Check. Quantity, numbers and figures, counting material

Teaching numeracy, systematized and methodologically justified by the Federal State Educational Standard (FSES), is included in the system of work with preschoolers in kindergarten. However, the age characteristics of children require particularly careful preparation of visual aids. The most important role is given to the counting material. We will look at the types of counting material used in mathematics classes in different age groups, and give advice on how to make it yourself as a demonstration and handout.

The validity of using visual counting material in kindergarten

In a preschool educational institution, children begin to master counting at the age of three, and this is their main mathematical activity. Learning takes place with the indispensable support of visual aids, since abstract logical operations performed during counting (merging and dividing sets, comparing quantities and numbers, comparing sets) are difficult for children to understand and require “objectification.” Visual counting material is a comprehensive didactic tool aimed at developing basic ideas about counting as part of targeted learning.

Famous teacher K.D. Ushinsky said: “Children’s nature itself requires visual learning.”

Such benefits are very diverse, and their application in each case depends on:

• specific content of educational material (for example, teach children of the second youngest group to distinguish between the concepts of many and few);
• the methods used (more precisely, certain gaming techniques, for example, illustrations for a fairy tale in which characters learn to count);
• the age of the children (if in the second younger group there may be cards with pictures of the same animal, then in the older group the pictures depict different animals, that is, the essence of the phenomenon being described becomes more complex).

Counting in kindergarten is mastered along with other didactic skills and concepts, for example, learning about colors: distribute the mushrooms into baskets of the corresponding colors and say which one has more/fewer of them

Visual material must meet the following requirements:

• scientific (correspond to scientific data on counting);
• pedagogical (carry an educational, developmental, educational load);
• sanitary and hygienic (do not contain harmful substances, do not cause eye strain;
• aesthetic (beautiful design, bright and clear images)

Features of demonstration and handout material for different age groups

Calculating material in mathematics, like other visual aids, can be of two types:

• large, that is, demonstration, which is used by the teacher to explain and show how to operate with it (magnetic boards, posters, paintings, etc.);
• small, that is, handout (cards, laptops, etc.), using which all children perform certain tasks at the same time, which allows organizing independent activities of children to develop the necessary mathematical skills and abilities.

Visual mathematical material differs in the type of counting activity, which is a priority for a specific age category.

1. Second junior group. To form the concept of singularity and multiplicity, you can use, for example, puzzle pictures, cubes in which numbers are surrounded by elements with the same number of fruits (vegetables, animals, etc.) or pictures with dots that need to be correlated with the number. By the way, the same material with dots is still used, only there are more numbers.
2. . Children must be able to give an accurate assessment of a set of objects, in this case counting to 5. For this, pictures depicting objects and numbers corresponding to their quantity are actively used, as well as a combination of a toy and a three-dimensional number. For example, to recognize the graphic image of a number, the task could be as follows: help the bunny find the number 3. Place a moth on a flower with five petals.
3. Senior group. Kids count to 10 and can add or subtract one at a time. For clarity, they use, for example, the game of dominoes, matching a number with a picture with the same number of objects.
4. Preparatory group. Children can compare numbers “more and less”, make up given numbers from two smaller ones - 5 from 2 and 3, for example. The demonstration material becomes more complex. These could be tasks for comparing the number of objects in pictures, composing a whole image after sequentially folding numbered cut parts, etc.

Counting sticks are a universal visual aid: they allow you to demonstrate and practice all types of counting activities.

Thus, the first manuals are aimed at ensuring that children learn to correlate the visual image of a number and the number of objects it denotes. In the middle group, this work is no longer on “recognizing” the image of a number, but on quantitative counting up to 5. In the older group, children learn to perform basic addition and subtraction operations, and in the preparatory task materials are comparative in nature, since children already know how to correlate quantities , indicated by numbers.

At any stage of training, it is necessary to think over a way to get acquainted with the graphic image of a number, for example, in the form of creating an application

Types of handouts

As already mentioned, manuals can be demonstration or handout. And there are also those that can be used in both cases (for example, Dienesh blocks). The teacher chooses the types of handouts depending on the age of the children. So, already in the first junior group, children get acquainted with cubes and counting sticks. True, so far the assessment level is “a lot or a little.” Typically, the gradation of the use of types of handouts depends on the age of the children: the younger, the more toys, and the older, the more drawings and diagrams. In general, the following counting aids are actively used in kindergarten:

• Cuisenaire sticks (multi-colored parallelepipeds of different sizes made of wood or plastic are used mainly in the second junior and middle groups, when the concept of quantity is introduced);
• Dienesh blocks (a set of geometric shapes of different sizes, which can be used by analogy with Cuisenaire sticks, as well as to introduce rectangles, triangles, circles, squares);
• cubes (in the younger group they practice the concepts of “many and few”);
• pyramids (as a budget, more affordable version of Cuisenaire sticks and Dienesh blocks);
• beads, buttons (in junior and middle groups);
• pictures, puzzle pictures, cards (for all ages);
• fan with numbers (for senior and preparatory groups, in which the children already clearly associate a number with its graphic image);
• lapbooks, tasks in which can combine all of the above manuals, etc.

Please note that there is no clear age division in the use of counting materials, since their use must be justified from the point of view of the educational goal. And yet, in the senior and preparatory groups, the emphasis is on cards, so that children get used to working with clarity “like at school.”

Photo gallery: examples of counting handouts

The capabilities of counting cubes allow them to be used up to the preparatory group. To master the skill of counting to 5, it is convenient to use special pyramids. A fan with numbers is a tool for school, but can also be used in kindergarten. On the blocks you can practice mastering basic geometric shapes and counting objects in groups Learn You can count on sticks completely unnoticed: for example, by laying out figures from them

Lapbook for FEMP “Quantity and counting”

A laptop is a folder that contains material on a specific topic. The organization of the material in such a manual is that the teacher arranges the visualization in the form of mini-books, accordion layouts, gift boxes, windows or pockets, etc. In addition, the lapbook necessarily includes tasks of a creative nature.

To form elementary mathematical concepts (EMP), laptops are also used - the fruits of the teacher’s creative approach to the implementation of learning tasks. Benefits are calculated for a specific stage of training. Since lapbooks were originally made by parents to teach their child, these manuals, put on a “methodological stream,” are now used for individual work, as well as for working in pairs or threes.

How to make didactic materials for a preparatory group with your own hands

First, you need to determine the goals of the Quantity and Counting lapbook.

1. Strengthen the ability to count to 10.
2. Practice ordinal and quantitative counting.
3. Practice the skill of comparing numbers with the number of objects.
4. Learn to write numbers.
5. Develop the ability to add, subtract and compare numbers within 10.
6. Develop active vocabulary, logic, memory and thinking.
7. Work on the ability to independently solve assigned problems.
8. Cultivate responsiveness, self-confidence and self-confidence.

After the organizational stage, you can proceed directly to production. This process begins with the preparation of the necessary materials. Moreover, methodological questions are developed first, and only then a suitable design is selected for them.

Typically a lapbook includes:

• pictures with numbers for visual perception of their graphic image;
• cards with numbers and objects (either separately or 2 in 1);
• puzzles (cut numbers or pictures, each piece of which shows a number, etc.);
• pictures of fairy tales with numbers in their titles;
• coloring books;
• copybook;
• riddles, counting rhymes, etc.

It is most convenient to organize materials into files, which, in turn, are stored in a folder. The cover of this manual frame should also be brightly designed. But with such packaging, it is troublesome to work with the materials: before use, part of the manual will have to be laid out. So you can take advantage of the experience of your colleagues and make the pages of the lapbook cardboard, and on these sheets you can attach files, pop-up books, and boxes with surprises.

Photo gallery: example of a homemade laptop

For a lapbook, using a folder is the most durable Cards with dots and numbers can be put in bright envelopes so that the child becomes interested in their contents When making such a manual, it is assumed that children know how to write By laying out numbers from elements, children remember the graphic image of numbers, and also train their eye With the help of a lapbook, children quickly and easily understand the essence of the comparison. Having solved the example in the garage and in the car, the child must correlate the same answers. Children, as a rule, get excited about playing dominoes.

Individual cards in mathematics for the second junior, middle, senior groups

Learning to count is something that requires maximum concentration and constant practice from a child. The latter is designed to provide individual cards - methodological aids for working on a topic one at a time or in mini-groups (2-3 people).

1. In the second younger group, to practice the concept of one-many, for example, a card may have a picture of a steam locomotive. The child receives a stack of trailers and distributes them according to the card. At the same time, the adult focuses the child’s attention on the fact that at first there were no carriages, then one appeared, and then “many.”
2. In the middle group, counting to 5 is very effectively trained by correlating elements of pictures (for example, dots on the back of a ladybug) and a graphic image of the number.
3. In the older group, to practice counting to 10, you can use tables with dots and small cards with numbers that children must correlate with each other. Or cards with numbers to restore counting order. By the way, the skill of writing numbers is trained in the same way.
4. In the preparatory group, cards can be graphic examples of addition and subtraction: the child counts the number of objects to the left of the + or - sign and writes the result in the cell provided for this.

For practical reasons, it is better to laminate cards. Then, even if the child needs to write something on an assignment (for example, the answer to the solution to an example), he will be able to do it with a marker that can be easily wiped off the cellophane.

To ensure that the numbers are always in the children’s field of view, you can install a “Fun Counting” folder in the group. She will introduce the kids to both numbers and the number of objects in a group.

Photo gallery: examples of individual cards and a picture for a mobile folder

In the younger group, children learn to evaluate sets by attaching different numbers of cars to locomotives. In the preparatory group, children perform addition and subtraction in the range from 1 to 10. A child in the middle group must count the spots on the back of a ladybug and connect it with the appropriate number. In the older group, children learn to perform simple arithmetic operations ranging from 1 to 10 Bright and beautiful pictures from the sliding folder will attract the attention of the children and teach them to relate the number to the number of objects

Pictures for teaching counting in senior and preparatory groups

There are no particular differences in the form of the pictures, only the tasks, that is, the content, differ.

Photo gallery: individual cards for the senior group

Cards with numbers can be made at home By rearranging the number of balls, the child will learn to count to 10, as well as sort things according to the “new/old” principle. An individual card can contain a creative task: fashion a number from plasticine. Such houses help children learn the composition of numbers

In order for a child to successfully comprehend the basics of mathematics, adults often have to use various visual aids. Among them, a special place is given to counting material. When choosing it from a huge variety, you need to choose the option that will be convenient for you and interesting for children.

Features of choice

In mathematics classes, objects are elements of sets with which certain actions must be performed. Regarding them, a specific question about their quantity can be raised. Some points that may be of interest in classes in another subject are not specified here. For example, if we are talking about birds on a branch, then it does not matter what kind of birds they are.

In mathematics, attention is paid only to quantity and quantitative relationships. In order for children to understand the material, counting material is often used.

This type of visual aids includes counting sticks, abacus, counting boards, or, as they are called differently, abaci, an arithmetic box, geometric mosaics, various sets of thematic or geometric figures for counting, cash registers of counting materials.

Choosing the right means for teaching children will make learning fun and exciting. The importance of this is due to the fact that children, right up to the start of primary school, learn and remember new things much more effectively if they are interested.

Among the factors that determine your choice should be the materials from which the sets are made, the appropriate age of the children, and the preferred shapes.

Manufacturing materials

A variety of materials are used to make counting material sets. These can be cardboard cards, high-strength plastic or wooden figures, or magnetic elements. When making a choice in favor of a particular material from which the counting material is made, you should first of all take into account its safety and environmental friendliness.

Thus, aids made of wood are considered environmentally friendly and pleasant to the touch. They are typically hand painted with safe, non-toxic paints. High-quality plastic figurines can last longer and are lighter in weight than wooden ones. You should choose only high-quality, high-strength plastic that has no foreign odors. It’s easy to make the necessary materials yourself from cardboard, and you can even involve your child in this process. Magnetic cards are convenient for teachers to use on the board to demonstrate to a large number of children. They are also suitable for those who have a small magnetic board at home.

Popular math sets

We offer an overview of the most popular and popular sets for teaching counting to young children.

Set “Learn to count” from the manufacturer “Red Star”

It is very convenient to store the kit at home or in the classroom in the plastic pencil case included in the kit. The counting material itself is wooden, which makes it absolutely safe. The kit includes:

• counting sticks (20 pcs);
• squares – green, red and blue colors;
• circles of red, yellow, green colors;
• squares (two types and colors);
• plates: numbers and signs (28 pcs).

This set can be used in classes with children 5-10 years old at home, in kindergarten and school. With its help, the baby will be able to get acquainted with the basics of geometry, numbers, and learn to perform simple counting operations. The child will be able to put together fancy pictures from geometric shapes, developing imagination and fine motor skills. He will also be able to learn to find patterns and continue the sequence, which will contribute to the development of logical thinking, teach him to compare, reason, classify and draw conclusions.

Cash register for numbers and counting materials “Learn to count” made of plastic from “Stamm”

A good set that can be used from the age of five. The set includes 132 elements made of high-quality plastic - geometric shapes, counting sticks and numbers, which are packed in a convenient plastic case.

With its help, you can introduce your baby to numbers and geometric shapes. Children will be able to form numbers and learn to solve examples and problems.

Mathematical typing on magnets Taruntaeva T.V.

The kit is designed to work on a magnetic board in the following sections:

• an account with a change in the basis of the account and according to the conceptual measure;
• development of the ability to classify;
• the ability to divide a whole into equal parts;
• relationship between the whole and the part;
• sets, union of sets;
• problem solving;

The set includes geometric shapes made from laminated cardboard - red, yellow, green and blue. The magnets must be attached to them yourself.

Set contents:

• circle division (diameter 20 cm) – 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/12.
• A square with a side of 12 cm and dividing it into parts in two ways: 1, 1/2, 1/4, 1/5, 1/8, 1/9.
• Circle, diameter 8 cm – 12 pcs. one color, 6 pcs. – other, 1 piece – 1/2+1/2.
• Counting sticks up to 10 in length in increments of 2.5 cm and up to 7 in width in increments of 1.5 cm.
• Geometric shapes: square, equilateral triangle, circle in two colors, 10 pieces each.
• Numbers and signs.
• Additional geometric shapes: rhombus (1 piece), trapezoid (2 pieces), equilateral (3 cm, 1 piece), obtuse (1 piece) and rectangular (1 large and 2 small) triangles, circle with a diameter of 3 cm (10 pieces) .

Counting materials cash register Fancy “Learn to count”

Selection by age

To work with counting material in kindergarten, you should choose bright and colorful aids. With the help of an interesting design, it is much easier to attract the attention of preschoolers and make learning a fun, interesting game. It needs to be changed periodically so that the children are constantly engaged in the learning process. Today you can work with hedgehogs; in the next lesson, count how many birds have arrived.

For younger children, choose beautiful bright figures and sets with which you can teach your child to count to 20. Older preschoolers are already eager to go to school as soon as possible. At this age, children may like sets in a beautiful pencil case, because it is a necessary attribute of school education.

Children 6-7 years old and elementary school students who have already become acquainted with the basics of counting in the preparatory groups of kindergarten can be offered various sticks, cash registers, and abacus. Using them, you are no longer attached to gaming activities. The manuals help the child visually and make it easier to understand the mathematical operations that need to be done. With their help, it is easier for a primary school student to navigate the connections between the abstract and the concrete.

The best forms for perception

For children under 5 years old, counting material in the form of various figures is suitable. These could be apples, mushrooms, nesting dolls, various vegetables, transport, animals. With the help of such forms, you can play out many different situations to teach your child to count. Today the hedgehog will bring mushrooms, and the squirrel will bring apples. Tomorrow you will count how many vegetables you will add to the soup. Later, distribute the carrots to the bunnies. The most important thing at this age is play, which should not be forgotten by an adult working with a child..

It is also necessary to use three-dimensional numbers so that the baby correlates the concept of number and numbers. He will remember each number much better if he can touch it, run his finger along each line. After all, tactile perception plays a huge role in the development of a baby from a very young age.

Children of senior preschool age and primary school students can already be offered various geometric shapes as counting material, which can also be used as mosaics. This way, the child will be able to remember the name of the shapes, learn the main colors, and will lay out various pictures from the details.

Also, children of this age may like sets with 1 cm cubes. Such sets can be used not only for counting. With their help, the child will learn to sort, construct graphic images, and become familiar with the concepts of “perimeter,” “volume,” and “area.”

Counting sticks are a universal educational tool for children of all ages. The youngest will need strict adult supervision. With their help, you can begin to develop a child as early as 9 months. They will help develop fine motor skills, learn colors, many different concepts, such as “one-many”, “wide-narrow”, “long-short”, etc.

They help teach a child to compare, find similarities and differences, promote sensory development, develop logic, imagination, and the ability to think outside the box. With the help of sticks, the child will be able to get acquainted with the basics of geometry. And, of course, they will help in teaching your child to count and become familiar with basic mathematical operations.

How to do it yourself?

Any parent can make counting material with their own hands, which will significantly save the family budget. You can make it from improvised materials that are at home:

• Numbers
• Counting from 1 to 10
• Number composition
• Subject pictures
• Geometric figures
• Math puzzles

11 photos

You can also use beads, clothespins, fabric appliqués, and various waste materials.

Lots of different options, All adults have to do is turn on their imagination and express themselves. You can cut and glue from cardboard, you can sew and knit, you can draw - do what you like. For a child, aids that are made with love by his mother will be the most beloved.

How to learn calculations?

In order to teach a child to calculate, you can use a wide variety of counting materials: abacus, abacus, sticks, cards, various ready-made sets of counting materials, etc. In primary school lessons, teachers also use all these aids to teach children various counting operations.

Advantages of using counting materials:

• visual demonstration of the computational actions performed;
• accessibility of understanding the meaning of arithmetic operations;
• the use of counting materials helps in the development of fine motor skills;
• accessibility - you can always find counting material at hand without purchasing anything special.

Disadvantages of using counting materials:

• the habit of using any objects for counting sometimes complicates the child’s transition from an objective environment to an abstract mental form;
• There is a wide choice of different counting materials. For adults who are not specialists, it is sometimes difficult to understand the teaching methods of a particular manual.

Using an abacus

The abacus is somewhat reminiscent of the Soviet abacus. It is a wooden frame with knitting needles, on which 5 dominoes are strung. The number of knitting needles may vary. The knitting needles pass through a bar that separates the knuckles. There is one domino above the knitting needle, and four below it.

When counting on an abacus The ability to work with the thumb and forefinger is very important. With the help of repeated repetitions it is necessary to bring it to automaticity. Keep in mind that this skill is quickly forgotten without regular training.

Arrangement of number lines: Each digit occupies its own spoke. The domino below the dividing bar indicates 1, above the dividing bar - 5. Let's look at a specific example. The number 3 on the abacus will be marked like this:

The number 15 looks like this:

Here, one domino is raised on the tens digit, and on the units we lower the domino, which represents 5.

Thus, numbers are deposited on the abacus and various counting operations are performed. With it you can add, subtract, multiply, divide and even raise to a power. However, such complex operations are already the basics of mental arithmetic, to get acquainted with which it is better to attend a course of relevant classes.

Counting material is necessary when teaching children mathematics at home, in kindergarten and school. It is presented in a wide variety in stores. But it is not always convenient to use purchased items. Among your things you can find something that your baby will like best. Learn the basics of mathematics with your little one with pleasure and always by playing, then the learning process will be much easier.

For information on what counting material is, see the following video.

Notes of mathematical classes and GCD, stories about making educational games, lapbooks, materials and manuals for confident development of numeracy skills.

Scenarios of entertainment, musical and theatrical events designed to consolidate these skills and abilities. The fairy tale “The Little Goat Who Could Count to Ten” has been around for many years. During this time, many stories appeared in the style of this “educational story.” They are also presented for you in the publications of this thematic section.

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