Fascinating mathematics: tasks and exercises for preschoolers. Logic problems

Teaching mathematics in a playful way develops and shapes the child’s cognitive interest. It is best to develop an interest in this science before teaching it at school.

Interesting and exciting tasks and exercises in mathematics for preschoolers will help with this.

Developmental tasks can instill in a child a number of useful qualities: perseverance, the ability to set goals and plan, follow rules, the ability to analyze, weigh the result, and give reasons.

Finding ways to solve non-standard problems helps stimulate creative and research activity.

Working with developmental math tasks is not at all difficult; parents are quite capable of handling it. But in order for the child to get the maximum benefit from classes, it is necessary to adhere to the rules of their organization:

Challenges help children understand that every potential challenge may contain a trick or a double meaning. To find the correct answer, you need to concentrate and look at the puzzle from different perspectives.

Before you begin the task, you need to give recommendations on how to complete it:

• Take into account the level of development and age characteristics of the child.
• For example, the attention span of preschoolers is lower than that of younger schoolchildren. They can maintain attention while doing an activity of interest for 30-50 minutes. If your baby's attention suddenly wanes, there is no need to force him to continue studying.
• Based on the interests of the child.
• Don't overuse hints.
• If a child cannot find a solution to a problem, there is no need to say the correct answers every time, you need to encourage him to search and be patient. To keep the child’s interest, an adult can offer a partial hint. As a rule, a preschooler does not manage to complete all tasks the first time, but this has positive aspects - if a child is forced to do something several times, the development of the volitional sphere occurs.
• Do not limit yourself to one type of exercise, but use a variety of material.
• This will help in diversified development. When organizing classes, you need to pay attention to training spatial-temporal relationships, counting skills, imagination, logical thinking, etc.
• Use different forms of organizing classes: individual work, games in pairs or team competitions.
• Proceed from the gradual complication of tasks.
• Use visual aids that will attract the child’s attention: bright pictures or photographs, images of favorite fairy-tale characters.
• Do not skimp on praise if the baby deserves it.
• Encourage independence.

Work with your child comprehensively. As you develop your math skills, also develop your reading skills. Find out from our article.

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Types of tasks in mathematics

Entertaining mathematical tasks include games, riddles, comic problems, puzzles, and exercises with geometric shapes. All of them are aimed at developing reaction speed, logical and innovative thinking, resourcefulness, and imagination.

Since preschool age is divided into junior and senior, tasks should be selected taking into account the degree of difficulty. The younger preschool age covers the age period of 3-4 years, and the older one - 5-7 years. Of course, the breakdown of tasks by age is conditional, since everything depends on the pace of development of the offspring, which is what we need to focus on.

Math games

Mathematical games include tasks that are based on the analysis of logical relationships and patterns.

To find the answer, you need to analyze the conditions of the problem, familiarize yourself with its content and understand what needs to be done.

The search for a solution involves the use of mental operations: analysis, synthesis, generalization.

A game “Make a sequence of numbers”. The child is given mixed cards with numbers from 1 to 5 or 10, and he must arrange them in the correct sequence.

Exercise . The child receives a form with pictures next to which there are numbers. You need to count the objects in the picture and circle the corresponding number.

Exercise . You need to draw the specified number of dots on the insect’s body.

Games for older preschoolers

A game "Compare the number". The adult asks the child to name the number, taking into account the conditions: it must be more than 5, less than 8. For each correct answer, you can give a sun or a flag.

Exercise . On a special form there are a series of pictures on the left, and examples on the right. It is necessary to choose a suitable example for the picture.

Mathematical problems for ingenuity

Puzzles are recommended for children of older preschool age. The most common are geometric problems with counting sticks. They are called geometric because the task is based on the composition and transformation of various figures. To complete the task, you need to prepare counting sticks and chart tables with images of figures.

You need to try to choose tasks with different conditions and solutions in order to stimulate the baby’s search activity.

Problems for preschoolers

A picture depicting some object is placed in front of the child. It could be a house, a bench,... The child must, focusing on the sample, put together a similar object from sticks. Subsequently, you can complicate the task by asking the child to add up the shown picture without having an example in front of his eyes, that is, from memory.

"Shape Transformation". The task is carried out in 2 stages. First, the adult shows the child a figure and asks him to make the same one out of sticks. Instructions for the second stage: you need to determine which and how many sticks should be removed to create a different figure.

The child needs to analyze the presented geometric shapes, imagine what the final result will look like and choose an answer.

The child is given an image of a complex geometric figure consisting of many details; he must count how many triangles, rectangles, and squares are in the figure.

Games for recreating figurative images from geometric shapes

Games with geometric shapes to compose various objects and animals are very useful for the development of analytical thinking and sensory skills. To conduct classes, you need to stock up on a set of shapes: a circle, a triangle, a rectangle or a square.

Games for younger preschoolers

“Make a picture.” The child is given a standard set of figures and simple pictures depicting various objects. Based on the example, the child must put together the pictures.

Games for older preschoolers:

“Make a silhouette of an animal or insect”. To play the game, take a circle, which is divided by lines into smaller and heterogeneous parts, and cut. Then, from the received parts of the circle, the children try to make a picture, and they are not given specific instructions - they must act according to their own plan.

"Items made from cubes." Looking at the image of the object, the preschooler builds the same one from cubes.

Riddles, comic problems, entertaining questions

Children meet riddles, comic problems and entertaining questions with extraordinary enthusiasm. They are able to activate the child’s mental activity, develop skills to notice the main and essential properties, separating them from the secondary ones.

Tasks belonging to this category are excellent for use at the beginning of a lesson to prepare the child for intellectual work and conduct mental gymnastics.

Comic tasks can create a favorable emotional background and lift your spirits. As a way to relax and switch attention, tasks can be used in the middle of the lesson.

Mathematical riddles are intricate questions or descriptions of some object or phenomenon that a child must guess. Since the riddles are mathematical, numbers will definitely appear in them, and computational actions will need to be performed.

Comic problems are game tasks with a mathematical meaning, to solve which you need to use ingenuity and resourcefulness, and in some cases have a sense of humor. It is recommended to study according to them from the senior preschool age. The content of the tasks is unusual, since along with the main characteristics they include secondary ones. It turns out that the search for an answer is, as it were, disguised by other conditions.

Examples of humorous problems

• 2 cars drove 5 km. How many kilometers did each car travel?
• If a stork stands on one leg, then it weighs 4 kg. How much will a stork weigh when it stands on 2 legs?
• What is heavier: 1 kg of concrete or 1 kg of wool?

Interesting questions

They are short questions asking people to count something.

• How many ears do three mice have?
• You, me, you and me. How many of us are there?

Games, mathematical entertainment

Games and mathematical entertainment are a great way to diversify the forms of work. If you choose a game with two participants, the child’s interest will increase due to the spirit of competition.

Games for younger preschoolers

“Finish the drawing.” The child is given a sheet of paper with geometric shapes depicted on it. The task is to draw a small picture based on the desired geometric figure. For example, from a circle you can draw a snowman or a clock, from a square - a TV, a briefcase.

An example of a game for older preschoolers

"Houses". For this game you will need 20 images of houses with 10 windows. You can judge the apartments by the presence of curtains on the windows. The essence of the game is to compare the houses with each other: how many residents need to be moved in so that all the apartments are fully occupied, how many residents need to be removed from the house so that the same number of apartments are occupied in it as in the fifth house.

Universal games

The older the child, the more numbers there can be.

Books on mathematics for preschoolers

1. A. Boloshistaya “Mathematics around you.” The workbook includes tasks to develop mathematical thinking. Intended for children 4-5 years old.
2. K.V. Shevelev “Mathematics for preschoolers.” The workbook consists of developmental tasks addressed to children aged 6-7 years. The classes are designed to prepare you for school.
3. L.G. Peterson “One is a step, two is a step.” The series of manuals is designed to develop a mathematical way of thinking, imagination, and the ability to analyze.
4. M. Druzhinin “The Big Book of Leisure.” The book includes rebuses, riddles, puzzles. The tasks are designed to develop analytical thinking, broaden your horizons, and activate your imagination.
5. O. Zhukova “Mathematics for preschoolers.” The coloring book contains game exercises that will teach your child to count to 10 and help develop perception and logic.

Arithmetic is the most basic, basic section of mathematics. It originated from people's needs for counting.

Mental arithmetic

What is called mental arithmetic? Mental arithmetic is a method of teaching quick counting that comes from ancient times.

Currently, unlike the previous one, teachers are trying not only to teach children how to count, but also trying to develop their thinking.

The learning process itself is based on the use and development of both hemispheres of the brain. The main thing is to be able to use them together, because they complement each other.

Indeed, the left hemisphere is responsible for logic, speech and rationality, and the right hemisphere is responsible for imagination.

The training program includes training in operation and use of tools such as abacus.

The abacus is the main tool in learning mental arithmetic, because students learn to work with them, move the dominoes and understand the essence of the calculation. Over time, the abacus becomes your imagination, and students imagine them, build on this knowledge and solve examples.

Reviews about these teaching methods are very positive. There is one drawback - the training is paid, and not everyone can afford it. Therefore, the path of a genius depends on one’s financial situation.

Mathematics and arithmetic

Mathematics and arithmetic are closely related concepts, or rather arithmetic is a branch of mathematics that works with numbers and calculations (operations with numbers).

Arithmetic is the main section, and therefore the basis of mathematics. The basis of mathematics is the most important concepts and operations that form the basis on which all subsequent knowledge is built. The main operations include: addition, subtraction, multiplication, division.

Arithmetic is usually studied at school from the very beginning of education, that is. from first grade. Children master basic mathematics.

Addition is an arithmetic operation during which two numbers are added, and their result is a new one - the third.

a+b=c.

Subtraction is an arithmetic operation in which the second number is subtracted from the first number, and the result is the third.

The addition formula is expressed as follows: a - b = c.

Multiplication is an action that results in the sum of identical terms.

The formula for this action is: a1+a2+…+an=n*a.

Division- This is the division of a number or variable into equal parts.

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Teaching arithmetic

Arithmetic is taught within the school walls. From the first grade, children begin to study the basic and main section of mathematics - arithmetic.

Adding numbers

Arithmetic grade 5

In the fifth grade, students begin to study topics such as fractions and mixed numbers. You can find information about operations with these numbers in our articles on the relevant operations.

A fractional number is the ratio of two numbers to each other or the numerator to the denominator. A fractional number can be replaced by division. For example, ¼ = 1:4.

Mixed number– this is a fractional number, only with the integer part highlighted. The integer part is allocated provided that the numerator is greater than the denominator. For example, there was a fraction: 5/4, it can be transformed by highlighting the whole part: 1 whole and ¼.

Examples for training:

Task No. 1:

Task No. 2:

Arithmetic 6th grade

In 6th grade, the topic of converting fractions to lowercase notation appears. What does it mean? For example, given the fraction ½, it will be equal to 0.5. ¼ = 0.25.

Examples can be compiled in the following style: 0.25+0.73+12/31.

Examples for training:

Task No. 1:

Task No. 2:

Games for developing mental arithmetic and counting speed

There are great games that promote numeracy, help develop math skills and mathematical thinking, mental counting and counting speed! You can play and develop! You are interested? Read short articles about games and be sure to try yourself.

Game "Quick Count"

The "quick count" game will help you speed up your mental counting. The essence of the game is that in the picture presented to you, you will need to choose a yes or no answer to the question “Are there 5 identical fruits?” Follow your goal, and this game will help you with this.

Game "Mathematical Comparisons"

The Math Comparison game will require you to compare two numbers against the clock. That is, you have to choose one of two numbers as quickly as possible. Remember that time is limited, and the more you answer correctly, the better your math skills will develop! Shall we try?

Game "Quick addition"

The game “Quick Addition” is an excellent quick counting simulator. The essence of the game: a 4x4 field is given, that is. There are 16 numbers, and above the field is the seventeenth number. Your goal: using sixteen numbers, make 17 using the addition operation. For example, above the field you have the number 28 written, then in the field you need to find 2 such numbers that in total will give the number 28. Are you ready to try your hand? Then go ahead and train!

Development of phenomenal mental arithmetic

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Preschoolers solve this problem in 5-10 minutes. Some programmers take up to an hour to complete it. But many people, after writing several sheets of paper, give up.

Parking space number

It usually takes a six-year-old child no more than 20 seconds to solve this problem. But it often confuses unprepared adults. So what number is hidden under the car?

Riddle for a genius

A genius finds a solution in 10 seconds. Bill Gates - in 20 seconds. Harvard University graduate - in 40 seconds. If you found the answer in 2 minutes, then you belong to the 15% of most gifted people. 75% of people are unable to solve this problem.

Ruler of the Island

The autocratic ruler of one island wanted to prevent aliens from settling on the island. Wanting to maintain the appearance of justice, he issued an order according to which anyone wishing to settle on the island must, after thinking carefully, make any statement, and after a preliminary warning that his life depended on the content of this statement. The order read: “If the alien tells the truth, he will be shot. If he tells a lie, he will be hanged." Can an alien become an island resident?

Project approval

According to the agreement, the procedure for approving a new project in the development of which institutions A, B, and C participate is as follows: if A and B participate in the approval first, then institution B must also participate. If approval occurs first in institutions B and C, Institution A also joins. The question is: are such cases possible when approving a project when only institutions A and B would take part in it, while the participation of institution B would not be necessary (while maintaining the agreement on the procedure for approving projects)?

Two tribes

There are two tribes living on the island: well done. Those who always tell the truth, and liars who always lie. The traveler met the islander, asked him who he was, and when he heard that he was from a tribe of fellows, he hired him as a guide. They went and saw another islander in the distance, and the traveler sent his guide to ask him to what tribe he belonged. The guide returned and said that he claimed to be from a tribe of fellows. The question is: was the guide a good guy or a liar?

Aborigines and Aliens

Three people stand before the court, each of whom can be either an aborigine or an alien. The judge knows that natives always answer questions truthfully, but aliens always lie. However, the judge does not know which of them is a native and which is an alien. He asks the first one, but does not understand his answer. Therefore, he asks first the second, and then the third, what the first answered. The second one says that the first one said he was an Aborigine. The third says that the first called himself an alien. Who were the second and third defendants?

Beetle on tape

The beetle went on a journey. He crawls along a tape, the length of which is 90 centimeters. At the other end of the ribbon, two centimeters from the end, is a flower. How many centimeters will the beetle have to crawl to the flower: 88 or 92 (provided that it crawls all the time on one side and only at the end can it cross the end of the tape to the other side)?

Purchase

Marina spent a long time choosing which jug to buy. Finally I chose. The saleswoman put the purchase in a box. What did Marina buy? How many jugs did the saleswoman put on the shelves, which ones they were on before?

Tourist

The tourist was walking towards the lake. He reached a crossroads, from where one road led to the right and the other to the left; one went to the lake, the other did not. There were two guys sitting at a crossroads, one of them always told the truth, the other always lied. Both of them answered either “yes” or “no” to any question. The tourist knew all this, but he did not know which of them was telling the truth and which was lying; he also did not know which road led to the lake. The tourist asked only one question to one of the guys. What kind of question was it, since he knew from the answer which road led to the lake?

broken window

During the break there were nine students left in the class. One of them broke the window. The following answers were received to the teacher's question:

How many triangles? What team?

Read carefully and do not write anything down: Torpedo tops the standings, Spartak is in fifth place, and Dynamo is right in the middle between them. If Lokomotiv is ahead of Spartak, and Zenit takes place immediately behind Dynamo, then which of the listed teams is in second place? You are given 30 seconds to think.

Project approval procedure

The enterprise has three workshops - A, B, C, which have agreed on the procedure for approving projects, namely: 1. If workshop B does not participate in the approval of the project, then workshop A does not participate in this approval. 2. If workshop B takes part in approval of the project, then workshops A and C take part in it. The question is: under these conditions, is workshop C obliged to take part in the approval of the project when workshop A takes part in the approval?

An evening walk

Which of these nine mustaches went for an “evening walk”?

7 buttons

Which of the 7 buttons should you press? For the bell to ring? It is recommended to find the path mentally.

Make a table

In the Moscow semi-final of the European Basketball Championship, held in Soviet times, the places were distributed as follows: USSR - 14 points, Italy and Czechoslovakia - 12 each, Israel - 11, Finland - 10, East Germany and Romania - 9 each and Hungary - 7 points. According to the regulations. Each team received 2 points for a win, 1 point for a loss, and 0 points for a no-show. No draws were allowed. Make a summary table of the results of the games if you know that the Finnish team won against the Italian team and lost to the Romanian team.

Explanation is inevitable

On Tuesday at about 10 o'clock in the morning a stranger burst into Inspector Warnicke's room. He was extremely excited. His hands were shaking, his tousled hair stuck out in all directions. A few minutes later, having lit a cigarette and calmed down, the visitor began his story: - This morning I returned from vacation. I had to shake on the train all night. I didn’t get enough sleep and, when I came home, I decided to lie down on the sofa. Because of fatigue, I did not immediately notice that the piano had disappeared from the room, and the coffee table and armchair had been moved out of place. On this piece of paper I drew a plan for the arrangement of furniture in the room before I left. “Here’s what, dear,” said Inspector Warnicke, quickly glancing at the drawing, “First of all, it’s absolutely clear to me that you didn’t have a piano at all.” Now let's find out why you needed this lie. Why did Inspector Warnicke doubt the veracity of the visitor's story?

LOGIC PROBLEMS

Logic problems, just like mathematics, is called “mental gymnastics.” But, unlike mathematics, logic problems is an entertaining gymnastics that allows you to test and train your thought processes in a fun way, sometimes from an unexpected perspective. Solving them requires intelligence, sometimes intuition, but not special knowledge. Solving logic problems consists in thoroughly analyzing the conditions of the problem, unraveling the tangle of contradictory connections between characters or objects. Logic problems for children- these are, as a rule, whole stories with popular characters, which you just need to get used to, feel the situation, visually imagine it and catch the connections.

Even the most difficult logic problems do not contain numbers, vectors, functions. But a mathematical way of thinking is necessary here: the main thing is to comprehend and understand the condition logical problem. The most obvious solution on the surface is not always the right one. But most often, solving a logic problem turns out to be much simpler than it seems at first glance, despite the confusing condition.

Interesting logic problems for children in a variety of subjects - mathematics, physics, biology - arouse their increased interest in these academic disciplines and help them in their meaningful study. Logic problems on weighing, transfusion, tasks on non-standard logical thinking will help in everyday life to solve everyday problems in a non-standard way.

In the process of solving logic problems you will get acquainted with mathematical logic - a separate science, otherwise called “mathematics without formulas”. Logic as a science was created by Aristotle, who was not a mathematician, but a philosopher. And logic was originally part of philosophy, one of the methods of reasoning. In his work “Analytics,” Aristotle created 20 patterns of reasoning, which he called syllogisms. One of his most famous syllogisms is: “Socrates is a man; all people are mortal; So Socrates is mortal." Logic (from ancient Greek. Λογική - speech, reasoning, thought) is the science of correct thinking, or, in other words, the “art of reasoning.”

There are certain techniques solving logical problems:

way of reasoning, with the help of which the simplest logical problems are solved. This method is considered the most trivial. During the solution, reasoning is used that consistently takes into account all the conditions of the problem, which gradually lead to a conclusion and the correct answer.

table method, used in solving text logic problems. As the name suggests, solving logical problems involves constructing tables that allow you to visualize the conditions of the problem, control the reasoning process, and help you draw correct logical conclusions.

graph method consists in sorting through possible options for the development of events and the final choice of the only correct solution.

flowchart method- a method widely used in programming and solving logical transfusion problems. It consists in the fact that first operations (commands) are allocated in the form of blocks, then the sequence of execution of these commands is established. This is a flowchart, which is essentially a program, the execution of which leads to the solution of the task.

billiards method follows from trajectory theory (one of the branches of probability theory). To solve the problem, you need to draw a billiard table and interpret the actions by the movements of the billiard ball along different trajectories. In this case, it is necessary to keep records of possible results in a separate table.

Each of these methods is applicable to solving logical problems from different areas. These seemingly complex and scientific techniques can be used in solving logic problems for grades 1, 2, 3, 4, 5, 6, 7, 8, 9.

We present you a wide variety logic problems for grades 1, 2, 3, 4, 5, 6, 7, 8, 9. We have selected for you the most interesting logic problems with answers, which will be of interest not only to children, but also to parents.

• choose for the child logic problems in accordance with his age and development
• take your time to reveal the answer, let the child find it himself logical solution tasks. Let him come to the correct decision himself and you will see what pleasure and feeling of delight he will have when his answer coincides with the given one.
• in progress solving logic problems Leading questions and indirect clues indicating the direction of reflection are acceptable.

Using our selection logic problems with answers you will really learn to solve logical problems, expand your horizons and significantly develop logical thinking. Go for it!!!

Solving logical problems - the first step towards child development.

E. Davydova

Logic is the art of arriving to an unpredictable conclusion.

Samuel Johnson

Without logic it is almost impossible to enter our world brilliant discoveries of intuition.

Kirill Fandeev

A person who thinks logically stands out nicely against the backdrop of the real world.

American saying

Logic is the morality of thought and speech.

Jan Lukasiewicz