Mathematics is perhaps the most difficult science for junior schoolchildren. But it is simply necessary to understand its basics in grades 1-2, otherwise it will be impossible to understand the intricacies later. Parents are interested in how they can teach their child to quickly and easily solve examples, because this is the first stone that little students stumble over.
How to teach solving examples within 10?
The easiest and fastest way is to explain to your child how examples within the first ten are solved. Mandatory conditions for this will be conscious verbal back and forth, knowledge of the previous and next number, as well as it, for example, 5 is 1 and 4 or 2 and 3.
At first, counting sticks are a good choice to help your child understand how to add or subtract numbers. It is not advisable to use your fingers or a ruler to count - this way the child does not learn to think. This is the opinion of most teachers, although in reality it turns out that this stage is simply necessary for some. Some people pass it faster, while others are delayed. The more the child does, the better the result will be.
Example
For children, dominoes are an excellent example for learning to count. With its help it is easy to explain: 4-4=0 or 5=5.
Examples can be visualized - draw a certain number of apples, candies and other things, subtracting or adding them.
How to teach a child to solve examples up to 20?
If counting within ten has already been mastered, it’s time to move on - learning to add and subtract numbers from the second ten. In fact, this is not at all difficult if the child knows by heart the composition of the number and has an understanding of what is greater and what is less.
Nowadays, visual examples are as important as in mastering the first ten.
Example 1
Let's look at an example of adding 8+5. This is where knowledge of the composition of the number is required, because 5 is 2 and 3. We add 2 to 8, we get the round number 10, to which adding the remaining 3 is no longer a problem.
Example 2
To learn subtraction, you will also need to divide numbers into their components. To subtract eight from fifteen, you need to divide the first number by the sum of the numbers 10 and 5. After this, divide the subtrahend by 5 and 3. Now the most interesting thing happens - from the first digit of the subtrahend (10) we subtract the last digit of the second of the terms of the number eight. We get seven.
How to teach a child to solve examples up to 100?
Children who have mastered counting within twenty will not find it difficult to figure out other tens. The program now requires that addition and subtraction be done in your head, not in a column. You need to show your child how to do this.
Example
43+25. To 3 units we add 5 units and write it slightly to the side of the equal sign, leaving room for one more digit. Then we add 2 tens to 4 tens and get 68. It is important that the child clearly understands that tens and ones cannot be mixed. The same example can be solved in a column using the same principle.
If a child is unable to solve examples, you should talk to the teacher so that she pays attention to this particular problem. But you shouldn’t relieve yourself of responsibility either - practicing at home, in a calm environment, will sooner or later give positive results.
With admission to primary school There is a change in the child’s main activity: more and more of his time is now spent on educational activities. During this period, much attention begins to be paid to teaching mental arithmetic. And in this matter, the actions of the teacher and the parent must be united: if a child is required to be able to count in his head in a lesson, but this process is not controlled at home, then the skill will take a very long time to develop.
How to develop mental counting skills?
Many teachers do not recommend it, because with this method they do not strive to remember the result, because necessary tool is always nearby. And if there are not enough fingers while counting, the child will experience difficulty.
It is not advisable to constantly use sticks to find results. When working with large numbers, a child may get confused and come to the wrong decision. Of course, it will not be possible to completely ignore these methods, but it is better to use them to explain the material, and not constantly. Gradually reducing their use, you need to achieve the skill of mental counting.
It is based on three components:
- Capabilities: In order for a child to learn to count in his head, he must first develop the ability to concentrate and remember several things at the same time.
- Knowledge of fast counting algorithms and the ability to choose the most effective one in a particular situation.
- Constant training , which will automate the solution of complex problems and improve the speed and quality of calculations.
The last component is the main one, but the importance of the first two should not be underestimated: knowing a convenient algorithm and having the necessary mathematical abilities, you can quickly solve the required example.
The development of mental arithmetic skills in primary schoolchildren is based on two types of activities:
- Speech – before performing an action, the child first says it out loud, then in a whisper, and then to himself. For example, when solving the example “2+1”, he says: “to add 1, you need to name the next number,” and in his head he determines that it is 3 and names the result.
- Motor – first adds or removes objects (sticks, cars) to calculate the result, then does this with a finger, and then last stage– with the eyes, performing the necessary actions in the mind.
You can invite your child to work with numbers using aids offered by different methods.
Zaitsev's technique
Allows you to raise a child who thinks logically, knows how to analyze information and generalize it, and highlight what is essential. For students in grades 1-2, these manuals will help them understand arithmetic operations with numbers.
To study mathematical techniques you will need special cards (“Counting”) with numbers 0 – 99 and tables that clearly show the composition of the numbers (the required number of cells is shaded).
First, the child gets acquainted with the numbers of the first ten, determines the composition of its number, and then proceeds to arithmetic operations with the learned numbers.
N.A. Zaitsev conducts a video lesson with children using his own methodology.
Work is carried out with colored cubes and boxes with cells that can fit 10 cubes . With the help of a set, children are explained the concepts of “composition of a number” and “ten” and taught the skill of mental counting.
Even a smart child may sometimes not understand the simplest things. This does not indicate his lack of understanding or lack of intelligence; most likely, it indicates a lack of interest.
After all, children can perceive information and remember it only when it evokes an emotional response in them. Bright positive emotions children experience during interesting game Therefore, it is better to teach mental arithmetic skills through play activities.
For example, children imagine that the blocks are gnomes and the box is their house. There were 2 gnomes in the house, 3 more came to visit them. The task is clearly demonstrated, the lid of the box is closed and the question is asked: “How many gnomes are there in the box?” To answer the question, children will have to count in their heads, without relying on cubes.
Gradually, the tasks become more complicated, children learn to add and subtract by moving through tens, and then two-digit numbers.
The video story will tell about teaching children using the methods of Sergei Polyakov
Algorithms
Knowledge of simple arithmetic rules and patterns will help you quickly find the result in your mind:
- To subtract 9 , you can first subtract 10 and then add 1. Similarly, subtract the numbers 8 and 7, only then add 2 and 3, respectively.
- The numbers 8 and 5 add up like this: First, 2 is added to 8 (to make 10), and then 3 (5 is 2 and 3). All examples of addition with passing through ten are solved in the same way.
The following algorithms are suitable for adding two-digit numbers:
27+38=(27+40)-2=65
27+38=(20+30)+(7+8)=50+15=65
In the first case, the second term is rounded to tens, and then the added number is subtracted. In the second, the bit terms are added first, and then the results.
When subtracting, it is convenient to round off the subtrahend:
Workout
For training you can use special computer programs or games:
- "Shop" . The child can play the role of both the seller and the buyer; all calculations must be carried out in the mind. Prices for goods are set depending on the student's abilities.
- "Merry Count" . An adult throws a ball to the child and names an example to which an answer must be given. Thus, the score is developed automatically.
- "Chains" . A chain of examples is given, children need to find the final result without writing down the intermediate results of the calculations.
If a child regularly counts in his head, this skill will develop. Such classes will be a good basis for those with three-digit numbers.
The video story will tell you how to teach a schoolchild to quickly count in his head - not mental arithmetic
What should a child be able to do before starting to learn to add and subtract?
Can count to 10 or more
"One, two, three... there are six apples here."
We didn’t count everything - the steps in the entrance, the Christmas tree in the yard, the bunnies in the book... It looked something like this. "How many bunnies? Point your finger. One, two, three. Three bunnies. Show three fingers. Good girl! That's right!" At first my son was not interested in counting; he liked searching more. The game of hide and seek is also not superfluous: “One, two, three... ten. I’m going to look. It’s not my fault who didn’t hide!” At the age of 3, we could not count to 10; instead of numbers, we pronounced unknown words with a similar intonation. But later, due to the fact that it was often necessary to show the number of fingers, numbers were associated with the number of objects.
Knows numbers
“One, two, three... there are six apples here. The number “six” is written like this “6.”
I don't remember any special exercises that we did. Everything happened in passing. “Which floor are we on? On the second. Look, his number is written on the wall. “2”. Show two fingers. Well done.” In the elevator: “What floor does grandma live on?” — “On the 3rd” — “Which button should you press?” - “This one” - “I guessed a little wrong. Here’s a three.” In the store: “We have the key to box number 9. You see, there’s a tag on the key. Which box has this number written on it?” Something similar with a wardrobe number. In line to see the doctor: “What is the office number? Here’s the number.” - “Two” (as far as I understand, at random) - “No, this is the number “5”. Show 5 fingers. Okay!” "When will daddy arrive?" - “In an hour. Look, now the short hand is at 6. When this hand is at 7, right here, then it will arrive.” "Please switch to Channel 1. Bring the remote control. It says one here. Press this button. Thank you." Interesting. The numbers determine any color. In addition to learning colors and numbers, fine motor skills are trained. The numbers written in mirror by the child must be corrected. There is such a diagnosis as “dysgraphia”. To exclude it, you should contact a speech therapist.
Can sort (name) numbers in ascending-descending order
"Baba Yaga came and mixed up all the numbers. Can you arrange them correctly?"
Until three or four years of age, a child needs to be taught comparison, namely: 1) to distinguish between the concepts of big-small, high-low, long-short, heavy-light, wide-narrow, thick-thin, old-new, fast-slow, far -close, hot-warm-cold, strong-weak, etc. Look for the smallest object, the longest... 2) combine objects: by color, shape and other characteristics (dishes, clothes, furniture, pets), find differences in the pictures. 4) remove an extra item in a row (for example, from several red apples there is one green one), continue the row (for example, ▷ ☐ ▷ ☐ ▷ ☐ ?), name the missing element (for example, ▷ ☐ ▷ ? ▷ ☐ ▷), distribute in pairs (for example, ▷ ☐ ▩ ☐ ▷ ▩), name what happened first, what came next (put on a sweater first, then a jacket, and not vice versa; first it’s autumn, then winter...). 5) fold a pyramid, a puzzle, place beads in a certain sequence. Only I have at least 20 books with similar tasks for kids. Previously with my son, now with my daughter we look through and talk through them with enthusiasm. “Show all the fruits” - “Here” - “Well done!” (clap our hands) - “What kind of fruit is this?” - “Orange” - “Uh-huh. Still there?”... By the age of 4, you can and should introduce Board games(there is already enough perseverance and attention): dominoes, cards, lotto, with chips (each player has a chip) and cubes (the move is made based on the number of dots rolled on the cube), where the winner is the first one to reach the finish line according to the drawn card. We used standard options, not children's ones. The cards were played in “The Drunkard” with a full deck (with 2 and 3): the deck is divided equally between the players, in the piles the cards are turned face up and the top one is drawn, there are no suits, the one whose card is larger takes the bribe (7- ka beats 4, 2 beats ace, two more cards are placed on two equal cards: one face down, the other face down, the second time the merits of only the top cards are assessed: “Who takes it?” How?! What's more: 5 or 10? Let's count..."), she joins the general pile, the one who has the whole deck wins. Joy knows no bounds if the whole family sits down to play (with dad, grandma, grandpa...). The child learns not only to play, but also to correctly perceive defeat. It is better to be able to count numbers from 1 to 10, and back, from 10 to 1, than to count to 100. When we were 5 years old, we confidently did both. The countdown can be said in a relay race: “Who will collect the most cubes? Get ready! Ten, nine, eight... one. Start!” We organized such competitions when it was time to clean up scattered toys. Pictures where we need to connect the dots in ascending numbers helped us learn to count to one hundred. If you speak it out, you get a good result. ""Forty-nine". Then what comes?" The appearance, pronunciation of the number and the sequence are remembered. You can interpret that the numbers in tens are the same, writing the numbers as follows:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
And it’s handy to consolidate the material on the way: “When will we arrive?” - “Not long left. Count to one hundred and we’ll arrive. Let’s go together. One, two...” We didn’t teach more than 100 before school. I answered questions only when the child himself was interested: “What comes after 100? And what is one thousand and one thousand?” Or if the numbers were encountered in everyday situations: “We are waiting for bus 205. Two zero five. Tell me when you see the 205th.” It is also useful to name the numbers before or after a given number or in a certain interval. The game will help with this: “I guessed a number from 1 to 20, try to guess it in 5 attempts, and I will tell you whether it is more or less than the number you named. I guessed.” — “Three” — “More” — “Seven” — “Less” — “Five” — “Well done! You guessed right! Now it’s your turn to guess the number.”
Knows the concepts of more and less
"Dad has 6 apples, mom has 8. Who has more apples?" - "Mom."
The clubs explain that the number 22 is greater than 18, since it is closer to 100. This is true, but at the same time we laid out piles of nuts and erected towers of cubes in order to connect the image of the number with the number of objects. More and less gradually become more complex, as does addition and subtraction. Almost simultaneously with the plus-minus-equal signs, the greater-than-less-equal signs are introduced. My son was just over 5 years old at the time. “There are a lot of apples on one side [intonation is required!], the distance between the fingers is large, there is a larger number next to the open side of the sign.” “On the other hand there are few apples, the distance between the fingers is tiny, the corner is looking at the smaller number.” “Equally”, “equally”, “at the same time”, “equally”, “as much” are the same: “You and dad have the same mugs”, “I have the same amount of soup”, “Share the candy equally with your sister”. There are no problems with this concept when there are two children in the family.
next example
It is most difficult to compare numbers consisting of the same digits. Almost always we solved them.
next example
How to teach a child to add (subtract) up to 10
Counting on fingers
"Dad has 3 apples. Unfold three fingers. Mom has 2 apples. Unfold two more fingers. How many apples are there? How many fingers? One, two, three, four, five. Mom and Dad have five apples."
"Dad has 3 apples. Unfold three fingers. He shared one apple with you. Bend one finger. How many apples does he have left? One, two. Dad has two apples left."
"Dad had 2 apples. Show two fingers. Dad got hungry and ate both apples. Take away two fingers. How many did he have left?" - “Dad ate everything. Dad didn’t give me an apple: (Dad needs to be put in a corner!” - “Uh-huh, Dad has no apples left. He has zero apples. Hee-hee, and yes, he needs to be put in a corner.”
The child must count all the objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.
+
=
The child must count all the objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.
-
=
With objects on paper
next example
The child must count all the objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.+ =
The child must count all the objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.
- =
We had difficulties not with finding the answer, but with pronouncing the entire example with signs, with the correct declination of objects. "One, two, three. Three candies. PLUS. One candy. How much is it? One, two, three, four. Four candies. Let's do it again. Three candies PLUS one candy EQUALS four candies."
With numbers on paper
Three examples a day is enough. In six months, their number can be increased to 5-7. The answers must not only be spoken, but also written down. points?The words “addition table,” which is crammed as “multiplication table,” make me itch. In my opinion, the child’s thinking and logic are completely switched off at this moment. Therefore, I tried to put my son in such conditions that he himself would guess that the result of adding different numbers can be the same number. "One plus two?" - "Three" - "Two plus one?" — “Three” — “That is, changing the places of the terms does not change the sum” (hmm, the last one came out automatically: I didn’t explain to my son what a “term” was). “Can you solve the examples: 2 + 3 = ? 1 + 4 = ?” - “Easy! Five. Oh, there’s five here too. And there and there are five!” You can also take seven spoons: “How many spoons are there?” - “One, two, three... seven.” Put one spoon aside: “How many spoons are in each pile?” - “One and one, two, three... six” - “And that’s all?” — “Seven” — “It turns out that 1 + 6 = 7.” Transfer another spoon: “Now how many spoons are in each pile?” - “Two and five” - “And that’s all?” — “Seven” — “Look, the number of spoons in the piles changes, but the total number remains the same.” Later in the club, he drew houses in which numbers live (without my participation). There are two apartments per floor. It is necessary to resettle all the residents so that on each floor their number is equal to the number indicated by the owner on the roof.
_ _ / \ / \ / \ / \ / 2 \ / 3 \ /_______\ /_______\ |_0_|_2_| |_0_|_3_| |_1_|_1_| |_1_|_2_| |_2_|_0_| |_2_|_1_| |_3_|_0_|
Without recalculating the first number
"Dad has 3 apples. Mom has 2 apples. How many apples are there in total? There are already three. Stretch three fingers. Now two more. Three, four, five."
I myself didn’t notice how my son stopped counting all the items. She explained it a couple of times, but did not insist.
Based on a given condition, formulate, write down and solve an example yourself
“Look. There is a problem. “You have 7 games loaded on your tablet. You’ve already played 5. How many unexplored games are there left?” - “Two” - “That’s right. It can be written as “7−5=2”. Interesting, Will you be able to write a similar problem yourself: “After dinner, you need to wash 10 dirty dishes. How many are already in the sink?” - “Six” - “How to write it down?” - ""10−4=6"" - "Well done!"
Problems should be simple and mundane, with items from Everyday life, with questions “how much”, “how much”. “You have 3 cars. They gave you 3 more for your birthday. How many cars do you have now?” (6) “You have 6 pencils, the girl you played with yesterday has 2. How many more pencils do you have?” (4) “You are 5 years old, Nikita is three years older than you. How old is Nikita?” (8) “There are five dogs and three balls. Is there enough ball for everyone? How many balls are missing?” (no, 2) “2 pears and 4 bananas grow on a birch tree. How many fruits grow on a birch tree?” (0, since fruits do not grow on birch trees)
Relationship between addition and subtraction
Subtraction is the inverse operation of addition. In other words, in order to more conveniently find the unknown variable x (pronounced “x”) in the equation x +1 = 3, the entry is reduced to the form x = 3−1 (when the number is moved ahead, it changes its sign from plus to minus and vice versa ) .
Full example: x + 1 = 3 x = 3 - 1 = 2 This is the connection that needs to be conveyed to the child. That is, to show that 2+1=3 is the same as 3−1=2 and 3−2=1. For this purpose, you can ask him to come up with 3 conditions for the task based on what he saw (instead of dots there could be bows, houses, cars, etc.).
Change Total points
"What kind of examples do you think can be written? Let's say 6 + 2 = 8 or 2 + 6 = 8 “How many dots are there in total?” 8 - 2 = 6 “How many green dots?” 8 - 6 = 2 “How many pink dots?” And now it's your turn."
- =
− =+ =
+ =
next example
Without counting fingers
When you have calculated quite a lot of examples, you simply already know that 2 + 3 = 5 and there is no need to double-check it with your fingers.
How to learn to count within 20
Counting by lines
"6 plus 8. First draw 6 lines then add 8 more. How many lines are there in total? Six, seven, eight... fourteen. Answer: 14"
Counting from 10 to 20
11 + 4 ----- 15
There were no problems, so I don’t even remember how I explained it. She also showed the solution in a column (tens under tens, ones under units). To prevent the numbers from slipping, I outlined six cells with a pencil. Even when my son gave the correct answer, she sometimes asked him to write it down in a column.
With numbers on paper
The statement that it is easier to count in tens was also transferred to the plane of trial and error. Why were 100 rubles exchanged for 1 ruble? A handful of coins was taken. The child was asked to count the number of rubles. Even counting 37 coins is difficult. But if you arrange the coins into piles of 10 coins, there will be fewer mistakes. "Ten, twenty, thirty, and in this pile there are seven. Thirty-seven in total." I also asked for some money for travel: “To get to the hospital and back I need 52 rubles. Count me out, please... Oh! There’s not enough for the trip back! How can I get back home?” Later, a problem was announced: “If you count how many steps up to the apartment, you will receive a prize” (there were exactly 10 steps between the flights).Imaginary fingers (within 12)
"What is 6+6? Imagine what you have on right hand two more fingers. Six, seven, eight... twelve." 
I didn’t expect that I would like the proposed idea so much.
On fingers
"What is 8+9? Bend eight fingers"
“Two fingers are already straightened. Let’s straighten them some more to make it 9. Three, four, five... nine.”
“There are already ten fingers: these are 8 previously bent and 2 straightened from 9. Now let’s count the number of fingers before the bent one. Eleven, twelve, thirteen... seventeen. Answer: 17.”
On a piece of paper
The child must count all the objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.+ =
The child must count all the objects. Don’t rush, the understanding that there are 5 fingers on one hand does not come immediately.
- =
7 + 8 = 7 + 3 + 5 = 10 + 5 = 15 ↙↘ 3+5
“How much do you need to add to 7 to make 10?” - "3" - "That's right. And eight minus 3?" — “5” — “We replaced 8 with 3+5. Where did 3 come from?” - "Out of 8"...
13 - 6 = 10 + 3 - 6 = 4 + 3 = 7 ↙↘ 10+3
“Thirteen can be written as 10 plus 3. From 10 we subtract 6. What happens?” — “4” — “Add 3”...
At the age of six, we solved such problems, but, as far as I saw, my son did not do it meaningfully, but in an image and likeness. But if, after, say, the example 6+7=13, you ask how much 6+8 is, the child gives the correct answer “14.” To the question "Why?" the laconic “Because 1” sounds.
In my mind
Repetition is the mother of learning. How more examples, the less often you turn to the above methods.
Practice!!!
You need to go with your child to the store for a single item (bread, pen, lollipop, ice cream) with a given amount of money. But in such a way that he is the buyer, and you are just an outside observer. You should ask him if there is enough money to buy the thing [more or less]. It must be explained that the seller must give change if the amount of funds transferred exceeds the price [by how much/subtraction]. After a while, replace one coin with two, and then with three [addition].
My son had 10 rubles in one coin. I was thirsty and I offered to buy him a bottle of water himself. The following dialogue ensued with the seller: “Can I buy water?” - “Yes. It costs 8 rubles.” - “Are there any for 10?” That is, he did not think about whether he had enough money or not. If they had said that there was no bottle for 10 rubles, he would probably have turned around and left.
Mathematics for preschoolers: what else will be useful in 1st grade?
Orientation in space
"Where left hand? Close your right eye. Grab your left ear. Jump on your left leg. How many cars are there on your right? And on the left? And in front (in front)? And behind (behind)? What color is the car between gray and green? What's under the table? On the table? Over the table? Near? Near? Inside (in)? Outside (s/s)? Who got up from the table? What did I get from under the table?
We played games like this. The leader (either me or my son) on the street gave instructions to the person who had closed his eyes: “Slow down, there’s a bump in front, two steps left, one, two, now raise your right leg high... A man is coming at you from behind, move to the left, a little more... "There's a cyclist coming towards you, quickly take two steps to the right." The presenter (either me or my son) drew a plan of the room, and on it marked with a cross where the toy was hidden, which the second player had to find using the plan. I laid out notes around the apartment indicating where the following piece of paper was located: “In the table in the kitchen”, “Under the sofa”, “Above your bed”... The last note said where the treasure was. The first one was given to my son.
I gave (plus they did something at the club) to make sure that there were no problems with it: “From the point, two cells up, one diagonally, to the right...” And checked on a piece of paper: “Draw in the upper right corner a star. In the center is a flower. To the left of the flower is a circle. Place a cross in the middle of the bottom edge of the leaf..."
Geometric figures
"What does a ball look like? What is the difference between an oval and a circle? What is the shape of a stool when you look at it from above?"
“Please name the even numbers? (2, 4, 6) And the odd ones? (1, 3, 5)” The definition that “Even numbers” are those that are divisible by 2 will not work here. Therefore, during a walk, I drew my son’s attention to the sign on the house “27 → 53”. "Do you know what she means?" - "..." - "It shows that the house numbers will increase if you go in this direction. But, since on this side there are only houses with odd numbers, they will increase like this: “27”, “29”, "31"... What number do you think will come after "31"?" - ""32"" - "Nope, "33". This is the odd side. And after "33"? - ""35"" - "Well done! Let's go check it out. So, this is "27". And that one?" - ""29"" - "Let's see... Well, what number is it, here it is?" - ““29”... By the way, I remember the question of a boy in the club, which puzzled the teacher: “Is zero an even or an odd number?” It is immediately clear that children do not memorize, but delve into it, their gray cells are working.Preparing for Multiplication
At the age of six, it is useful to study how the minutes on the clock are grouped (by 5), why by pointing to “2” we talk about 10 minutes.
Problems involving groups of two are also interesting: “Six legs are visible from under the fence. How many chickens are hiding behind the fence?” or “How many mittens do 4 kids need?”
next example
Three flowers can stand in 4 vases, six fish can swim in 3 aquariums, etc.
At what age should you start learning mathematics?
The level of education in Russia is now such that it is the parent who will have to explain the basics of mathematics to a first-grader. In order to have time to maneuver, to enter into this process gradually (it’s not for nothing that first-graders’ eyesight declines), so that tasks are perceived as entertainment and not labor, one should begin before the child goes to school. If the baby doesn’t understand (doesn’t remember) some point, then it’s worth either trying to explain it differently, or quitting and returning to the material after a while, or finding a suitable incentive (“If you solve the example without my hint, you’ll get a prize”). It is better to write examples on paper rather than looking at the monitor.
From the age of three or even two years, parents begin to think about how to properly teach their child to read and count? The fact is that it is during this period that children become the most inquisitive and positively perceive the desire of adults to teach them something, new knowledge falls on fertile soil - children quickly assimilate new information and they begin to actively use it in their games and communication with others peace. However, explaining to a child the principles of counting, the basic principles of geometry and orientation in space is not so easy. A child may miss some numbers or swap them without understanding the logic of counting. This happens because the memory of a little person is designed in such a way that they remember only what interested them, scared them or made them happy.
In psychology there are certain age periods when to correctly master some principles of counting with your child:
- at the age of two years, the child is able to carry out ordinal counting, that is, count objects in turn from one to ten;
- at three or four years old, children learn to count consciously, group objects, divide, etc.;
- When the age reaches four or five years, the ability to count in the mind is formed and children become capable of understanding abstract concepts.
If parents stick to age characteristics, then it will be much easier to teach counting.
The task of parents is to make the learning process as interesting as possible for children; it is in this case that mastering the principles of mathematics will be easy and unnoticed.
Principles of teaching mental arithmetic
At early preschool age, parents begin to wonder: how to teach a child to count in his head? Psychologists and teachers have developed several rules and exercises, the use of which will quickly teach children to count in their heads.
The basis on which the development of new knowledge should be built is the child’s readiness for exercises with a mathematical bias, the excitement of the classes, and their frequency. It is possible to simply teach a child to count in his head step by step, maintaining the sequence of exercises:
- Before you start learning, you need to explain to your child the concepts of “more” and “less.” For example, when reading books, pay his attention to the drawings - which objects are depicted more, which colors are fewer, etc.
- Use the concept of “equally” in games. Ask your child to divide items between family members or peers in equal shares.
- At this stage, it is right to start learning addition and subtraction. Use well-known objects: fruits, toys, sticks. At 3-4 years old, the child should understand that when adding objects, the result is more, and when subtracting, the result is less.
- Also, using known objects, show that if you swap them, the total quantity will not change.
- Proceed to counting up to 10. Show different kinds addition and subtraction within this number. Double-digit numbers will come later - when the child easily navigates single-digit numbers.
- A ruler will help you learn to count in your head. Use your fingers to mark the steps on it and show it to your child. Subsequently, the ruler will become an indispensable assistant in school.
- Learn in a game format - memorization will not give the desired effect, and after a while will provoke a negative attitude towards learning.
- At this stage, the baby should understand the principles of counting order, i.e. how much was in the beginning, how much was then added or subtracted, and how much was the end result. Try to wean him off from adding and subtracting on an abacus, or using objects as visual aids and try to teach him to carry out these operations in his mind.
Learning to count can be taught by parents in any situation: during a game, a walk, or when an adult is doing household chores.
You don't have to use numbers - count everything you see, for example: how many trees do you see? Or, after dinner, ask the question: how many plates do you see on the table?
Exercises for learning to count
- Learning to count within 10
At home you can play the following games with your child:
- Teach the basics of finger counting by introducing your child to numbers up to five. However, remember that teaching this is easy, but unlearning it is much more difficult. Many children under 5th grade count using their fingers, which negatively affects their further development. To subsequently wean your child from this simplest method of counting, use special methods developed by psychologists and teachers.
- Draw or find pictures with one to five objects depicted on them; do not show the numbers to the baby yet - this may confuse him. Mastering new knowledge using pictures is considered the most effective method when children are under three years of age.
- Watch educational cartoons and programs together - there is a specialized program and videos on the Internet that use various techniques and techniques for mastering counting.
- You can teach addition and subtraction using abacuses - toy stores offer colorful and interesting options for children.
- Read rhymes for little ones that include counting and other mathematical techniques.
- Well, don’t forget to use the opportunity to count the objects around you with your baby in any free time and at any moment.
- Learning to count to twenty
Once the baby has mastered counting on fingers to five and numbers to ten, and does not “float” in their sequence, you can begin to teach counting to twenty by using the following technique:
- First of all, explain to your child that the following numbers after 10 consist of two digits. Explain that the first digits represent tens, and the second digits represent units.
- Take two containers or boxes. In one place put a two-digit number (for example, 12 or 13) of objects familiar to the child, and in the other several units or one object. This technique will allow children to clearly see the difference.
- Tell us that units always follow one another - first 11, then 12, 13, etc.
- After your child understands the basics of counting to twenty and follows the sequence of numbers well, give him tasks to strengthen the acquired skill: for example, ask him to give you 12 forks, or to pick 15 berries.
- Learning to count to one hundred
When the baby enters the elder preschool age(4-6 years old), you can teach counting up to one hundred.
- First, talk about the numbers 10, 20, 30, 40 and then up to 100, that there are only nine tens. Explain that from 10 to 20, from 20 to 30, etc. There are still a few, give examples.
- Learn one ten every day. At the end of the day - repeat, first using any available items. If learning goes poorly, return to the beginning of your studies..
- Don’t forget about educational games - when most of the numbers have been mastered, write the numbers in a row one by one, skipping one. The baby's task is to find it.
- Be sure to praise! Try not to use the phrases “you are doing it badly”, “you are not capable”, etc. Do your best to maintain a positive motivation for learning.
Mathematics is the queen of sciences
Don't forget that mathematics is not limited to addition and subtraction. In the third and fifth grades, children begin to be introduced to other rules of mathematics - multiplication and division, as well as the basics of geometry - they are taught to distinguish between different geometric figures, highlight longer or shorter ones, which are smaller or larger, etc. Parents who want to independently teach the basics of mathematics before their child enters first grade must adhere to several rules:
- First, determine the time for your classes: firstly, you need to study for at least 30 minutes a day, and secondly, the duration of one of your “lessons” should be no more than 10-15 minutes, so as not to overwork someone who is not yet ready for active brain activity. baby's activities. This can provoke a negative attitude towards the subject, which may manifest itself later when the child enters first grade.
- Regular repetition of the material covered in the context of new exercises. This means don't just memorize - if you've mastered 2+2, come back to it as you go through the length or width of the segments.
- If you notice that the child is not coping well with the task, or he does not understand you, you should not persist, it is better to return to simpler tasks and after some time use more complex examples again. Adapt to children's thinking, it differs significantly from the thinking of an adult. First, they get used to the new knowledge, then understanding comes, and only then the information is remembered.
We count as a column
It is necessary to carry out addition and subtraction in a column when these actions are impossible or difficult to perform in the mind.
It is necessary to begin learning to count in a column with an explanation of how single-digit and multi-digit numbers are obtained and how they should be written. Then show that operations with numbers are carried out by digits - ones with units, tens with tens, etc.
When adding numbers that form a sum greater than 10, the baby may have difficulty. Let’s say you need to add 12 and 29. 9+2=11 – explain to your child that when writing down one unit, the second one needs to be left “in the mind” in order to then add it to the sum of the next column of numbers, i.e. 1+2=3 and + 1 (which was “in the mind”), the total is 4 in the first column and 1 in the second, i.e. the sum of 12 and 29 is 41. If leaving “in the mind” is bad for the baby, you can write these numbers above the first column.
The one who walks will master the road!
If you are wondering how to teach your child to count quickly, you are in for a long and difficult task. Classrooms can be tedious, and many children struggle to learn the material and fall behind, unable to cope with the workload.
It is you who can form a thirst for learning, interest in mathematics and lay the foundations of practical thinking.
Let you have a development program for your baby - make a game out of learning, use educational materials, create comfortable conditions and you baby will go to first grade with positive motivation and a desire to learn new things.
