COMPOSITION OF A NUMBER FROM 2 NUMBERS LESS THAN THIS NUMBER
In terms of preparing children for the activity of calculation, it is necessary to introduce them to the composition of a number from 2 smaller numbers. Children are introduced not only to decomposing a number into 2 smaller numbers, but also to obtaining a number from 2 smaller numbers. This helps children understand the features of a sum as a conditional combination of 2 terms.
Children are shown all the options for the composition of numbers within the heel.
The number 2 is 1 and 1,
- 3 is 2 and 1, 1 and 2,
4 is 3 and 1, 2 and 2, 1 and 3,
5 is 4 and 1, 3 and 2, 2 and 3, 1 and 4.
The teacher lays out 3 circles of the same color in a row on a typesetting canvas, asks the children to say how many circles there are, and indicates that in this case the group is made up of 3 red circles: 1, 1 and 1 more. “A group of 3 circles can be made up differently,” says the teacher and turns the third circle back. “How is the group composed now?” - asks the teacher. Children answer that the group is made up of 2 red circles and 1 blue circle, and in total - of 3 multi-colored circles.
The teacher concludes that the number 3 can be made up of the numbers 2 and 1, and 2 and 1 together make 3. Then he turns the second circle back, and the children tell him that the group is now made up of 1 red and 2 blue circles. Summarizing the children's answers in conclusion, the teacher emphasizes that the number 3 can be composed in different ways: from 2 and 1, from 1 and 2. This exercise clearly reveals the composition of the number, the relationship between the whole and the part, so it is advisable to begin introducing children to the composition of numbers with it .
To consolidate children's knowledge about the composition of a number from 2 smaller numbers, use a variety of exercises with objects and models of geometric shapes. Children are offered story-tasks, for example: “3 swallows were sitting on the top wire, 1 swallow moved to the bottom wire. How many swallows are there in total? How are they sitting now? How can they still sit?” (The swallows on the typesetting canvas are moved from wire to wire.) Or: “Vera was given 4 pencils. She shared with Anya. How could she separate the pencils? For the same purpose, they are given tasks: one child takes 3 pebbles (acorns) in both hands, and the rest guess how many pebbles he has in each hand; divide a group of 3 (4, 5) toys between 2 children; draw 2 types of shapes, for example circles and squares, 4 shapes in total; It is useful to look at number figures with children, in which the circles are divided into 2 groups.
Having completed one or another task, each time the children talk about what 2 groups the set is divided into, how many objects are included in it, and make a generalization about the composition of the number from 2 smaller numbers. For example, a child says: “I took 2 green and 1 yellow ribbon, and there are 3 ribbons in total. The number 3 can be made from 2 and 1; 2 and 1 together make 3."
It is important to teach children to construct answers in different ways: to go both from the particular to the general, and from the general to the particular: “In total, I drew 4 figures: 3 squares and 1 oval figure.”
It is equally important to encourage children to establish a relationship between the whole and the parts, that is, to draw a conclusion about the composition of the number: “The number 4 can be made from 3 and 1; 3 and 1 together make 4."
To lead children to a generalization, they are given the following tasks: the teacher shows a card on which from 3 to 5 objects are depicted, but he covers some of them and says: “There are 4 bunnies drawn on the card. Guess how many bunnies I closed.” The teacher takes 2 number figures, shows one of them, for example with 3 circles, to the children, and turns the second one to them with the reverse side and asks: “How many circles are on an inverted card, if there are 5 circles on 2 cards together? How did you guess?
You can encourage children to find examples in the group room of dividing numbers into 2 groups. For example, in a group room there may be 2 cabinets with toys and 1 with manuals, but 3 cabinets in total; 2 big bears and 3 small ones, for a total of 5 bears, etc.
Familiarity with the composition of a number from 2 smaller numbers provides the transition to teaching children to calculate.
Teaching children problem solving
Previous work allows children to move on to a new activity - calculations. Learning addition and subtraction is one of the main goals of first grade math. In kindergarten, mainly preparatory work is carried out. Children learn calculation by composing and solving arithmetic problems. This work allows you to understand the meaning of arithmetic operations and consciously resort to them, to establish relationships between quantities.
Preschoolers solve simple problems in one action, mainly direct ones, that is, those where the arithmetic operation (add, subtract) directly follows from the practical action with objects (added - it became more, subtracted - it became less). These are problems to find the sum and remainder. Children are introduced to cases of addition, when a smaller number is added to a larger number, they are taught to add and subtract first the number 1, then the number 2, and then the number 3. (Numerical material is used in the amount of the first ten.)
Stages of learning to solve problems. Teaching computational activities and introducing preschoolers to tasks is carried out in stages, giving children knowledge in small doses.
At the first stage, it is necessary to teach children to compose tasks and help them realize that the content of the tasks reflects the life around them. They assimilate the structure of the task, highlight the condition and question, and realize the special significance of numerical data. In addition, they learn to solve problems, consciously choose and formulate the action of addition or subtraction, and understand the meaning of what quantitative changes result from practical actions with the objects mentioned in the problem (more or less has become or remains).
Children learn to give a complete, detailed answer to the question of a problem. Numerical material during this period is either limited to the first heel, or within the second heel 1 is added or subtracted. At the second stage, children learn not only to reasonably choose the action of addition or subtraction, but also to correctly use the techniques of counting and counting by 1, adding or subtracting the number first 2, and later 3.
Teaching children how to write problems. In order for children to learn to identify the numerical data of a task, practical actions and understand the meaning of the quantitative changes to which they lead, complete substantive visualization is necessary. In the first lesson, the teacher gives the children a general idea of the problem, teaches them how to practically draw up a condition and pose a question to it. The main attention is paid to children’s understanding of the meaning of quantitative changes that certain actions with objects lead to. We connected 2 groups of objects: we added another to one group - there are more objects than there were. They separated so many objects, reduced them - there were fewer objects than there were.
The first 1-2 tasks are compiled by the teacher, describing in them the actions that the children performed according to his instructions: “Seryozha put 3 nesting dolls on the table. Vera brought 1 more matryoshka doll. How many nesting dolls did Vera and Seryozha bring in total?”
It is important to immediately attract children’s attention to the quantitative relationships between the numerical data of the problem: “How many nesting dolls did Seryozha put on the table? How many nesting dolls did Vera bring? Are there more or fewer nesting dolls after Vera brought 1 more? How many nesting dolls did Vera and Seryozha bring? Did we get more or fewer nesting dolls than Seryozha supplied? Why?"
The teacher says: “I made up a problem, and you solved it. Now we will learn to compose and solve problems.” They remember the problem that the children just solved. The teacher explains how the task is composed: “First, it is told how many nesting dolls Seryozha put on the table and how many nesting dolls Vera brought, and then the question is asked how many nesting dolls Seryozha and Vera brought in total. You answered that Seryozha and Vera brought 4 nesting dolls. Having solved the problem, you have answered the question correctly.”
Another task is created in the same way. It is important to emphasize the need to give an accurate, detailed answer to the question of the problem. If the child misses something, for example, he only talks about the number of objects (“4 nesting dolls”), the teacher notices that it is not clear which dolls he is talking about.
It is useful to give tasks to all children at the same time, asking them to come up with a problem about what they did. This creates better conditions for establishing quantitative relationships between numerical data. The teacher suggests: “Put 5 circles on the top strip of the card, and 1 circle on the bottom. Tell us what you did.” The teacher makes sure that the story is brief, coherent, and specific. He points out that such a story is not yet a task: “This is what we know. What can you find out? What should I ask?” As a rule, children do not feel the need to ask a question and often immediately give the answer: “In total, I added 6 circles.” The teacher reminds you that you just had to tell them what you did and think about what question to ask.
You can also use this technique. The teacher invites the children sitting on the right side to perform some action, for example, move 1 to 6 circles. Children sitting on the left are asked to think about what question they can ask a friend next to them. Each time, the teacher highlights numerical data and draws the children’s attention to the quantitative changes that occurred as a result of the practical actions described in the task conditions.
By encouraging children to make connections and relationships between numbers, they are taught to anticipate the outcome. After the children give an answer to the question of the task, the teacher asks: “Has it become more or less?” Compares the numerical data of the problem condition with the number obtained as a result of the action.
In the first two lessons, children should learn to elementary analyze problems.
Familiarization with the structure of the task. Children become familiar with the structure of the problem in the second or third lesson: they learn that the problem contains a condition and a question, and the presence of at least 2 numbers in the problem condition is especially emphasized.
The teacher, addressing the children, says: “I will now tell you what the task is about, and you will show everything that I will tell you about. Children placed 6 flags on the card on the left, and 1 flag on the right. How many flags did you put on the card? We have created a task. Let's repeat it and separate what we know from what we don't know. What do we know? The guys answer that they have 6 flags on the left and 1 flag on the right. “We know that. This is the condition of the problem,” explains the teacher. “What is asked in the problem?” “How many flags are there on the card,” the children answer. “We don’t know that. This is what you need to find out. This is a matter of task. Each problem has a condition and a question. What numbers are we talking about in our problem? What question did you ask? Let's repeat our task." The teacher invites one child to repeat the condition of the problem, and asks the other to pose a question, and clarifies what 2 parts the problem consists of. This makes up 2-3 tasks. Each time the teacher suggests dividing the task into a condition and a question. Sometimes he himself tells the children the condition and asks if everything is said in the problem, what is missing. You can repeat the task by role: one child tells the condition, another poses a question, the third gives an answer to the question of the task.
The teacher, participating in this game, changes roles with the children: some children come up with the condition of the problem, others pose a question, and the teacher gives an answer to the question of the problem, and vice versa.
It is important to reveal the arithmetic meaning of the question in the problem. To this end, when considering the next task, the teacher specifically focuses the children’s attention on the nature of the question. For example, the children told the condition of the problem: “Oli had 4 balls, and Dima gave her 1 more ball. This is the condition of the problem, this is what we know. What new things can you learn about balls? It turns out that you can find out a lot: what color the balls are, whether they are large or small. But the main thing is to find out their total number. So what question should be posed to the problem?” Children pose a question about the total number of balls. The problem question usually begins with the question how much? The teacher sometimes deliberately asks about the color, size, location of the object. Children notice the mistake and correct the teacher.
It is necessary to emphasize the importance of the numerical data of the problem. For this purpose, the following technique is recommended: when talking about the condition of the problem, the teacher omits one of the numbers or both numbers and asks: “Is it possible to solve the problem?” Children are practically convinced that the problem statement must contain at least 2 numbers.
After children learn to compose problems without visual material, to consolidate knowledge about the structure of the problem, it is useful to compare it with a story and a riddle: “Dad gave Tanya some beautiful pebbles, and her brother shared his pebbles with her. What did I tell you? Are there numbers here? Is there a question here? “Dad gave Tanya 8 pebbles, and her brother gave her 1 more pebble. How many pebbles were given to Tanya? What is this? As you may have guessed by now, this is a task. How is it different from a story?”
The children explain: “The story does not say how many pebbles dad gave Tanya and how many pebbles her brother gave her. And the problem says that dad gave Tanya 8 pebbles, and her brother gave her 1 more pebble. The problem contains 2 numbers. There is not a single number in the story and there is no question. There is a question in the problem.” - “Can we solve this problem? What do we know? It's good to compare problems with riddles. They select riddles in which numbers are indicated: One speaks, two look, and two listen (mouth, eyes, ears); Four brothers live under one roof (table). Together with the children, the teacher discusses what questions can be asked here: “What is this? How many legs does the table have? Etc. They find out that in the riddle you have to guess what object is being talked about, but in the task they want to find out about the quantity, how many objects will be obtained or left.
Comparing a problem with a riddle allows us to emphasize the arithmetic meaning of the problem question. It is useful to teach children to use a general method by which they can distinguish a problem from a story or riddle. You can analyze the text according to the following plan: “Are there numbers here? How many numbers are there? Is there a question here?
In conclusion, children are asked to transform a riddle, story, etc. into a task, and think about what needs to be done for this.
At this stage of training, in the first lesson, children solve addition problems, and in subsequent lessons, they solve addition and subtraction problems, and the addition and subtraction problems alternate. The answer is found based on an understanding of the connections and relationships between adjacent numbers.
Dramatization tasks. Depending on what visual material is used, the following tasks are distinguished: dramatization tasks, illustration tasks and oral tasks that children solve without relying on visual material (1). Much attention is paid to dramatization tasks. In them
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1. This division of tasks is arbitrary, since preschoolers solve problems only orally.
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actions that children observe, and most often directly perform themselves, are reflected. It is important that the numerical data is clearly presented here, and not the answer to the question.
First-graders sometimes cannot solve a problem simply because they do not understand the meaning of the words denoting this or that action: spent, shared, donated, etc. Therefore, in the preparatory group for school, special attention should be paid to revealing the semantic meaning of the words denoting certain actions. To this end, it is necessary to take into account what practical actions form the basis of the task. In this case, it is advisable to compare tasks for finding the amount and the balance that involve actions of the opposite meaning: came - left, approached - moved away, took - gave, raised - lowered, brought - carried away, arrived - flew away.
It is most important to compare words with the same root of opposite meaning, the meaning of which is difficult for children to grasp: gave (he) - gave (to him), gave (he) - gave (to him), took (he) - took (from him). During dramatization, actions are named.
From lesson to lesson, children's knowledge about actions with objects expands and becomes more precise, and the idea accumulates that tasks always reflect what is happening in life.
Illustration problems. Further development of independence and accumulation of experience in establishing quantitative relationships in various life situations are provided by illustration tasks based on pictures and toys.
First, children are shown pictures that present the theme, plot, and numerical data. The teacher creates the first problem based on the picture himself. It teaches children to look at a drawing, highlight numerical data and those life actions that led to a change in quantitative relationships. For example, in the picture there is a boy with 5 balls, he gives 1 ball to the girl. Looking at the picture, the teacher asks: “What is drawn here? What is the boy holding? How many balls does he have? What is he doing? If he gives the ball to the girl, will he have more or fewer balls left? What do we know? Match the problem conditions. What can I ask?”
At first, the teacher helps the children with leading questions, then gives them only a plan: “What is drawn? How many? What changed? Will it be more or less? And then the children independently look at the pictures and make up problems.
To compose problems, you can use pictures that show a general background (forest, river) or objects such as a vase, basket, spruce, apple tree. In the drawings, cuts are made into which flat color images of objects are inserted: cones, apples, balls, pears, cucumbers, boats, houses, trees, etc. The teacher inserts images of objects into the cuts so that numerical data is clearly presented.
Thus, in this case, only the topic and numerical data of the task are predetermined; the plot of the task can be varied by children.
By changing numerical data, the teacher encourages children to come up with problems for finding the sum and remainder of different content on the same topic, and to compose problems for any plot picture used for teaching storytelling.
Even more scope for developing imagination and independence is provided by composing problems about toys. The teacher encourages children to recall various facts from life that they have seen or read about. He gives an example - he comes up with several versions of problems on one topic. At the same time, he makes sure that children create tasks of varied content on one topic (not similar to one another) and reliably convey the facts of life, encourages independence and creativity. Children choose the most interesting problems and solve them. The material for composing tasks can be the environment, familiar objects. For example: “In a group room, 6 tables are in the middle and 1 table is against the wall. How many tables are there in the group?”, “The attendants placed 8 cans of water on the children’s tables, and 1 can on the teacher’s table. How many cans did the attendants put in?"
Oral tasks. Previous work creates the conditions for the transition to composing tasks without relying on visual material (oral tasks). There is no need to rush into writing oral tasks. Children, as a rule, easily grasp the scheme of a task, begin to imitate it and sometimes distort the truth of life, not understanding the logic of quantitative relationships that are the basis of the task.
After the meaning of the actions that need to be performed is well mastered, the children will be able to solve problems that are based on their experience. Tasks of various contents make it possible to clarify and consolidate knowledge about the environment, teach them to establish connections and relationships, that is, to perceive phenomena in their interconnections and interdependencies.
The teacher gives the children the first oral problems: “There were 5 glasses of water in the decanter, Seryozha drank 1 glass. How much water is left in the decanter?”, “For the holiday, the builders delivered 5 houses on one side of the street and 1 house on the other. How many houses did the builders deliver for the holiday?”, “The pioneers planted 6 apple trees and 1 pear tree near the school. How many fruit trees did the pioneers plant? In some cases, the following technique can be used as a transitional step to solving oral problems: the teacher tells the children the problem and invites them to depict the condition using circles, squares, or putting aside bones on an abacus.
Children should be taught to remember a task the first time and repeat it without expecting additional questions. When teaching children how to compose problems, the teacher determines the volume of numerical material. It is necessary to ensure that children correctly reflect life connections and dependencies in their tasks. Each time we should discuss whether it really happens as one of the children came up with.
Summary of GCD in the middle group. Digit and number 3
Lesson summary for children 4-5 years old “Number and number 3”
Author: Khashaeva Albina Aleksandrovna, teacher, Secondary School No. 74 (d/o), Moscow. Description of the material I offer you a summary of direct educational activities for children of the middle group on the topic “Number and number 3.” This is a summary of a lesson in which children become familiar with the concept of a number series, numerals from 1 to 3, and also learn to name them correctly and navigate them correctly. Purpose To familiarize yourself with the formation of the number 3 and the number of the same name;
teach to name the numerals 1, 2 and 3; arrange and count things from left to right with the right hand; learn to navigate in space. Materials
Materials for
the teacher : * ball * cards with numbers Materials for children : * cards with numbers 1, 2 and 3 * identical cubes - 6 pieces * cards with raspberries - 4 pieces * cards with strawberries - 4 pieces * number card Instead of the corresponding cards, you can take toys in the form of raspberries and strawberries.
Progress of the lesson
At the table (sitting) To begin, invite the children to place one cube. — How many dice did you bet? - Now show me this figure. — What figure did they show and why exactly? - Now to the right of the cube, make a column of 2 cubes. - How many cubes are there in this column? That's right, one, two, just two cubes. - What number should be used to denote 2 cubes? Show the number 2. - Now make another column of two cubes next to it and place another one on it. Are there more cubes? - Let's count together how many cubes are in the last column: one, two, three - 3 cubes in total. — The number 3 is indicated by the number 3 ( show
).
— Make sure that the 2nd and 3rd columns have an equal number of cubes - 2 each. Check the correctness of the task.
— What is the number of cubes in the 2nd column?
And in the 3rd? Place another cube in the 3rd column. How many cubes are there in the 3rd column now? Where are there more cubes: in the 2nd or 3rd column? Show the number that represents the number 3. Place the numbers 1 and 2 on the board.
- Where should the number 3 be? After what digit in the number series should it be placed?
Let's play the game
Game “What has changed?” On the board there is a row of numbers from 1 to 3. The guys close their eyes, the teacher removes the number 2. Opening their eyes, they name the “disappeared” number and put it in the right place in the row.
The next time, when the game is repeated, one of the children removes the number. For the first time, it is the number 2 that should be removed, because the children must see the boundaries of the number series. Physical education lesson
“Who is faster?”
— outdoor game Working with a card
The teacher allows the children to raise their right hand and tell individual children which hand they demonstrated.
After this he asks to demonstrate his left hand. Next, the children are asked to place their left hand on the card on the left side, and with their right hand to arrange the berries from left to right. — Place this many strawberries on the top “shelf” of the card. Indicates the number 2.
- How many strawberries are on the card?
Show me 2 strawberries. The guys make a circular gesture, circling two strawberries.
- Place the same number of raspberries at the bottom. How many raspberries did you put in? — What can you say about raspberries and strawberries? — Place another raspberry in the row. Which berries have become smaller? Which ones are there more? — What needs to be done to make them equal, 3 each? — What number should be placed next to raspberries and strawberries? Why this number?
Tips for parents
After the lesson, you can recommend to parents how to help children fix the number 3 in everyday life. For example, put 3 cups on the table and ask the question: “How many plates and spoons should be placed if there are 3 people eating?”
We recommend watching:
Summary of a comprehensive lesson on FEMP with elements of application in the middle group. Summary of a lesson in mathematics in the middle group of kindergarten. Synopsis of a game-based cognitive lesson on FEMP in the middle group. Synopsis of joint activities on mathematical development for children of the middle group.
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