# Counting with children

## How Children Learn to Count

• Education
• Maths Tips
• 5 and under

Counting is easily taken for granted but there's a lot of fascinating research into how we learn to count - and there's more to it than you may think.

### The mathematical brain

It’s first worth considering where our capacity to do mathematics comes from.

Neuropsychologist Brian Butterworth in his book “The Mathematical Brain” suggests we’re born with an innate sense of number hard-wired into our brain and he attributes this to a small region of the brain behind the left ear he calls "the number module". He compares this idea to colour – in the same way we perceive the “greenness” of a leaf we can also perceive the “twoness” or “threeness” of a group of objects.

Take counting. Like times tables and algebra, we tend to think it's something kids have to be taught. Wrong, says Butterworth - it's an instinct. Sure, we have to learn the names and symbols of numbers to develop that instinct, but, because the number module is hardwired into the brain, basic counting comes naturally.

Remote tribes can count even when they have no words for numbers. In maths as in language he believes, "kids start off with little starter kits" And their maths starter kit is the number module.

There are other theories too - such as maths being an extension of our spatial awareness – but there’s something nice in the idea of a “little maths starter kit”.

A Word of warning - All this doesn't mean a child is predestined to be either good at maths or not. Far from it, we’re all born ready to learn maths – and it’s what happens in the first 10 years or so that sets us up.

### Counting with toddlers

Research suggest that toddlers - even as young as 12 months - have a sense of how many there are in a set - up to around three objects. This comes from their innate sense of number.

Counting is learned when the toddler starts making the connection between this innate sense of "how many there are" and the language we use to count "one, two, buckle my shoe". This is the first stage in learning maths and it's the building block for many early concepts.

Should parents count with their toddlers? Absolutely, using a variety of real objects. And since counting and language are interlinked reading to your toddlers is equally, if not more, important.

### Counting - early learning milestones

Here are some stages of learning to count that you may notice your child going through at ages 3 to 5:

• Recognising how many objects are in a small set without counting. So if you show your child four apples they won't have to count them to tell you there's four.
• Knowing the "number words" from one to ten and their order.
• Know the sequence regardless of which number they start on. So if you say "start counting at four" they will count "four, five . ." as opposed to always counting from one.
• Conservation of quantity - This is where children realise that the number of objects in a set stays the same unless any are added or removed. So if they count six cans of beans in a straight line, then you rearrange the beans ( in front of their eyes ) into say two stacks of three - they will realise there's still six without recounting.
• Counting non-visible objects - your child will realise they can count things they can't touch or even see - such as sounds, members of someone else's family, or even ideas.
• Cardinality, not to be confused with carnality - This is knowing that the last number counted is equal to the quantity of the set. If your child counts six oranges 1,2,3,4,5,6 and then you ask "how many oranges are there"? and they count them again then they haven't grasped "cardinality".

### Counting on - as a step towards adding

Learning to add comes as an extension of counting. Here are some stages a child goes through to make this connection:

• Counting all - For 3 + 5, children will count "one, two, three" and then "one, two, three, four, five"  to establish the quantity of the sets to be added – for example, three fingers on one hand and five fingers on the other. The child will then count all the objects "one, two, three, four, five, six, seven, eight"
• Counting on from the first number - Some children come to realise that it is not necessary to count the first number to add. They can start with three, and then count on another five to get the solution. Using finger counting, the child will no longer count out the first set, but start with the word ‘Three’, and then use a hand to count on the second added: ‘Four, five, six, seven, eight’.
• Counting on from the larger number -  It's more efficient when the smaller of the two numbers is counted. The child now selects the biggest number to start with which is "five", and then counts on "six, seven, eight".
• The final stage isn't really counting - it's where learners know their number facts and skip the time-consuming counting altogether.

Number lines are great visual tools for making this connection between "counting on" and addition or subtraction - we use them in Komodo a lot. Here's an earlier blog article all about number lines.

### Beyond basic counting

Counting is the first mathematical pattern learners encounter. From here they soon begin to count backwards which is a step towards subtraction and they'll also count in twos, fives and tens which are a foundation for multiplication.

The next big step is the idea of place value and counting to base 10. Learners often make this leap simply because it's an obvious and efficient way to count large numbers. In Komodo, we use practice examples like this to help learners make the connection to counting in tens and ones.

It's easy to forget that counting is a key concept in maths with many stages before it's mastered. There's certainly a lot more to it than one, two, three!

I'm Ged, Co-founder of Komodo, ex-maths teacher and dad. If you have any questions please get in touch.

About Komodo - Komodo is a fun and effective way to boost primary maths skills. Designed for 5 to 11 year olds to use in the home, Komodo uses a little and often approach to learning maths (15 minutes, three to five times per week) that fits into the busy routine. Komodo users develop fluency and confidence in maths - without keeping them at the screen for long.

Find out more about Komodo and how it helps thousands of children each year do better at maths - you can even try Komodo for free.

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## What Children Know and Need to Learn about Counting

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Children Develop an Everyday Math

Context and overview
Young children, even infants, develop essentially non-verbal basic concepts of quantity: more/less, order, same, and adding/subtracting. Children learn most of these things on their own, without much adult help. Children often use these concepts in everyday life, for example, to determine who has more or less ice cream.  Children’s concepts and procedures are useful under certain conditions but need to be enriched. (Perhaps that’s why number was invented: the shepherd needs to know not only that he has a lot of sheep, but exactly how many.) This is what children know and what they need to learn at roughly ages three, four and five.

More/less
Children need to be able to see that there are more objects here than there. They often solve this problem not by counting but by physical appearance. "This flock of geese in the sky must be larger because it covers a greater area than does the other flock." This approach is often adequate but can lead to wrong answers and confusion.

Order
Judgments of more or less are sufficient for many purposes, but sometimes a comparison between more than two things needs to be made. Thus the idea of order, which includes subtle ideas:

• In a group of three objects, the second item is larger than the one preceding it but smaller than the one following it.
• Also, the item that was first can become last under a new order.

Again young children tend to rely too much on appearances to solve the problems.

Same number
The idea of same number evolves, even without adult assistance, through several stages:

• The first step is seeing that two groups identical in shape and arrangement are also the same in number. Thus, if a brown bear and a yellow canary are placed directly below another brown bear and yellow canary, both rows are the same in number (as well as in shape, color, and arrangement).
• The second step is seeing that two groups differing in color or shape can still be the same in number. Thus, if a brown bear and a yellow canary are placed directly under a pink pig and blue heron, both rows are the same in number (and arrangement, although they differ in shape and color).
• The third step is seeing that two groups differing only in arrangement are the same in number. Thus, if a brown bear and a yellow canary are not placed directly under a pink pig and blue heron but instead lie elsewhere, both groups are the same in number (although they differ in arrangement, shape and color).
• The fourth is seeing that one group, when rearranged, has the same number as it did before it was moved around. Thus, if the child first sees a brown bear and a yellow canary in one arrangement, which is then transformed, the child realizes that the number did not change from what it was before the rearrangement.
• The fifth is first seeing that two amounts are the same number when they look similar, for example five eggs in a row and five egg cups in a row both have the same number. But then if there is a transformation (for example spreading the eggs apart so that the line of eggs is longer than the line of egg cups), the child has to be able to understand that the eggs and egg cups are the same in number even though the two lines look different.

The idea of adding as resulting in more and subtracting in less
Children learn that:

• When you add something to an existing set, the result is that you have more than you had at first.
• If you start with two groups of the same number, and by magic (while the child is not looking), one set is now more numerous than the other, you must have added to one or subtracted from the other
• You don’t have to count to arrive at these judgments concerning more and concerning addition and subtraction: you can solve the problem by reason alone.

Later instruction needs to build on all of these ideas when written numbers are introduced.

Learning the Counting Words

Context and overview
In everyday life, we use counting words all the time, selecting items from the supermarket (“we need two bananas”) or playing “10, nine, eight, … blast off!” Children love counting as high as they can, like grown-ups.  They may even be interested in the name of the highest number. Fluency in the counting words aids later computation.

Rote memory plus
At first, children memorize the counting words from about one to 10 or so. But their learning doesn’t involve only memory. Children learn some ideas and rules about number too, namely that proper order is essential; numbers are different from letters; and you are not supposed to skip or repeat numbers when you count.

Structure
Later, children pick up the underlying structure of number: ten is the basic unit (20, 30, etc.) and we tack units onto the tens (twenty-one etc.). The rules for saying the English counting words from eleven to nineteen are especially hard to learn because they are poorly designed. Eleven should be "ten-one," just like twenty-one. Fifteen should be "ten-five," like twenty-five. The East Asian languages get this right, but English and many other languages do not. By contrast, English is fairly well designed for the number words beginning with twenty.  Each of the tens words resembles a unit word. Forty is like four; eighty like eight, and so on. Fifty comes before sixty. (A fairly minor problem is that twenty should sound more like two and ideally should be “two-ten;” thirty should be “three-ten” and so on). After saying a tens word, the child appends the unit words, one through nine. Learning to count to 20 and beyond is a child's first experience with base-ten ideas. In this case, teaching needs to stress the base-ten pattern underlying the counting numbers: the structure. We need to “instructure” (teach the structure) not “instruct.”

Counting Things: How Many Are There?

Context and overview
Children’s ideas about same, more, less, and order are heavily influenced by perception and by their own imperfect logic (for example, that what looks like more is more).  These are good ideas but lack precision, so children need help in taking the next step. The counting words that children learn early on can be used for enumeration; in determining the exact number of a collection, it is the cardinal number that tells how many. Accurate enumeration and understanding of cardinal number are fundamental for all arithmetic (and measurement) and are not as simple as they seem. Rather they involve key mathematical ideas and strategic thinking.

Principles needed to understand enumeration
Enumeration refers to using the counting words to figure out the number of objects. (This includes any object, from imaginary monsters to marbles.) Children must learn to follow several rules and principles to enumerate accurately. This set of rules is fundamental:

• Say number words in their proper order.
• Match one number word with only one thing (one-to-one correspondence between number word and thing).
• Count each thing once and only once.

Given these rules and principles, there are several ways to enumerate with accuracy. Children need to be able to:

• "See” small numbers (up to four or so) without counting. This is subitizing, which can reduce the drudgery of counting.
• Count one object at a time.
• Point at objects.
• Push objects aside to keep track of which ones have been counted.
• Put objects in a line or other orderly arrangement.
• Count on the fingers.
• Group objects into convenient groups that can be subitized or counted.
• Group by 10s.

Children need to learn to use these approaches in appropriate situations. For example, if there are only two objects, subitizing may useful, but if there are nine, then pushing objects aside may be indicated.

Understanding cardinality
Children who enumerate accurately also need to understand the result achieved.  Suppose a child accurately counts five things. Correct enumeration alone does not necessarily mean that the child understands cardinality. Asked how many there are, the child may simply count the objects another time. For that child, answering the question of how many simply activates the counting routine but does not provide an understanding of the result. Children need to learn several things about cardinal number. The core idea is that correct enumeration yields the cardinal value of set. The last number word does not refer to the last object counted but to the set as a whole. When we count, the number one refers to the first object; two refers not to the second object counted but to the two objects in the new group, and so on. Furthermore, once the child has determined that there are five objects in the set, it does not matter if they are hidden, or if the objects are simply rearranged (say from a straight line to a circle). There are still five objects. This is conservation of number.

Common mistakes or misconceptions
When counting, children often rely too heavily on physical appearance, just as they did in determining more or less. One goal of teaching should be to help children learn that reason must trump appearance. Children need to think abstractly about tangible things. Eventually, they need to embed understanding of cardinal number (for example, the abstract idea that there are five objects here) within the larger system of number, for example, that five comes after four and is half of 10.

Context and overview
Next we need to understand how concepts of more/less, order, same, adding and subtracting without exact number (knowing that adding means making a set larger even if you don't know of the exact number), and enumeration get elaborated to create numerical addition and subtraction.  Children learn some of this on their own, but adults can and should help.

These concepts need to be learned to understand addition (subtraction is similar):

• Addition can be thought of in several ways, including combining two sets, increasing the size of one set, and jumping forward on a number line.
• Simple counting is also adding, one at a time.
• The order of addition makes no difference (the commutative property).
• Different combinations of numbers can yield the same sum.
• Addition is the inverse of subtraction.

Strategies used to add (or subtract)
Children often begin by using concrete objects and fingers to add but gradually learn mental calculation and remember some of the sums.

• Using concrete objects, children may do the following to solve a simple problem like 3 + 2: They may count all ("I have three here and two there and now I push them together and count all to get five") or they may count on from the larger ("I can start with three and then say, four, five. ")
• Approaching the problem mentally, children may solve the problem by derived facts, building on what is known ("I know that two and two is four, so I just add one to get five") and by memory ("I just know it!").

More features of numerical addition and subtraction

• It’s always useful to have backup strategies in case one doesn’t work. For example, if unsure about memory, the child can always count to get the answer.
• It’s important for the child to be able to check the answer.
• It’s important for the child to explain why 3 + 2 gives five as the answer, since proof is a social act requiring language.
• The child needs to learn different strategies for different set sizes. (Counting one by one is good for adding small sets but tedious and inefficient for larger sets.)
• The child should also be able to describe how he got the answer. (Self-awareness is one aspect of metacognition. Of course, remembering what you just did is essential for describing it in words. )
• Language is vital for describing one’s work and thinking, and to convince others; children need to learn mathematical vocabulary.
• The child should be able to apply the math in real situations or stories about real situations (such as word problems).

Number Sense

Context and overview
Children need to develop number sense, a concept that is notoriously difficult to define in a simple and exclusive way. I like to think of it as mathematical street smarts, which can be used in just about any area of number, including those discussed above. Number sense, which helps the child to make sense of the world, has several components, each of which undergoes a process of development.

Number sense involves using basic ideas to avoid computational drudgery, as when the child knows that if you add two and three and get five, then you don’t have to calculate to get the answer to three-and-two.

Use what is convenient
Number sense involves breaking numbers into convenient parts that make calculation easier, as when we mentally add 5 + 5 + 1 instead of 5 + 6.

Knowing what’s plausible or impossible
Number sense may involve a “feel” for numbers in the sense of knowing whether certain numbers are plausible answers to certain problems (if you are adding two and three you know that the answer must be higher than three; anything lower is not only implausible but impossible).

Understanding relationships
Number sense involves intuitions about relationships among numbers. (For example, "this is 'way bigger' than that.")

Fluency
Number sense involves fluency with numbers, as when the child knows immediately that eight is bigger than four, or sees that there are three animals without having to count.

Estimation
This involves figuring out the approximate number of a group of objects and is related to the notion of plausible answers.

The Transition to Written, Symbolic Math

Context and overview
Formal, symbolic mathematics can provide children with more powerful tools and ideas than those provided through their informal everyday math. Formal math (and its use of symbols) developed in several cultures and is now virtually universal. Children need to learn it.

Everyday origins and formal math
Children encounter math symbols in everyday life: elevator numbers, bus numbers, television channels and street signs are among the many. Often parents, television, and software activities introduce some simple symbolic math, such as reading the written numbers on the television or on playing cards.

Schools certainly have to teach formal math. But doing so is not easy. Even if they are competent in everyday math, children may have trouble making sense of and connecting their informal knowledge to what is taught in school. Teachers often do not teach symbolism effectively.  If children get off on the wrong symbolic foot, the result may be a nasty fall down the educational stairs. So the goal for teachers is to help children, even beginning in preschool, to understand why symbols are used, and to use them in a meaningful way to connect already-known informal mathematics to formal symbolic mathematics. The teacher needs to “mathematize” children’s everyday, personal math; that is, help children connect their informal system with the formal mathematics taught in school. It’s not ill-advised or developmentally inappropriate to introduce symbols to young children, if the activity is motivating and meaningful. On the contrary, it is crucial for the teaching of symbols to begin early on, but again, if and only if it is done in a meaningful way.

Here are key issues surrounding the introduction of formal math to young children:

Young children have a hard time connecting numerals and the symbols of arithmetic (+ and -) to their own everyday math
They may add well but be confounded by the expression 3 + 2.  It is as if the child is living in alternate realities: the everyday world and the “academic” (in the pejorative sense) world. The everyday world makes sense and the world of school does not. You think for yourself in the former and do what you are told in the latter.

The equals sign (=) is a daunting challenge
The teacher intends to teach the equals sign as "equivalent," and thinks she has, but the child learns it as “makes” (e.g., 3 + 2 makes 5). This is a tale of how child egocentrism meets teacher egocentrism but neither talks with the other.

The solution
We should not avoid teaching symbols but need to introduce them in a meaningful way. This means taking account of what children already know and relating the introduction of symbols to that prior knowledge. It also means motivating the use of symbols. Thus if you want to tell a friend how many dolls you have at home, you need to have counted them with number words (symbols) and then use spoken words (“I have five dolls”), written words (“I have five dolls” written on a piece of paper or a computer screen), or written symbols (5) to communicate the result.

Manipulatives can help
Use of manipulatives can be effective in teaching symbolism and formal math, but they are often utilized badly. The goal is not to have the child play with concrete objects but to use these objects to help the child learn abstract ideas. The goal of manipulatives is to get rid of them by putting them in the child’s head to use as needed in thought. For example, suppose the child learns to represent tens and ones with base-ten blocks. Given the mental addition problem 13 plus 25, the child may understand that each number is composed of 10s (the 10 by 10 squares) and some units (the individual blocks), and that solving the problem involves adding one 10 and two more, which is easy, and then figuring out the number of units. The mental images of the 10s and ones provide the basis for her calculation, part of which may be done by memory (one plus two is three) and part of which may be done by counting on her fingers (five fingers and three more give eight).

Conclusion

The basics of number are interesting and deep. Although young children develop a surprisingly competent everyday mathematics, they have a lot to learn and teachers can help.

Resource Type

Handout

## Lesson 3. Preparing for counting for the little ones: tips, activities, games, books

Any child can be taught to count. The only question is how to do it. Despite the fact that counting (including quick calculations) is not a serious difficulty, some children are given it almost in the blink of an eye, while others understand the information with difficulty. Not knowing how to convey seemingly elementary things to the baby, some parents resort to all sorts of tricks, while others give up altogether. In the matter of the full-fledged upbringing and development of the personality, neither one nor the other is completely suitable, and there is only one way out of the situation - to know how, when and what to do. We will talk about this.

Contents:

• Peculiarities of learning to count babies
• Initial steps for teaching children to count
• Tasks for the little ones in pictures
• Children's educational games
• Educational literature for children

### Peculiarities of teaching kids to count

First of all, it should be said that a child's memory has one special property - selectivity. Therefore, children learn some skills on the fly, without making any effort, and with others, as they say, they have to “tinker”.

It is important to know and always keep in mind that many things cause children to associate with emotional sensations, such as joy, fear or surprise. It is possible to teach a child to count competently and quickly only when this process will also cause him emotional reactions (positive, of course) and interest.

At first, you should make every effort to get your child interested in counting, numbers and numbers. If this is done successfully, even the most fidget will be able to master the skill. A huge plus is that while the development of reading and writing in most cases requires intensive work with notebooks and books, then with the account all this can be relegated to the background. By the way, an interesting fact: thanks to scientific research, it was possible to establish that when studying any language, children remember numerals best of all. But let's continue.

You can start training from the first months of your baby's birth. Of course, this cannot yet be called a full-fledged training - it is rather a preparation. In the period up to about two years, you can play fingers with your child, hum all kinds of songs and counting rhymes, so that the child's consciousness fixes that there are generally such "things" as numbers and numbers. When the baby is two years old, you can move on to more specific methods and techniques. We’ll talk about the methods a little later, but for now, let’s briefly dwell on how to behave with the child in terms of the issue we are considering.

### Getting started in teaching children to count

So you've decided to start teaching your child to count. It's time to get started.

First you need to teach the child the simplest number sequence, consisting of five numbers. Remember that almost everything in life can be calculated. Watch a cartoon - count the number of characters on the screen, dress the baby on the street - pay attention to the wardrobe, and tell him that you can only wear one coat on him, that he has two legs, but only one pair of shoes is put on them.

When reading a book, linger on the illustrations longer, count the number of elements depicted in it, animals, little men, houses. When you walk down the street, count the dogs and cats running by, the cars passing by. Doing this every day, and even at every opportunity, your little miracle will definitely learn the order of counting. In addition, auditory and visual memory, as well as attention, will develop.

When a child gets acquainted with numbers and counting, he must understand that he is performing some actions or tasks not because you ask him to, but because it will be useful to him. Show the kid the practical benefits of the ability to count, and then giving out two cookies to everyone at home will not be difficult for him.

Involve your child in household chores as often as possible. For example, when you are going to have dinner, ask him to serve you a specific number of glasses, plates or cutlery. While cooking, explain that a specific amount of ingredients is required to prepare a particular dish, otherwise the dish will not work.

Dust the bottom shelf - draw a number with a rag and ask the young mathematician to tell you. You can even write an example and then present its solution. Walking around the store will also be a great way to exercise for the baby. Make a grocery list with the baby, clearly pronouncing the amount of everything you need to buy, and bending your fingers on the handles. Let the baby try to remember the information, at least a couple of lines.

Already at the store, remind your tiny assistant that he has to help you and refresh the shopping list in his head. This will activate his brain centers, which means that he will learn to count faster. In addition, you will show the baby that you cannot do without him, and, realizing his importance, he will show more eagerness to help you.

And wind on one important rule: all your actions will not bring any result if you do them randomly. In the matter of training, regularity and perseverance are important. By systematically studying with your child, inventing new forms of elementary everyday learning to count, you will achieve high results.

Now let's get acquainted with more systematic methods of teaching children to count, namely: tasks for the smallest in pictures and children's educational games. Let's start with pictures, because. they are the easiest to work with.

### Tasks for the little ones in pictures

Tasks related to pictures are very common and very popular. We offer you a small list of those and brief instructions for use:

• Special cards for learning to count and study mathematical symbols. You can find them in any bookstore in a large assortment. You just need to show such cards to the child, explain what is shown on them, and use them to illustrate the performance of mathematical operations.

• Pictures with images of various objects. They can not only be counted, but also painted and compiled in the correct sequence. You can buy didactic material in the store, or you can make it yourself (we recommend the first option).

• Images that involve matching pictures and numbers. It is very simple to use: the kid looks at the picture, determines the number of objects and draws a line with a pencil to the corresponding number. Collections of similar images are also available in bookstores.

• Pictures of different objects and you want to determine the number (little or many), size (small or large) and height (high or low).

• Images with specific tasks, such as walking through a maze, finding the same items, finding differences, etc.

Toddlers are very fond of tasks with pictures, because they are funny, cheerful and colorful. But for you, as teachers, it is more important that they clearly show the child what is what, thanks to which he easily remembers the material, understands the meaning of his actions and can explain it to you. Be sure that the kid will look forward to each new lesson with pictures.

### Children's educational games

We will not surprise you if we say that the best form of learning for children is the form of play. If you build the learning process based on the game, the child will be involved and interested in it. And even numbers that may seem boring will delight and bring pleasure. But we want to introduce you not to simple games, but to interactive ones, i.e. with those that you can safely download and install on your computer or tablet, or simply open on the Internet.

1

#### The game "Masha and the Bear answer questions"

A very exciting and colorful game where the kid will have to be smart and use the ability to add and subtract. The bottom line is that a small player must help Masha give the correct answers to mathematical questions. By doing this, he will help her get to visit her grandparents. If the child answers incorrectly, the bear sits on a stump, preventing Masha from passing. You need to give as many correct answers as possible.

2

#### The game "Math with Luntik"

Luntik is one of the favorite cartoon characters of children. If your little one plays this game, he will quickly learn to add numbers up to ten. With the correct answer, Luntik rejoices, and with the wrong answer, he is sad. Tasks in the game like this: Luntik writes an example with a plus sign, and the player must find the correct answer (several options are offered). The game is accompanied by pleasant music that helps the baby to concentrate.

3

#### Bouquet game

The meaning of the game is as follows: flowers bloom in the garden, which you want to put in vases. The player is given three vases with different numbers. In each vase you need to put the appropriate number of flowers. So, while happily manipulating virtual objects, your child will quickly learn to identify numbers and correlate them with the number of objects.

4

#### Piggy treats game

Another wonderful toy, the main characters of which are Piggy and his friends. The task of the game is to properly distribute treats to guests. For example, you need to help Piggy to share the nuts for everyone. There is a number next to the plate of each guest, and the correct number of nuts should be put on each plate. The interface of the game is designed so that the child can easily learn to count and memorize the images of numbers.

5

#### Animal Count Game

This game is suitable for toddlers who can count to five. Your child is presented with four pictures and one number, and he must find the picture, the number of animals in which corresponds to this number.

By and large, you can find a lot of similar games. All that is required for this is to type the desired request on the Internet. But games, of course, should not be limited, because they should be only an accompanying element of classes. In addition to them, we strongly recommend that you do not neglect children's poems and rhymes that activate children's thinking and make it more flexible. Be sure to connect the numbers when your beloved gold draws, paints, sculpts from plasticine or cuts something. And don't forget about children's books that contain counting tasks, drawings of numbers, simple examples, and other attributes of mathematics.

Speaking of literature, at the end of the lesson we want to present some good teaching aids that will help you learn many interesting features of the process of teaching children to count and build the process even more effectively.

### Educational literature for children

A variety of manuals are used today to teach kids to count. As a rule, they describe all kinds of techniques that develop mathematical abilities, memory and attention, logic and thinking in general, and also allow children to instill a love of mathematics.

Given that there are a lot of such manuals today, you need to find one that will be of interest to you and your little one. Therefore, you need to be prepared to spend some time studying thematic literature (if, of course, you have a desire).

We offer you a small list of excellent books that you can choose without fear that time will be wasted:

• Alla Kharchenko “Mathematics for kids. I count to 10"
• Daria Denisova "Mathematics for kids"
• Svetlana Gavrina "Mathematics for the little ones"
• Alexander Zvonkin "Kids and Mathematics"
• Elena Kolesnikova "Mathematics for children 3-4 years old"
• Elena Bakhtina "Mathematics for kids from 2 to 5"

In the fifth lesson you will learn a little more about how to work with preschoolers, how to introduce the child to the world of numbers and the composition of the number, and some simple tasks that can be given to children to solve.