic operations in various combinations. Names of numerical expressions: sum, difference, product, quotient.

Reading and writing simple numerical expressions.

23h

Coins and banknotes of various denominations.

Units of length and area.

Discriminate
Russian coins and paper bills of various denominations.

Calculate
cost, price or quantity of a product based on two given known values.

Control
correct calculations using a microcalculator.

Discriminate
units of length.

Choose
unit of length when making measurements.

Compare
lengths expressed in the same or different units.

Distinguish
the perimeter of a rectangle (square) from its area. Calculate
perimeter of a polygon (including a rectangle).

Choose
unit of area for calculating the areas of shapes. Call
units of area. Calculate
area of ​​a rectangle (square). Distinguish
area of ​​a rectangle (square) from its perimeter

During the year

Algorithm for analyzing and solving various types of problems

Select
multiplication or division to solve a problem.

4. Arithmetic problem and its solution

Arithmetic problem and its solution

Simple problems solved by multiplication or division. Compound tasks that require two actions in different combinations.

Problems with missing or extra data.

Recording the solution to a problem in different ways (in the form of an expression, in question-and-answer form). Examples of problems solved in different ways. Comparison of texts and solutions to seemingly similar problems.

Drawing up and solving problems in accordance with given conditions (number and types of arithmetic operations, given relationships between quantities). Formulation of the modified task text. Recording a solution to a new problem

Analyze

the text of the problem in order to find a way to solve it.

Plan

Justify

Play

written or oral progress in solving a problem.

Rate

ready-made solution (true, false).

Compare

proposed options for solving the problem in order to identify a rational method.

Analyze

Construct

5. Logical and mathematical training



algorithm for solving the problem.

selection of necessary arithmetic operations to solve the problem.

texts and solutions to problems, indicate their similarities and differences.

texts of simple problems

Patterns

Determination of the rule for selecting mathematical objects (numbers, numerical expressions, geometric figures) for a given sequence.

Compiling number sequences in accordance with a given rule.

Evidence

True and false statements. Carrying out simple proofs of the truth or falsity of these statements.

Choice situation

Selecting the correct answer among several given plausible options. Simple logical (including combinatorial) problems.

Consideration of all options for solving a logical problem.

Logical problems, the text of which contains several statements (including negation) and their solution

Throughout the year

Name
the next few objects in this sequence

Characterize
this statement (true, false), justify
your answer, giving supporting or refuting examples.

Prove
the truth or falsity of statements based on the results of calculations, properties of mathematical objects, or their definitions.

Update
your knowledge to justify choosing the correct answer.

Design
algorithm for solving a logical problem.

Search
and find
all options for solving a logical problem.

Highlight
logical statements from the text of the problem and, based on their comparison , draw the necessary conclusions


6. Working with information

7. Repetition

Presentation and collection of information

Tables with two inputs containing ready-made information. Filling tables with specified information.

Drawing up tables, diagrams, drawings based on the texts of educational problems (including arithmetic) for the purpose of their subsequent solution

Throughout the year

21h

Algorithm for adding and subtracting single-digit numbers

Comparison rule.

Concept:

arithmetic operation inverse to this one

Select
from the tables the necessary information for solving various educational problems.

Compare
and
generalize

information presented in the rows and columns of a table

Calendar and thematic planning.

No.

Section names

Lesson topics

Content Items

Number of parts

owls

Calendar dates

Numbers 10, 20, 30, …, 100.

Read numbers within 100; write down and compare numbers within 100.

Perform simple mental calculations within 100.

Add and subtract numbers within 100 using written calculation techniques.

Model the decimal composition of a two-digit number.
Reading and writing two-digit numbers using digits.

1

04.09.

2


Numbers 10, 20, 30, …, 100. Solving problems.

1

05.09.

3

Two-digit numbers and their writing. And CT

Representation of two-digit numbers using colored sticks.

1

06.09.

1

18.09


10

Ray and its designation.

1

19.09

11

Number ray. And CT

The concept of a unit segment on a number line. Coordinate of a point on the ray. Construction of points with given coordinates.

1

20.09

12

Number ray.

1

21.09



13

Test No. 2 “Number Ray”

1

25.09.

14

according to plan actually


1


Addition and subtraction within 100 (42h)

4-5

Two-digit numbers and their writing.

2

07.0911.09.

6

Two-digit numbers and their writing.

1

12.09.

7

Test No. 1 “Writing and comparing two-digit numbers”

1

13.09

8

Ray and its designation. And CT

Introducing the concept of a ray as an infinite figure. Showing the beam using a pointer. Illustration of the beam using a ruler and designation of the beam

letters.

1

14.09

9

Ray and its designation.


Meter. Relationships between units of length. And CT

Measuring lengths and distances using various measuring instruments: ruler, meter ruler, tape measure. Relationships between units

lengths: meter, decimeter and centimeter.

1

26.09

15

Meter. Relationships between units of length.

1

27.09.

16

Polygon and its elements.

Introduction to the concepts of a polygon, its vertices, sides and angles. Labeling a polygon with letters.

1

28.09.

17

Polygon and its elements.

1

02.10

18


Polygon and its elements.


1

03.10.


19


Addition and subtraction of the form 26±3; 65±30.

Particular and general techniques for adding and subtracting two-digit numbers, based on digitwise addition and subtraction. Practical implementation

actions using colored sticks. Subsequent recording of calculations in a column.

1

04.10


Recording addition in a column.

1

10/12.

25


Recording subtraction in a column.

Particular and general techniques for adding and subtracting two-digit numbers, based on digitwise addition and subtraction. Practical implementation
actions using colored sticks. Subsequent recording of calculations in a column.

1

20

Addition and subtraction of the form 26±3; 65±30. And CT

1

05.10

21

Addition and subtraction of the form 26±3; 65±30.

1

09.10.

22

Test No. 3 on the topic “Adding two-digit numbers. Polygon”

Particular and general techniques for adding and subtracting two-digit numbers, based on digitwise addition and subtraction. Practical implementation

actions using colored sticks. Subsequent recording of calculations in a column.

1

10.10.

23

Writing addition in a column. And CT

1

11.10.

24


16.10.

26

Recording subtraction in a column.

1

10.17.

27

Addition of two-digit numbers (general case). And CT

Addition of two-digit numbers (general case).

Particular and general techniques for adding and subtracting two-digit numbers, based on digitwise addition and subtraction. Practical implementation

actions using colored sticks. Subsequent recording of calculations in a column.

1

10.18.

28

Addition of two-digit numbers (general case).

1

10.18.



29

Test No. 4 on the topic “Addition of two-digit numbers”



1

10.19.

30

Analysis of test work. Work on mistakes.

Problem solving.

Subtraction of two-digit numbers (general case).

Particular and general techniques for adding and subtracting two-digit numbers, basic in place value

addition and subtraction. Practical execution of actions using colored sticks. Follow-up

recording calculations in a column.

1


23.10.

31


Subtraction of two-digit numbers (general case).

1

24.10.

32

Subtraction of two-digit numbers (general case).

1

10.25.

33

Perimeter of a polygon. And CT

Introduction of the term “perimeter”. Calculation of perimeters of any polygons.

1

26.10.

34

Perimeter of a polygon.

1

30.10

35

Perimeter of a polygon.

1

31.10.

36

Circle, its center and radius. And CT

Introducing the concept of “circle”. Introduction of the terms “center”, “radius of a circle”. Constructing a circle using a compass.

1

01.11.

37

Circle, its center and radius. Circle and Circle

1

02.11.

38

Circle, its center and radius Circle and circle.

1


13.11.



39


The relative position of figures on a plane. And CT

The concept of intersecting and non-intersecting figures. Solving practical problems.

1

14.11.



40

The relative position of figures on a plane.

1

11/15.

41

Test No. 5 on the topic “Addition and subtraction of two-digit numbers”



1

16.11.

42


Analysis of test work. Work on mistakes. Problem solving.


1

20.11.


43

Single-digit multiplication table. (54h)


Multiplication and division by 2. AND CT

Tabulated cases of multiplication and division by 2. Use knowledge of the multiplication tables to find division results. Finding a fraction
numbers by division. Preparing to introduce the concept of area of ​​a figure (recalculating squares, into which the figure is divided using the multiplication table).

1

21.11.


44

Multiplication and division by 2.

1

22.11.

45

Multiplication and division by 2. Half a number.

1

23.11.

46

Multiplying three and by 3. And CT

Table cases of multiplication and division by 3. Use knowledge of the multiplication tables to find division results. Finding the beat

numbers by division. Preparing to introduce the concept of area of ​​a figure (recounting squares,

into which the figure is divided using the multiplication table).

1

27.11.

47

Multiplication and division by 3.

1

28.11.

48

Multiplication and division by 3. Third of a number.

1

29.11.

49

Multiplying four and by 4. And CT

Table cases of multiplication and division by 4. Use knowledge of the multiplication tables to find division results. Finding the beat

numbers by division. Preparing to introduce the concept of area of ​​a figure (recounting squares,

into which the figure is divided using the multiplication table).

1

30.11.

50

Multiplication and division by 4.

Quarter number.

1

04.12.

51

Test No. 6 “Table cases of multiplication by 2, 3 and 4”

1

05.12.

52

Multiplying five and by 5. AND CT

Table cases of multiplication and division by 5. Use knowledge of the multiplication tables to find division results. Finding a beat

numbers by division. Preparing to introduce the concept of area of ​​a figure (recalculating squares,
into which the figure is divided using the multiplication table).

1

06.12.

53

Multiplication by 5. Solving problems.

1

07.12.

54

Multiplication and division by 5. Solving problems.

1

11.12.

1

12.12.

55

Multiplication and division by 5. The fifth part of a number.

56


Multiplication and division by 5. The fifth part of a number. Independent work.


1

13.12.

57


Multiply by 6. AND CT

Tabulated cases of multiplication and division by 6. Use knowledge of the multiplication tables to find division results. Finding a fraction
numbers by division. Preparing to introduce the concept of area of ​​a figure (recalculating squares,

1

14.12.


58


Multiplying by 6. Solving problems.

1

12.18.

59

Multiplication and division by 6.

into which the figure is divided using the multiplication table).

1

12.19.

60

Multiplication and division by 6. The sixth part of a number.

1

20.12.

61

Multiplication and division by 6. The sixth part of a number.

1

21.12.

62

Test No. 7 on the topic “Tabular multiplication and division by 4, 5 and 6”

1

25.12.

63

Analysis of test work. Work on mistakes. Problem solving.

1

26.12.

64


Area of ​​the figure. Units of area. And CT

Introduction of the concept of “area of ​​a figure.” Familiarization with units of area (square meter, square decimeter, square centimeter) and
their designations are m², dm², cm².

1

27.12.

65



Area of ​​the figure. Units of area.

1

28.12.

66


Area of ​​the figure. Units of area.

1

15.01.

67

Test No. 8 “Area of ​​a figure”

1

16.01.


68


Analysis of test work. Work on mistakes. Multiplying seven and by 7.

Tabulated cases of multiplication and division by 7. Use knowledge of the multiplication tables to find division results. Finding a fraction

numbers by division.

1

17.01.

69


Multiplication by 7. Solving problems.

1

18.01.

70

Multiplication and division by 7. AND CT

1

22.01.

71

Multiplication and division by 7. The seventh part of a number.

1


23.01.

72

Multiplying eight by 8.

Table cases of multiplication and division by 8. Use knowledge of the multiplication tables to find division results. Finding a fraction

numbers by division.

1

24.01.

73

Multiplication by 8. Solving problems.

1

25.01.

74

Multiplication and division by 8. AND CT

1

29.01.

75-76

Multiplication and division by 8. The eighth part of a number.

2

30.01.

77

Multiplying nine and by 9.

Table cases of multiplication and division by 9. Use knowledge of the multiplication tables to find division results. Finding the beat

numbers by division.

1

31.01.

78

Multiplication by 9. Solving problems.

1

01.02.

79

Multiplication and division by 9. AND CT

1

05.02.

80


Multiplication and division by 9. The ninth part of a number.

1

06.02.

81



Multiplication and division by 9. The ninth part of a number.


1

02/07.

82

Test No. 9 on the topic “Multiplication and division by 7, 8, 9”

1

08.02.

83


Analysis of test work. Work on mistakes. Problem solving.


1

12.02.

84-88

How many times more or less? ICT

Multiple comparison of numbers. Solving problems to find a number that is several times greater or less than a given number. Practical techniques for comparison

numbers.

5

13.02.
14.02.
15.02
02.19.,02.20



89-90

Solving problems involving increasing and decreasing several times.

Multiple comparison of numbers. Solving problems to find a number that is several times greater or less than a given number. Practical techniques for comparison

numbers.

2

21.02
22.02

91-95

Finding several fractions of a number. And CT

Using division and multiplication to find multiple fractions of a given number or quantity. Solution of the inverse problem. Using division and multiplication to find multiple fractions of a given number or quantity. Solution of the inverse problem.


5

26.02.
27.02.

28.02

01.03

05.03

96

Test No. 10 on the topic “Solving multiple comparison problems. To increase and decrease several times”

1

06.03

97-99

Expressions (23h)

Analysis of test work. Work on mistakes.

Name of numbers in action records. And CT

Introduction of the names of the components of addition, subtraction, multiplication, division. Concepts about numerical expression and its meaning. Composition of numbers

expressions from numbers and action signs. Calculating the values ​​of numeric expressions.

3

07.03

12.03.

13.03.

100

Numerical expressions. And CT

Introduction of the names of the components of addition, subtraction, multiplication, division. Concepts about numerical expression and its meaning. Composition of numbers

expressions from numbers and action signs. Calculating the values ​​of numeric expressions.

1

14.03.


Numerical expressions.

1

101

Numerical expressions.

1

15.03.

102


19.03.

103


Compiling numerical expressions.

Introduction of the names of the components of addition, subtraction, multiplication, division. Concepts about numerical expression and its meaning. Composition of numbers
expressions from numbers and action signs. Calculating the values ​​of numeric expressions.

1

20.03.

104


Compiling numerical expressions.

Compiling numerical expressions.

1

21.03.

105

Test No. 11 on the topic “Numerical Expressions”



1

22.03

106

Analysis of test work. Work on mistakes.

Angle. Right angle. And CT

Introduce the concept of angle. Introduction of the terms “right angle”, “indirect angle”. A practical way to determine and construct a right angle with

using: a) models; b) drawing square.

1

02.04.




107


Angle. Right angle.

1
03.04.

108

Variable.

Formation of the concept of a variable, as well as an expression containing one variable. Designation of variables with Latin letters

alphabet. Finding the values ​​of expressions with a variable for a given set of values ​​of this variable. Problem solving.

1

04.04.

109

Variable.

1

05.04

110

Rectangle. Square. And CT

Introducing the definitions of a rectangle and a square (as a rectangle with equal sides). Familiarization with the properties of opposites

sides and diagonals of a rectangle.

1

09.04.

111

Rectangle. Square.

1

10.04.

112

Rectangle. Square.

1

11.04.

113-114

Properties of a rectangle. And CT

Introducing the definitions of rectangle and square (as a rectangle with equal sides). Familiarization with the properties of opposite sides and diagonals of a rectangle.

2

12.04.

16.04.

115

Area of ​​the rectangle. And CT

Rule for calculating the area of ​​a rectangle (square). Problem solving.

1

17.04.

116


Area of ​​the rectangle.

1


18.04.

117

Area of ​​the rectangle.

1

19.04.

118



Test No. 12 on the topic “Rectangle. Square. Perimeter and area of ​​a rectangle””

1

23.04.



119


Analysis of test work. Work on mistakes.


1

24.04.



120-127

Repetition

(21h)

Repetition on the topic “Addition, subtraction, multiplication and division of numbers within 100” ICT

Solving problems along the main content lines of the course.

8

25.04.
26.04.
03.05.
07.05.
08.05.

10.05.

14.05.
15.05.

128


Final test No. 13

1

16.05.



129-132


Repetition on the topic “Arithmetic problems”


4

17.05.

21.05

22.05.

23.05.

133-137

Repetition on the topic

“Expressions”

4

24.05.

25.05.

27.05.

28.05.

138-140

Reserve lessons.

3

29.05.

30.05.

31.05.

Contents of the mathematics program. 2nd class

Addition and subtraction within 100 (42 hours)

Numbers 10, 20, 30, …, 100. Two-digit numbers and their writing. Ray and its designation. Number beam. Meter.

Relationships between units of length. Polygon and its elements. Addition and subtraction of the form 26±3; 65±30.

Writing addition in a column. Addition of two-digit numbers (general case). Subtraction of two-digit numbers (general case).

Perimeter of a polygon. Circle, its center and radius. Circle and Circle

The relative position of figures on a plane.

Single digit multiplication table (54 hours)

Tabular multiplication of numbers and corresponding cases of division.

Multiplication property: numbers can be multiplied in any order.

Area of ​​the figure. Units of area.

How many times more or less?

Relationships “less in .” and “more in .”.

Solving problems involving increasing and decreasing several times.

Fraction of a number. Finding multiple fractions of a number.

Expressions (23 hours)

Name of numbers in action records. The names of the components of the operations of addition, subtraction, multiplication and division.

Numerical expressions. Numerical expression and its meaning. Numeric expressions containing parentheses Compose numeric expressions.

Finding the values ​​of numerical expressions. Compiling numerical expressions. Corner. Right angle. Determining the type of angle (direct, indirect), finding a rectangle among given quadrilaterals using the right angle model. Variable.

Rectangle. Square. Properties of a rectangle. Rectangle (square). Properties of opposite sides and diagonals of a rectangle.

Area of ​​a rectangle. The rule for calculating the area of ​​a rectangle (square). . Area units: square decimeter, square centimeter, square meter and their designations (dm 2
, cm 2
, m 2
).

Repetition(21h)

.

Requirements for the level of training

Planned learning outcomes

name:

– natural numbers from 20 to 100 in forward and reverse order, the next (previous) number when counting;

– a number several times greater or less than a given number;

– units of length, area;

– one or more parts of a given number and a number according to its share;

– components of arithmetic operations (addend, sum, minuend, subtrahend, difference, multiplier, product, dividend, divisor, quotient);

– a geometric figure (polygon, angle, rectangle, square, circle);

compare:

– numbers within 100;

– numbers in multiples (how many times one number is greater or less than another);

— lengths of segments;

distinguish:

– relations “more in” and “more on”, “less in” and “less on”;

– components of arithmetic operations;

– numerical expression and its meaning;

– Russian coins, banknotes of various denominations;

– right and indirect angles;

– perimeter and area of ​​the rectangle;

– circle and circle;

read:

– numbers within 100, written in digits;

– records of the form 5 2 = 10, 1 2 :
4 = 3;

play:

– results of tabular cases of multiplication of single-digit numbers and corresponding cases of division;

– relationships between units of length: 1 m = 100 cm, 1 m = 10 dm;

give examples:

– single and double digit numbers;

— numerical expressions;

model:

– decimal composition of a two-digit number;

– algorithms for adding and subtracting two-digit numbers;

– a situation presented in the text of an arithmetic problem, in the form of a diagram, drawing;

recognize:

– geometric shapes (polygons, circle, rectangle, angle);

order:

– numbers within 100 in increasing or decreasing order;

characterize:

– numerical expression (name, as composed);

— polygon (name, number of angles, sides, vertices);

analyze:

– the text of a training problem with the aim of finding an algorithm for solving it;

– ready-made solutions to problems in order to choose the right solution, a rational method of solution;

classify:

– angles (straight, indirect);

– numbers within 100 (single-digit, double-digit);

design:

– texts of simple arithmetic problems;

– algorithm for solving a compound arithmetic problem;

control:

— your activities (find and correct errors);

rate:

– a ready-made solution to a learning problem (true, false);

solve educational and practical problems:

– write two-digit numbers in digits;

– solve compound arithmetic problems in two steps in various combinations;

– calculate the sum and difference of numbers within 100, using learned oral and written calculation techniques;

— calculate the values ​​of simple and compound numeric expressions;

— calculate the perimeter and area of ​​a rectangle (square);
– construct a circle using a compass;

– select from the table the necessary information to solve a learning task;

– fill out tables, having some data bank.

By the end of training in second grade

student can learn
:

formulate:

– properties of multiplication and division;

– definitions of rectangle and square;

— properties of a rectangle (square);

name:

– vertices and sides of the angle, indicated in Latin letters;

– polygon elements (vertices, sides, corners);

– center and radius of the circle;

— coordinates of points marked on the number line;

read:

– designations of ray, angle, polygon;

distinguish:

– ray and segment;

characterize:

– location of numbers on the number line;

– relative position of figures on the plane (intersect, do not intersect, have a common point (common points);

solve educational and practical problems:

— select the unit of length when taking measurements;

– justify the choice of arithmetic operations for solving problems;

– indicate in the figure all the axes of symmetry of the rectangle (square);

– draw a polygon on paper using a ruler or by hand;

– create simple numerical expressions;

– perform simple mental calculations within 100.

Personal, meta-subject and subject results

Personal

Student learning outcomes are:

the ability to establish which educational tasks a student can successfully cope with independently;

readiness and ability for self-development;

the ability to characterize one’s own mathematical knowledge and skills;

interest in expanding and deepening the acquired mathematical knowledge;

readiness to use the mathematical training received in educational activities and in solving practical problems that arise in everyday life;

express your own judgments and give reasons for them;

Metasubject

learning outcomes are:

mastery of basic methods of understanding the world around us (observation, comparison, analysis, synthesis, generalization, modeling);

accepting a learning task, searching and finding ways to solve it;

mastery of planning, control and evaluation of educational activities; determining the most effective way to achieve results;

performing educational activities in various forms (practical work, working with models, etc.);

creating models of studied objects using sign-symbolic means;

understanding the reasons for unsuccessful educational activities and the ability to act constructively in conditions of failure;

active use of mathematical speech to solve various communicative problems;

willingness to listen to the interlocutor, conduct a dialogue;

Subject

student results:

mastering the basics of mathematical speech;

the ability to apply acquired mathematical knowledge to solve educational, cognitive and educational and practical problems;

mastery of oral and written algorithms for performing arithmetic operations with non-negative integers, the ability to calculate the values ​​of numerical expressions, solve word problems, measure the most common quantities in practice, recognize and depict the simplest geometric figures;

Universal learning activities:

compare objects (figures) according to their shape and size;

distribute a given set of objects into groups according to given characteristics (perform classification);

compare sets of objects according to their numbers (by making pairs of objects)

Number and counting

count objects; express the result as a natural number;

compare numbers;

order a given set of numbers.

Arithmetic operations with numbers and their properties

simulate a situation illustrating a given arithmetic operation;

reproduce oral and written algorithms for performing four arithmetic operations;

predict the results of calculations;

control your activities: check the correctness of calculations using the studied methods;

evaluate the correctness of the presented calculations;

compare different calculation methods, choose the most convenient one;

analyze the structure of a numerical expression in order to determine the order in which the arithmetic operations contained in it are performed.

Values ​​

compare the values ​​of homogeneous quantities;

arrange given quantity values;

establish a relationship between data and desired quantities when solving various educational problems.

Working with word problems

model the dependencies contained in the text of the problem;

plan the progress of solving a problem;

analyze the text of the problem in order to select the necessary arithmetic operations to solve it;

predict the outcome of a decision;

control your activities: detect and eliminate errors of a logical nature (during the solution) and errors of a computational nature;

choose the correct solution to a problem from several presented solutions;

observe how the solution to a problem changes when its conditions change.

Geometric concepts

navigate on a plane and in space (including distinguishing directions of movement);

distinguish geometric shapes;

characterize the relative position of figures on a plane;

construct the indicated figure from parts;

classify triangles;

Logical-mathematical preparation

determine the truth of simple statements;

Working with information

collect the required information from specified sources; record results in different ways;

compare and summarize information presented in tables, graphs and diagrams;

convert information from text form to tabular form.

Educational and methodological support

Collection of programs for the set of textbooks “Primary School XXI
century.” – 3rd ed., revised. and additional – M.: Ventana – Graf, 2021.

Conversations with the teacher. First grade of a four-year primary school.

Mathematics: 2nd grade: teaching methods / V. N. Rudnitskaya, E. E. Kochurova, O. A. Rydze, – M.: Ventana-Graf, 2021.

Kochurova E. E., Rudnitskaya V. N., Rydze O. A. Mathematics: 2nd grade: Textbook for students of general education institutions: in 2 hours. Part 1. – M.: Ventana-Graf, 2021.

Rudnitskaya V.N. Mathematics: 2nd grade: Textbook for students of general education institutions: in 2 hours. Part 2. – 3rd ed., revised. – M.: Ventana-Graf, 2021.

Mathematics: 2nd grade: workbook No. 1 for students of general education institutions /

E. E. Kochurova. – M.: Ventana-Graf, 2021.

Mathematics: 2nd grade: workbook No. 2 for students of general education institutions /

E. E. Kochurova. – M.: Ventana-Graf, 2021.

Knowledge assessment. Mathematics in primary school: Tests and tests. – M.: Ventana-Graf, 2021.

Further reading

Planned results of primary general education/[L. L. Alekseeva, S. V. Anashchenkova, M. Z. Biboletova, etc.]; edited by G.S. Kovaleva, O. B. Loginova. – 3rd ed. – M.: Education, 2021.

How to design universal learning activities in primary school. From action to thought: a manual for teachers / [A. G. Asmolov, G. V. Burmenskaya, I. A. Volodarskaya and others]; edited by A.G. Asmolov. – 3rd ed. – M.: Education, 2021.

Collection of programs for the set of textbooks “Elementary school XXI
century.” – 3rd ed., revised. and additional – Ventana – Count, 2021.

Conversations with the teacher: 2nd grade of a four-year elementary school / Ed. L.E. Zhurova. – Ventana-Graf, 2008.

Rudnitskaya V. N., Yudacheva T. V. Mathematics: 2nd grade: Teaching methods. – M.: Ventana-Graf, 2008.

Rudnitskaya V. N. Mathematics in elementary school: tests and tests / V. N. Rudnitskaya, T. V. Yudacheva. – 2nd ed., revised. – M.: Ventana-Graf, 2021.

Mathematics: 2nd grade: textbook for students of general education institutions: in 2 hours – 5th ed., revised. – M.: Ventana – Graf, 2021.

Workbook “Mathematics”, 2nd grade, No. 1, No. 2. Authors: Rudnitskaya V.N., Yudacheva T.V., M.: Publishing house. Ventana-Graf Center, 2021

Workbook for differentiated learning “We are friends with mathematics”, 2nd grade, Author: Rudnitskaya V.N., Yudacheva T.V., M.: Publishing house. Ventana-Graf Center, 2021.

Digital educational resources:

Self-developed presentations ( CD
ROM
)

Equipment:

Study tables.

Marker board

Projector

Large universal board (with the possibility of magnetic fastening).

Computer.

Teaching materials:

counting material;

chips;

set of geometric shapes;

diagrams;

set of numbers;

tables for adding numbers within 10, 20; 100

didactic dolls;

didactic games;

task cards;

tests.

Forms of control

Testing


1

Item

Number of tests by class

1st grade

2nd grade

3rd grade

4th grade

Russian language

Control cheating

1

1

Dictation

1( see footnote
)

4

4

4

Exposition

1

Vocabulary dictation

4

4


4

2
1

Test

4

4

4

Total

1

14

14

14

Mathematics

1

13

13

14

Literary reading

1

4

8


8









The world around us


1


4

4

4







(Material taken from methodological letter 2021)

Publication address:

https://www.obumage.net/metodicheskie-razrabotki/209294-rabochaja-programma-po-uchebnomu-kursu-matema

§

§

Testing and measuring materials in mathematics for 4th grade students

Option 1

Part A

Represent the number 462 as a sum of digit terms.

400 62

460 2

450 10 2

400 60 2

What property is common to the numbers 38, 237, 934, 731?

All numbers are three-digit

All numbers are even

All numbers are greater than 200

Each number has a 3 in the tens place.

The length of the rectangle is 12 cm and the width is 4 cm. Find its perimeter.

16 cm

48 cm

3 cm

32 cm

In which row is the solution to the problem written?

5 jars contain 20 kg of honey. How much does one jar of honey weigh?

20 .

5 = 100 (kg)

20 : 5 = 4 (kg)

20 5 = 25 (kg)

20 – 5 = 15 (kg)

What is not a unit of length?

Centimeter

Millimeter

Kilometer

Kilogram

Which example was solved correctly?

805 – 467 = 348

923 – 516 = 407

720 – 380 = 440

511 – 103 = 418

What action should be performed last when finding the value of the expression

– 40 .

5 14?

1) addition

2) subtraction

3) multiplication

4) division

Calculate: 236 .

4

844

904

944

834

Calculate: 984 : 4

146

246

236

248

145 kg of strawberries, 135 kg of currants were brought to the store, and raspberries were 2 times less than strawberries and currants together.

What expression can be used to find out the mass of raspberries brought to the store?

( 145 135) . 2

( 145 – 135) .

2

(145 135): 2

4) (145 – 135): 2

Calculate: 486,136

1) 92

2) 522

3) 612

4) 622

What expression can be used to calculate the area of ​​a rectangle with sides 6 cm and 3 cm?

6 3 6 3

(6 3) .

2

6 .

3

6 .

2 3

.

2

The flower shop had 42 red roses and 48 white ones. A third of all roses were collected into bouquets and sold. How many roses did you sell?
90

12
72

30

. The length of the room is 6 m 5 cm. Express the length of the room in centimeters.
1) 655 cm
2) 65 cm
3) 605 cm

4) 650 cm

Part B

One box holds 12 juice packs. Are four boxes enough to hold 50 of these bags?

Enough, there will still be room for two more packages

Not enough, two bags won’t fit

Enough, all packages will fit

Not enough, not enough space for 20 bags

Solve the problem by briefly writing the condition.

13 tents for 4 people

? tourists

15 tents for 3 people

__________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Answer__________________________________________________________________________

The table shows the results of a survey of 3rd grade students about which juices they prefer.

Names

Apple

Cherry

Peach

Orange

Ira

Natasha

Dima

Seryozha

Katya

Fedya

Lenya

Sveta

Using the data in the table, answer the questions.

a) How many boys like peach juice?

Answer: ________________________________________________

b) How many children don’t like apple juice?

Answer: ____________________________ __________________

c) Which of the guys likes cherry and orange juices?

Answer: ________________________________________________________________________________

Write down the expression and calculate its value.

Increase the quotient of numbers 91 and 3 by 10 times.

Testing and measuring materials in mathematics for 4th grade students.

September 2021-2021 academic year

Option 2

Part A

Represent the number 783 as a sum of digit terms.

700 83
780 3

740 40 3

700 80 3
What property is common to the numbers 38, 237, 934, 731?
All numbers are three-digit
All numbers are even

All numbers are greater than 200

Each number has a 3 in the tens place.

The length of the rectangle is 15 cm and the width is 3 cm. Find its perimeter.

18 cm

45 cm

5 cm

36 cm

In which row is the solution to the problem written?

Three boxes of apples weigh 36 kg. How much does one box of apples weigh?

36

.

3 = 108 (kg)

36 : 3 = 12 (kg)

36 – 3 = 33 (kg)

36 3 = 39 (kg)

What is not a unit of mass?

Gram
Centner

Kilometer

Kilogram
Which example was solved correctly?
1) 412 493 = 805
2) 587,234 = 811

3) 348 256= 614
4) 823 177 = 990 What action should be performed last when finding the value of the expression 300 40

.

5 – 14?

1) addition

2) subtraction

3) multiplication

4) division

Calculate:478

.

2

856

956

946

846
Calculate: 717 : 3
248

229
239

139

Three friends were sledding down the mountain. Igor drove 200m. Sasha is 2 times less than Igor, and Petya is 70 m more than Sasha. Using what expression can you find out how many meters Petya traveled?

200 – 2 (m)

200 : 2 70 (m)

200 : (2 70) (m)

( 200 70) : 2 (m)

Calculate: 704 – 368

1) 346

2) 436

3) 1072

4) 336

What expression can be used to calculate the area of ​​a rectangle with sides 5 cm and 7 cm?

5 7 5 7

(5 7 )

.

2

5 .

7

5 .

2 7 .

2

There are 180 windows in the school building. A sixth of all windows were replaced with new double-glazed windows. How many windows are left to replace?

60

6

174

150

The distance from the house to the garage is 2 m 4 cm. Express this distance in centimeters.

1) 24 cm

2) 204 cm

3) 240 cm

4) 244 cm

Part B

Only 22 books can be placed on each shelf. Will 67 books fit on three such shelves?

Will not fit, 1 book left

They will fit, there will be room for one more book

Will fit 20 more books

Will not fit, there is not enough space for 10 books

§

Sedova Margarita Vladimirovna

MANOU “Gymnasium No. 2” Mariinsk

Primary school teacher

Composite problems for price, quantity, cost.

A bun costs 2 rubles. How much do 6 of these buns cost?

Luda has 9 coins of 10 rubles. How much money does the girl have?

Three identical notebooks cost 21 rubles. How much does one notebook cost?

How many candies of 9 rubles can you buy for 45 rubles?

Six buttons cost 18 rubles. How much does one button cost?

Vitya has 3 coins of 2 rubles. How much money does the boy have?

We bought 4 chocolates for 10 rubles. How much does the purchase cost?

How much does one album cost if 5 albums cost 30 rubles?

The girl paid 27 rubles for 9 pencils. How much does 1 pencil cost?

The housewife bought 8 bunches of dill for 3 rubles. How much did she pay for the purchase?

Vera has 4 coins of 2 rubles. How much money does the girl have?

We bought 3 chocolates for 10 rubles. How much does the purchase cost?

How much does one album cost if 4 albums cost 24 rubles?

For 7 pens we paid 35 rubles. How much does 1 pen cost?

The housewife bought 7 bunches of parsley for 4 rubles. How much did she pay for the purchase?

A bun costs 4 rubles. How much do 5 of these buns cost?

Luda has 7 coins of 10 rubles. How much money does the girl have?

Three identical pens cost 21 rubles. How much does one pen cost?

How many chocolates at 9 rubles can you buy for 45 rubles?

Five buttons cost 15 rubles. How much does one button cost?

For labor lessons, we bought 4 spools of white thread for 10 rubles and the same number of spools of black thread for 12 rubles. How many rubles did you pay for the entire purchase?

Kolya had 20 rubles, Misha had 25 rubles. How many balls can they buy if a ball costs 5 rubles?

Grandmother bought 4 m of silk for 9 rubles and 3 m of cotton. She paid 54 rubles for the entire purchase. How much does a meter of chintz cost?

Misha had 13 rubles, and Olya had 14 rubles. How many movie tickets can they buy if 1 ticket costs 3 rubles?

For school we bought 10 rulers for 6 rubles and the same number of pencils for 4 rubles. How many rubles did you pay for the entire purchase?

The boy bought 6 albums for 12 rubles. How many albums will he buy with 8 rubles?

One sketchbook costs 5 rubles, and a jar of glue costs 2 rubles. How much more expensive are 3 albums than 4 jars of glue?

My sister bought 3 notebooks for 6 rubles, and my brother bought the same number of notebooks for 10 rubles. How much did all these notebooks cost?

Asya had 98 rubles. She bought a photo album for 42 rubles and several notebooks for 4 rubles. How many notebooks did the girl buy?

Two girls bought 10 erasers at the same price. One paid 16 rubles, and the second 4 rubles. How many erasers did each girl buy?

Publication address: https://www.obumage.net/metodicheskie-razrabotki/209212-sostavnye-zadachi-na-cenu-kolichestvo-stoimos

§

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

7 x 3= 48 : 6 = … : 4 = 7

8 x 5 = 42 : 7 = 36 : …=9

9 x 6 = 35: 5 = …x 7 = 70

7 x 8 = 24: 4 = …x 7 = 63

9 x 7 = 32 : 8 = 14 :… = 7

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

6 x 7 = 27 : 3 = …. : 7 = 7

8 x 4 = 30 : 5 = 32 : … = 4

9 x 5 = 28: 4 = … x 7 = 21

7 x 4 = 54: 6 = …x 6 = 60

9 x 3 = 56 : 7 = 48 : …= 8

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

7 x 3= 48 : 6 = … : 4 = 7

8 x 5 = 42 : 7 = 36 : …=9

9 x 6 = 35: 5 = …x 7 = 70

7 x 8 = 24: 4 = …x 7 = 63

9 x 7 = 32 : 8 = 14 :… = 7

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

6 x 7 = 27 : 3 = …. : 7 = 7

8 x 4 = 30 : 5 = 32 : … = 4

9 x 5 = 28: 4 = … x 7 = 21

7 x 4 = 54: 6 = …x 6 = 60

9 x 3 = 56 : 7 = 48 : …= 8

Mathematical dictation No. 1.

1 option.

The minuend is 44, the subtrahend is expressed as the product of the numbers 8 and 3. What is the difference?

Find the sum of two products: 8 and 4, 6 and 3.

Increase the product of numbers 9 and 5 by 4 tens and 5 ones.

How many times are there 6s in the number 48?

Increase the product of numbers 6 and 5 by the same amount.

Increase the quotient of numbers 63 and 9 by the product of numbers 7 and 4.

The product of numbers is 35. One of the factors is 7. What is the second factor?

From the number 45, subtract the product of the numbers 9 and 4.

Sewing 7 suits requires 42 meters of fabric. How many of these suits can be made from 54 meters of fabric?

56 yogurts were packaged in 7 boxes. 5 boxes of yogurt were sent to the school cafeteria. How many pieces of yoghurt were sent to the school cafeteria?

Mathematical dictation No. 1.

2nd option.

Reduce the sum of numbers 38 and 16 by 6 times.

How many times 7 are there in 49?

The minuend is expressed by the product of the numbers 9 and 6, the subtrahend is 24. What is the difference?

Increase the product of 7 and 8 by 4 tens and 3 ones.

Find the sum of two products: 6 and 6, 7 and 4.

Increase the quotient of numbers 42 and 7 by the product of numbers 8 and 4.

The product of numbers is 28. One of the factors is 7. What is the second factor?

From the number 46, subtract the product of numbers 3 and 7.

There were tomatoes in 4 boxes, 9 kg each. How many boxes of tomatoes were sent to the market?

Yulia bought 7 notebooks for 6 rubles and 4 identical notebooks for 9 rubles. How much money did Julia pay in total?

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

2 x 7 = 63: 9 = 8 x…. = 40

4 x 8 = 72: 8 = … x 7 = 49

6 x 3 = 10: 1 = 8 x … = 56

9 x 7 = 27: 3 = …: 9 = 8

7 x 4 = 48 : 8 = … : 8 = 10

5 x 9 = 20: 2 = 7 x…. =35

9 x 9 = 28 : 7 = 42 : … = 6

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

6 x 8 = 27 : 9 = 8 x ….= 64

1 x 7 = 18: 3 = … x 6 = 42

4 x 6 = 81 : 9 = 4 x … = 24

9 x 8 = 70 : 7 = … : 2 = 9

7 x 5 = 32 : 8 = … : 9 = 7

6 x 7 = 56: 7 = 7 x… = 21

3 x 8 = 30 : 6 = 80 : … = 10

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

2 x 7 = 63: 9 = 8 x…. = 40

4 x 8 = 72: 8 = … x 7 = 49

6 x 3 = 10: 1 = 8 x … = 56

9 x 7 = 27 : 3 = … : 9 = 8

7 x 4 = 48 : 8 = … : 8 = 10

5 x 9 = 20: 2 = 7 x…. =35

9 x 9 = 28 : 7 = 42 : … = 6

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

6 x 8 = 27: 9 = 8 x ….= 64

1 x 7 = 18: 3 = … x 6 = 42

4 x 6 = 81 : 9 = 4 x … = 24

9 x 8 = 70 : 7 = … : 2 = 9

7 x 5 = 32 : 8 = … : 9 = 7

6 x 7 = 56: 7 = 7 x… = 21

3 x 8 = 30 : 6 = 80 : … = 10

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

19 x 5 = 100 : 10 = 6 x 16 =

16 x 4 = 88 : 2 = 8 x 11 =

18 x 3 = 84 : 7 = 4 x 12 =

27 x 3 = 75: 5 = 7 x 14 =

15 x 5 = 36 : 3 = 5 x 17 =

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

4 x 18 = 46 : 2 = 21 x 3 =

5 x 13 = 48 : 4 = 14 x 5 =

6 x 14 = 72 : 3 = 26 x 3 =

7 x 14 = 64: 4 = 34 x 2 =

3 x 18 = 36 : 3 = 27 x 2 =

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

19 x 5 = 100 : 10 = 6 x 16 =

16 x 4 = 88 : 2 = 8 x 11 =

18 x 3 = 84 : 7 = 4 x 12 =

27 x 3 = 75: 5 = 7 x 14 =

15 x 5 = 36 : 3 = 5 x 17 =

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

4 x 18 = 46 : 2 = 21 x 3 =

5 x 13 = 48: 4 = 14 x 5 =

6 x 14 = 72 : 3 = 26 x 3 =

7 x 14 = 64 : 4 = 34 x 2 =

3 x 18 = 36 : 3 = 27 x 2 =

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

3 x 7 = 81 : 9 = 6 x …= 30

5 x 8 = 60 : 10 = … : 9 = 8

6 x 4 = 24: 8 = … x 7 = 35

8 x 8 = 56 : 8 = …. : 3 = 9

7 x 6 = 28: 7 = 9 x… = 36

9 x 8 = 16 : 2 = … : 6 = 9

2 x 9 = 18: 6 = 3 x… = 15

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

7 x 9 = 48 : 6 = … : 7 = 9

6 x 3 = 45: 5 = …: 2 = 7

9 x 6 = 42 : 7 = 36 : … = 4

8 x 4 = 80: 10 = … x 8 = 72

7 x 7 = 56 : 7 = … : 6 = 6

5 x 3 = 24: 4 = … x 6 = 12

9 x 10 = 40 : 8 = 18 : … = 6

Last name, first name________________________________________________________________
Number__________________________________________________________________________

1 option.

3 x 7 = 81 : 9 = 6 x …= 30

5 x 8 = 60 : 10 = … : 9 = 8
6 x 4 = 24: 8 = … x 7 = 35

8 x 8 = 56 : 8 = …. : 3 = 9

7 x 6 = 28: 7 = 9 x… = 36

9 x 8 = 16 : 2 = … : 6 = 9

2 x 9 = 18: 6 = 3 x… = 15

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

7 x 9 = 48 : 6 = … : 7 = 9

6 x 3 = 45 : 5 = … : 2 = 7

9 x 6 = 42 : 7 = 36 : … = 4

8 x 4 = 80: 10 = … x 8 = 72

7 x 7 = 56 : 7 = … : 6 = 6

5 x 3 = 24: 4 = … x 6 = 12

9 x 10 = 40 : 8 = 18 : … = 6

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

28 : 9 =….(rest….) 44 : 8 =….(rest….)

52 : 6 =….( rest….) 77: 8 = ….(rest….)

67 : 9 =….(rest……) 68 : 7 =….(rest….)

46 : 6 =….(rest….) 25 : 9 =….(rest….)

70 : 9 = ….(rest….) 58 : 9 =….(rest….)

79: 8 = ….( rest….) 14: 4 =…. (rest….)

Last name, first name________________________________________________________________

Number________________________________________________________________________________

Option 2.

16 : 5 =….(rest….) 78 : 9 =….(rest….)

74 : 8 =….(rest….) 61 : 8 = ….(rest….)

23 : 9 =….(rest….) 39 : 7 = ….(rest….)

58 : 6 =….(rest….) 62 : 8 = ….(rest….)

31 : 4 =….(rest….) 69 : 7 = ….(rest….)

66 : 7 =….(rest….) 53 : 7 =….(rest….)

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

28 : 9 =….(rest….) 44 : 8 =….(rest….)

52 : 6 =….( rest….) 77: 8 = ….(rest….)

67 : 9 =….(rest……) 68 : 7 =….(rest….)

46 : 6 =….(rest….) 25 : 9 =….(rest….)

70 : 9 = ….(rest….) 58 : 9 =….(rest….)

79: 8 = ….( rest….) 14: 4 =…. (rest….)

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

16 : 5 =….(rest….) 78 : 9 =….(rest….)

74 : 8 =….(rest….) 61 : 8 = ….(rest….)

23 : 9 =….(rest….) 39 : 7 = ….(rest….)

58 : 6 =….(rest….) 62 : 8 = ….(rest….)

31 : 4 =….(rest….) 69 : 7 = ….(rest….)

66 : 7 =….(rest….) 53 : 7 =….(rest….)

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

Mathematical dictation No. 52

Increase the next number 199 by one hundred.

Write down a number consisting of 3 hundreds and 9 tens.

Write down the previous number 8 hundreds.

Increase the number 58 10 times.

Reduce the number 500 by 100 times.

Subtract 2 tens from the number 720.

Reduce the number 730 by 10 times.

How many tens are in the number 910?

How many units are there in 810?

How many hundreds are there in the number 900?

________________________________________________________________________________

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

Mathematical dictation No. 51

How much greater is the product of the numbers 26 and 2 than their sum?

Write down a number consisting of 2 hundreds and 4 ones.

Write down a number consisting of 3 hundreds and 3 tens.

Add 6 tens to 7 hundreds.

Write down the previous number of 2 hundreds.

Increase the number 42 10 times.

Reduce the number 380 by 10 times.

Reduce the number 800 by 100 times.

Increase the number 600 by 40 units.

Increase the number 700 by 7 units.

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

Mathematical dictation No. 53

Reduce the number 420 by 4 hundreds.

Write down the previous number for the number 380.

Add 6 tens to 7 hundreds.

Reduce the number 370 by 7 tens.

Reduce the previous number 241 by 10 times.

Reduce the number 900 by 100 times.

How many hundreds are in the number 730?

Subtract 8 hundred from the number 842.

Subtract 8 tens from the number 384.

Write down any number that contains 43 tens.

________________________________________________________________________________

Last name, first name________________________________________________________________

Number________________________________________________________________________________

Option 2.

Mathematical dictation No. 54

Reduce the number 394 by 3 units.

Increase the number 520 by 8 tens.

Reduce the number 648 by 4 tens.

Increase the number 742 by 2 hundreds.

Reduce the next number 699 by 100 times.

Find the sum of 9 tens and 3 tens.

How many hundreds are there in 840?

Subtract 9 hundreds from the number 948.

Subtract 7 tens from the number 674.

Write down a number that contains 54 tens.

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

800 50 1= 936 – 30= 650 – 200 =

746 – 40 = 600 40= 550 400 =

763-60= 264 – 4= 800 100 =

100 40 6= 581 – 500= 370 – 20 =

623 – 600= 659 40 1= 30 420 =

689 – 80= 600 50 8= 420 60 =

________________________________________________________________________________

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

593 – 90= 726 – 20= 990 – 500 =

888 – 80= 300 10 4= 570 300 =

500 30 6= 564 – 500= 190 700 =

600 70 5= 540 – 500 9= 700 200 =

249 – 9= 400 60 – 1= 780 – 40 =

526 – 500= 344 – 4 = 70 240 =

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

800 50 1= 936 – 30= 650 – 200 =

746 – 40 = 600 40= 550 400 =

763-60= 264 – 4= 800 100 =

100 40 6= 581 – 500= 370 – 20 =

623 – 600= 659 40 1= 30 420 =

689 – 80= 600 50 8= 420 60 =

________________________________________________________________________________

Last name, first name________________________________________________________________

Number________________________________________________________________________________

2nd option.

593 – 90= 726 – 20= 990 – 500 =

888 – 80= 300 10 4= 570 300 =

500 30 6= 564 – 500= 190 700 =

600 70 5= 540 – 500 9= 700 200 =

249 – 9= 400 60 – 1= 780 – 40 =

526 – 500= 344 – 4 = 70 240 =

Last name, first name________________________________________________________________

Number________________________________________________________________________________

1 option.

Mathematical dictation No. 56.

Reduce the number 930 by 10 times._________________________________________________________

The sum of the numbers is 640, one of the numbers is 410. Find another number.___________________________

How many units are there in 73 tens?__________________________________________________________

Increase the number 375 by two tens.________________________________________________

Find the sum of the numbers 380 and 60._______________________________________________________

How much is 430 greater than 390?

370 kg of potatoes were harvested from the garden. 90 kg of potatoes were left for seeds. How many kg of potatoes did the family leave for food?________________________________________________

The number 30 is 5 times less than the unknown number. What is the unknown number?____________

Reduce the sum of numbers 560 and 340 by 10 times.__________________________________________

175 kg of cherries were collected in the garden, which is 25 kg less than plums were collected. How many kg of plums were collected in the garden?________________________________________________________________

Last name, first name________________________________________________________________

Number________________________________________________________________________________

Option 2.

Mathematical dictation No. 54.

Increase the product of numbers 335 and 0 by 65.__________________________________________

Increase the number 684 by 2 tens.________________________________________________

The sum of the numbers is 530, the first term is 220. Find the second term.____________________

Increase the number 642 by 3 tens.________________________________________________

How many units are there in 95 tens?___________________________________________

Find the sum of the numbers 480 and 70._______________________________________________________

How much is 290 less than 540?_________________________________________________

Dad bought three apples. The weight of the purchase is 1 kg. Two apples weigh 300 g. What is the weight of the third apple?________________________________________________________________

Julia took 65 photos about her summer holidays. She pasted them into a 13-page album. How many photos did Yulia post on each page?_______________________________________________________________________

The third part of the number is 25. What is the whole number?________________________________

Mathematical dictation No. 20.

Last name, first name__________________________________________________________________________

Date________________________________________________________________________________

option.

1. The height of the poplar is 18 meters. The cypress is 2 times higher than the poplar, and the pine is 20 m lower than the cypress. What is the height of the pine?

2. Reduce the product of numbers 120 and 6 by 6 tens.

3. Increase the quotient of 420 and 3 by the same amount.

4. Find the fourth part of the product of numbers 80 and 6.

5. The area of ​​the room is 36 m², its width is 4 m. What is the perimeter of this room?

6. Increase the quotient of 720 and 8 by 910.

7. 180 kg of apples were collected from one apple tree, and 2 times more from another apple tree. How many kilograms of apples were collected from 2 trees?

8. Increase the third part of the number 660 by 780.

9. Increase the quotient of 720 and 8 by 11 tens.

10.6 pens cost the same as 18 pencils. One pencil costs 5 rubles. How much does one pen cost?

________________________________________________________________________________

Mathematical dictation No. 20.

Last name, first name_________________________________________________________________

Date__________________________________________________________________________

option.

In the confectionery shop, 6 hundred Easter cakes were baked for the holiday. Half of all Easter cakes were sent to stores, the rest of the Easter cakes were divided equally between three orphanages. How many Easter cakes did each orphanage receive?

Increase the product of numbers 14 and 30 by 2 times.

Increase the quotient of 810 and 9 by 5 times.

The intended number is 3 times less than 540. What is the intended number?

The width of the rectangle is 35 mm, the length is 2 times greater. What is the perimeter of this rectangle?

Increase the number that is less than 530 by two hundred by 3 times.

The hall has 20 rows of chairs with 16 seats in each row. How many seats are there in total?

How much more is the number 860 than twice the number 180?

Reduce the number 800 by the product of the numbers 720 and 1.

The mass of three boxes of onions is 39 kg, and the mass of four boxes of garlic is 48 kg. How many kilograms is a box of onions heavier than a box of garlic?

Mathematical dictation No. 21.

Last name, first name_________________________________________________________________

Date__________________________________________________________________________

option.

1. Sveta washed 24 plates, which was 1/3 of all dirty plates. How many dishes does Sveta need to wash?

2. Reduce the number 640 by the quotient of the numbers 120 and 3.

3. Increase the product of the numbers 60 and 8 by 2 tens.

4.1/7 part of the number 84 is increased 10 times.

5. Three kiosks were brought 24 kg of fruit each, and the fourth – 28 kg. How much fruit did they bring to all the stalls?

6. From the product of numbers 17 and 4, subtract the difference of the same numbers.

7. What is the side of the square if its perimeter is 32 cm?

8. Increase the number that contains 3 hundreds and 7 ones by 3 times.

9. Reduce the difference between the numbers 700 and 340 by 6 times.

10. The minuend is 9 hundreds, the difference is the product of the numbers 250 and 3. What is the subtrahend equal to?

Mathematical dictation No. 21.

Last name, first name________________________________________________________________

§

“Implementation of a competency-based approach in the process of working on quantities in the 4th grade based on the teaching materials “Elementary school of the 21st century”.”

The goal of modern education is to prepare competitive specialists who are able to think and act systematically, have creative activity, leadership qualities, and are characterized by initiative and independence, i.e. possessing key competencies. In this regard, the terms “competence” and “competence” are becoming increasingly widespread in the educational environment.

The “Concept for the Modernization of Russian Education” states: “A developing society needs modernly educated, moral, enterprising people who can independently make decisions, predicting their possible consequences, who are characterized by mobility, who are capable of cooperation, who have a sense of responsibility for the fate of the country, its social economic prosperity.”

Competence in the Federal State Educational Standard is understood as the ability to apply knowledge, skills, personal qualities and practical experience for successful activities in a certain area.

The concept of “competence” as a pedagogical problem is relatively new.

The concept of “competence” refers to the area of ​​skills, not knowledge. As T.V. Ivanova notes, “competence is a general ability based on knowledge, experience, values, and inclinations that are acquired through training. Competence is neither knowledge nor skill; to be competent does not mean to be learned or educated.”

A. G. Asmolov states that “competence is understood as the result of cognitive learning, and competence is the general ability and willingness to use knowledge, skills and generalized methods of action learned during the learning process in real activities. Competence is “knowledge in action.” Competence means a person’s ability to establish connections between knowledge and the real situation, make decisions under conditions of uncertainty and develop an algorithm of actions for its implementation. Depending on the nature of the tasks facing a person, types of competence are distinguished: personal, communicative, intellectual, social, and general cultural.”

According to the program for introducing a competency-oriented approach into the educational process, the following key competencies are identified.

“1. Value-semantic – readiness to see and understand the world around us, to navigate it, to realize one’s role and purpose, to be able to choose goals and meaning for one’s actions and actions, and to make decisions.”

“2. General cultural – the student’s awareness of the features of national and universal culture, the spiritual and moral foundations of human life and humanity, individual nations, the cultural foundations of family, social, public phenomena and traditions, the role of science and religion in human life, their influence on the world, effective methods of organization free time”.

“3. Educational and cognitive – the student’s readiness for independent cognitive activity: goal setting, planning, analysis, reflection, self-assessment of educational and cognitive activity, the ability to distinguish facts from speculation, mastery of measurement skills, the use of probabilistic, statistical and other methods of cognition.”

“4. Information – the student’s readiness to independently work with information from various sources, search, analyze and select the necessary information, organize, transform, save and transmit it.”

“5. Communicative – includes knowledge of the necessary languages, ways of interacting with surrounding and distant people and events, provides skills for working in a group, mastery of various special roles in a team. The student must be able to introduce himself, write a letter, questionnaire, application, ask a question, etc.”

“6. Social and labor – possession of knowledge and experience in civil and social activities (playing the role of a citizen, observer, voter, representative), in the social and labor sphere (the rights of a consumer, buyer, client, manufacturer), in the field of family relations and responsibilities, in matters economics and law, in professional self-determination.”

“7. Personal (self-improvement) – readiness to carry out physical, spiritual and intellectual self-development, emotional self-regulation and self-support” [33].

The formation of key competencies in the educational process of schoolchildren at the level of mathematics is considered as a specially organized model of interaction between participants in the educational process at the “teacher-student”, “student-student” level.

In the textbook by V. N. Rudnitskaya (“Primary School of the 21st Century”) there is given a large number of tasks of an algorithmic nature, tasks on translations, and many applied tasks. The study of quantities in first grade begins with the study of a segment and its parts (lesson No. 21, part 1). At this stage, children learn to correctly measure segments, draw segments of a given length, that is, they have acquired knowledge of how to measure and acquire measuring skills. At the next stage, the topic “Length” is studied (lesson No. 22, part 1). Hereˎ childrenˎ measureˎ segmentsˎ usingˎ variousˎ measures, determine the length of the segments by eye, and then check by measurement, thus developing the student’s ability to establish connections between knowledge and the real situation. Students are offered tasks such as, for example, determining by eye the distance between cabinets and determining what can be placed between them: a chair, a desk, two desks, two chairs, or a chair and a desk. Students make assumptions, and then confirm them with practical actions, prove them, and develop an algorithm of action. In the future, work of a general cultural nature is carried out, children are offered some information about the history of units of measurement of length. Then the firstˎ unit of measurementˎ of lengthˎ is enteredˎ -ˎ centimeter. Nextˎ it is proposedˎ to find outˎ the lengthˎ of the givenˎ segmentsˎ usingˎ a rulerˎ andˎ expressˎ the obtainedˎ resultˎ inˎ centimeters. Atˎ the nextˎ stageˎ childrenˎ beginˎ toˎ compareˎ segments, come up with questions with words for how much, the same ˎ (lessonˎ No. 22, partˎ 1). Work is underway on information; children independently look for those objects in the classroom that correspond to a given length.

The next quantity is the decimeter (lesson No. 26, part 1), students are learning a new unit of measurement of length – the decimeter. Here children learn the relationship between the two studied units of length: the centimeter and the decimeter. In the future (lesson No. 33 part 1) children measure length in decimeters and centimeters. For example, the teacher gives the task to measure in decimeters and centimeters the desk at which they are sitting, the teacher’s desk, the width of the bookcase, etc. In the second part of the mathematics textbook, the following tasks are periodically encountered: “Estimate the length of the segment by eye. Check your answer: take a measurement” (part 2, p. 74 No. 18, p. 93 No. 9, p. 102 No. 9). At this stage, educational and cognitive activity is being developed – mastery of measurement skills.

In the second grade, children study the meter (lesson No. 19, part 1), the ratio of the units of length studied: centimeter, decimeter, meter. Children are asked to use a meter ruler or tape measure to measure: the length and width of the classroom, the chalkboard, the length of their step, their height (part 1, p. 36, No. 4). Children learn to read notes (part 1, p. 36, no. 2). At this stage, work takes place in a group, and this is a communicative activity. Subsequently, there is a journey into the past (general cultural competence, personal competence), students become familiar with the following units of length: span, arshin, vershok, oblique fathom and solve an ancient problem (part 1, p. 40). Learn to express numerical values ​​of quantities in various units of measurement. They learn to express numerical values ​​of length expressed in units of one name by values ​​expressed in units of two names, and vice versa (Part 1, p. 46, No. 17).

In the second grade, the study of the area of ​​​​figures begins (lesson No. 19, part 2). Observations on the area of ​​the figures were carried out at an earlier stage – in the first grade. For example, “Find equal figures”, “Which of the figures has more cells? Why?”. At this stage, children measure the area of ​​a figure using different standards and compare the numerical values ​​of the areas of figures measured by different standards. In the next lesson (lesson No. 20, part 1) children become familiar with the units of measurement of area: square centimeter, square decimeter, square meter and the relationships between them. Getting to know the units of area is similar to getting to know the units of length. Then the area of ​​a rectangle is studied (lesson No. 25, part 1). Here children learn the formula for finding the area of ​​a rectangle, and then establish connections between knowledge and the real situation, use knowledge in real activities. Students are given the task of finding out the area of ​​the classroom, the surface area of ​​the desk, the area of ​​the classroom stand, and homework of the following kind: find out the area of ​​each room and the entire apartment. In this case, work is being done on the following competencies: informational, communication, personal, and labor.

In the third grade, new units of measurement of length are studied – the millimeter (lesson No. 7, part 1) and the kilometer (lesson No. 7, part 1). Here children find out why such measurements are used. Examples are given: the road from school to home, from home to the dacha, from the dacha to the river is measured in kilometers, and the thickness of a notebook or diary is measured in millimeters. Children independently search, analyze, and demonstrate understanding of the information provided. And this is information competence. They perform exercises on the ratio of units of length, convert small units into larger ones and vice versa, work on converting information. In the future, the concepts of nautical mile and mile are given and ancient problems are solved (general cultural competence).

The next step is to study the unit of measurement of mass – gram, kilogram (lessons 17-20, part 1). At this stage, tasks of a social and labor nature are given, and children are offered the game “Shop”. In the following, historical information is given about which units of mass were used previously in Russia (pood, pound) and ancient problems are solved (general cultural competence). Then capacity, liter, is studied (lessons 21-23, part 1). Here children get acquainted with the unit of measurement of capacity – liter (educational and cognitive competence). Children bring different containers (plastic bottles, glass jars, cans, etc.) and measure the capacity – these are social and labor tasks. The following is a historical background (this is general cultural competence).

The next unit of measurement is time (lesson No. 92, part 2). Here measures of time are studied, historical information is given about the emergence of units of time change, and the calendar is also studied. Each child has a calendar in his hands, he finds his date of birth, public holidays, school holidays, etc. It also offers tasks on the ratio of time units: year, month, day. In the second lesson (lesson No. 93, part 2) students begin to study the week. In the next lesson (lesson No. 94, part 2) the table of time measures is studied, such units of time as hour, minute, second and their relationships are studied. In the fourth lesson on this topic (lesson No. 95, part 2) clocks are studied. Here children get acquainted with clock hands and their purpose, learn to tell time using a clock. The fifth lesson is about comparing, adding and subtracting units of time. Here children’s knowledge of relationships between units of time is generalized and systematized. Children learn to perform arithmetic operations with numerical values ​​of time. At this stage, work is underway on such competencies as general cultural, informational, communicative, and value-semantic.

In the fourth grade it is studied – ton, centner (lessons No. 43-45, part 1), during lessons children do exercises on the ratio of units of mass, convert small units into larger ones and vice versa, solve problems (competence educational – cognitive).

The study of quantities in elementary school ends with the topic “Exact and approximate values ​​of quantities.” Throughout our lives, we use approximate values, for example: when we are asked what time it is, we answer without seconds, we measure length without millimeters, in a store when buying a product we say about so many grams or about a kilogram. In this block, tasks of a social and labor nature are given.

In the considered program, much attention is paid to the formation in students of the concept of quantity and its measurement. In more detail than in the traditional program, quantities and units of their intention are studied. The connection of this topic with life is clearly visible, for example, practical activities when studying the topic “Meter”: a) “measure the length and width of the classroom, chalkboard, width of the door, window with a meter”; b) “measure two cords 2m and 3m long. Which cord is longer and by how much?”; c) “measure the length and width of your room with a meter.”

Tasks of a social and labor nature in the 4th grade according to the textbook by V. N. Rudnitskaya:

1. How many square ceramic tiles with an area of ​​1 dm2? needed to cover part of a wall with an area of ​​1 sq. m? (p. 35 No. 26*)

2. The length of the rectangular platform is 18 m and the width is 9 m. How many steps must be taken to go around it if the step length is 75 cm? (page 35 No. 28)

3. Misha has 45 rubles. He spent a ninth of this money on buying an eraser, and with the rest of the money he bought 4 notebooks. What is the price of an eraser? What is the price of the notebook? (page 36№33)

4. A kilogram of sweets costs: 250 rubles, 125 rubles. What is the cost of 200 g and 500 g of sweets at the indicated prices? (p.36 No.32*)

5. 480 berry bushes were brought to the nursery for planting. The pie chart shows what portion of the number of all bushes is occupied by each species of these shrubs. Count the number of currant, raspberry, gooseberry and blueberry bushes using the chart. (p.128 no. 2)

Tasks for the formation of educational and cognitive activity in the 4th grade according to the textbook by V. N. Rudnitskaya:

1. Consider the graph of Yura’s mass versus its age. In the textbook, the graph is by X
– age, according to Y
– weight. Answer the questions: What was the mass of Yura at 2 years, 5 years, 7 years, 9 years? By how many kilograms did his weight increase in 3 years (from 2 to 5 years), in 2 years (from 7 to 9 years)? At what age did Yura’s mass become 25 kg, 45 kg? In how many years did Yura’s mass increase from 25 kg to 40 kg? (p. 99 No. 22, part 1)

2. The boat was moving in a straight line between two piers on Lake Baikal. The figure shows a graph of the boat’s movement. X
-time of day, Y
– distance from the pier (km). Calculate how fast he was walking. At what distance from the pier was the boat at 13 o’clock, at 14 o’clock, at 11:30 am? At what time was the boat 105 km from the pier? (page 150 No. 21, part 1)

Thus, this program provides a high level of scientific character and connection between mathematics and life, that is, the introduction of any quantity is based on the life experience of children. The proposed program is aimed not only at the formation of mathematical knowledge, skills and abilities, but also at the general development of children. An example of this is historical information about quantities, their units of measurement, information from the history of the occurrence of quantities and the need to measure them.

Thus, when conducting a lesson, the teacher strives to ensure that the student clearly understands what and how he is studying today, in the next lesson, and how he can use the acquired knowledge in his future life.

Publication address: https://www.obumage.net/metodicheskie-razrabotki/209171-realizacija-kompetentnostnogo-podhoda-v-proce

§

§

§

Topic:
“Roman numbering”.

Goal:
introduce Roman numeration and the basic rules for writing numbers.

Lesson type:
learning new material.

Problems:
introduce children to Roman numerals and their writing, give an idea of ​​how to use them in practice; develop mental activity; develop an interest in mathematics.

Teacher Equipment:
cards with images of different written numberings, cards with the topic and objectives of the lesson, cards with Roman numerals, images of a clock with Roman numerals, a picture of a pedestal, pictures of three girls, a graphic diagram of the task, a card for reflection; pointer.

for students:
cards in white, blue and yellow colors.

Work form:
frontal, individual.

Personal universal learning activities:
to generate interest in educational activities.

Meta-subject results:

Regulatory universal educational actions:
plan your actions in accordance with educational objectives and teacher instructions; take into account the action guidelines identified by the teacher in the educational material; in collaboration with the teacher, find a solution to the educational problem presented at a visual-figurative level;

Cognitive universal learning activities:
make comparisons (visually and by presentation), draw conclusions based on comparison; use a schematic version of mathematical notation; draw an analogy and draw conclusions based on it;

Communicative universal learning activities:
take an active part in educational activities using verbal communication means; allow for the existence of different points of view; come to a common decision; understand the content of the questions and reproduce the questions.

Subject results:
get acquainted with Roman numbering (symbols I, V, X); write numbers using Roman numerals; solve the problem using graphical modeling.

Lesson plan:

Lesson stage

Teacher activities

Student activities

I
Self-determination for activity.

2 minutes

Creating a situation for inclusion in activities; creating a positive emotional orientation.

Concentrate attention. Check your preparedness for the lesson. Write down the date, “Cool work.”

II
Updating knowledge. Setting a learning task.

5 minutes

Using the front form of work. Creating a situation to pose a problem.

Perform tasks that train individual abilities for learning activities, mental operations and learning skills.

III
Learning new material.

12 minutes

Organizes work on writing Roman numerals (frontally).

Analyze the way numbers are written in Roman numeration.

IV
Primary fixation

15 minutes

Physical education

1 minute

Organizes the application of new knowledge.

Organizes the repetition of educational content necessary to ensure meaningful continuity.

Compare Roman numerals and Arabic numerals.

Complete the educational task in accordance with the goal. Analysis of the way numbers are written in Roman numeration.

V
Backup job.

3 minutes

Organization of independent work with self-test using a standard on cards

Do written work on cards.

VI
Lesson summary. Reflection

2 minutes

What did we learn about in the lesson? Where can you find Roman numerals?

Evaluate their work. Answer the teacher’s questions.

Lesson progress

1. Self-determination for activity.

(Teacher’s greeting.)

I’m very glad to see everyone.

Success awaits you today.

And I’ll also tell you:

Smile for everyone – all of us.
Pull yourself together, pull yourself together

And sit down quietly.

– Write the date and “Cool work” in your notebook.

2. Updating knowledge. Setting a learning task.

Problematic question:

– Think about what is shown on these cards?

– What do you think the signs depicted on these cards could mean?

(Listen to students’ guesses)

– Maybe the next couple of cards will help you answer this question?

Of course, these cards have numbers on them. On the first card is the numbering of the Mayan Indians. The second card has Chinese numbering. She is one of the oldest. On the third card there is Arabic numbering – the most common today. Although the name “Arab” was given to it conditionally, since its real homeland is India. But it was brought to Europe from Arab countries, hence the name. The fourth card has Roman numbering. These are numbers that came to us from ancient Rome.

– Guys, guess the topic of the lesson. (Lesson topic: Roman numbering. Posted on the board).

– Guys, what should we learn in class? (Tasks are posted on the board: get to know Roman written numbering; learn the rules for writing numbers in Roman numerals; learn to read numbers written in Roman numerals; arrange them in ascending order).

3. Learning new material

– Imagine that you are ancient Romans and don’t know numbers. What would you use to represent the number 1? 2? 3? ( Using fingers)

– Indeed, fingers played a significant role in the history of counting. Do you understand the numbers of Roman numeration I
, II
, III
. (Image is posted).

– Let’s write them down.

– What next?

– There are 5 fingers on a person’s hand. In order not to write 5 sticks, they began to depict a hand. The hand drawings were made very simple. Did you guess it? Instead of drawing the entire hand, it was depicted V
– number 5.

– Think about how you would suggest writing the number 4 in Roman numerals? What about the number 6? If the stick ( I
) is written to the right of the number 5, then we add 1 to 5, and if the stick ( I
) is written to the left of the number, then 1 is subtracted from the number. (The work with numbers 7, 8 is similar.)

– In Roman numbering, you cannot write more than three identical digits in a row.

– How to write the number 10? You know that 10 consists of two fives, so 10 in Roman numbering was represented by two fives: one five stands as usual, and the other is turned down – X
.

(Working with the number 9, remember the rule for the number 4.)

– Some Roman numerals can be written by repeating the numbers. If the digits are written to the right of the number, then the numbers they represent are added to the first written number, and if the digits are written to the left of the number, then the corresponding numbers are subtracted.

– Write down in your notebook the natural number series that we always use (Arabic numbers) with a gap of 1 cell. (Writing on the board).

– Using familiar numbers, let’s read the numbers. They are arranged in ascending order.

4. Primary fixation

– Where have you come across Roman numerals? (On the clock.)

– Determine the time using a clock with Roman numbering.

– What time is it on the clock? (Three hours.)

Physical education

We are starting exercises,
We stretch our hands,
Stretch your back, shoulders,
To make it easier for us to sit.
Let’s jump together, jump and jump!
Who will get the ceiling?
Now walk in place.
We all stomp loudly together.
We’ve finished charging,
Let’s return to the notebooks.

– Take a white card and read the problem to yourself.

– Hold the card in front of you, and I will read the problem. (Reading the problem aloud by the teacher.)

Masha, Valya and Lena competed in the long jump. Masha jumped 80 cm. Lena is 30 cm shorter than Masha. And Valya is 40 cm further than Lena. How far did Valya jump?

– Who is the problem talking about? (That Masha, Valya and Lena were long jumping.)

– Today we will denote the condition with a diagram using segments. Take the blue card.

– What do we know about Masha? Valya? Lena?

– What do the letters mean and what do the segments mean?

– Remember the conditions of the problem, what is known about Masha. I show on the board, and you show on the diagrams.

– What does 30 cm shorter mean? (The same amount, but without 30 cm.)

– What does 40 cm further mean? (The same amount, and even 40 cm.)

– What do you need to find in the problem? (How far did Valya jump?)

– Can we immediately answer the question of the problem? (No, we don’t know how far Lena jumped)

– How many actions are there in solving a problem?

– What will you find with the 1st action? 2nd?

– Write down the solution. Check it out. Write down your answer.

80-30=50 (cm) Lena jumped. 2)50- 40=90 (cm) Valya jumped.)

§

7

Academic subject: mathematics

Class 4

GBOU secondary school No. 13

g.o. Chapaevsk

Batenok Olga Gennadievna

Lesson topic: “Multiplying a three-digit number by a three-digit number”

Lesson objectives:

Continue working on developing computational skills when multiplying a three-digit number

to a three-digit number.

Develop logical thinking, the ability to raise children’s interest in the subject.

Foster the desire to lead a healthy lifestyle.

Equipment: route sheets, multimedia.

Lesson progress:

I
. Organizing time.

Look at me!
I am your guide today.
Without wasting a minute,
I invite you on a journey!
Take all your knowledge on the road!
And don’t forget to smile!

II
. State the topic and purpose of the lesson.

Today in the lesson we continue to multiply a three-digit number by a three-digit number, we will consider cases when the number contains a zero, and we will also consolidate previously acquired knowledge . (Slide No. 1)

III
. Updating students’ basic knowledge.

Mathematical dictation (3 people at the board with route sheets). (Slide No. 2)

a) The height of the football goal is 2 meters 40 centimeters. Express the height of the gate in centimeters.

b) The height of a hockey goal is 1 meter 20 centimeters, it is 2 times less than the height of a football goal. Find out the height of the football goal.

c) The width of the school skating rink is 8 meters, length is 20 meters. What is the area of ​​the skating rink?

d) At school, 84 students are involved in gymnastics. Half of them are girls. How many girls do gymnastics?

e) A speed skater runs an average of 700 meters in one minute. How many meters does a speed skater run in 3 minutes?

2. Checking the work (pictures with a certain sport appear on the multimedia, in accordance with the tasks and answers: 240 cm, 2m 40cm, 180 sq.m, 42 girls, 2100 meters). (Slide No. 3)

Name the extra number

Increase the round numbers by 4 times.

What were the tasks about?

What is sport for?

What is health?

(Health – correct, normal, activity of the body).

S. I. Ozhegov (Slide No. 4)

And today we will also talk about health, how to preserve and increase it. After all, health is a priceless gift, and this gift cannot be wasted; without it it is very difficult to make life interesting and happy. At the same time, we will increase our knowledge.

What do you think will help you stay healthy? By solving the examples, you will find out the answer to the question. (Slide No. 5)

3. Oral counting.

406×7=2842

309×5=1545

207×9=1863

208×2=416

704×3=2112

Checking the work. (Slide No. 5)

Put the numbers in ascending order

What word did you get? (Slide No. 5)

What is a mode?

Regime – the established order of something

(S. I. Ozhegov). (Slide No. 6)

A daily routine will help you develop a certain habitual rhythm of life: work and rest. A conveniently organized regime will help you maintain good performance, vigor and cheerfulness. Everything will work out for you without much stress.

Now I will find out how you carry out your daily routine.

Oral problem solving.

a) How long does it take you to get to school? How many minutes is this?

b) What time should children your age go to bed? If a boy starts getting ready for bed at 8:45 p.m. and goes to bed at 9:00 p.m., how much time does he spend getting ready for bed?

c) How long does it take you to do your homework? (Average 2 hours). How many minutes is this?

After an hour of studying, be sure to rest your eyes while doing the exercises.

(Color relaxation). (Slide No. 7-10)

Follow the regime of work and life – your health will be stronger than granite. (Slide No. 11)

IV
. Work on the topic.

Now let’s see how the knowledge that you applied will help you solve examples of a new type during mental calculation.

What did you notice in the recording of these examples (specifically in the 1 multiplier). (Slide No. 12)

Which rule with zero is appropriate in our particular case?

(Slide No. 12)

1×a =a a×0=0

0: a =0 a 0=a 0×a=0

Working with the textbook p.42

Explanation of solutions to examples.

Solution at the board with explanation No. 209.

We talked about the daily routine, which, if followed, maintains health. But there is also a diet, the implementation of which is also necessary for our health.

Work in pairs

Perform No. 210 in pairs.

-By solving the examples, you will learn what foods you need to eat to grow, have energy for work, be healthy and feel good.

4. Checking the work. (Slide No. 13)

456×803=366168 fruits 105×420=44100 meat, fish

605×102=61710 vegetables 521×180=93780 eggs, nuts

528×330=174240 bread, cereals 907×203=184121 dairy

products

All these products are very important. What valuable food product is being discussed in the riddle:

Liquid, not water,

White, not snow

(Milk).

Milk is the first food of man. First the mother’s, and then the cow’s. Medical scientists have proven that drinking milk daily reduces the occurrence of caries (a dental disease).

Let’s solve the equation and find out how much milk you need to include daily in your diet.

(Slide No. 14)

5. Solving equations.

1 option. Option 2.

x×15=18000:6 60×x=300×40

6. Solving problems (independently, to choose from).

How many grams of milk do the students in our class need per day? For a week? (Slide No. 15)

Drink milk, children,

you will be healthy! (Slide No. 16)

There is a saying: “A healthy mind in a healthy body.” How do you understand it?

The famous medical scientist Speransky, who lived a long life and was never seriously ill, was asked: “What is your secret?” He replied that he had a “secret weapon,” and the weapon was physical education.

Every person is obliged to fight for longevity, to think about how to stay cheerful and fit. Before classes we do daily exercises. (Slide No. 17)

7. Physical education minute.

Have you ever thought that one set of morning exercises on average includes:

squat twists

32 36 24

8. Oral problem solving. (Slide No. 18)

What will we know if:

32 36 24 34-32

(32 36 24)×7 36 32

Remember! (Slide No. 19)

The river begins with a stream,

and health from exercise!

9. At school we have many sports clubs. Make up a problem using a short note and solve: (Slide No. 20

Total – 534 students

Tennis – 1/6 of all students

Judo – 1/3 of all students

Swimming – ?

10. Checking the work. (Slide No. 21-23)

Sun, air and water are our best friends!

V
. Lesson summary. (Slide No. 24)

What did you do in math class? What were they talking about?

Do:

Daily routine.

Power mode

Play sports

And then:

1. You will multiply and divide,

2. Solve problems and equations.

3. And most importantly, you will be healthy!

Publication address: https://www.obumage.net/metodicheskie-razrabotki/208903-urok-matematiki-v-4-klasse-umnozhenie-trjohzn

§

Work program for the course “Mathematics”

Explanatory note

Work program of the curriculum in mathematics for grade 4b. Compiled in accordance with the requirements of the Federal State Educational Standard for Primary General Education on the basis of the Approximate Basic Educational Program in Mathematics and the author’s approximate program for 4th grade students by the authors T. E. Demidova, S. A. Kozlova, A. G. Rubin, A. P. Tonkikh.

General characteristics of the subject:

The construction of this course is based on the idea of ​​humanizing mathematical education, which corresponds to modern ideas about the goals of school education and pays special attention to the student’s personality, his interests and abilities. The selection of teaching methods and means is based on an activity-based approach.

The course allows you to provide the required level of training for schoolchildren, provided for by the state standard of mathematical education, and also allows you to prepare them in such a way that is sufficient for in-depth study of mathematics.

Learning Objectives

development of figurative and logical thinking, imagination; formation of subject skills necessary for successfully solving educational and practical problems, continuing education;

mastering the basics of mathematical knowledge, forming initial ideas about mathematics;

nurturing an interest in mathematics, the desire to use mathematical knowledge in everyday life.

The goals of teaching mathematics are determined by the general goals of education, the concept of mathematical education, the status and role of mathematics in science, culture and the life of society, the values ​​of mathematical education, new educational ideas, among which developmental education occupies an important place.

The main goal of teaching mathematics is to form a comprehensively educated and proactive individual who has a system of mathematical knowledge and skills, ideological, moral, cultural and ethical principles, norms of behavior that develop during the educational process and prepare the student for active work and continuing education in modern society.

Based on the general provisions of the concept of mathematical education, the initial mathematics course is designed to solve the following problems:

ensure strong and conscious mastery of the system of mathematical knowledge and skills necessary for application in practical activities, for studying related disciplines, for continuing education;

ensure intellectual development, form the qualities of thinking characteristic of mathematical activity and necessary for a full life in society;

develop the ability to learn;

to form an idea of ​​the ideas and methods of mathematics, of mathematics as a form of description and a method of understanding the world around us;

to form an idea of ​​mathematics as part of universal human culture.

Personal, meta-subject and subject results of mastering a mathematics course.

3rd-4th grades

Personal results
studying the educational and methodological course “Mathematics” in grades 3–4 is the formation of the following skills:

Independently determine and express the simplest rules of behavior common to all people in communication and cooperation (ethical standards of communication and cooperation).

In independently created situations of communication and cooperation, based on simple rules of behavior common to everyone, make a choice about what action to take.

The means to achieve these results are the educational material and textbook assignments aimed at the 2nd line of development – the ability to determine one’s attitude to the world.

Meta-subject results
studying the educational and methodological course “Mathematics” in the 3rd grade are the formation of the following universal educational actions.

Regulatory UUD:

Formulate independently
lesson objectives after preliminary discussion.

Study together with the teacher, discover and formulate an educational problem.

Make a plan for solving a problem (task) together with the teacher.

Working according to the plan, check your actions with the goal and, if necessary, correct mistakes with the help of the teacher.

The means of forming these actions is the technology of problem dialogue at the stage of learning new material.

In dialogue with the teacher, learn to develop evaluation criteria and determine the degree of success in performing your own work and the work of everyone, based on the existing criteria.

The means of forming these actions is the technology of assessing educational achievements (academic success).

Cognitive UUD:

Navigate your knowledge system: independently guess what information is needed to solve a learning problem in one step.

Select
sources of information necessary to solve the educational problem among the dictionaries, encyclopedias, and reference books proposed by the teacher.

Acquire new knowledge: extract
information presented in different forms (text, table, diagram, illustration, etc.).

Process received information: compare
and group
facts and phenomena; determine the causes of phenomena and events.

Process the information received: draw conclusions
based on generalization of knowledge.

Convert information from one form to another: compose
simple plan
educational and scientific text.

Convert information from one form to another: represent information
in the form of text, tables, diagrams.

The means of forming these actions are the educational material and textbook tasks aimed at the 1st line of development – the ability to explain the world.

Communication UUD:

Convey your position to others: formalize
your thoughts in oral and written speech, taking into account your educational and life speech situations.

Convey your position to others: express
your point of view and try to justify it
, giving arguments.

Listen to others, try to accept another point of view, be willing to change your point of view.

The means of forming these actions is the technology of problem dialogue (inviting and leading dialogue).

Read textbook texts aloud and silently and at the same time: conduct a “dialogue with the author” (predict future reading; pose questions to the text and look for answers; test yourself); separate the new from the known; highlight the main thing; to make plan.

The means of forming these actions is the technology of productive reading.

Subject content

4th grade (4 hours per week, total – 136 hours)

Numbers and operations on them.

Fractional numbers.

Fractions. Comparing fractions. Finding part of a number. Finding a number from its part.

What part one number is of another.

Addition of fractions with like denominators. Subtracting fractions with like denominators.

Numbers from 1 to 1000000.

Numbers from 1 to 1000000. Reading and writing numbers. Class of units and class of thousands. I, II, III categories in the class of units and in the class of thousands. Representation of a number as a sum of its digit terms. Comparison of numbers.

Numbers from 1 to 1000000000.

Oral and written numbering of multi-digit numbers.

Number beam. Movement along a number line. Location of points with given coordinates on a numerical ray, determination of the coordinates of given points.

Exact and approximate values ​​of quantities. Rounding numbers, using rounding in practice.

Adding and subtracting numbers.

Addition and subtraction operations on numbers ranging from 1 to 1,000,000. Techniques of rational calculations.

Multiplication and division of numbers.

Multiplying and dividing numbers by 10, 100, 1000.

Multiplication and division of numbers ending in zeros. Oral multiplication and division of numbers by a single digit in cases reducible to operations within 100.

Written multiplication and division by single digit numbers.

Multiplication and division by two-digit and three-digit numbers.

Quantities and their measurement.

Area estimation. Approximate calculation of areas. Areas of composite figures. New units of area: mm², km², hectare, are (area). Area of ​​a right triangle.

Work, labor productivity, working time.

Functional dependencies between groups of quantities. Formulas expressing these dependencies.

Word problems.

Simultaneous movement along the number beam. Oncoming traffic and traffic in the opposite direction. Moving in pursuit. Movement with lag. Problems with an alternative condition.

Elements of geometry.

Changing the position of volumetric figures in space.

Volumetric figures made up of cubes and parallelepipeds.

Rectangular coordinate system on a plane. Correspondence between points on the plane and ordered pairs of numbers.

Elements of algebra.

Calculate the values ​​of numerical expressions containing up to six operations (with and without parentheses), based on knowledge of the rule about the order of execution of actions and knowledge of the properties of arithmetic operations. Using equations to solve word problems.

Elements of stochastics.

Collection and processing of statistical information about the phenomena of the surrounding reality. Public opinion polls as the collection and processing of statistical information.

The concept of the probability of a random event.

Stochastic games. Fair and unfair games.

The concept of the arithmetic mean of several numbers. Problems on finding the arithmetic mean.

Pie charts. Reading information contained in a pie chart.

Entertaining and non-standard tasks.

Dirichlet principle.

Mathematical games.

Final repetition.

Requirements for student learning outcomes by the end of 4th grade

Subject results
Studying the “Mathematics” course in the 4th grade is the formation of the following skills.

1st level (required)

Students
will learn

:

use the name and sequence of numbers in the natural series within 1,000,000 when solving various problems (what number does this series begin with, how is each subsequent number in this series formed);

explain how each subsequent counting unit is formed;

use the names and sequence of digits in writing numbers when solving various problems;

use the names and sequence of the first three classes when solving various problems;

tell how many digits are contained in each class;

explain the relationship between categories;

use knowledge about the number of digits contained in each class when solving various problems and justifying their actions;

use knowledge of how many units of each class are contained in the number notation when solving various problems and justifying their actions;

use knowledge about the positionality of the decimal number system when solving various problems and justifying their actions;

use knowledge about units of measurement of quantities (length, mass, time, area), the relationship between them when solving various problems;

use knowledge about the functional relationship between quantities when solving various problems. Price, quantity, cost. Speed, time, distance. Labor productivity, working time, work.

perform oral calculations (within 1,000,000) in cases reducible to calculations within 100, and written calculations in other cases, check the correctness of the calculations;

perform multiplication and division with 1000;

solve simple and compound problems that reveal the meaning of arithmetic operations, relationships between numbers and relationships between groups of quantities. Price, quantity, cost; speed, time, distance.

solve problems related to the movement of two objects: towards and in opposite directions;

solve problems in 2-3 steps on all arithmetic operations in an arithmetic way (based on diagrams, tables, short notes and other models);

consciously create algorithms for calculating the values ​​of numerical expressions containing up to 3-4 actions (with and without parentheses), based on knowledge of the rules about the order of actions and knowledge of the properties of arithmetic operations and follow these algorithms, including analysis and verification of their actions ;

read the simplest expression written using letters (sum, difference, product, quotient), when one of the components of the action remains constant and when both components are variable;

consciously use the algorithm for finding the value of expressions with one variable for a given value of the variables;

use knowledge of the relationship between the components and results of addition, subtraction, multiplication, division when solving equations of the form: a ± x = b
; x − a = b
; a ∙ x = b
; a : x = b
; x: a = b
;

be able to compare the meanings of expressions containing one action; understand and explain how the result of addition, subtraction, multiplication and division changes depending on a change in one of the components.

calculate the volume of a parallelepiped (cube);

calculate the area and perimeter of figures made from rectangles;

select rectangular and obtuse, isosceles and equilateral triangles from a set of triangles;

construct a circle along a given radius;

identify flat and three-dimensional figures from a variety of geometric shapes;

recognize geometric shapes. Point, line (straight, curve), segment, ray, broken line. A polygon and its elements (vertices, sides, angles), including a triangle. Rectangle (square), corner, circle, circle (center, radius). Parallelepiped (cube) and its elements (vertices, edges, faces). Pyramid, ball, cone, cylinder;

find the arithmetic mean of two numbers.

2nd level (software)

Students will be able to learn:

use knowledge of the name and sequence of numbers within 1000000000 when solving various problems and justifying their actions.

Students should have an understanding of how to read, write and compare numbers within 1000000000;

Students should be able to
:

estimate the results of arithmetic operations when solving practical and subject problems;

consciously create algorithms for calculating the values ​​of numerical expressions containing up to 6 actions (with and without parentheses), based on knowledge of the rule about the order of actions and knowledge of the properties of arithmetic operations, and follow these algorithms, including analysis and verification of their actions;

find a part of a number, a number by its part, find out what part one number is of another;

have an idea of ​​solving problems into parts;

understand and explain the solution of problems related to the movement of two objects: following and lagging;

read and build auxiliary models for compound problems;

recognize flat geometric figures when their position on the plane changes;

recognize volumetric bodies – parallelepiped (cube), pyramid, cone, cylinder – when their position in space changes;

find the volume of figures made up of cubes and parallelepipeds;

use given equations to solve word problems;

solve equations in which the relationship between the components and the result of an action must be applied several times: a ∙ x ± b = c
;

(x ± b): c = d
; a ± x ± b = с
and etc.;

read information recorded using pie charts;

solve the simplest problems using the Dirichlet principle;

find the probabilities of the simplest random events;

find the arithmetic mean of several numbers.

By the end of training in fourth grade

student can learn
:

name:

— coordinates of points marked in the coordinate angle;

compare:

– quantities expressed in different units;

distinguish:

numerical and letter equalities;

types of angles and types of triangles;

the concepts of “several solutions” and “several ways to solve” (tasks);

play:

– methods of dividing a segment into equal parts using a compass and ruler;

give examples:

true and false statements;

rate:

measurement accuracy;

explore:

— problem (presence or absence of a solution, presence of several solutions);

read:

information presented on the chart;

solve educational and practical problems:

calculate the perimeter and area of ​​a non-standard rectangular figure;

– explore objects of the surrounding world, compare them with models of spatial geometric figures;

– predict the results of calculations;

– read and write any multi-digit number within the class of billions;

measure length, mass, area with specified accuracy,

compare angles by superposition using models.

List of educational and methodological support
:

Mathematics T. E. Demidova, S. A. Kozlova, A. P. Tonkikh. Textbook for 4th grade: in 3 parts / – M.: Balass, – (Educational system “School 2100”)

Kozlova S. A., Rubin A. G. Mathematics. Grade 4: Methodological recommendations for teachers. – M.: Balass,

Tests for the textbook “Mathematics” (“My Mathematics”). S. A. Kozlova, A. G. Rubin, 4th grade. – M.: Balass, – (Educational system “School 2100”).

Didactic material for the textbook “Mathematics” for grade 4 by T. E. Demidova, S. A. Kozlova, A. P. Tonkikh – M.: Balass, – (Educational system “School 2100”).

“Diary of a schoolchild,” 4th grade.

“Diagnostics of meta-subject and personal results of primary education.” Test work 4th grade (authors R. N. Buneev and others).

“Summer notebook for a future fifth-grader” (authors R. N. Buneev and others).

“I will learn everything, I can do everything” – a manual from the series “How we learn” (authors A. V. Goryachev, N. I. Iglina).

J. “Primary school plus before and after…”

J. “Elementary school”

Technical training aids

Visual aids:

– natural aids (real objects of living and inanimate nature, substitute objects);

– visual visual aids (drawings, diagrams, tables).

Equipment for multimedia demonstrations:

– computers;

– media projector;

-DVD projector;

-TV.

Electronic educational set on disk “Games and tasks” (grades 1-4).

Internet – a unified collection of digital educational resources (http: school – collection.edu/ru).

Calendar and thematic planning of lessons in the course “Mathematics”

(136 hours, 4 hours per week).

ONZ
– a lesson in discovering new knowledge

RU
– skill development lesson;

PR
– lesson – practical work

OU
– general lesson;

UK
– a lesson in control.

No.

p/p

Name

sections, topics

Lesson type

Activities

students

Development

UUD

Calendar dates

Plan.

Fact.

Section 1. Numbers from 1 to 1000.

1. Repetition and generalization of material studied in 3rd grade. (9 hours)

1

Tournament 1. TEST – control No. 1.

UK

Independent completion of tasks

Name a sequence of numbers within 1000; count in hundreds;

read, write and compare numbers within 1000; write numbers in descending and ascending order; establish a pattern of arrangement of numbers in a number series; compare values; to solve problems.

Perform addition and subtraction of three-digit numbers; explain the relationship between categories; find unknown components of addition and subtraction; compare the areas of figures; find the perimeter.

Apply learned properties of multiplication when solving word problems; choose the most convenient solution; determine the truth and falsity of statements; solve equations of the studied types; perform calculations within 1000; compare literal mathematical expressions.

2

Repetition of what has been covered. Numbers from 1 to 1000. Writing and reading numbers. Bit terms.

OU

Reading and writing numbers within 1000. Solving problems. Comparison of quantities.

3

Arithmetic operations on numbers

OU

Performing exercises to review what was learned in third grade.
Checking and self-testing the assimilation of the studied material.

4

Arithmetic operations on numbers

OU

5

Arithmetic operations on numbers

OU

6

Arithmetic operations on numbers

OU

7

Arithmetic operations on numbers. Mathematical dictation No. 1

OU

8

Revision of 3rd grade

UK

15.0911

9

Arithmetic operations on numbers

OU

11

Fractions. Finding part of a number

ONZ

Independently completing tasks to find part of a number.

Solve problems on finding a part of a number and a number from its part with an explanation of the method of action; solve inequalities of studied species; find the meaning of expressions in 3-4 steps; solve logical problems.

12


Finding a part of a number Finding a number by its part

ONZ

Formulating a rule and working out a method for finding a number by its fraction.


13

Finding a number from its part. Finding a number by its part

RU, OU

Solving problems with fractions. Observation of changes in the solution of a problem when its conditions change.

14

Comparison of fractions

ONZ

Comparing and ordering fractions.

Compare fractions with the same denominators or numerators; arrange fractions in descending (ascending) order; solve equations to find an unknown factor.4 select schemes for the equations. Highlight in the text of the problem the quantity that will be taken as the main unknown; express other quantities through the unknown; choose a scheme for a problem from several options.

15

Comparison of fractions

RU, OU

Formulation and independent application of rules with the same numerators and denominators. Skill development. Peer review.

16

Comparison of fractions

RU


17


Solving problems on the topic “Fractions”

OU

Finding a number by its part and part of the number. Explanation of the progress of solving the problem. Using auxiliary models.

18

Addition of fractions with like denominators

ONZ

Perform arithmetic operations with fractions. Solving word problems.

Add fractions with like denominators; find fractions that are equal to each other using a diagram; find the meanings of expressions containing 3-4 actions, explaining the choice of the order of actions.

19

Subtracting fractions with like denominators

ONZ

Subtract fractions with like denominators; find fractions that are equal to each other using a diagram. Highlight in the text of the problem the quantity that will be taken as the main unknown; express other quantities through the unknown; choose a scheme for a problem from several options.

21

Dividing a smaller number by a larger number

ONZ

Description of phenomena and events using numbers. Simulation of situations illustrating an arithmetic operation and the progress of its execution.

Divide a smaller natural number by a larger one. Solve problems on finding part of a number and a number from its part with explanation

22

What part is one number of another

ONZ

Checking and self-testing the assimilation of the studied material.

Apply a rule for determining what part one number is of another; solving the equation of the studied types; select an equation for the problem; find the meaning of expressions containing 3-4 actions; compare letter expressions containing 3 actions.

23

Test – control No. 2

UK

24

Solving problems on the topic “Fractions” “Not only mathematics…”

OU

Solving word problems with fractions; explanation for choosing a solution plan. Peer review.

Divide a smaller natural number by a larger one. Solve problems on finding a part of a number and a number from its part with an explanation of the method of action; solve inequalities of studied species; find the meaning of expressions in 3-4 steps; solve logical problems.

25

. Reinforcement on the topic: Fractions”

OU, RU

Section 2. Numbering of multi-digit numbers 12 hours

26

Multi-digit numbers. Rank and classes.

ONZ

Reading and writing round multi-digit numbers.

Name a sequence of numbers within 1000000; count in hundreds; read, write and compare numbers within 1,000,000; explain how each subsequent counting unit is formed; represent numbers as digit terms.

27

Reading and writing multi-digit numbers

ONZ

Use the names and sequence of numbers within 1,000,000 when solving educational problems (what number does the natural series of numbers begin with, how is each subsequent number in this series formed); explain how each subsequent counting unit is formed; use the names and sequence of digits in writing numbers when solving various problems.

28

Comparison of numbers. Arithmetic dictation

ONZ

Description of phenomena and events using numbers

Use knowledge of how many units of each class are contained in the notation of a number when solving problems; compare and order multi-digit numbers.

29

Bit terms.

ONZ

Practicing the skills of representing multi-digit numbers in the form of place value terms.

Checking and self-testing the assimilation of the studied material.

Use knowledge about the positionality of the decimal number system when solving various problems and justifying their actions; represent multi-digit numbers as a sum of digit terms

22

30

Multi-digit numbers. Bit terms

UK

33-34

Reading and writing multi-digit numbers

Test for the 1st quarter.

ONZ

Reading and writing multi-digit numbers.

Use the names and sequence of numbers within 1,000,000 when solving various problems (what number does the natural series of numbers begin with, how is each subsequent number in this series formed); explain how each subsequent counting unit is formed; use the names and sequence of digits in writing numbers when solving various problems.

223


31

Multiplying the number 1000. Multiplying and dividing a number by 1000, 10000, 100000Analysis of work on errors

OU

32

Reading and writing multi-digit numbers

ONZ

Formulation of rules for multiplication and division by 1000,10000,100000 based on the algorithm of multiplication by 100

Multiply the number 1000, multiply and divide by 1000,10000,100000; solve composite problems of the studied types; find the perimeter of a rectangle; choose the most convenient way to solve the problem; determine the truth and falsity of statements.

2

113

35

Million. Million class. Billion.

ONZ


Introducing new counting units





36


Test control No. 3.

ONZ, RU

Reading and writing multi-digit numbers

37

Reading and writing multi-digit numbers. “Not only mathematics…”

UK

Checking and self-testing the assimilation of the studied material.

38

Length units

OU

Clarification of ideas about the relationship between previously studied units of length.

Have an idea of ​​the relationship between units of length (mm, cm, dm, m, km); compare quantities by their numerical values; express these quantities in the studied units of measurement; draw a figure according to the model; find the perimeter.

1

39

Units of mass. Gram, ton.

ONZ

Introducing new units of mass: gram, ton

40

Units of measurement

ONZ

Clarification of ideas about the relationship between previously studied units of length

Use knowledge about the relationship between units of length and mass; compare values; perform arithmetic operations with named numbers; draw segments, finding the size of a segment based on its part; solve equations of the studied types.

41-42

Area units.

ONZ

Repetition of the relationship between previously studied units of length

Correlate different units of area measurement with each other; convert large units of measurement into smaller ones and vice versa; perform arithmetic operations with named numbers; name various geometric shapes, describe their similarities and differences; find the area of ​​figures.

13

43

Area of ​​a right triangle.

ONZ, RU

Clarification of ideas about the types of triangles. Formulating a generalized method for finding the area of ​​a right triangle

Use knowledge about units of measurement of quantities (length, mass, time, area), the relationship between them when solving various problems; distinguish between types of triangles; name the sides of a right triangle (legs, hypotenuse); find the area of ​​a right triangle.

44


Approximate calculation of areas. Palette.

ONZ

Finding the area of ​​shapes using a palette.

Understand that sometimes using already known methods it is impossible to accurately determine the area of ​​a figure; find the area of ​​flat figures using a palette; perform arithmetic operations with named quantities; find the area of ​​a square; compose expressions based on the proposed conditions of the problem

.

45

Volume units

ONZ


Clarification of ideas about the relationship between previously studied units of volume.

Use knowledge about units of volume measurement when solving various problems (m 3
, dm 3
,liter), the relationship between them; convert large units of measurement into smaller ones and vice versa; perform arithmetic operations with named numbers; create a line chart using a table.

46

Solving problems on the topic “Magnitudes”

RU, OU

Solving problems with quantities; comparison and ordering of units of mass, volume, area, length.

Solve simple and compound problems that reveal relationships between numbers and dependencies between groups of quantities (price, quantity, cost; speed, time, distance; labor productivity, work time, work).

47

Exact and approximate values ​​of quantities

ONZ

Introduction to the concept of “approximate value of a quantity.”

Solving word problems using an arithmetic method; planning the progress of solving the problem; presentation of the task text (diagram, table, diagram and other models).

Know a general algorithm for rounding numbers (finding an approximate value of a quantity); find the approximate value of the area; compose tasks yourself using a table; express these quantities in the studied units of measurement.

48

Solving problems on the topic “Quantities”. Arithmetic dictation.

RU, OU

49

Addition and subtraction of multi-digit numbers. Estimation of the sum and difference

ONZ

Calculating the sum and difference; development of computing skills.

Apply algorithms for addition and subtraction of multi-digit numbers; estimate the results of arithmetic operations when solving practical and subject problems; solve simple and compound problems that reveal the meaning of arithmetic operations, relationships between numbers and relationships between groups of quantities.

50-53

Addition and subtraction of multi-digit numbers

RU, OU

Development of computational skills and ability to solve word problems.

Consciously create algorithms for calculating the values ​​of numerical expressions containing up to 3-4 actions (with and without parentheses), based on knowledge of the rules about the order of actions and knowledge of the properties of arithmetic operations and follow these algorithms, including analysis and checking your actions.

54

Productivity. The relationship between work, time and productivity

ONZ

Solving word problems using an arithmetic method; planning the progress of solving the problem; presentation of the task text (diagram, table, diagram and other models).

Apply algorithms for adding and subtracting multi-digit numbers. Functional connection between quantities. Price, quantity, cost. Time, speed, distance. Labor productivity, working time. Calculate the results of arithmetic operations when solving practical and subject problems.

55-56

Independent work Solving problems on the topic “Adding and subtracting multi-digit numbers”

RU, OU

Solving word problems using an arithmetic method. Planning the progress of solving a problem. Presentation of the task text (diagram, table, diagram and other models).

Apply algorithms for addition and subtraction of multi-digit numbers. Functional connection between quantities. Price, quantity, cost. Time, speed, distance. Labor productivity, working time.

57

Multiplication of numbers. Grouping of multipliers

ONZ

Perform multiplication based on grouping of factors.

Understand that the product does not depend on the order of the factors and the order of operations; explain how many digits are contained in each class; name the number of digits contained in each class; orally find the meaning of round number expressions based on learned properties of addition and multiplication.

58

Arithmetic operations on numbers

RU, OU

Practice learned multiplication techniques with round numbers. Solving word problems.

Apply algorithms for multiplying and dividing multi-digit numbers; solve simple and compound problems that reveal the meaning of arithmetic operations, relationships between numbers and dependencies between groups of quantities (price, quantity, cost; speed, time, distance; labor productivity, work time, work); solve equations of the studied types.

59

Multiplying multi-digit numbers by single-digit numbers

ONZ

Practice learned multiplication techniques with round numbers. Solving word problems.

Multiply a multi-digit number by a single-digit number; solve problems in 2-3 steps on all arithmetic operations in an arithmetic way (based on diagrams, tables, short notes and other models); consciously create algorithms for calculating the values ​​of numerical expressions containing up to 3-4 actions (with and without parentheses).

60-61

Multiplying numbers

ONZ

Practice learned multiplication techniques with round numbers. Solving word problems.

Perform oral and written calculations with multi-digit numbers based on learned properties of addition and multiplication; using given expressions, compose problems with quantities: price, quantity, cost; time, speed, distance; productivity, time, work; find approximate meanings of expressions.

UK

Checking and self-testing the assimilation of the studied educational material.

Independently analyze the text of the problem and choose a solution; draw up a program of action and find the meaning of the expression; apply rules when finding the meaning of expressions; solve equations of the studied types; perform written calculations with three-digit numbers; Find the area and perimeter of a rectangle.


62

Cont. work No. 2 (for the 2nd quarter)

63

Analysis of bug fixes.

RU, OU

Working on mistakes made in the test.

Detect and eliminate errors of a logical (during solution) and arithmetic (in calculation) nature; use various techniques for checking the correctness of finding the value of a numerical expression (based on rules for establishing the order of actions, algorithms for performing arithmetic operations, estimating the result).

64

Problem solving (“Not only mathematics…”)

RU,

65

Tournament 4. Test – control. School workshops

UK

Checking and self-testing the assimilation of the studied educational material.

Compare values; arrange quantities in descending and ascending order; choose an expression to solve a problem presented in the form of a table from several options proposed in the textbook; perform approximate calculations; round numbers to the thousandth place; find false and true statements.

66

Division of round numbers

ONZ

Using various techniques for checking the correctness of finding the value of a numerical expression (based on rules for establishing the order of actions, algorithms for performing arithmetic operations, estimating the result).

Detect and eliminate errors of a logical (during solution) and arithmetic (in calculation) nature; divide round multi-digit numbers by a single-digit number; select several solutions to inequalities; find approximate values ​​of quantities; use mathematical terminology

67

Arithmetic operations on numbers

RU, OU

Description of phenomena and events using numbers. Simulation of situations illustrating an arithmetic operation and the progress of its execution.

Consciously create algorithms for calculating the values ​​of numerical expressions containing up to 3−5 actions (with and without parentheses); solve problems involving the oncoming movement of two objects; find and choose a convenient way to solve a word problem; act according to a given and independently drawn up plan for solving a problem.

68

Dividing a number by the product

ONZ

Solving examples of dividing a number by a product in different ways. Choosing a convenient calculation method.

Understand three ways to perform division of a number by a product; explain which of the three methods is convenient; solve equations of the studied types; find a part of a number; use mathematical terminology to write numerical expressions; transfer information from a table to a graph.

69

Dividing round multi-digit numbers into round numbers

Arithmetic operations on numbers

ONZ

Description of phenomena and events using numbers. Simulation of situations illustrating an arithmetic operation and the progress of its execution.

Divide multi-digit numbers into round numbers with step-by-step commentary on the general method of action; use all known algorithms for oral and written calculations when finding the meanings of expressions; find true and false statements, justifying your choice; solve problems involving the oncoming movement of two objects.

70

Division with remainder by 10, 100, 1000

ONZ

Practicing computational skills. Solving fun problems.

Divide round numbers with a remainder (with verification). Evaluate simple statements as true or false. Determine the membership of elements of a given population (set) and part of the population (subset); find part of a segment from the whole; draw segments of a given length; independently create and use auxiliary models

No.

p/p

Name

sections, topics

Lesson type

Types of activities

students

Development

UUD

Fact.

71

Division of round numbers with remainder

ONZ

Explanation of the reasoning when dividing round numbers with a remainder. Composing letter expressions.

Divide round numbers with a remainder (with verification); evaluate simple statements as true or false; explain the choice of the course of solving a word problem based on the table; perform arithmetic operations with named numbers; write mathematical expressions using the names of the components of arithmetic operations.

72

Equations

ONZ

Solving equations of the studied types.

Solve equations in which the relationship between the components and the result of an action must be applied several times: a ∙ x ± b = c; (x ± b) : c = d; a ± x ± b = c; detect and eliminate errors of a logical (during solution) and arithmetic (in calculation) nature; compose letter expressions according to conditions specified verbally, in drawings or in tables; calculate the numerical value of a letter expression given the values ​​of the letters.

73

Arithmetic operations on numbers

RU

Development of computational skills and ability to solve word problems.

Select (by estimation) and solve equations with the smallest and largest roots; find approximate values ​​of quantities; find the probabilities of the simplest random events; perform a search of all possible options for recalculating objects and combinations, including combinations that satisfy the specified conditions; convert information from one type to another.

74

Equations

OU

Solving equations of the studied types.

Solve equations in which the relationship between the components and the result of an action must be applied several times: a ∙ x ± b = c;



(x ± b) : c = d; a ± x ± b = c; detect and eliminate errors of a logical (during solution) and arithmetic (in calculation) nature; compose letter expressions according to conditions specified verbally, in drawings or in tables; calculate the numerical value of a letter expression given the values ​​of the letters.

2

75

Arithmetic operations on numbers

OU

Development of computational skills and ability to solve word problems.

Find and solve equations with equal roots; choose an equation and diagram for the problem from several options proposed in the textbook; perform arithmetic operations with multi-digit numbers; find the volume of a figure consisting of several cubes; perform actions with named numbers.

76-77

Dividing multi-digit numbers into single-digit numbers

ONZ

Use of well-known algorithms for oral and written calculations.

Find errors made when dividing a multi-digit number by a single-digit number; perform division with multiplication check; recognize flat geometric figures when their position on the plane changes; solve problems involving the movement of two objects in the opposite direction; draw up diagrams and equations for problems.

9

78

Arithmetic operations on numbers

RU, OU

Development of computational skills and ability to solve word problems.

Perform arithmetic operations (addition, subtraction, multiplication and division) with multi-digit numbers; solve problems with quantities; compare values; recognize types of triangles; determine the membership of elements of a given population (set) and part of the population (subset); compose and solve equations using the notation suggested in the textbook.

79

Current book No. 3 on the topic “Multiplication and division of numbers”

UK

Checking and self-testing the assimilation of the studied educational material.

Apply knowledge about the functional relationship between quantities

speed, distance; labor productivity, work time, work) when solving word problems; draw up diagrams and equations for problems; enter data into tables

80

Analysis of bug fixes

RU

Independent work. Peer review.

Detect and eliminate errors of a logical (during solution) and arithmetic (in calculation) nature. Apply knowledge about the functional relationship between quantities (price, quantity, cost; time, speed, distance; labor productivity, work time, work); find and correct errors made when solving a problem.

81

Written division of multi-digit numbers into single-digit numbers

ONZ


Development of computational skills and ability to solve word problems.

Use an algorithm for written division of a multi-digit number by a single-digit number; draw up an equation as a mathematical model of the problem; find the surface area of ​​a cube; perform actions with named quantities; recognize flat and three-dimensional geometric shapes

82

Dividing multi-digit numbers into single-digit numbers

ONZ

Development of computational skills and ability to solve word problems.

Explain the reasoning when dividing multi-digit numbers by single-digit numbers (using the textbook algorithm); solve the equation of the studied species; solve word problems using diagrams and tables; explain the choice of order of actions in mathematical expressions.

83

Arithmetic operations on numbers

RU, OU

Development of computational skills and ability to solve word problems.

Explain the reasoning when dividing multi-digit numbers by single-digit numbers (using an algorithm); find true and false statements by estimating calculation results; solve movement problems; perform division with remainder; recognize different types of triangles; find their perimeter and area.

eee

84

Dividing multi-digit numbers into single-digit numbers

RU, OU

Working on computational skills. Development of logical thinking.

Consciously create algorithms for calculating the values ​​of numerical expressions containing up to 3-4 actions (with and without parentheses), based on knowledge of the rule about the order of actions and knowledge of the properties of arithmetic operations and follow these algorithms, including analysis and checking your actions; present information in the form of tables.

85

Written division of multi-digit numbers into single-digit numbers

ONZ

86-87

Dividing multi-digit numbers into round ones

ONZ

Introduction to the algorithm for dividing multi-digit numbers by round ones.

Perform written division of multi-digit numbers into round numbers using a reasoning model; solve equations of the studied types; solve word problems on oncoming traffic using a drawing; express some units of length and area in others; solve non-standard weighing problems; use knowledge about the bit composition of multi-digit numbers.

88

Solving problems on the topic “Multiplication and division of numbers”

RU, OU

Solving word problems using an arithmetic method; planning the progress of solving the problem; presentation of the task text (diagram, table, diagram and other models).

Use knowledge of the name and sequence of numbers within 1,000,000 when solving various problems and justifying their actions; estimate the results of arithmetic operations when solving practical and subject problems; find a part of a number, a number by its part, find out what part one number is of another; solve problems into parts.

Multiplying by a two-digit number

ONZ

89

Using various techniques to check the correctness of finding the value of a numerical expression.

Use knowledge of the rule for multiplying a sum by a number to multiply a multi-digit number by a two-digit number; estimate the calculation results; distinguish between statements of a general statement; correctly formulate refutations of statements, i.e. carefully select counterexamples.

90-91

Multiplying multi-digit numbers by a two-digit number

ONZ

Using various techniques for checking the correctness of finding the value of a numerical expression (based on rules for establishing the order of actions, algorithms for performing arithmetic operations, estimating the result).

Rate

its computing capabilities; perform multiplication of multi-digit numbers by two-digit numbers with a detailed explanation of the calculations;
compare different calculation methods, choosing the most convenient one; predict the result of calculations ; solve word problems involving the movement of two objects in the opposite direction.

92

Problem solving

RU

Clarification of the concept of “removal speed”. Solving word problems using an arithmetic method; planning the progress of solving the problem; presentation of the task text (diagram, table, diagram and other models).

Solve problems involving the movement of two objects in opposite directions; compose tasks using diagrams; choose a convenient way to solve a problem; draw a diagram for the problem; detect errors in reasoning and calculations made when solving a problem independently; build figures based on given points; perform division with remainder.

93-95

Multiplying multi-digit numbers by a three-digit number

ONZ

Development of computational skills and ability to solve word problems.

Understand that multiplication by a three-digit number is performed using the same algorithm as multiplication by a two-digit number; estimate the results of arithmetic operations when solving practical and subject problems; find the most convenient way to calculate.

96-100

Solving problems on the topic “Multiplication of multi-digit numbers by a three-digit number”

OU

Development of computational skills and ability to solve word problems.

Understand that multiplication by a three-digit number is performed using the same algorithm as multiplication by a two-digit number; estimate the results of arithmetic operations when solving practical and subject problems; find the most convenient way to calculate.

101

Test for the 3rd quarter on the topic “Multiplication and division of numbers”

UK

Checking and self-testing the assimilation of the studied educational material.

Apply knowledge about the functional relationship between quantities (price, quantity, cost; time, speed, distance; labor productivity, time


work, work) when solving word problems; draw up diagrams and equations for problems; enter data into tables.

102

Working on mistakes. Written division of multi-digit numbers by two-digit numbers

OU

Independent work. Peer review.

Detect and eliminate errors of a logical (during solution) and arithmetic (in calculation) nature; apply knowledge about the functional relationship between quantities (price, quantity, cost; time, speed, distance; labor productivity, work time, work); find and correct errors made when solving a problem.

103-104

Problem solving (“Not only mathematics…”)

RU,OU

Solving word problems using an arithmetic method; planning the progress of solving the problem; presentation of the task text (diagram, table, diagram and other models).

Apply knowledge about the functional relationship between quantities (price, quantity, cost; time, speed, distance; labor productivity, work time, work); find and correct errors made when solving a problem.

105

Tournament No. 5 Test – control

UK

Checking and self-testing the assimilation of the studied educational material.

Apply knowledge about the functional relationship between quantities (price, quantity, cost; time, speed, distance; labor productivity, work time, work) when solving word problems; draw up diagrams and equations for problems; enter data into tables; choose a convenient way to solve the problem.

106

Written division of multi-digit numbers into two-digit numbers

ONZ

Development of computational skills and ability to solve word problems.

Perform written division and multiplication of multi-digit numbers by a three-digit number; divide multi-digit numbers with a remainder; find part of a number from a whole; perform arithmetic operations with named quantities; distinguish figures on a plane; draw three-dimensional figures.

107-111

Arithmetic operations on numbers

RU, OU

112

Arithmetic mean

ONZ

Introduction to the method of finding the arithmetic mean of several numbers

Read information given using bar charts;



find the arithmetic mean of several numbers to solve practical problems; draw figures at given points; perform multiplication and division of multi-digit numbers.

113

Written division of multi-digit numbers by a three-digit number

ONZ

Development of computational skills and ability to solve word problems.

Round numbers to given digits; perform written division of multi-digit numbers by three-digit numbers, performing detailed reasoning; invent and solve problems using diagrams; select an equation for a problem from several proposed options.

114

Dividing multi-digit numbers by a three-digit number

ONZ

Development of computational skills and ability to solve word problems.

Perform written division of multi-digit numbers by three-digit numbers, performing detailed reasoning; draw flat figures and find their perimeter; have basic survey skills; processing its data and presenting it using tables.

115-117

Arithmetic operations on

By numbers

RU,

OU

Development of computational skills and ability to solve word problems.

Perform written division and multiplication of multi-digit numbers by a three-digit number; divide multi-digit numbers with a remainder; find part of a number from a whole; perform arithmetic operations with named quantities; distinguish figures on a plane; draw three-dimensional figures.

118

Pie chart

ONZ

Introduce the way of presenting information using a pie chart.

Read information given using pie, line and column charts, tables, graphs; transfer information from a table to pie, line and column charts; create questions for diagrams; find the arithmetic mean of several numbers.

119

Arithmetic operations on

By numbers

RU,OU

Exercises in performing arithmetic operations with multi-digit numbers.

Perform written addition, subtraction, division and multiplication of multi-digit numbers; compare fractions

using diagrams; read pie charts; solve problems with quantities; present information in table form; Perform calculations on values ​​in expressions with and without parentheses.

120

Number ray. Coordinates of a point on a number line.

ONZ

Arrangement of numbers on the number line. Exercises in performing arithmetic operations with multi-digit numbers.

Build a number beam; have an idea of ​​the concept of “point coordinate”; mark points with given coordinates on a numerical line; fill out the table using the data in the pie chart; compare literal expressions without performing calculations; perform division with remainder (with check); solve word problems.

121

Address in the table. A couple of numbers.

ONZ

Introduction to the concept of “cell coordinate”.


Find the cell address in the table; explain what the first and second numbers in the cell address mean; place figures, numbers and pictures in the table at given addresses; perform arithmetic operations with named numbers; mark points with given coordinates on a numerical line.

122

Coordinates of points on the plane

ONZ

Introducing the coordinate angle.

Have an idea of ​​the coordinate angle; locate points with given coordinates on the number line and on the coordinate plane; determine the coordinates of points; understand that when determining the coordinates of a point, you should not confuse the order of numbers in a pair.

123

Consolidation of what has been learned on the topic “Multiplication and division of numbers”

RU,

OU

Solving non-standard, logical and entertaining problems. Expanding your mathematical horizons.

Have initial ideas about the essence and features of mathematics
about knowledge, the history of its development, its generalized nature and role in the knowledge system.

124

Test No. 4 on the topic “Multiplication and division of numbers”

UK

Checking and self-testing the assimilation of the studied educational material.

Use various techniques for checking the correctness of finding the value of a numerical expression (based on rules for establishing the order of actions, algorithms for performing arithmetic operations, estimating the result);

125

Working on bugs

Non-standard tasks

RU, OU

Independent work. Work in pairs.

Perform arithmetic operations within 1,000,000; solve word problems of the studied types; construct figures on a plane; distinguish studied geometric shapes; perform operations with fractions and quantities; convert quantities; determine the coordinates of points on the plane; compare literal expressions.

126

REPEATING AND GENERALIZING WHAT YOU LEARNED IN 4TH CLASS. Repetition on the topic “Numbering multi-digit numbers”

RU, OU

Finding a number by its part and part of the number. Explanation of the progress of solving the problem.

Using auxiliary models to solve a problem.

Compare fractions with the same numerators and denominators; arrange fractions in descending and ascending order; solve problems on finding a part of a number and a number from its part; perform arithmetic operations with fractions (cases studied).

127

Final test

UK

Checking and self-testing the assimilation of the studied educational material.

Perform arithmetic operations within 1,000,000; solve word problems of the studied types; construct figures on a plane; distinguish studied geometric shapes; perform operations with fractions and quantities; convert quantities; determine the coordinates of points on the plane; compare literal expressions.

128

Working on bugs

OU

Independent work. Work in pairs.

Perform arithmetic operations within 1,000,000; solve word problems of the studied types; construct figures on a plane; distinguish studied geometric shapes; perform operations with fractions and quantities; convert quantities; determine the coordinates of points on the plane; compare literal expressions.

129

REPEATING AND GENERALIZING WHAT YOU LEARNED IN 4TH CLASS.

RU,OU

Named number arithmetic, comparison and ordering

Compare values; arrange quantities in descending order and.

RU, OU

136


Repetition on the topic “Actions with named numbers”

values.

ascending; choose an expression for solving a problem presented in the form of a table from several options proposed in the textbook; perform approximate calculations; round numbers to the thousandth place;

130

REPEATING AND GENERALIZING WHAT LEARNED IN 4TH CLASS. Exercise in addition and subtraction of multi-digit numbers.

RU, OU

Exercise in addition and subtraction of multi-digit numbers.

Perform addition and subtraction of multi-digit numbers; use various techniques for checking the correctness of finding the value of a numerical expression (based on rules for establishing the order of actions, algorithms for performing arithmetic operations, estimating the result); perform arithmetic operations with named numbers; compare numeric and alphabetic mathematical expressions.

131

Revision on the topic “Written techniques for adding, subtracting, multiplying and dividing multi-digit numbers”

RU, OU

Exercise in dividing and multiplying multi-digit numbers.

Perform written division and multiplication of multi-digit numbers by a three-digit number; use various techniques for checking the correctness of finding the value of a numerical expression (based on rules for establishing the order of actions, algorithms for performing arithmetic operations, estimating the result); perform arithmetic operations with named numbers; compare numeric and alphabetic mathematical expressions.

132

Repetition on the topic “Order of actions in expressions”

RU, OU

Solving logical, non-standard and entertaining problems.

Use the knowledge gained during the study of mathematics in the fourth grade to solve logical, entertaining and non-standard problems.

133

Repetition on the topic “Order of actions in expressions”

RU, OU

134

Repetition on the topic “Solving equations and inequalities”

RU

135

Repetition on the topic “Geometric material”


RU, OU

Schedule of tests and tests.

At the end II
quarters.


Page 25


3

K/R or test number

Lesson number

Note

Page number of this notebook

Math tests

1

1

Conducted during the first lesson of the academic year

Page 2

2

23

Held after the topic “Fractions”

Page. 5

3

34

Conducted during the first lesson in II
quarters

Page 8

4

65

Conducted during the first lesson in III
quarters

Page 10

5

105

Conducted during the first lesson in IV
quarters

Page 14

Current control work

1

8

Entrance test

2

Administrative control work based on the text of the administration

3

79

Held in III
quarters.

Page. 17

Quarter tests

1

30

At the end I
quarters

Page 21

2

64

101

At the end

III

quarters.

Page 29


§

The student will learn

:

Cognitive

UUD

model
methods for finding the perimeter;

compare

different ways to find the perimeter as a result of using the commutative property of multiplication, choose
The most convenient;

classify
objects, numbers, geometric figures according to a given characteristic;

identify a pattern
constructing series containing numbers;

execute
creative tasks, applying knowledge in changed conditions.

The student will have the opportunity to learn

:

understand and perform simple generalizations and use them to gain new knowledge;

establish mathematical relationships between objects and groups of objects, record this orally, using the features of mathematical speech (accuracy and brevity;

apply knowledge and methods of action in changed conditions

;

explain the found methods of action when solving new educational problems and find ways to solve them (in the simplest cases);

extract information from the proposed text according to a given condition.

Regulatory
UUD

understand and accept
learning task;

take into account
guidelines for action identified by the teacher in collaboration with him;

explain
and justify the action
, chosen to solve the problem ;

jointly highlight evaluation criteria
and evaluate
work result;

control
and evaluate
my job.

The student will have the opportunity to learn

:

understand, accept and retain various educational and cognitive tasks;

identify known knowledge and skills from the topic of the lesson, determine the range of unknowns on the topic being studied.

Communication
UUD

build
simple reasoning, formalize
them in the form of understandable simple logical statements;

work
in pairs when playing the mathematical game “Make a Rectangle”;

take into account
different opinions,

negotiate
and come
to a common decision;

explain
and justify
action chosen to solve a problem.

The student will have the opportunity to learn

:

apply mathematical knowledge and mathematical terminology
when expressing your opinion and proposed courses of action;

engage in dialogue with the teacher and peers, in a collective discussion of problems, show initiative and activity in the desire to speak out;

together with peers, set the task of working in pairs, distribute functions in pairs when completing tasks;

assist a friend in cases of difficulty;

listen to your activity partner;

express your opinion with reason.

§

§

Municipal budgetary educational institution “Basic comprehensive Kaplinskaya school”

WORK PROGRAM

WITH GIFTED STUDENTS

2 “B” class

for the 2021-2021 academic year

Teacher Grudkova G.V.

Stary Oskol

2021

EXPLANATORY NOTE

Creating a system for working with gifted and talented children is one of the directions of the national educational initiative “Our New School”, therefore, providing conditions for the identification and development of gifted and talented children and the realization of their potential is one of the priorities in the field of education of the MBOU ” OO Kaplinskaya School”

The program of work with gifted children provides for the creation of equal starting conditions for the identification, development, social support of gifted children, the realization of their potential, ensuring comprehensive development and education.

The identification of gifted children in my class began already in the first grade on the basis of observations, the study of psychological characteristics, speech, memory, and logical thinking. Various methods for identifying talented children help to establish their priorities, inclinations and interests. Much depends on the parents. The child’s personality is formed in the family, and it also plays a big role in its formation. Parents must strive to develop the following personal qualities in their children:

Confidence that is based on the consciousness of self-worth.

Understanding the strengths and weaknesses in oneself.

Intellectual curiosity and willingness to take research risks.

Respect for kindness, honesty, friendliness, empathy.

The habit of relying on one’s own strengths and the willingness to take responsibility for one’s actions.

The ability to help find a common language and joy in communicating with people.

A gifted child will not be able to realize his abilities without the conditions created for this. The environment must be such that the child can draw information from it, constantly expand his zone of proximal development and form a motivational sphere. Participation in various competitions, olympiads, and conferences outside of school greatly stimulate the development of gifted children. A reasonable system for encouraging the success of a gifted child is needed. It is important to formulate the concept of result not for the sake of reward, but for the sake of self-improvement and self-development.

The training program is designed for 34 hours (once a week). Lesson duration 45 minutes.

GOAL

Creation of a system of activities for gifted children to develop the intellectual and creative abilities of students.

Problems

implementation of the principle of a person-centered approach in the training and education of students with an increased level of learning,

activation of their intellectual qualities for the purpose of the harmonious development of man as a subject of creative activity,

creating optimal conditions for identifying support and development of gifted children;

introduction into the educational process of all types and forms of creative self-realization, non-standard scientific and artistic thinking of students.

Work in mathematics lessons is supplemented by extracurricular activities.

GROUP LIST

1. Vinnikova Darina

2. Ilya Karapuzov

Classes are open to all students who wish to study mathematics.

Characteristics of students

Vinnikova Darina, born in 2007. Darina came to school well prepared. From the first days of school, she showed diligence and activity in her educational activities. She is inquisitive and enjoys reading books on various topics. She took part in various competitions. The girl has a good memory. He was brought up in a large, prosperous family. Parents pay great attention to the upbringing and education of the child.

Ilya Karapuzov, born in 2008. I came to school prepared. Has extraordinary thinking, thinks logically. He was brought up in a complete, prosperous family. Parents pay great attention to raising their son. Ilya loves mathematics and finds various solutions to problems.

The boy takes an active part in the life of the class and school. In the 2021-2021 academic year, he was the winner of various all-Russian and school competitions.

Program content

(34 hours, once a week)

Introductory lesson. Safety regulations. (1h)

Problems on finding an unknown term. (3h)

Mathematical expressions (4h)

Arithmetic puzzles (3h)

Numerical expressions (2h)

Cut and put together (2h)

Logic problems (6h)

Word problems

Compiling mathematical puzzles (2 hours)

Solving Olympiad tasks (5 hours)

Thematic planning

Item no.

Theme

Number of hours

1.

Safety rules in the classroom. Introductory lesson.

1

2.

Problems on finding an unknown term.

3

3.

Mathematical expressions

4

4.

Arithmetic puzzles

3

5.

Numerical expressions

2

6.

Cut and put together

2

7.

Logic problems

6

8.

Word problems

6

9.

Compiling mathematical puzzles

2

10.

Solving Olympiad tasks

5

Calendar and thematic planning

No.

Lesson topic

Planned date

Fact

Note

1

Introductory lesson. Safety regulations.

09/07/15

2

Problems on finding an unknown term.

09/14/15

3

Problems on finding an unknown term.

09/21/15

4

Problems on finding an unknown term.

09.28.15

5

Solving advanced mathematical expressions

05.10.15

6

Solving expressions.

10/12/15

09.11.15


7

Mathematical expressions.

10/19/15

8

Mathematical expressions.

02.11.15

9

Arithmetic puzzles

10

Arithmetic puzzles

11/16/15




11

Arithmetic puzzles

11/23/15

12

Numerical expressions

11/30/15

13


Numerical expressions

07.12.15

14

Cut and put together.

12/14/15

15

Cut and put together.

12/21/15

16

Logic problems

12/28/15

17

Logic problems

01/18/16

18

Logic problems

01/25/16

19

Logic problems

02/01/16

20

Logic problems

02/08/16

21

Problems involving cutting a figure into equal parts.

02/15/16

22

Word problems.

02.22.16

23

Word problems.

02.29.16

24

Word problems.

03/07/16

25

Problem solving.

03.14.16

26

Problem solving.

03/28/16

27

Weighing problems.

04.04.16

28

Compiling mathematical puzzles.

04/11/16

29

Compiling mathematical puzzles.

04/18/16


30

Solving Olympiad tasks.

04/25/16

31

Solving Olympiad tasks.

05/02/16

32

Solving Olympiad tasks.


05/02/16



33

Solving Olympiad tasks.

05.16.16

34

Olympics

05/23/16


Expected results

Be able to read, compose and solve arithmetic puzzles
Count geometric shapes, isolating small ones from large ones.
Be able to solve problems of all types independently.

Be able to compose logical problems using your own experience and observations.

Know the order of execution of arithmetic expressions, compose and solve expressions in several steps.

Be able to perform complex calculations orally.

Used literature

Belova E. “Gifted Children.” J. “Preschool education” No. 4 1991, p. 69-75

Burmenskaya G.V., Slutsky V.M. “Gifted Children”, M. Progress, 1991

Vygotsky L. S. “Imagination and creativity in childhood.” Psychological essay. Book for teachers. M., Education, 1991

Geidman B. P., Misharina I. E. “Preparation for the Mathematical Olympiad. Elementary School. 2-4 grades. – M., Iris-press, 2008

Gilbukh Yu. Z. “Attention, gifted children”, M., Znanie, 1991

Publication address: https://www.obumage.net/metodicheskie-razrabotki/208773-plan-raboty-s-odarennymi-detmi-2-klass

§

EXPLANATORY NOTE

FOR CERTIFICATION MATERIAL IN MATHEMATICS

IN 1st CLASS

Interim annual certification is carried out with the aim of establishing the actual level of students’ theoretical knowledge in mathematics, their practical skills and abilities, establishing the compliance of students’ subject universal educational activities with the requirements of the Federal State Educational Standard for the 1st grade course in mathematics in the following sections:

Solving simple problems.

Addition and subtraction within 20.

Construction of segments.

Comparison of numbers.

Certification material is compiled on the basis of the educational complex “School of Russia”

1. Moro M. I., Bantova M. A., Beltyukova G. V., Volkova S. I., Stepanova S. V. Mathematics. Working programm. (Collection of work programs “School of Russia” grades 1-4. A manual for teachers of general education institutions. – M.: Prosveshchenie, 2021)

2. Mathematics. 1 class. Textbook for general education institutions with adj. per electron carrier. At 2 p.m. / [Moro M.I., Bantova M.A., Beltyukova G.V., Volkova S.I., Stepanova S.V.]. – 3rd ed. – M.: Education, 2021.

When compiling the certification material, the following teaching aids were used:

Tests in mathematics: to the textbook by M. I. Moro et al. “Mathematics. 1st grade” / V. N. Rudnitskaya. – 9th ed., revised. And additional – M.: Publishing House “Exam”, 2021. – 127, [1] p. (Series “Teaching and Methodological Kit”)

Krylova O. N. Final certification in mathematics: 1st grade. M.: Exam 2021

Volkova S. I. Mathematics. Test work. – M.: Education, 2021)

Form of implementation: combined test.

The test includes 4 tasks.

1 task is aimed at testing computational skills in solving examples of addition and subtraction within 20, operations with the number 0.

Tasks 2 and 3 are aimed at testing the skill of solving simple addition and subtraction problems within 20.

4 task is aimed at testing the skills of finding the length of segments and constructing them.

TEST 1ST CLASS

                                    1 option

1 . Complete the steps:

1 9 =                                     10 7 =                                          
8 0 =                                     12 – 2 =                                          
5 4 =                                     13 -10 =                                            
10 -7 =                                     4- 4 =                                          

2
. Draw 4 circles. Draw triangles under the circles so that there are 3 more triangles than circles.

3 . Solve the problem:
There are spoons and forks on the table. There are 5 spoons, and there are 2 more forks than spoons. How many forks are on the table?

4
. The length of the first segment is 8 cm, and the length of the second is 3 cm less. How many cm is the second segment? Draw these segments.

2nd option

1 . Complete the steps:

5 0 =                                   1 4 – 4 =                            

2 7 =                                   1 7- 7 =                            

6 4 =                                16 – 10 =                            

10 -5 =                                   7 – 7 =                              

                                    
2
. Draw 5 circles. Draw triangles under the circles so that there are 2 fewer triangles than circles.

3
. Solve the problem:
There are spoons and forks on the table. There are 7 spoons, and there are 2 less forks than spoons. How many forks are on the table?

4 .
The length of the first segment is 4 cm, and the length of the second is 1 cm less. How many cm is the second segment? Draw these segments.

3rd option

1. Follow the steps:

10-3 = 10 4=

7 2= 17-7=

5 3= 15-10=

6 0= 1 9=

2. Draw the first segment 5 cm long, and the second 2 cm less than the first.

3. Solve the problem:
Vanya and Petya went fishing. Vanya caught 8 fish, and Petya caught 2 fish more. How many fish did Petya catch?

4. Compare the numbers:

17 * 12

8 * 10

2 * 13

4th option

1. Find the meaning of the expression:

12 1= 4 3 3=

10 3= 5 (2 2)=

14-4= 8- (4 4)=

2. Draw a triangle and a quadrilateral

3. Solve the problem:

Daffodils bloomed at the dacha. 7 daffodils were cut for a bouquet and 7 more remained. How many daffodils have bloomed?

Criteria for assessing certification work, grade 1

Errors:

computational errors in examples and problems;

incorrect solution to the problem (skipping an action, not
correct choice of actions, unnecessary actions);

ignorance or incorrect application of properties, rules, algorithms, existing dependencies underlying the execution of a task or used during its execution;

incorrect choice of actions, operations;

incorrect calculations when the purpose of the task is to test computational skills;

discrepancy between the measurements and geometric constructions performed and the specified parameters.

Shortcomings:

incorrect writing of data (numbers, signs, symbols, quantities);

errors in the recording of mathematical terms and symbols when preparing mathematical calculations;

incorrect calculations when the purpose of the task is not related to testing computational skills;

incorrect formulation of the question for action when re
completing the task;

lack of answer to the task or errors in recording the answer.

§

§

§

The teacher gives each group a geometric figure in the shape of a house. What geometric shapes does the house consist of?

Draw a line so that you have a triangle and a square.

What shape does the window have? (Rectangle)

Each group has different sized windows.

Task: measure the sides of the window, find the perimeter.

The perimeter of a rectangle is the sum of the lengths of all its sides.

What properties of a rectangle do you know?

(A rectangle has equal opposite sides)

What units of measurement will we work with?

Guys, can we say that this is a task? What will be the conditions of the task? (Length and width of rectangle)

What is the question in the problem? (What is the perimeter)

What else is in the problem? (Solution and answer)

Don’t forget to write the formula by which we are looking for the perimeter. ( P
= a
b
a
b
)

The teacher invites the children to complete this task independently.

One person from each group comes to the board and shows the answer they received, which corresponds to the letter on the roof of the house. Then the children line up in descending order of perimeter values. The result is the word “Harbor”.

§

The Lion Cub and the Turtle lay on the beach and sang a song:

“I’m lying in the sun, I’m looking at the sun.

I lie and lie and look at the sun.”

At 12 o’clock in the afternoon the radio said that the weather would be sunny for the next three days. Do friends need sunglasses after 36 hours?

Select:
Yes No Explain your answer
_________________________________

: OOD summary of the applique “friends for tumbler. learning to cut circles”

Natalia Sedova

OOD summary for the application “Friends for Tumbler. Learning to cut circles”

Theme « Friends for Tumbler
»

Program content

Problems

Educational
:

• Teach children to cut out a circle
from a square by cutting corners

• Improve your child’s skills in applique

Educational
:

• Develop coordination, creativity, color perception and accuracy

Educational
:

• Cultivate interest in applications

Methods and techniques
: interesting moment, literary word (riddle about tumbler
, game technique (let’s make friends for the tumbler
, examination tumbler
, verbal methods and techniques (instructions, comments, etc.)

Introductory part
: communicating the purpose and objectives of the task, examining the toy, repeating safety precautions when working with scissors, repeating the rules of gluing

Main part
: individual instructions and explanations

Preliminary work
: didactic game for determining the shapes of objects, conducting classes in drawing and modeling tumbler
, learning songs and poems about tumbler
.

Materials and equipment
: toy – tumbler
, tassels, oilcloths, coasters according to the number of children; red squares with sizes 7×7, 4×4 and 2×2 according to the number of people, white squares with sizes 3×3, album sheets and scissors according to the number of people, colored paper in green, yellow, blue, light blue, black, brown for decorating a matryoshka doll according to the number of children.

-Children, a Guest came to us today. But to find out who it is, you need to solve the riddle. Listen to me carefully
:

This toy doesn’t like to sleep at all,

You put it down, it gets up again,

Beautiful cutie

Called.

( Tumbler
)

– That’s right, children! Tumbler came to visit us
. She wants us to help her. She lives alone in a toy house, and Tumbler is bored there
. How can we help her?

– Make her tumbler friends
!

– Exactly! Look closely at the tumbler
. What parts does the tumbler consist of
?

(Head, body, two arms)

– What figure do the toy’s body parts resemble? (On circle
)

– Note the circles
, are they the same or different? (Various)

– What size are they? (Torso from the largest circle
, the head is from the middle one, and the arms are from the small ones)

-What color is the face of the tumbler
? (White)

-And what else does the tumbler have?
? (Eyes, hair, buttons.)

-You liked tumbler
?

-Let’s make friends for her
?

This applique
we show it to the children for examination before starting work on application
.

– But first I will show you how to get a circle from a square
. circle has no corners
, which means that for the square to turn into a circle, the corners need to be cut off
. I’ll start cutting out a circle
from the middle of one side of the square, I will smoothly round
corner to the middle of its other side, so that the corner falls off. You will get something like this, quite even, circle
.

– Before you start working on applique
, let’s remember how to hold scissors correctly
: the thumb and middle fingers of the right hand are inserted into the rings of the scissors, the index finger supports them from below, the ends of the blades are directed away from you, forward.

Scissors must not be brought to the face, left with open blades, or thrown. Teach how to properly pass scissors to another person
: hold by the closed blades and pass the rings forward.

Don’t forget that you first need to lay out the items, only then start gluing.

Do you remember how to apply glue correctly?

(From center to edges)

– Now let’s get to work.

-Look what we got tumblers
. How beautiful and elegant they all are.

Now our tumbler will not be bored
.

After all, she has so many friends
!

How to make three-dimensional geometric shapes from paper (diagrams, templates)?

Here are a few patterns that can be used to make three-dimensional geometric shapes.

The simplest is the tetrahedron.

It will be a little more difficult to make an octahedron.

But this three-dimensional figure is a dodecahedron.

Another one is the icosahedron.

More details about the production of three-dimensional figures can be found here.

This is what three-dimensional figures look like not assembled:

And this is what the finished ones look like:

You can make many original crafts from volumetric geometric shapes, including gift wrapping.

So that children can better remember what geometric shapes are and know what they are called, you can make three-dimensional geometric shapes from thick paper or cardboard. By the way, you can use them to make beautiful gift wrapping.

The most difficult thing is to develop and draw developments; you need at least basic knowledge of drawing. You can take ready-made scans and print them on a printer.

To keep the fold line straight and sharp, you can use a blunt needle and a metal ruler. When drawing a line, the needle must be bent strongly in the direction of movement, almost laying it on its side.

This is a development of a trihedral pyramid

This is a development of a cube

This is the development of an octahedron (tetrahedral pyramid)

This is the development of a dodecahedron

This is the development of an icosahedron

Here you can find templates for more complex figures (Platonic Solids, Archimedean Solids, polyhedra, polyhedra, different types of pyramids and prisms, simple and oblique paper models).

By the way, to calculate the parameters of the pyramid, you can use this program.

By making three-dimensional figures from paper yourself, you can not only use them for entertainment, but also for learning.

https://www.youtube.com/channel/UCQRYdu-8IU0hbWCXFOe7BhA

For example, you can clearly show your child what a particular figure looks like and let him hold it in his hands.

Or you can print out diagrams with special symbols for training purposes.

So I suggest below that you familiarize yourself with the dodecahedron symbol, both simple and with small drawings that will only attract the baby’s attention and make learning more fun and entertaining.

The cube diagram can also be used to teach numbers.

A pyramid diagram can help you learn the formulas that apply to a given figure.

In addition, I suggest you familiarize yourself with the diagram of the octahedron.

The tetrahedron diagram will also help you learn colors.

As you understand, the above templates must be printed, cut out, folded along the lines, and glued along special narrow strips adjacent to selected sides.

Before you start making three-dimensional geometric figures, you need to imagine (or know what it looks like) the figure in 3D dimension: how many faces does this or that figure have.

First you need to correctly draw a figure on paper along the edges that must be connected to each other. Each shape has edges that have a specific shape: square, triangle, rectangle, rhombus, hexagon, circle, etc.

More interesting articles about paper: