## 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.

– 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 |

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 blackmistakes, 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

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. |

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 | 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 |

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 equalities43:8=[ ](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 = [ ] cm5. 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 | B | KO | |

5 | skill | 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.

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

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.

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, | B | KO | |

4 | ability to write numbers in ascending order | B | KO | |

5 | skill | 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 Solve | 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 Solve Execute | 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 Execute | 1 | ||||||||||||||||

8 | Consolidation of what has been learned. Pages for the curious. | Solve Execute | 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 | 1 | ||||||||||||||||

13 | Relationship between multiplication and division | Solve | 1 | ||||||||||||||||

14 | Even and odd numbers. | Play | 1 | ||||||||||||||||

15 | Multiplication and division table with number 3 | Solve | 1 | ||||||||||||||||

Relationship between proportional quantities (10 hours) | |||||||||||||||||||

16 | The relationship between the quantities price, quantity, cost | Analyze | 1 1 | ||||||||||||||||

17 | Relationship between quantities mass, quantity | ||||||||||||||||||

18 | The order of execution of actions in expressions with brackets. | Apply Calculate Use | 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 Act Explain Watch |

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 Execute | 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 Execute | 1 | ||||||||||||||||

Multiplication and division tables with numbers: 4, 5, 6, 7. (26 hours) | |||||||||||||||||||

26 | Multiplication and division table with number 4 | Play Apply | 1 | ||||||||||||||||

27 | Reinforcing what has been learned | 1 | |||||||||||||||||

28 | Problems to increase a number several times | Compare Act Explain Watch | 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 Act Explain Watch | 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 |

1 | |||||||||||||||||||

35 | Problems involving multiple comparisons of numbers | Compare Act Explain Watch | 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 | 1 | ||||||||||||||||

39 | Multiplication and division with numbers 5,6 | Solve Play | 1 | ||||||||||||||||

40 | Problems for finding the fourth proportional | Compose Act Explain Solve | 1 1 | ||||||||||||||||

41 | Solving problems to find the fourth proportional | ||||||||||||||||||

42 | Multiplication and division table with number 7 | Play Solve | 1 | ||||||||||||||||

43 | A page for the curious. Math games. | Find Play Find Solve | 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 |

1 | |||||||||||||||||||

47 | Project “Mathematical Tales” | Compose | 1 | ||||||||||||||||

48 | Area. Ways to compare figures by area. | . Compare Analyze Model Rate | 1 | ||||||||||||||||

49 | Units of area are square centimeter. | Play | 1 | ||||||||||||||||

50 | Area of the rectangle. | Calculate | 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 | 1 | ||||||||||||||||

53 | Solving examples of multiplication and division with the number 8 | Solve | 1 1 | ||||||||||||||||

54 | Solving problems of the studied types | ||||||||||||||||||

55 | Multiplication and division table with number 9. | Play |

1 | |||||||||||||||||||

56 | Units of area – square decimeter. | Compare | 1 | ||||||||||||||||

57 | Multiplication table. Consolidation. | Play | 1 | ||||||||||||||||

58 | Solving multiplication and division examples using the summary multiplication table. | Analyze Apply | 1 | ||||||||||||||||

59 | Unit of area – square meter | Compare Apply | 1 | ||||||||||||||||

60 | Solving problems with proportional quantities. | Analyze Apply | 1 | ||||||||||||||||

61 | A page for the curious. Problem solving. | Execute | 1 | ||||||||||||||||

62 | Repetition of what has been learned. | Solve Apply | 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 |

Apply | 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 Apply | 1 | ||||||||||||||||

71 | A page for the curious. | Execute | 1 1 | ||||||||||||||||

72 | Consolidation of the studied material. | ||||||||||||||||||

Shares (11 hours) | |||||||||||||||||||

73 | Shares. Formation and comparison of shares. | Solve Play Apply | 1 | ||||||||||||||||

74 | Circle. Circle. | Draw Apply | 1 1 | ||||||||||||||||

75 | Circle diameter. Problem solving. | ||||||||||||||||||

76 | Problems on finding the fraction of a number and a number from its fraction. | Find Solve Play Apply | 1 | ||||||||||||||||

77 | Time units – year, month, day | Describe Play Apply | 1 1 | ||||||||||||||||

78 | A page for the curious. Problems in pictures. | ||||||||||||||||||

79 | Repetition of what has been covered on the topic “Shares”. | Solve Play Apply |

1 | |||||||||||||||||||

80 | Test on the topic “Shares” | 1 | |||||||||||||||||

81 | Analysis of test work. Problem solving. | Execute Apply | 1 | ||||||||||||||||

82 | Solving word problems in three steps | Solve Apply | 1 | ||||||||||||||||

83 | A page for the curious. We are preparing for the Olympics. | Rate Execute | 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 Solve | 1 | ||||||||||||||||

85 | Reception of division of the form 80:20. | Solve | 1 | ||||||||||||||||

86 | Multiplying the sum by the number | Solve | 1 | ||||||||||||||||

87 | Solving problems in different ways | Solve Execute | 1 | ||||||||||||||||

88 | Multiplication techniques for cases of the form 23 ∙ 4, 4∙ 23 | Use | 1 1 | ||||||||||||||||

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

90 | Solving problems with quantities | Use Calculate Solve | 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 | 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 | 1 | ||||||||||||||||

94 | Solving division problems. | Solve | 1 | ||||||||||||||||

95 | Division techniques for cases of the form 69:3, 78:2 | Use Solve | 1 | ||||||||||||||||

96 | Relationship between numbers when dividing | Compare Solve | 1 | ||||||||||||||||

97 | Division check | Solve | 1 | ||||||||||||||||

98 | Division techniques for cases of the form 87:29, 66:22 | Solve Execute | 1 | ||||||||||||||||

99 | Multiplication check | Solve Execute | 1 | ||||||||||||||||

100 | Solving equations based on the connection between numbers in division | Compose | 1 1 | ||||||||||||||||

101 | Solving equations. Consolidation. | ||||||||||||||||||

102 | A page for the curious. Solving logical problems. | Execute Compose Conduct | 1 | ||||||||||||||||

103 | Repetition of what has been covered on the topic “Non-tabular multiplication and division” | Solve Execute | 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 Solve Compose | 1 | ||||||||||||||||

106 | Division with remainder | Explain Solve Compose Execute | 1 | ||||||||||||||||

107 | Division with remainder by selection method | Explain Solve | 1 1 | ||||||||||||||||

108 | Performing division with remainder in different ways | ||||||||||||||||||

109 | Solving examples of division with remainder. | Explain Solve | 1 | ||||||||||||||||

110 | Solving division problems with remainder | Explain Solve | 1 | ||||||||||||||||

111 | Cases of division with a remainder when the divisor is greater than the dividend | Explain Solve Execute | 1 | ||||||||||||||||

112 | Checking division with remainder | Explain Solve | 1 | ||||||||||||||||

113 | Repetition of what has been covered on the topic “Division with remainder” | Explain Solve Rate | 1 | ||||||||||||||||

114 | Test on the topic “Division with remainder | 1 | |||||||||||||||||

115 | Analysis of test work. Project “calculation problems” | Execute |

Compose Conduct | 1 | ||||||||||||||||||

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

116 | Oral numbering. Thousand | Count Analyze | 1 | ||||||||||||||||

117 | Formation and name of three-digit numbers. | Read Compare called Solve | 1 | ||||||||||||||||

118 | Counting unit digits | . Arrange Read | 1 | ||||||||||||||||

119 | Relationship between proportional quantities: consumption per day, number of days, total consumption. | Compose Act Explain Detect and install of a computational nature, made in the solution. | 1 | ||||||||||||||||

120 | Natural sequence of three-digit numbers | Arrange Install Group | 1 | ||||||||||||||||

121 | Increase and decrease the number by 10 times, 100 times. | Execute Read Increase and decrease | 1 | ||||||||||||||||

122 | Replacing a three-digit number with a sum of digit terms | Replace | 1 | ||||||||||||||||

123 | Representation of numbers as a sum of digit terms. | replace | 1 | ||||||||||||||||

124 | Comparison of three-digit numbers. | compare | 1 | ||||||||||||||||

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

Determine | 1 | ||||||||||||||||||

126 | A page for the curious. Roman numerals. | Read and Write Compare Read | 1 | ||||||||||||||||

127 | Units of mass: kilogram, gram | translate | 1 | ||||||||||||||||

128 | A page for the curious. Problem solving. | Execute | 1 | ||||||||||||||||

129 | Repetition of what has been learned on the topic “Numbering” | Arrange Install Group | 1 | ||||||||||||||||

130 | Test on the topic “Numbering” | 1 | |||||||||||||||||

131 | Analysis of test work. A page for the curious. Solving logic problems | Execute | 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 Use . Solve | 1 | ||||||||||||||||

133 | Different methods of calculations. | Execute | 1 | ||||||||||||||||

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

1 | |||||||||||||||||||

135 | Different calculation methods | Execute | 1 | ||||||||||||||||

136 | Techniques for written calculations | Execute | 1 | ||||||||||||||||

137 | Written addition algorithm | Apply | 1 | ||||||||||||||||

138 | Written subtraction algorithm | Apply | 1 | ||||||||||||||||

139 | Types of triangles. | Discriminate Apply | 1 | ||||||||||||||||

140 | Written addition and subtraction of three-digit numbers. | Apply | 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 Work your point of view, evaluate | 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 |

1 | |||||||||||||||||||

Multiplication and division (18 hours) | |||||||||||||||||||

145 | Techniques for oral multiplication and division. | Use Solve | 1 | ||||||||||||||||

146 | Different calculation methods | Solve | 1 | ||||||||||||||||

147 | Oral techniques for multiplying and dividing by round numbers | Solve Use | 1 | ||||||||||||||||

148 | Types of triangles | Solve Distinguish | 1 | ||||||||||||||||

149 | Method of written multiplication by a single-digit number. | Solve Use | 1 | ||||||||||||||||

150 | A page for the curious. Solving logic problems | Execute | 1 | ||||||||||||||||

151 | Algorithm for written multiplication of a three-digit number by a single-digit number | Solve Use | 1 | ||||||||||||||||

152 | Written multiplication of three-digit numbers by one-digit | Solve Use | 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 Use | 1 | ||||||||||||||||

156 | Algorithm for written division of a three-digit number by a single-digit number. | Solve Use | 1 1 | ||||||||||||||||

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

158 | Checking division by multiplication. | Solve Apply Use |

1 1 | |||||||||||||||||||

159 | Solving problems of the studied types. | ||||||||||||||||||

160 | Introducing the calculator. Consolidation of what has been learned. | Solve conduct | 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 Read Compare called | 1 | ||||||||||||||||

164 | Repetition. Addition and subtraction. | Solve Execute | 1 | ||||||||||||||||

165 | Repetition. Multiplication and division | Solve Apply Use | 1 | ||||||||||||||||

166 | Repetition. Rules on the order of actions | Solve Apply Calculate Use | 1 | ||||||||||||||||

167 | Final test | 1 | |||||||||||||||||

168 | Analysis of test work. Repetition. Geometric figures and quantities | Solve Calculate | 1 | ||||||||||||||||

169 | Repetition. Written single-digit multiplication and division | Solve Play Apply | 1 | ||||||||||||||||

170 | Repetition. Units of length, mass, time | Solve translate | 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 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 T. N. Sitnikova, I. F. Yatsenko Lesson developments in mathematics. 3rd class M: “VAKA”2021 |

Electronic tutorials: (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: |

– 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);

– 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

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 Characterize Call Compare Execute |

(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. |

Justify

calculation methods based on studied propertiesDistinguish

and

callcomponents 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 |

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 Compare 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

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 }

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. |

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

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.

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.

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

using: a) models; b) drawing square.

1

02.04.

^{}

107

^{ }

Angle. Right angle.

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

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.

21.0522.05.

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 |

^{}

Test

4

4

4Total

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