Part and whole tasks for preschoolers. Abstract of a lesson in mathematics

Abstract of OOD on FEMP on the topic "Part and whole ”for children of the older group.

Educational area: "Cognition".

Target: Formation of the concepts of part and whole.

Educational tasks:

1. To consolidate the skills of forward and backward counting within 10.

2. To consolidate the ability to make a whole from parts.

3. Continue to form the idea that the subject can be divided into two equal parts, learn to name the parts and compare the whole and the part.

4. Continue to acquaint with dividing a circle into 4 equal parts, to learn to name the parts and compare the whole and the part.

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Synopsis of organized educational activities on the topic "Part and Whole" for children of the older group.

Educational area: "Cognition" FEMP.

Theme: "Part and Whole".

Objectives of educational areas:

1. EDUCATIONAL TASKS:

Strengthen the knowledge of geometric shapes in children.
Strengthen the skills of forward and backward counting within 10.
Strengthen the ability to make a whole from parts.
Continue to form the idea that an object can be divided into two equal parts, learn to name the parts and compare the whole and the part.
Continue to introduce the division of a circle into 4 equal parts, teach how to name the parts and compare the whole and the part.

2. CORRECTIVE TASKS:

Development mental processes(concentration and switching of attention, increasing the volume of attention, formation mental operations- analysis, synthesis, generalization).
To achieve the activity of all functions of the eye during the lesson.
Develop oculomotor functions.
Promote the restoration of blood circulation in the area of the eye muscles.
Develop auditory and visual attention, memory, logical thinking.

3. EDUCATIONAL TASKS:

Build motivation learning activities focused on the satisfaction of cognitive interests and the joy of creativity.
To cultivate the ability to listen and hear the task the first time.
Maintain interest, attention, and good humor.
Cultivate interest in classes in the formation of elementary mathematical concepts.

DEMONSTRATION MATERIAL:

Flanelegraph;

pictures with the image of Masha and her friends, cake, plate, sausage;

excerpts from cartoon "Masha and the Bear" - "Once a Year" (44th episode);

song " in the afternoon birth and I, and I, and I, and I Congratulations you "(Barbariki);

the song "Happy Birthday to Me" ("Masha and the Bear");

sweet treat for children.

HANDOUT:

"Plate" (a circle of paper), cut into pieces;

"Sausage" (a strip of paper);

"Cake" (a circle of paper); scissors.

STROKE OOD:

1.Masha asks children to help prepare for her birthday

An excerpt from the cartoon "Masha and the Bear" (01: 36-02: 22), where a bear treats its guests with a cake.

What should we teach Masha? (share the cake equally for all guests) Can we help Masha prepare for her birthday? (Yes)

2. Visual gymnastics "Count the guests"

Direct and reverse counting within 10.

3. "Collect the plate"

Guys, Masha was in such a hurry that she broke all the plates. Let's help her and collect them. In front of each part of the circle. Make whole circles from the parts. (On children's tables, circles are divided into 3 parts)

4. "Divide the sausage in half"

Guys, Masha cooked sausages, but they turned out to be very large.

Let's help her divide each sausage in half so that they fit on our plates.

Before each strips (sausages).

How to divide a strip into two equal parts?

I have a paper strip, I will fold it in half, precisely trim the ends, iron the fold line and cut along the fold line.

How many pieces have I divided the strip into? (in two parts)

Each of the parts is called one half or half, because it was divided into two equal parts.

How many parts are there in a whole strip? (two)

How did we get 2 equal parts?

Which is bigger: a whole strip or one of its 2 equal parts?

Which is smaller: a whole strip or one of its halves?

5.Physical training "Happy Birthday"

Dance to the song "in the afternoon birth and I, and I, and I, and I Congratulations you »Barbariki

6. "Divide the cake into pieces"

Masha invited a bear and two wolves to her birthday.

Let's help Masha share the cake between friends and learn how to divide the circle into four equal parts.

How many guests do you need to divide the cake into? ( by 4).

What should be the parts? (equal, equal).

How many parts can we already divide the circle into? (on 2)

How many parts did it make? (2)

What is the name of each part? (half or one half)

Which is bigger: a whole circle or a part of it? (whole circle)

Which is smaller: part of a circle or a whole circle? (part of the circle)

How do you get four equal parts? That's right, you need to cut each half in half again.

How many parts did it make? (4)

What can you name each part? (one quarter.)

Which is bigger: a whole circle or one fourth? (whole circle)

Which is less: one fourth of a circle or one second of a circle?

Which is bigger: one second circle or one fourth?

Take circles on the tables. Think and try to divide the circle into four equal parts? (first into two parts, then again into two).

How many pieces did you get?

What is this part called? ( half).

What's more (less) whole cake or half?

Which part is it? ( fourth).

What is less (more) a quarter or a whole cake?

What are the parts?

Now, tell us what you think is important in this work (connect the sides evenly). Why is it important?

7. Masha's birthday

An excerpt from the cartoon "Masha and the Bear" (05: 52-06: 37), where Masha treats guests with a cake.

Was Masha able to divide the cake equally among the guests? (Yes)

8. Summary

Masha: Well done guys, your knowledge and skills helped me prepare for my birthday.

What did you do in class?

Which assignment did you like?

Thank you very much! I have prepared a surprise not only for my guests, but also for you!

Distributes refreshments (the song "Happy Birthday to Me" from the cartoon "Masha and the Bear" sounds).

ANGELA BATYROVA
"Part and Whole". Summary of a lesson in mathematics for the preparatory group

Abstract

Classes in mathematics. Preparatory group.

Educator: Batyrova A. V. MKDOU number 22

Software content.

1. The development of substitution actions by children « parts» and « whole» using strips of different sizes.

2. Development of ideas about affirmative sentences in children.

3. Development in children of ideas about the days of the week.

Material: Matryoshka, apple, knife

Dispensing material: Cards with days and weeks written on them, stripes, digital fans.

Course of the lesson:

The first part

Educator: Guys, this morning the postman handed me a letter. Let's see where this letter comes from. We received a letter from the city of Tsifrograd. And when they sent us a letter on February 1. What's the date today?

Educator: How many days the letter came to us, let's count.

Children: 5 days.

Educator: What day of the week is it today?

Children: Tuesday.

The second part

The game "Name the day of the week"

Educator: Now let's guys play a game.

Children are given cards with the names of the days of the week. The teacher asks to go to the board "First day of the week", monday, then next "Day of the week" asking what it is called, then the next one again, and so on. "days of the week" lined up, the teacher asks to raise their name (jump, sit down, stand on tiptoe) "Day of the week" that comes after some or before some. Then we invite all the children to disperse and, upon a signal, stand up again one after another, starting a row, for example, from Tuesday (Wednesday, Friday).

Educator: Well done guys, go to your seats. Guys, let's see what is in the envelope and who wrote the letter to us.

I read the letter: Hello guys, group number 9... Znayka writes to you from the city of Tsifrograd. In our city we learned that you are very smart guys, you think well. Try to solve my tasks. Best regards, Znayka.

Third part

Problem number 1. Two numbers - 1 and 3, quickly add them up and say the answer (4)

Problem number 2. Sitting on a tree 4 birds: 2 sparrows, the rest are crows. How many crows (2)

Problem number 3. There were 4 apples on the table. One of them was cut in half and placed on the table. How many apples are on the table? (4)

FIZMINUTKA.

Fourth part

New topic

Educator: Guys, here we have an apple - it is whole, and now I will cut it and get 2 unequal pieces - this is parts... So connecting 2 parts of an apple make a whole, and when I disconnect it turns out 2 apple parts... There are 2 strips in front of you, one long strip is whole, and 2 smaller is parts... Tell me, what kind of apple is it?

Children: Whole.

Educator: Show which strip we designate.

Children: One.

Educator: Guys, when I sever the apple. What do we get?

Children: 2 parts.

Educator: Show which strip we designate?

Children: Two.

Educator: Guys, look what is this?

Children: Matryoshka.

Educator: And what kind of nesting doll?

Children: Whole.

Educator: And if I split it, what will we get?

Children: 2 parts.

Educator: These parts what strip do we designate?

Children: Two stripes.

Educator: And when is it whole?

Children: One.

Educator: Well done!

Fifth part

The teacher says several sentences. He says that there are such proposals, when they ask something, they ask a question, for example: "How old are you? Are you 5 years old? " These are interrogative sentences. And there are such proposals when just something they say: “You are 6 years old. Your name is Olya. " The caregiver says that he will call different offers... When the sentence is interrogative, the children will raise such a sign (shows a question mark, it is called "question mark" when non-questioning (other types of offers are not named)- do not lift anything. Each time after completing the assignment, the children are asked to explain why the sentences are interrogative or non-interrogative. “In an interrogative in something, it is asked, in the intonation of a voice a question sounds, they want to know something, to ask.

Problem number 4. 7 candles burned. 2 candles were extinguished. How many candles are left?

Analysis: What did you learn today at occupations? What have you learned?

Promotion. Guys, let's make a circle. We celebrate the Day of Love in mid-February, let us now join hands and give warmth and love to each other. And now to our guests and I to you guys I will give you my warmth and love, (music sounds, I distribute valentines).

Dividing the whole into parts is an important direction in preparing preschoolers for computational activity, the ability to understand the meaning of problems and in solving them. With the need to divide children preschool age collide very early - in Everyday life, game. For example, who among us did not share an orange, tangerine, apple and so on.

Or, all children know that they have different toys, they take the necessary toy and act with it. In theory, this means that they have allocated a certain part of the toys. But this does not mean at all that they are able and can divide the whole into parts.

Dividing the whole into parts of the problem

Pedagogical experience suggests that without purposeful teaching of dividing the whole into parts, preschoolers will not form the concepts of "whole" and "part". If you take a deeper interest in this topic, it will become clear that the process of familiarizing children with the division of the whole into parts in a preschool educational institution consists of three main tasks:

Dividing a set into subsets;
Practical division of objects into parts by folding, cutting, based on measurement, etc.
Getting a whole from parts, i.e. establishing relationships between part and whole.

Solving the first problem - dividing a set into subsets - adults simply generalize the practical skills of children, helping them to practically combine many objects into one whole and showing how to do this. For example, collect toys in the amount of 8 pieces: 4 pyramids, 4 cars put them in one box and make a generalization - “toys, 8 pieces in total, take pyramids”, then ask: “what is more: pyramids and cars combined or only pyramids? " In this case, the parts will be 4 pyramids and 4 cars. Each part is smaller than the whole, since there were 8 toys in the box, and there were 4 cars left. Almost all children know how to do this, and verbal conclusion, conclusion must be taught to them, consolidated in practice in everyday life, play, in work.

Teaching children to divide into parts

Teaching preschoolers to divide the whole into parts, almost always goes unnoticed, but they understand what is required of them to do and learn this requirement.

For example, in everyday life - you have a set of vegetables for a salad (many), ask your kid to sort vegetables into groups (subsets): cucumbers, tomatoes, lettuce, etc. Ask your child to select from this set, for example, tomatoes that make up one part of the salad. Ask: "what is more tomato or other salad parts combined?" Next, say the conclusion - vegetables for a salad are one whole, and tomatoes are a part that should be put in a salad with other vegetables. In exactly this way, you can teach how to distinguish some dishes from its total number, pieces of furniture, work equipment, and so on.

Dividing the whole into parts is a game like "collect a bouquet for mom (grandmother, sister)".

A set of flowers is one whole (a bouquet), let your son or daughter single out from this set, for example, asters. Conclusion: a bouquet is a "whole", asters are a "part". If the bouquet consists of one type of flowers, then the flowers are distinguished by color. For example, select red from a bouquet of gladioli.

Bouquet - "whole", red flowers - "part". A didactic game with puppets will help you solve all software problems. For example, the doll Natasha came to visit the doll Katya, and Katya has only one piece of cake (one apple, pear, pancake, etc.). What should be done to treat Natasha? The answer is obvious, but an adult will tell you the conclusion. Work experience suggests that dolls must be matched with the same attractiveness. In the practice of kindergarten work, there were such cases when children shared pieces of different sizes and most of the treats were given to a doll that was more attractive in appearance.

The sequence of dividing the whole into parts

The practical sequential division of the whole into two parts occurs first, as a rule, using the example of geometric flat figures by folding them in half (2 equal parts), then the halves are divided in half, etc.

In this case, it is necessary to strictly ensure that the children bend the shape correctly, imposing one half on the other. The process of division itself occurs by tearing the whole or cutting with a clerical knife or scissors. In this case, the adult needs to ensure that the form given to the child is divided equally. There is one more point to which special attention should be paid, children usually speak not “in half”, but “in half”, and their parts often turn out not to be equal, but even, as they strive to do the work neatly and often cut irregularities. Therefore, you should pay attention to the child's speech and the correct use of mathematical terms. Exact science requires an accurate designation of the results of an action. By the same principle, various stripes, ribbons, etc. are divided.

Further, there is training in composing a whole from parts, and emphasis is placed on the concepts of "whole" and "part". At this stage, it is important to show the children how the part relates to the whole: the part is less than the whole, and the whole is more than the part. This is best learned in practice: children are given, say, 2 circles - one is divided into parts, and the other remains whole. By attaching a part of the circle to the whole, we find out that the part is less than the whole and vice versa. When the children understand the ratio of the whole and the part, they are asked to make up a whole object of a circle (square, rectangle) from parts, counting its parts. Together with adults, they learn and clarify that the number of parts is different, the more parts, the smaller the parts themselves. Later, offer the kids a geometric mosaic, which, by the way, children love to play. Pay attention to the fact that flat objects cannot be bent. A piece of tape, a strip of paper of the required length and so on can serve as a conditional measure. If you did not divide the object into equal parts, then using the method of superimposing parts to each other, specify which part is larger and which is smaller, and add these parts so as to get the whole object. The conclusion suggests itself - an object can be divided into unequal parts, but then it cannot be said that it is equally divided. We just say: "Divide the circle into 2 (4.8) parts."

Question: What does this knowledge give to preschool children? Is it necessary to give the concept of whole and part? Yes, it is necessary. Teaching children to divide the whole into parts allows them to see the relationship between the whole and the part and to assimilate the regularity in things and phenomena hidden for direct perception of objects (looking at the square, we do not think that it can be divided, but by dividing the square, we perceive it already by -other). In addition, knowledge of the relationship between the whole and the part contributes to the formation logical thinking, ability to find causal links, to judge by the total of the initial data. In a word, it will give a broad general developmental effect.

Didactic games for dividing the whole into parts

Dividing the whole into parts in kindergarten fixed with didactic games... These same games are good to use at home.

Fold a picture from parts - you can play with geometric shapes, you can collect cut pictures, plots, etc .;
Assemble the figure - figures are different in shape, color or color;
Place the dishes in their places ”- it is better to use when setting the table, playing with the doll;
Find the superfluous - for example, we divide the circle, but there is also a part of a triangle or other shape;
All equally - dividing apples, cake, pancake, etc .;
Connect the parts - you get the whole;
Whose face? - drawing up cut pictures;
Modeling animals - we sculpt an animal from parts;
"Fold the boards", "In which box?", "Who is the first?", "Arrange in order", etc.

A complete encyclopedia of modern educational games for children. From birth to 12 years old Voznyuk Natalia Grigorievna

"Part - whole"

Ask your child to guess which part of which object or creature you are calling:

propeller - helicopter, airplane;

wheel - car;

steering wheel - bicycle;

sail - boat;

carriage - train;

roof - house;

arrow - hours;

button - call;

page - book;

window sill - window;

heel - boot;

visor - cap;

keyboard - computer;

door - room;

rod - handle;

branch - tree;

petal - flower;

pine cone - tree;

seeds - plants;

the tail is a beast;

scales - fish;

wings - a bird;

shell - turtle;

the mane is a lion.

Or vice versa. You name the object, and the child names one or more of its parts:

house - roof, door;

ship - steering wheel, anchor;

bicycle - pedals, wheel;

magazine - pages, letters;

computer - mouse, keyboard;

coat - collar, sleeves, buttons;

refrigerator - ice, food;

kettle - lid, spout;

fishing rod - float, hook;

flower - petals, stamens, pollen;

tree - branches, bark, leaves;

mushroom - cap, leg;

beetle - legs, antennae, wings;

butterfly - wings, proboscis;

fox - tail, paws;

apple - peel, seeds;

head of cabbage - leaves, stump.

If the child finds it difficult to give an answer, help him, give your example or ask a leading question.

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Very often, younger students have difficulties in solving arithmetic problems. In order to understand the reasons for these difficulties, let's first understand what types of tasks exist. To begin with, we can distinguish two large groups of problems, depending on the way they are solved. These are problems that are solved using addition or subtraction, and problems that we will solve using multiplication or division. Children begin to get acquainted with the problems of the latter type in grade 3, when they study the multiplication table. Tasks for comparing the number of objects can be distinguished into a separate type. In such tasks there are necessarily words ON (?) LESS or MORE and questions (?) TIMES MORE or LESS. How to solve such problems will be discussed in a separate article.

You can also divide tasks into simple and complex, depending on the presence of intermediate questions and, accordingly, on the number of actions in the solution. Simple tasks are solved in one step, and in order to solve a complex task, several steps must be performed sequentially. Before dwelling in more detail on solving problems of a certain type, it should be remembered that any problem has a condition and a question. After the child has read the problem, be sure to invite him to re-read the question and repeat it in your own words. Thus, you will immediately make sure that the child understands what exactly needs to be found in the problem. Then discuss with your child what you need to know in order to be able to answer the question on the problem. Re-read the condition again and find out what is known for sure, and what else needs to be learned. This step is especially important when solving complex problems.

In order to briefly and clearly record all the data from the condition of the problem and its question, a short note or drawing of the problem should be made. Children are often reluctant to do this because it takes extra time and effort. When the child is already good at solving a certain type of problem, then a short note can be omitted, it is enough to write an explanation in each action. But if a child is just getting to know a new type of problem or solves such problems incorrectly, then a short note is simply necessary.

Moreover, in cases where the child does not understand the course of solving the problem, it is necessary to use not only a short note and a drawing, but also try to beat the condition of the problem so that the child is the main character in this problem. Often, children understand better the solution to the problem, acting with objects, so you can give counting sticks, matches, toothpicks and the like, let them put them in piles, connect them, remove or add objects, depending on the condition of the problem. But you should not use such solutions too often. It is much more important to explain the general principle of problem solving. And for this, the child must very clearly understand what a part and a whole are. By the way, these concepts will help in solving not only problems, but also equations.

Let's take a closer look at how to explain to a child what a part and a whole are. It is important for us that the child understands a part not only as a separate piece of something whole, but also in the meaning of a set and a subset. These terms themselves will be used only in grades 4-5, but a first grader is also quite capable of realizing the essence of these concepts, if explained on specific, available examples, using actions with objects.

This is very easy to do.

For example: place 4 red mugs and 3 mugs in front of the child of blue color... The mugs should be the same size and differ only in color. This is a prerequisite. Objects should differ in only one feature .. All these are circles. What is the difference? Divide the circles into groups. What bands did you get?

All circles are whole. The whole can be divided into parts. What parts have you divided all the circles into? (For red circles and blue circles). What is the whole and what is the part is the main question of the exercise.

Take circles of 3 colors of the same size and repeat the exercise. Then take circles of the same color in two or three sizes and repeat the task. Remember that the main goal of these exercises is for the child to clearly understand the concepts of whole and parts. The items for performing such tasks should be very diverse: buttons of the same size, but different in color or shape, and, moreover, there must be groups of completely identical buttons. Tea, dessert and table spoons, saucers, plates and cups - dishes and so on. Along the way, when performing these exercises, consolidate the classification of objects and repeat the words-generalizations and differentiation of objects (clothes and shoes, furniture and household appliances, passenger and freight transport, vegetables, fruits and berries, etc.).

It will be necessary to teach the child to answer the questions:

How, in one word, can all these objects be correctly named?

What parts can these items be divided into?

What shall we call the whole? What shall we call the part? Or what is the whole and what is the part?

As soon as you notice that the child can freely distinguish and name the whole and the parts, start using the same objects to add the parts and subtract the part from the whole. Now the main goal of learning is to understand and memorize two basic rules, on the basis of which you can solve any problems and equations for addition and subtraction.

The formula for these rules should be explained and learned:

1) To find the whole, you need to add all these parts: C = H + H

2) To find a part, you need to subtract another (known) part from the whole H = C - H

I will explain a little more about how to do this using an example with red and blue circles. What is the whole and what is the part? What needs to be done so that only red circles remain on the table? (Remove blue circles).

Remember the rule: To find one part, you need to subtract the other (known) part from the whole. What needs to be done so that all the mugs are on the table? (Put the red and blue circles together).

Remember the rule: To find an integer, you need to add all the parts.

Be sure to repeat these rules each time you exercise with different objects.

Now, let's see how to apply these rules to simple problems.

There were 3 sparrows and 4 titmouses on a branch. How many birds were there on the branch?
There were 2 cups and the same number of saucers on the table. How many dishes are on the table?
Nastya dried 3 maple, 4 oak and 2 birch leaves. How many leaves did Nastya dry in total?
7 birds were sitting on the tree, 3 flew away. How much is left?

Read the question again. What do you need to know a part or a whole?

Repeat the rule. What parts do we know and what do we know about them? (If you need to find the whole).
Or offer to name known part and the whole, if you need to find a part.

How to solve the problem?

Such, as a rule, do not cause difficulties. But the tasks given below turn out to be more difficult to solve, due to the fact that it is more difficult to present the conditions of the problem in the form of a picture or a film:

Ira had 9 new notebooks. When she had filled several such notebooks, she had only 6 pure notebooks left. The question is, how many notebooks did the girl Ira fill up?
When Vitya painted 5 pictures in the book, there are 3 of them left. How many pictures are in the book?

To analyze the problem, we start with a question. If the child does not quite understand the question, clarify it by asking: "Has Ira filled up all the notebooks or only a part?" or "The problem asks about all the pictures in the book, or only about a part of the pictures?" Then proceed according to the above algorithm.

_______________?______________
/ _____ sparrows _____ | ____ titmice ___ \
3 4

9 tetras .____________________
/ ___ completed ______ | _______ left _____ \
? 6

In such a drawing, the whole is signed from above, and parts from below. The drawing allows you to visualize the condition of the problem, and you should start using it already when solving simple problems. In the first grade, while the children count within 10, it is possible to lay as many cells as there are objects indicated in the task (for example, 4 sparrows and draw a straight line in 4 cells). But it is not worth dwelling on this for a long time, since when the numbers are more than 20, it will be impossible to postpone the same number of cells. A drawing will be especially necessary when solving complex problems. But this is a topic for another article.