Pythagorean table of addition and subtraction up to 10. How to teach a child to count? Teachers advise

First stage. We do not use number notation

The primary task is to teach counting to 10 , n e using the corresponding numbers. Actions with objects come to the fore. For example, there was one spoon, they put another one - there were two spoons. Then you can increase the number of spoons by saying the name of the number.

Practical tasks will help in solving this problem. For example, ask your child more often about the quantity of something: how many plates, how many slippers, how many birds are on that branch. You can count anything, even the steps of a staircase.

Second phase. Getting to know the numbers themselves.

In the first grade, the numbers 1, 2, 0 are first studied, and then 3, 4, 5, 6, 7, 8, 9. The position of zero is determined by the fact that at first it is difficult for the student to understand why emptiness is indicated by a number. And then, when operations with numbers are already practiced, it becomes clear why zero is needed. For example, there were five apples on the table, five were eaten. There is nothing left, that is, zero.

Another option: These drawings are shown, and the teacher asks the children: “What has changed?” They will note: “Nothing.”

The second example shows that if three dots are completely removed from one square, then there will be an empty square and no dots left at all.

The main rule that children must understand when counting to ten is that each number is less than the next number by one and more than the previous number by one.

Techniques for learning to count to ten:

• Train game. A common practice for learning numbers in first grade. One student comes out in front of the class, he says that he is the first car. After that, another one comes out and says: one and one more will be two. And this continues until ten. Then the operation is done in reverse order. The cars “fall apart” one by one. The purpose of this exercise is to remember the order of numbers in forward and reverse order.
• Display on the line. This is an outdated method based on rote memorization and visual proof of the order of numbers.
• Counting on fingers. Traditional and easiest for children. Can be used at first until the child understands the order of the numbers. Then you need to wean them off your fingers by telling them the “secrets” of converting numbers.

• Using funny poems and cartoons about numbers. It will be interesting to watch the cartoon “How the Little Goat Learned to Count” or recite rhymes.

Memory poems for learning counting

Berry count

A fox walked along the edge of the forest:
- One, there’s a strawberry in the basket,
Two are like blueberries in the sky,
Three - ruddy lingonberries,
And four is a cloudberry,
Five - a little currant,
Six is ​​like a viburnum bead,
Seven is like a rowan tree like the sun,
Eight - blackberries in the paw,
Nine is blue blueberry,
Ten - juicy raspberries.
That's a full basket!

One - hand, two - hand -
We're making a snowman!
Three is four, three is four,
Let's draw the mouth wider!
Five - let's find a carrot for the nose,
Let's find coals for the eyes.
Six - let's put our hat on askew.
Let him laugh with us.
Seven and eight, seven and eight
We'll ask him to dance.
Nine - ten - snowman
Over the head - somersault!
What a circus!

Let's go for a walk, fingers
And the second to catch up,
Third fingers run,
And the fourth on foot,
The fifth finger jumped
And at the end of the road he fell.

• Game "Name the neighbors of the number". For example, you need to name the neighbors of the number 4.
• Exercise "The numbers got lost". You need to put the randomly arranged pictures with numbers in order. There is another interpretation of this exercise: Baba Yaga mixed up all the numbers. Help me arrange them correctly.

• There were 10 chicken legs visible under the fence. Question: How many chickens are there in total? - Counting in twos: 2, 4, 6, 8, 10 - five chickens.
• How many boots should three goslings be given? Similar to the previous problem.
• The most convenient way to count in fives is by watching the clock.

How to learn the table of addition and subtraction within ten?

After the child knows the order of numerals, it is useful to use tasks on the composition of numbers. You can, of course, memorize the composition of the number 5, for example, but it is better to use game actions with objects with a parallel focus on memorization.

For example:

There were 4 oranges in one plate and 2 in the other. How many oranges are there in total? (Task to find the sum)

There are only 6 apples, and three friends. Divide equally to everyone.

You can also combine small diagrams with simple tasks that are easy to use in the classroom and at home.

It is not difficult to give the following example of the commutative law of addition: one plate with two apples lies on the table, and another plate with four apples lies side by side; if you swap them, the total number of apples will still remain the same.

How to teach a child to add and subtract by passing through tens?

In the example below, to add the numbers 8 and 5, the second addend is expanded to complete the first addend to ten, and then the remainder is added to ten.

As for subtraction, the minuend is decomposed according to its digit composition. Using the example of 15 minus 8, we see that the number 15 is decomposed to its digit units. The result is always 10 and digit ones - 5. Now: the subtrahend must be decomposed into terms. The first term will be the digit units from 15, and the second term will be selected (children know the composition of the number 8). Now all that remains is to subtract the second term from the eight from 10. And the answer is ready. With a little practice, you can easily solve such examples in your head.

Learn table of addition and subtraction within 10

One of the important objectives of the 1st grade mathematics course is for children to firmly master the tables of addition and subtraction within ten. When studying the composition of numbers, an important point is to rely on visualization and gaming activity. Work on studying the addition and subtraction tables should be carried out systematically, the forms of work should be varied. Only under such conditions can boredom and monotony be avoided and children’s strong memorization of the composition of numbers is guaranteed.

Of course, these are paper simulators for the composition of numbers.

But most of all, children like interactive or online games! Play is one of the important means in the acquisition of knowledge, development and education of children. It can be applied within different teaching methods. A very important point in the game is overcoming obstacles, achieving goals, and searching independently. All these elements of the game develop the mental abilities of the student. It is with the help of various computer games and simulators, tasks for the interactive table that a modern teacher can diversify the types of work aimed at children mastering the addition and subtraction tables. They will help students not only bring the skill of mental calculation to automaticity, but will also give them the opportunity to consolidate the rules of working in a group.

Composition of number 5

Composition of number 6

Composition of number 7

Composition of number 8

Composition of number 9

Composition of the number 10

The following are online games aimed at consolidating and automating the composition of numbers - these are mathematical simulators that include examples and equations that will help bring knowledge of the composition of numbers to automaticity.

However, do not forget about other ways to memorize the composition of numbers, since being in front of a computer screen for a long time is harmful for a child.

The very first examples that a child gets acquainted with even before school are addition and subtraction. It is not so difficult to count the animals in the picture and, crossing out the extra ones, count the remaining ones. Or move the counting sticks and then count them. But for a child it is somewhat more difficult to operate with bare numbers. That is why practice and more practice are needed. Don’t stop working with your child in the summer, because over the summer the school curriculum simply disappears from your little head and it takes a long time to make up for lost knowledge.

If your child is a first-grader or is just entering first grade, start by repeating the composition of the number by house. And now you can take on examples. In fact, addition and subtraction within ten is the child’s first practical use of knowledge of the composition of a number.

Click on the pictures and open the simulator at maximum magnification, then you can download the image to your computer and print it in good quality.

It is possible to cut A4 in half and get 2 sheets of tasks if you want to reduce the load on the child, or let them solve a column a day if you decide to study in the summer.

We solve the column and celebrate our successes: cloud - not solved very well, smiley - good, sunshine - great!

Addition and subtraction within 10

And now randomly!

And with passes (windows):

Examples for addition and subtraction within 20

By the time a child begins to study this topic of mathematics, he should know very well, by heart, the composition of the numbers of the first ten. If a child has not mastered the composition of numbers, he will have difficulty in further calculations. Therefore, constantly return to the topic of composition of numbers within 10 until the first grader masters it to the point of automaticity. Also, a first grader should know what the decimal (place value) composition of numbers means. In mathematics lessons, the teacher says that 10 is, in other words, 1 ten, so the number 12 consists of 1 ten and 2 ones. In addition, units are added to ones. It is on knowledge of the decimal composition of numbers that the techniques of addition and subtraction within 20 are based. without going through ten.

Examples for printing without going through the tens mixed up:

Addition and subtraction within 20 with a transition through ten are based on techniques for adding to 10 or subtracting to 10, respectively, that is, on the topic “composition of the number 10,” so take a responsible approach to studying this topic with your child.

Examples with passing through tens (half a sheet of addition, half a subtraction, the sheet can also be printed in A4 format and cut in half into 2 tasks):

In this lesson you will learn how to add and subtract single-digit numbers using place value. By solving interesting problems, you will study the algorithm for adding and subtracting numbers by passing through ten and get acquainted with the table for adding single-digit numbers up to 20. You will have the opportunity to practice the previously studied material using interesting examples.

Subject:Introduction to basic concepts in mathematics

Lesson: Adding and subtracting single-digit numbers using place value. Addition table up to 20

Using a graphical model, you can explain addition of single-digit numbers passing through tens.

How can you add 9 and 7?(Fig. 1)

Rice. 1

The graphical model shows that the first term 9 must be added to 10. To do this, we divide the second term into two parts, one of which is equal to the number 1, since

9 + 1 = 10, which means 7 = 1 + 6. (Fig. 2)

Rice. 2

Let's do the addition by parts:

9 + 7 = (9 + 1) + 6 = 10 + 6 = 16

Answer: 9 + 7 = 16.

You can add these numbers differently. (Fig. 3)

Rice. 3

The second term 7 can be added to 10. To do this, we divide the first term into two parts, one of which is equal to the number 3. Therefore, 9 = 3 + 6.

Rice. 4

Let's do the addition by parts:

7 + 9 = (7 + 3) + 6 = 10 + 6 = 16

The first term is 9, it lacks one unit to 10, so we break the second term into parts. 5 is 1 and 4. We add to 9 first one unit, and then the remaining four units.

9 + 5 = 9 + (1 + 4) = 14

The first term is 6, it lacks up to 10 four units, so we divide the second term into parts: 4 and 2. We add 4 to 6 first and get ten units, and then the remaining two units.

6 + 6 = 6 + (4 + 2) = 12

The first term is 4, it lacks up to 10 six, so we divide the second term 8 into parts: 6 and 2. We first add six units to 4 and get ten units, and then the remaining two units.

4 + 8 = 4 + (6 + 2) = 12

In the minuend 15 there are five units, so we divide the subtracted 7 into parts: 5 and 2. We first subtract five units from 15, we get 10. Then we subtract the remaining two units from ten.

15 - 7 = 15 - (5 + 2) = 8

In the minuend 16 there are six units, so we divide the subtracted 9 into parts: 6 and 3. First we subtract six units from 16, we get 10. And then from 10 we subtract the remaining three units.

16 - 9 = 16 - (6 + 3) = 7

In the minuend 12 there are two units, so we divide the subtracted 4 into parts: 2 and 2. From 12 we subtract 2, we get 10. And from 10 we subtract 2.

12 - 4 = 12 - (2 + 2) = 8

Answer: 12 - 4 = 8.

Using the technique of addition and subtraction by parts with passing through ten is not always convenient, so you need to learn table for adding single digit numbers up to 20 by heart.

The figure shows a table that will make it easier for you to learn cases of adding single-digit numbers up to 20. (Fig. 7)

Rice. 7

In each column, the first term is the same, and the second increases by one, which means the sum will also increase by one. Let's find the value of these amounts.

9 + 2 = 11, therefore: 9 + 3 = 12, reasoning this way, we fill out the entire table. (Fig. 8)

Rice. 8

Each line contains amounts with the same answers. Choose the way it will be easier for you to remember the answers: by columns or by rows. If you learn the table for adding single-digit numbers up to 20 well, then it will not be difficult for you to subtract single-digit numbers within 20.

Bibliography

1. Alexandrova L.A., Mordkovich A.G. Mathematics 1st grade. - M: Mnemosyne, 2012.
2. Bashmakov M.I., Nefedova M.G. Mathematics. 1 class. - M: Astrel, 2012.
3. Bedenko M.V. Mathematics. 1 class. - M7: Russian Word, 2012.

1. Social network of educators ().
2. 5klass.net ().
3. Self-taught ().

Homework

1. Remember how to correctly add and subtract single-digit numbers using place value.

2. Help the frog solve the examples.

3. Solve the examples and color the picture.

Preparing for the game - settings

1. Any parameters and settings can be changed at any time, even during the game.
2. Initially the game is set up like this:
   • Computation type - Addition up to 10
   • Prize 1- chocolate, bonus 2- cookie
   • In a gaming session 10 calculations (arithmetic examples)
   • Percentage of examples that must be solved correctly to receive Prize 1 - 90%
   • Percentage of examples that must be solved correctly to receive Prize 2 - 70%
3. You can choose any other type of calculation - depending on what the child knows and what is being taught at school at the moment. Types of calculations in the game:
   • Addition, subtraction, addition and subtraction (mixed):
     • To 10
     • Up to 20 (with transition through ten)
     • Up to 20 (with and without passing through ten)
     • Up to 30
     • Up to 100
   • Multiplication, division or any combination - by 1, - by 2, - by 3.......etc. up to 10
   • Comparison of numbers
4. Set how many examples there will be in a game session. It is better to start with a small number of attempts - 5 or 10, so as not to discourage the child from continuing the game. When the child increases milk yield:) improves performance, you can move on to a serious game with 100-200 examples.
5. Enter the percentage of correctly solved examples for which 1st and 2nd prizes are awarded. To begin with, it is better to lower the percentage. For example, choose 70 and 50 percent for 1 and 2 premiums, respectively. Later, the rates can be increased to 90 - 70. Or even to 98% - 95% for very terribly smart children :). Enter only numbers, without the % sign!
6. Write down the bonuses your child will receive for 1st and 2nd place.
7. The settings will be saved using a cookie (a small script) and restored the next time you open the game page in your browser.

Now you can start the game!

1. To start the game, press the START button
2. When an example appears on the screen, the child must enter the answer after the "=" sign.
3. If we play “comparisons”, we need to enter the appropriate sign: . To do this, it is most convenient to use the buttons that appear next to the NEXT button
4. After entering the result, you need to press the OK button (or ENTER on the keyboard) to check whether the example was solved correctly.
5. If the example was solved correctly, "Correct" will appear on the screen. If no, “Wrong” is the correct answer. At the same time, the game will calculate the percentage of correctly solved examples
6. To move on to the next example, you need to click NEXT
7. When the session ends, the prize that the child won (or “didn’t win anything”) and the percentage of correctly solved examples during the session will appear on the screen.
8. To start a new session, click the START OVER button.

Big hopes:)

What can you expect from this game? Great help in completing the school curriculum! As a rule, within 5-7 days, in which the child plays for 30-40 minutes, he firmly masters the next type of calculation (for example, adding to 20 and passing through ten). And he practically stops making mistakes in class.