Addition and subtraction up to 100. Count correctly. Mathematics workbook. G.V.Belykh

"Addition and subtraction within 100"

Completed by: primary school teacher Akhmetyanova A.I.

Neftekamsk 2016

From the history of mathematics

Numbers from 21 to 100

Verbal counting

Examples for addition and subtraction

Addition and subtraction problems

Oral addition and subtraction techniques

Written addition and subtraction techniques

Rebuses

Coloring pages

10.Literature

FROM THE HISTORY OF MATHEMATICS

The world is built on the power of numbers.

PYTHAGORAS

How old are you? How many friends do you have? How many paws does a cat have?

A long time ago, many thousands of years ago, our distant ancestors lived in small tribes. They wandered through fields and forests, along river and stream valleys, looking for food. They ate leaves, fruits and roots of various plants. Sometimes they fished, collected shells or hunted. They dressed in the skins of killed animals.

The life of primitive people was not much different from the life of animals. And people themselves differed from animals only in that they spoke and knew how to use the simplest tools: a stick, a stone or a stone tied to a stick.

Primitive people, just like modern small children, did not know counting. But now children are taught to count by their parents and teachers, older brothers and sisters, and comrades. And primitive people had no one to learn from. Their teacher was life itself. Therefore, training went slowly.

Observing the surrounding drive, on which his life completely depended, our distant ancestor from among the many various items First I learned to isolate individual objects. From a flock of wolves - the leader of the pack, from a herd of deer - one deer, from a brood of swimming ducks - one bird, from an ear of grain - one grain.

At first they defined this ratio as “one” and “many”.

Frequent observations of sets consisting of a pair of objects (eyes, ears, horns, wings, hands) led man to the idea of number. Our distant ancestor, talking about seeing two ducks, compared them to a pair of eyes. And if he saw more of them, he said: “Many.” Only gradually did a person learn to identify three objects, and then four, five, six, etc.

Life required learning to count. To get food, people had to hunt large animals: elk, bear, bison. Our ancestors hunted in large groups, sometimes with the whole tribe. For the hunt to be successful, it was necessary to be able to surround the animal. Usually the elder placed two hunters behind the bear’s den, four with spears against the den, three on one side and three on the other side of the den. To do this, he had to be able to count, and since there were no names for numbers then, he showed the number on his fingers.

By the way, fingers played a significant role in the history of counting, especially when people began to exchange objects of their labor with each other. So, for example, wanting to exchange a spear with a stone tip that he had made for five skins for clothing, a man would put his hand on the ground and show that a skin should be placed against each finger of his hand. One five meant 5, two meant 10. When there were not enough arms, legs were used. Two arms and one leg - 15, two arms and two legs - 20.

Traces of counting on fingers have been preserved in many countries.

Thus, in China and Japan, household items (cups, plates, etc.) are counted not in dozens and half a dozen, but in fives and tens. Counting in twenties is still used in France and England.

At first there were special names for numbers only for one and two. Numbers greater than two were named using addition: 3 is two and one, 4 is two and two, 5 is two, two more and one.

The names of numbers among many peoples indicate their origin.

So, the Indians have two - eyes, Tibetans - wings, other peoples have one - the moon, five - a hand, etc.

HOW PEOPLE LEARNED TO WRITE NUMBERS

IN different countries and in different times this was done in different ways. When people did not yet know how to make paper, notes appeared in the form of notches on sticks and. animal bones, in the form of deposited shells or pebbles, or in the form of knots, tied on a belt or rope.

…Take a close look at the drawing. A man raised both hands up. He had something to be surprised about. After all, it meant a whole million. And it's not a joke. The ancient Egyptians drew such a man when they wanted to depict a million. The little man performed the duties of a number.

Now we, accustomed to writing numbers, can’t even believe that there was some other system for writing numbers. These “numbers” were very different and sometimes even funny among different peoples. IN Ancient Egypt the numbers of the first ten were written down with the corresponding number of sticks. And “ten” was indicated by a bracket in the shape of a horseshoe. To write 15, you had to use 5 sticks and 1 horseshoe. And so on up to a hundred. For hundreds, a hook was invented, for thousands, an icon like a flower. Ten thousand was indicated by a finger pattern, one hundred thousand by a frog, and a million by the familiar figure with raised hands.

It was not very convenient to write large numbers in this way and it was completely inconvenient to add, subtract, multiply, and divide them. There was a lot of fuss with these hieroglyphic icons!

It was different for the Babylonians. They wrote down the numbers by pressing the symbols with a stick on a clay tablet. And therefore all their numbers were made up of combinations of wedges. If it was necessary to write one, they put one wedge, if two, they put two wedges next to each other, five - five.

Much later, the numbers began to be depicted differently. Look at the Roman numbering: I - one, II - two, III - three. There are five fingers on a person's hand. In order not to write five sticks, they began to depict a hand. However, the hand drawing was made very simple. Instead of drawing the entire hand, it was depicted with a V, and this symbol began to represent the number 5. Then they added one to five and got six. Like this: six - VI, seven - VII.

And how many are written here: VIII? That's right, eight. Well, how can we write four in short? It takes a long time to count four sticks, so we subtracted one from five and wrote it down like this: IV is five minus one.

How do you write ten?

You know that ten consists of two fives, so in Roman numbering the number “ten” was represented by two fives: one five stands as usual, and the other is turned down - X. Otherwise, ten can be written with two intersecting sticks.

If next to X you write one stick on the right - XI, then it will be eleven, and if on the left - IX - nine.

Remember the peculiarity of Roman notation: the smaller number to the right of the larger one is added to it, the one to the left is subtracted. Therefore, sign VI means 5+1, that is, 6, and sign IV means 5-1, that is, 4. Learning to read numbers written in Roman numeration is not difficult, and we advise you to do this without fail.

Roman numerals are used quite often these days. For example, Roman numerals are sometimes used on a watch dial; in books, they often indicate the volume or chapter number.

Solve these examples:

V+II= V+I=

IIX+I=X-II=

VI+II= VIII-III=

X-I= IХ+I=

Roman numbering was a great invention for its time. Still, it was not very convenient for writing and performing arithmetic operations.

After people created the alphabet, in many countries they began to write numbers using letters.

The Greeks and Slavs added special symbols to the letters so as not to be confused with ordinary letters. IN Ancient Rus' the letter “a” stood for one, “c” for two, and “d” for three. And so on. A special dash above the letter (title) indicates that it is not a letter, but a number. Also, the letter “a” with a special symbol on the left meant a thousand, and the letter surrounded by a circle meant ten thousand, or “darkness,” as such a number was called then.

However, letter numbering was also inconvenient for indicating a large number. At that time, people had not yet realized that the same number could mean different numbers depending on its position in a series of other numbers, as it is now with us. A great achievement was the introduction of zero into counting, which made it possible to indicate the missing digit when writing numbers. (More on zero in a moment.)

A way to write numbers in just a few characters (ten); which is now accepted throughout the world, was created in Ancient India. The Indian counting system then spread throughout Europe, and the numbers were called Arabic (as opposed to the Roman numerals that are sometimes used). But it would be more correct to call them Indian.

And now, I think you will be interested in listening to the story...

IT ALL STARTED WITH FIVES

I remember when I had to sit at the first desk, right in front of the teacher's table, I tried my best to look at the class register and tell my classmates who got what mark. But you can’t talk during the lesson, so I had to resort to using my fingers.

They gave Favorsky a high five - I, spreading my fingers, showed five. They gave Korolkov a four - I raised four fingers. If it was necessary to report a three, three fingers were used, and about a two, two, and one, about a one.

I was terribly proud that I had come up with such an ingenious method. The fact that it is the oldest that can be did not even occur to me then.

It turns out that in. In the old days, among all nations, only such manual calculation existed - there was no other. It was necessary to write down numbers - fingers were replaced with sticks. What number - so many sticks. Sometimes they were placed lying down, sometimes standing. Roman numerals, which are especially similar to manual, stick, counting, were written like that - standing up. And in our current numbers that came to us from the Arabs, there is, like an outstretched finger, only one. The rest lay down on their sides. Deuce - two lying sticks, connected only by quick writing with an oblique stroke; three - three sticks lying on their sides with two oblique strokes. Five is like the outline of a five with a thumb and the rest bent. It’s not for nothing that our words “five” and “pastern,” which in Old Russian means “hand,” are so similar to each other.

And the four, doesn’t it look like four sticks lying next to each other?

It doesn’t look like those lying in a row, but it does look like a broken cross, where each stick is connected to the other with a cursive stroke.

These first five numbers are the most important, because all the rest are made up of them.

The fact that most peoples depicted numbers with sticks is best illustrated by the unit. It was written differently in different countries. But everywhere it was similar to the current unit.

Soon you will learn in more detail about each number and understand that it is impossible to do without knowledge of mathematics. How, for example, can you calculate how many bricks are needed to build a house, how much metal is needed for a ship, or how much wood is needed for a children’s cube? That is why mathematics is called the queen of all sciences. Learn it better - you will become “kings”!

So, let's begin our unusual journey into the fairy-tale kingdom of mathematics, where all ten numbers live happily. We are sure that you will make friends with them and learn a lot of interesting things. So, let's go!

Without an account there will be no light on the street.
Without counting, a rocket cannot rise.
Without an invoice, the letter will not find the addressee
And the boys won’t be able to play hide and seek.

Our arithmetic flies above the stars
Goes to the seas, builds buildings, plows,

Plants trees, forges turbines,
It reaches right up to the sky.

Count, guys, or rather count,
Feel free to add a good deed,
Quickly read out the bad things,
The textbook will teach you accurate counting,
Hurry up to work, hurry up to work!

(Yu. Yakovlev)

Examples

1) 70 – 3 4 + 20
35 + 5 67 – 60
32 – 9 100 – 1
94 – 5 38 – 8 67 – 20

83 – 40 60 – 27 80 – 4 67 – 27 83 – 43

2) For oral counting:

Reduce the number 73 by 70.

Find the difference between the numbers 57 and 7.

Increase the number 50 by 8.

Find the sum of the numbers 49 and 1.

How much must be subtracted from 64 to become 60? How about making it 4?

How much must be added to 90 to become 99? How about making it 100?

* * *

* * *

Reduce 12 by 6.

Find the sum of numbers 8 and 7

Reduce 60 by 2.

What number must be increased by 9 to make 17?

Find the difference between the numbers 12 and 8.

What number must be subtracted from 4 to get 7?

How many tens and how many units are there in the numbers: 42, 51, 60, 94, 8.

Name the number in which: 6 dec. and 2 units; 7 units; 5 units; 8 units; 3 dec. 1 unit; 4 units

3) Verbal counting.
1. Calculate the sum of the numbers 15 and 19.
2. Find the difference between the numbers 55 and 13.
3. Reduce 27 by 3 times.
4. One factor is 5, the other is 4. What is the product of these numbers?
5.Look at the series of numbers: 27, 18, 54, 9, 10, 90, 36, 50, 70. What two groups can these numbers be divided into?

6. Name a number that has 7 tens.
7. Name a number that has 9 units.
8. Name a number that has 9 tens and 4 units.
9. Name a number that has 5 tens and 6 ones.

4) Counting starts according to the arrow.

Oral counting (problems in verse)

1) The squirrel was returning from the market and met a fox.
-What are you talking about, squirrel? - the fox asked a question.
– I bring 3 nuts and 7 cones to my children.
- You, fox, tell me: what is 7 + 3?
The fox quickly counted and counted exactly eight.
- Oh you, Red-haired cheat, deceived the squirrel cleverly!
– You guys, don’t believe her and check her answer!

2) Mushrooms were drying on the trees.
Well, they got wet in the rain.
Forty yellow butternuts,
Eight thin mushrooms,
Yes, three red foxes -
Very sweet sisters.
You guys are not silent.
Tell me how many mushrooms there are.

3) -minuend is 80, subtrahend is 25, what is the difference?

1st term – 15, 2nd term – 15, sum = ?

Added 4 numbers, each of which is equal to 25, how much is the total? How to calculate in a convenient way?

I thought of a number, added 70 to it and got 100. What number did I think of?

The number 60 was reduced by 8, how much did you get?

What number comes before the number 57? Follows the number 57?

4) On branches decorated with snow fringe,
The ruddy apples grew in winter.
The bullfinches have landed on the apple tree, look!
About three dozen of them arrived cheerfully.
Look here, they are flying.
There are now fifty of them.
Think about it
How many birds came later?

5) The sea lion cleaver said, reasoning:
My family is very small, -
Me, seven wives, and six children...
How many suits do you need for the summer?

6) Challenges for ingenuity:

Lena is Anna's daughter, and Anna is Natalya's daughter. Who is Lena Natalia related to? (Granddaughter.)

The assembly shop received 70 cans and 80 handles for them. How many ready-made cans can be assembled from them? (70 cans.)

You need to bring 9 logs from the forest. You can put no more than 4 logs on the machine. How many times will you have to go to the forest to transport all the logs?

In 5 years Kostya will be 13 years old. How old was Kostya 3 years ago?

Tanya had 7 pencils. She gave her brother 1 more pencil than she kept for herself. How many pencils does Tanya have left?

When a heron stands on one leg, it weighs 12 kg. How much will she weigh if she stands on two legs?

There are 10 fingers on two hands. How many fingers are there on eight hands?

“How many girls are there in our class?” - Yasha asked Gali. Galya, after thinking a little, answered: “If you subtract the number written as two eights from the largest two-digit number, and add the smallest two-digit number to the resulting number, then you will get exactly the number of girls in our class.” How many girls were there in this class? (21, 99-88=11, 11+10=21).

One rooster woke up 2 sleeping people. How many roosters does it take to wake up 10 people?

The hares (2) and the squirrel got tired of playing burners and sat down in one row. In how many ways can they do this? (6)

The staircase to the ship consists of 13 steps. What step do you need to stand on to be in the middle? (7)

Of the three brothers, December was taller than January, and January was taller than February. Which brother is tallest? Who's lower?

There are 4 apples on the table. One was cut in half. How many apples are on the table?

Two collective farmers were walking into the garden and met three more collective farmers along the way. How many collective farmers went to the garden?

Nina is shorter than Roma, Masha is shorter than Tolya, but taller than Roma. Who is the tallest?

7) 1. A California cuckoo can run 40 km in 1 hour, and an ostrich can run 30 km more. How many kilometers can an ostrich run in 1 hour?

2. A small bird, a hummingbird, makes 30 beats per second with its wings, and the eagle makes only 1 beat. How many more beats does a hummingbird make than an eagle?

3. It is estimated that one pair of woodpeckers brings 90 caterpillars to their chicks in 1 hour, and a pair of starlings brings 60 more to their chicks. How many caterpillars do starlings bring in 1 hour?

8) The sun sheds light on the earth,
Ryzhik is hiding in the grass.
Nearby, right there in yellow dresses,
There are 12 more brothers.
I hid them all in the box,
Suddenly I look - there is butter in the grass.
And 15 of those are oily,
They are already in the box.
And you have the answer ready:
How many fungi did I find?

9) Entertaining tasks

1. A cat sits in each of the 4 corners of the room. Opposite each of these cats are three cats. How many cats are there in this room?

2. The father has six sons. Every son has a sister. How many children does this father have in total?

3. In a tailoring workshop, 20 m were cut from a piece of cloth 200 m apart every day, starting from March 1. When was the last piece cut?

4. There are 3 rabbits in a cage. Three girls asked to give them one rabbit each. Each girl was given a rabbit. And yet there was only one rabbit left in the cage. How did this happen?

5. 6 fishermen ate 6 pike perch in 6 days. How many days will it take 10 fishermen to eat 10 pike perch?

6. There were 40 magpies sitting on one tree. A hunter passed by, shot and killed 6 magpies. How many magpies are left on the tree?

7. Two diggers will dig 2 m of a ditch in 2 hours of work. How many diggers does it take to dig 100 m of the same ditch in 100 hours of work?

8. Two fathers and two sons divided 3 oranges among themselves so that each got one orange. How could this happen?

9. A caterpillar crawls from the ground along the stem of a plant whose height is 1 m. During the day it rises by 3 dm, and at night it drops by 2 dm. How many days will it take for the caterpillar to crawl to the top of the plant?

1)45 + 14 =

2)73 - 2 =

3)57 + 38 =

4)19 + 51 =

5)97 - 54 =

6)59 - 25 =

7)18 + 30 =

8)42 + 20 =

9)66 + 16 =

10)42 + 5 =

11)48 + 19 =

12)13 + 59 =

13)86 - 1 =

14)11 + 76 =

15)79 + 59 =

16)43 - 9 =

17)14 + 4 =

18)38 + 13 =

19)37 + 44 =

20)81 −41 =

21)94 −85 =

22)86− 66 =

23) 6 + 23 =

24)26 - 7 =

25) 3 + 60 =

26) 4 + 13 =

27)74 +11 =

28)52 + 15 =

29)60 + 5 =

30)81 -56 =

31)97 + 3 =

32)80 + 1 =

33)47 + 39 =

34)77 −42 =

35)20 + 60 =

36)77- 57 =

37)32+ 13 =

38)83 + 7 =

39)54+ 21 =

40)21 -19 =

41) 5 + 76 =

42)87 - 1 =

43)42 + 50 =

44) 4 + 31 =

45)73 − 26 =

1) 1. Write down the numbers: thirty, fifty, eighty, forty.
2. Write down the number in which: six tens, two tens and five units, nine tens one unit, ten tens.
3. Choose neighbors of numbers 48 and 47; 45 and 47; 47 and 49; 49 and 50.
4. Write down the numbers in descending order: 75, 18, 24, 31, 90.52
5. Find the correct entry and check the box: number 27 contains
- seven tens and two units;
  two tens and seven units.
- 2) Find the meaning of expressions using the commutative property of addition:
  a)20+2+8+40 b)17+5+5+3
  
  c)18+11+2+9 d)40+1+9+50
  e)40+28+2 f)30+26+4
  g)63+7+20
  3) Read the entries using the words “more than” and “less than” so that the entries are correct and put a sign (<,>).
  15…17 17…71
- 21…12 34…65
  19…61 76…98
  25…56 56…54
  67…74 87…13
  43…34 20…40
  54…65 50…48
  4) Decipher and write the name of the ancient Russian measure of length, putting the answers in decreasing order.
  5) Write the correct answer.
  a) How many centimeters are in 1 meter? In 1 m =
  
  b) How many decimeters are in 1 meter? In 1 m =
- c) How can you write a word abbreviated as a number?meter ?
- d) Write down 10 meters, 12 meters, 7 meters.
  
  e) Express in decimeters:
  1) 8 m 1 dm; 2) 3 m 9 dm; 3) 6 m.
  
  f) Express in meters and decimeters:
  a) 54 dm; b) 77 dm.
- 6) Decipher the recording.
- 7) Help the squirrel collect mushrooms in the basket. To do this, you need to solve the examples and connect the cards with the correct answer with lines.
- 8)
- Addition and subtraction problems within 100
  Tasks:
  1 .What numbers are missing? Give the number following each missing one.
  2 .What number follows the number20,68,78,45,65,90,47,39,75,87,60,94,63,81,29,83,76.
  3. How many sticks are there in each picture?
- 4. There are twenty-nine sticks in the picture. Let's put another one. How many sticks are there?
- 5. Name all the numbers from 20 -39; 65-78; 76-81; 34-56; 55-67.
- 6. Decide orally.
  There were 15 willows growing by the pond. 6 old willows were cut down and 9 young ones were planted. How many willows are there at the pond?
  For lunch, mom served 3 cucumbers and 6 more tomatoes. At lunch we ate 4 tomatoes. How many tomatoes are left?
  There were 15 buckets of water in the barrel. To water the trees, 6 buckets were used, but then 9 buckets of water were added to the barrel. How many buckets of water are there in the barrel?
  There were 14 students in the class doing their homework. Then 6 children left and 9 came. How many children are there in the class?

When learning addition and subtraction V within 100 sobl! All the requirements for learning to understand actions within 20 are met.

Many of the difficulties that schoolchildren with intellectual disabilities experience when performing addition and subtraction operations within 20 do not disappear when performing the same deist! within 100. As experience and special research show, students still experience great difficulties when performing the subtraction operation. Largest quantity errors (occurs when solving examples of addition and subtraction by moving through the digit. A characteristic error when subtracting, the units of the subtrahend are subtracted by the units of the minuend. For example, 35-17 = 22. There is also a tendency to replace one word with another. For example: 64-16 = 80 , 17+2=15 (instead of subtraction, addition is performed and vice versa).When performing actions < With two-digit numbers, students often take into account only the units of one category; the units of another category (the first or second components) are rewritten without change (36+11=46, 85-24=64). The following mistakes are also made: students add or subtract without paying attention to the digits: units are added with tens (37+2=57, 38-20=36), a larger number is subtracted from a smaller number (17-38=21), with When solving complex examples, only one action is performed (12+14-8=26).

It is characteristic that students of the VIII type school for a long time do not master rational methods of calculation, lingering on the methods of counting specific objects and counting by unit.

The reasons for the errors lie in insufficiently solid knowledge of the addition and subtraction tables within 10 and 20 (39-7=31, 42+7=48), insufficiently solid knowledge and understanding of the positional meaning of numbers in a number, or in the inability to use one’s knowledge in practice, as well as in the peculiarities of thinking of schoolchildren with intellectual underdevelopment.

The sequence of studying the operations of addition and subtraction is determined by the increasing degree of difficulty when considering various cases.

1.Addition and subtraction of round tens (30+20, 50-20,
the solution is based on knowledge of the numbering of round tens).

2. Addition and subtraction without jumping through the digit.
154

B+5 35-5=30 41-2=45

|B+30 3.5-20=5 47-32=47-30-2

5+26=30+20+6 56-20=5 47-42=47-40-2

86+30 56-26=56-20-6 47-27=47-20-7
145+2=40+5+2
145+32=45+30+2

p8. Adding a two-digit number to a single-digit number, when the sum adds up to round tens. Subtracting No-digit and two-digit numbers from round tens:

4. Addition and subtraction with transition through digit.

D All actions with examples of groups 1, 2 and 3 are performed using methods of oral calculations, that is, calculations must begin with units of higher ranks (tens). Examples are written on a line. Calculation techniques are based on students' knowledge of numbering, decimal composition of numbers, tables of addition and subtraction within 10.

The operations of addition and subtraction are studied in parallel. Each case of addition is compared with the corresponding case of subtraction, their similarities and differences are noted.

Such addition cases as 2+34, 5+45, etc. are not considered independently, but are solved by rearranging the terms and considered together with the corresponding cases: 34+2, 45+5.

An explanation of each new case of addition and subtraction is carried out using visual aids and didactic material with which all students in the class work.

Let's look at techniques for performing addition and subtraction operations within 100:

1) 30+20= 50-30=

The reasoning goes like this: 30 is 3 tens (3 bunches of sticks). 20 is 2 tens (2 bunches of sticks). To 3 bunches of sticks we add 2 bunches, in total we get 5 bunches of sticks, or 5 tens. 5 tens is 50. So 30+20=50.

The same reasoning is carried out when subtracting circle/i.g tens.

A detailed record at first allows you to consolidate the consistency of your reasoning:

3 dec.+2 dec.=50 dec.=50,._. _ ^^.-^ ds1..=oi

All aids, which and<

used when studying numbering. Actions are carried out o6>

definitely on the accounts.

2) 30+26 26+30 „„ „„

The solution to examples of this type is also explained using manuals (abacus, arithmetic box, abacus). It is useful to show students a detailed recording of the action:

56=50+ 6 50-30=20 20+ 6=26

or 30+26=30+20+6=50+6=56.

The teacher uses this recording only when explaining. Students need to be shown a short form of recording, but require verbal commentary when performing actions, and when recording - underlining the tens:

The above cases of addition and subtraction are solved responsibly using the same techniques. However, in terms of difficulty they are not significant. For a student with an intellectual disability, it is much easier to add a larger number to a smaller number. (2+7)-9-7 is |the most difficult case of table subtraction. All this suggests that, observing the requirement of a gradual increase in difficulties in solving examples, it is necessary to take into account not only the calculation methods, but also the numbers on which the actions are performed. Explanation:

“In the number 45 there are 4 tens and 5 ones. Let's put the number on the abacus. [Add 2 units. We get 4 tens and 7 ones, or the number 47.”

12=10+ 2 45+10=55 55+ 2=57

45+12=45+10+2 57-12=57-10-2

This technique is advisable because when subtracting with a transition through a digit, the use of the technique of decomposition into digit terms of two components will lead to the subtraction of a larger number of units of the subtrahend from a smaller number of units of the minuend (43-17, 43 = 40 + 3, 17 = 10 + 7, 40 -10, 3-7).

30+26=56 26+30=56

It is useful to perform actions on accounts.

It should be noted that some students for a long time cannot learn to carry out reasoning when solving examples, but they can easily cope with solving them on abacus and do not mix up the digits. These students may be allowed to use an abacus.

For greater clarity and a better understanding of the positional meaning of numbers in a number, writing units and tens on the board and in notebooks can be done in different colors for some time. This is important for those students who have difficulty distinguishing digits.

3) 45+2 42+7

47-2 49-7

4) 45+12 42+17

57-12 59-17 57-52

50- 5 70-25, 50+45

50-5 _ 70-25

45=40+ 5 5+ 5=10 40+10=50

25=20+ 5 45+20=65 65+ 5=70

50=40+10 10- 5= 5 40+ 5=45

25=20+ 5 70-20=50 50- 5=45

The reasoning when solving these addition examples is no different from the reasoning when solving addition examples of the two previous types, although the latter are more difficult for students.

When considering cases of the form 50-5, it is necessary to point out that it is necessary to take one ten, since in the number 50 the number of units is 0, split the ten into units, subtract 5 from ten, and add the remaining tens with the difference.

For convenience and greater clarity of presentation of computational techniques, we examined each new case in isolation. 1 the process of teaching students oral computing techniques! It is necessary to look at each new case of addition or subtraction in inextricable connection with the previous ones, post-hatch incorporating new knowledge into existing ones, constantly comparing them. For example, 45+2, 45+5, 45+32, 45+35. Compare examples find general and different. Give examples of this type.

This kind of task will allow you to see the similarities and differences in examples, will force students to think, to consider each addition not in isolation, but in connection and interdependence. This will make it possible to develop a generalized method of mental calculations. (Solve, compare calculations and compose similar examples: 40-6, 40-26, 40-36, 40-30.)

4) Addition and subtraction with transition through rank (2nd group of examples) are performed using written calculation techniques, i.e., calculations begin with units of lower ranks (from ones), with the exception of division, and the entry is given in a column.

Students become familiar with notation and algorithms for written addition and subtraction and learn to comment on their activities. It is necessary to compare different cases of first addition, then subtraction, establish similarities and differences, involve students in the process of composing similar examples, and teach them to reason. Only such techniques can give a corrective effect.

When students learn to perform the operations of addition and subtraction with the transition through place value to column, they are introduced to performing these actions using mental calculation techniques.

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The explanation is usually carried out on an abacus, sticks, bars or cubes of an arithmetic box, and an abacus. 158

Stele suggests reading the example, putting 38 on the abacus, having first found out its decimal composition. First, I units need to add 3 units: the number 8 is added: yatka, i.e. 2 units are added; the resulting ten iiis are replaced by one ten, resulting in 4 tens. 1 more unit is added to 4 Gntkas.

When subtracting a single-digit number from a two-digit number with a transition through the digit, first all the units of the minuend are subtracted, I then the remaining units of the Counted are subtracted from the round tens.

Detailed 38+3=41 38+2=40 40+1=41

Both when adding and when subtracting, you need to decompose the second addition or minuend into two numbers. When adding, the second addition is decomposed into two numbers such that the first complements the number of units of a two-digit number to a round ten.

When subtracting, the subtrahend is decomposed into two Numbers such that one is equal to the number of units of the minuend, i.e., I so that when subtracting, a round number is obtained.

When performing actions, the difficulty for students is the ability to correctly decompose a number, perform the sequence of necessary operations, remember and add or subtract the remaining units.

For example, by performing the action 54 + 8, the student can correctly add 54 to 60. The difficulty is caused by decomposing the number 8 into 6 and 2. The student uses the number 6 to get a round number, but how many more units are left to add to the round tens (to 60), he forgets.

Taking this into account, it is necessary, before considering cases of this type, to repeat again and again the composition of the numbers of the first ten, to carry out exercises on adding numbers to round tens, for example: “How many units are missing to 50 in the numbers 42, 45, 48, 43, 4? What number must be added to 78 to get 80? We need to consider cases of the form 37+3+2=40+2=42 and seek an answer to the question: “How many units in total were added to the number (37)?”

“How many units were subtracted from the number 43?” This means that 43-5 = I For some students of the VIII type school, when solving the tal type of examples, partial clarity is used, for example 38 + 7. The student puts 7 bones on the abacus or draws sticks and reasons like this: “I’ll add 2 to 38, it will be 40 (and removes or crosses out 2 sticks), now I’ll add 5 more sticks to 40.”

Another example: 45-8. The student puts down 8 sticks and judges

It goes like this: “First, subtract 5 from 45, it becomes 40 (removes 5 sticks^

all that remains is to subtract 3. Subtract 3 from forty, leaving 37. 45-8=3?

Solving examples of this type is based on the solution techniques already known to students:

38+24 24=20+ 4 38+20=58 58+ 4=62

The solution to these examples is based on the second expansion! addend and subtract into bit addends and successor | by adding and subtracting them from the first component of the action.

Schoolchildren with intellectual disabilities due to instability!
attention, inability to concentrate often make mistakes
of this nature: they will add or subtract tens, but forget about
add or subtract units. I

Having not firmly grasped the technique of calculations, positional values | digits in a number, students add tens with ones, subtract tens from the units of the minuend: 54-18 = 43. I

Students should be able to perform addition and subtraction by moving through digits on an abacus.

For example: 56+27. First, let's set aside the number 56. Let's add 20. The result is 76. Let's add 7. Let's add 76 to 80, replace 10 units with one ten, add 3 more units to 8 tens.

Let's do the subtraction on the abacus (Fig. 11): 41-24.

In order for students to acquire the skills and abilities to solve the application of addition and subtraction with transition through rank, it is necessary to complete quite a lot of exercises. Examples can be given

with two and three components, alternating the actions of addition and reading. The following examples are also solved: 48+(39-30).

The arrangement of material with a gradually increasing degree of content allows students to master the necessary techniques when performing addition and subtraction operations. The success of mastering computational techniques largely depends on activity | lmikh students.

In a Type VIII school there will always be a group of children for whom mastering oral computational techniques when solving examples with transition through rank (27+38, 65-28) is inaccessible. Such students will solve examples using written calculation techniques (in a column).

When studying hundreds, the names of the components and results of addition and subtraction are fixed. In order for the names of the components to be included in the active vocabulary of students, it is necessary to use these names when reading expressions, for example: “The first term is 45, the second term is 30. Find the sum. The minuend is 80, the subtrahend is 32. Find the difference. Find the sum of three numbers: 30, 18, 42. What are numbers called when adding? Subtract 40 from the sum of the numbers 20 and 35,” etc.

Studying the Hundred introduces students to finding the unknown components of addition and subtraction.

When studying the operations of addition and subtraction within 10 and 20, students solved examples with unknown components using the selection technique, for example: P+3=10, 4+P=7, P-4=6, 10-P=4.

When studying hundreds, an unknown component is designated by a letter and students become familiar with the rule for finding unknown components.

Before introducing students to the solution of examples containing an unknown component, it is necessary to create a situation, come up with a vital and practical problem that would give students the opportunity to understand that using two known components and one unknown one, this third unknown component can be found.

6 Perova M. N.

For example: “There are several pencils in the box, but there. 3 more pencils lived. There are now 8 pencils in the box. Were there any chipped pencils in the box?

This task should be dramatized. The student takes a box of pencils (the number of pencils in it is unknown), says; 3 pencils there. Counts all the pencils in the box. I turns out to be 8. The teacher suggests that the number of pencils in which there was 1 (that is, unknown), be designated by the letter X. and recording x+3=8. If we subtract from 8 pencils the 3 pencils that were added, then 5 pencils will remain: *+3=8, x=8- 3, x=5.

Examination. 5+3=8 8=8

After solving several more problems with real objects, we can conclude: “To find the unknown term! you need to subtract a known term from the sum.”

Finding an unknown minuend is also best demonstrated, as experience shows, by solving a practical problem, for example: “There are several mushrooms in the basket.” (X), d she took 5 mushrooms (we take), there are 4 mushrooms left in the basket (count 1). How many mushrooms were in the basket?

The task is being played out. Let us designate the mushrooms that were in the basket with the letter X and write: X- 5=4. “What action can you use to find out how many mushrooms there were?” (Addition.)

Examination. 9-5=4 4=4

Questions and tasks

1.Make a thematic plan for studying the numbering of the first hundred numbers
in the 3rd grade of the VIII type school.

2.Name the stages of studying the numbering of numbers of the first hundred.

3.What is the sequence of learning addition and subtraction within
100?

4.Make a summary of the lesson, the purpose of which is to familiarize the student
involving an algorithm for written addition or subtraction within 100.

5.Copy out 3-5 types from the mathematics textbook for 3rd grade
development and correction exercises analysis and synthesis, comparison. Co
do 5 exercises aimed at solving similar problems.

Chapter 11

In mathematics, of course, it is important to be able to think and think logically, but practice is no less important. Half of the mistakes in math exams are made due to incorrect calculations of simple operations with numbers - addition, subtraction, multiplication, division. And it is important to develop these skills in primary school. In order not to miss anything, it is necessary to systematically work with the child using special exercise books. They allow you to practice mathematical skills and abilities and bring them to automaticity. There are a variety of simulators, you don’t have to download them all, just one or two you like is enough. The manuals can be used when working with younger schoolchildren regardless of the program under which the training is conducted.

Mathematics. We solve examples with passing through tens.

A notebook for practicing addition and subtraction skills with passing through tens. Not just examples, but Interesting games and tasks.

Task cards. Mathematics. Addition and subtraction. 2nd grade

Convenient cards for teachers of second graders. 2 options for addition and subtraction of the same type. Suitable for organizing independent work in mathematics, depending on progress in the program.

Mathematics. Addition and subtraction within 20. Grades 1-2. E.E. Kochurova

In various mathematics courses, the topic of addition and subtraction within 20 is studied either at the end of the 1st grade or at the beginning of the 2nd. In any case, the manual will help to consolidate the learned methods of manipulating numbers; in some tasks these methods are presented in the form of unique hints. During independent work with a notebook, the child is guided by the sample implementation and algorithmic instructions. The ability to use such tips in studying will allow the student not only to find and use the necessary information while completing a task, but also to carry out self-test.

The notebook begins with practicing addition and subtraction skills within 10; this part is also suitable for first-graders.

Mathematics exercise book for 2nd grade

The notebook contains not only examples of addition and subtraction, but also conversion of units into each other, and comparison of calculation results (more or less).

3000 examples in mathematics (counting within 100 part 1)

Timed counting simulator. Time it to solve one column of examples and write it down in the box below. Pay attention to the columns that the child took more than 5 minutes to solve, which means he has difficulties with this type of example. Examples are given for addition and subtraction within ten and with transition through ten, addition and subtraction of tens, manipulation within hundreds.

Counting from 0 to 100

This copybook gives many examples of addition and subtraction to strengthen mental counting skills within 100.

We think it's correct. Mathematics workbook. G.V.Belykh

The notebook is also made in the form of a simulator, full of examples and equations. It starts with counting within ten, then within a hundred (addition, subtraction, multiplication and division), and ends with comparing equations (examples with greater than, less than, equal signs).

The manuals will be useful both for primary school teachers in their work and for parents to study at home with their children, in particular during the summer holidays. Tasks of different difficulty levels will allow you to complete differentiated approach to learning.