In mathematics, of course, it is important to be able to think and think logically, but practice is no less important in it. Half of the mistakes on exams in mathematics are due to incorrect calculation of simple operations with numbers - addition, subtraction, multiplication, division. And it is important to practice these skills even in elementary school. In order not to miss anything, it is necessary to systematically engage with the child using special exercise books - simulators. They allow you to work out mathematical skills and abilities and bring them to automatism. The simulators are varied, it is not necessary to download all of them, one or two of your favorites are enough. The manuals can be used in work with younger students, regardless of the program in which the training is conducted.
Maths. We solve examples with the transition through a dozen.
A notebook for practicing the skills of addition and subtraction with the transition through a dozen. Not just examples, but interesting games and tasks.
Task cards. Maths. Addition and subtraction. 2nd grade
Convenient cards for second graders teacher. 2 options for addition and subtraction of the same type. Suitable for organizing independent work in mathematics, depending on the progress in the program.
Maths. Addition and subtraction within 20. Grades 1-2. E.E. Kochurova
In different courses of mathematics, the topic of addition and subtraction within 20 is studied either at the end of grade 1, or at the beginning of grade 2. In any case, the manual will help to consolidate the studied methods of manipulating numbers; in some tasks, these methods are presented as a kind of hints. In the course of independent work with a notebook, the child is guided by the execution pattern and algorithmic instructions. The ability to use such prompts in learning will allow the student not only to find and use the necessary information during the assignment, but also to carry out self-examination.
The notebook begins with practicing addition and subtraction skills within 10, this part is also suitable for first graders.
Math exercise book for grade 2
The notebook contains not only examples of addition and subtraction, but also the conversion of units to each other, and the comparison of calculation results (more or less).
3000 examples in mathematics (counting within 100 part 1)
Simulator with a time count. Time to mark one column of examples for the solution and write down in the window below. Pay attention to the columns that the child solved for more than 5 minutes, which means that he had difficulties with this type of examples. Examples are given for addition and subtraction within ten and with a transition through ten, addition and subtraction of tens, manipulations within a hundred.
Score from 0 to 100
In this recipe, many examples of addition and subtraction are given to consolidate the skills of oral counting within 100.
We count correctly. Workbook on mathematics. G.V. Belykh
The notebook is also made in the form of a simulator, solid examples and equations. It starts with counting within ten, then within a hundred (addition, subtraction, multiplication and division), ends with a comparison of equations (examples with signs greater than, less than, equal).
The manuals will be useful both for primary school teachers in their work, and for parents to study at home with children, in particular, during the summer holidays. Tasks of different levels of complexity will allow for a differentiated approach to learning.
"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 tricks of addition and subtraction
Written tricks for addition and subtraction
Rebus
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 the fields and forests, along the valleys of rivers and streams, looking for food for themselves. They ate leaves, fruits and roots of various plants. Sometimes they caught fish, collected shells, or hunted. They put on the skins of slain 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 possessed speech and knew how to use the simplest tools of labor: a stick, a stone or a stone tied to a stick.
Primitive people, like modern small children, did not know the count. 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. Life itself was their teacher. Therefore, the training was slow.
Observing the surrounding drive, on which his life completely depended, our distant ancestor first learned to distinguish individual objects from many different objects. From a pack of wolves - the leader of the pack, from a herd of deer - one deer, from a brood of floating ducks - one bird, from an ear with grains - 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 a person to the idea of \u200b\u200bnumber. Our distant ancestor, talking about seeing two ducks, compared them with a pair of eyes. And if he saw more of them, then he said: "A lot." Only gradually did a person learn to distinguish three objects, and then four, five, six, etc.
Life required learning to count. Getting 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 beast. Usually the elder put two hunters for the bear 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 made by him for five skins for clothes, a man put his hand on the ground and showed that a skin should be placed against each finger of his hand. One five meant 5, two - 10. When there were not enough hands, the legs were also used. Two arms and one leg - 15, two arms and two legs - 20.
Traces of counting on fingers have survived in many countries.
So, in China and Japan, household items (cups, plates, etc.) are considered not dozens and half a dozen, but fives and tens. In France and in England, the counting of twenties is still in use.
Special names for numbers were initially only available for one and two. Numbers more than two were called using addition: 3 is two and one, 4 is two and two, 5 is two, two more and one.
The names of numbers in many peoples indicate their origin.
So, the Indians have two eyes, the Tibetans have wings, other peoples have one - the moon, five - a hand, etc.
HOW PEOPLE LEARNED TO RECORD NUMBERS
In different countries and at different times, this was done in different ways. When people did not yet know how to make paper, the notes appeared in the form of nicks on sticks and. bones of animals, in the form of deposited shells or pebbles, or in the form of knots. Tied to a belt or rope.
…Look closely at the drawing. A man raised both hands up. He had something to be surprised at. After all, he meant a million. And it's not a joke. The ancient Egyptians drew such a man when they wanted to portray a million. The little man acted as a number.
Now we, accustomed to drawing numbers, do not even believe that there was any other system of writing numbers. These "numbers" were very different and sometimes even funny among different peoples. In ancient Egypt, the numbers of the first ten were recorded with the corresponding number of sticks. And “ten” was designated by a horseshoe-shaped bracket. To write 15, you had to put 5 sticks and 1 horseshoe. And so on up to a hundred. For a hundred, a hook was invented, for a thousand - an icon like a flower. Ten thousand was denoted by a finger pattern, one hundred thousand by a frog, and a million by a familiar figure with raised arms.
It was not very convenient to write down large numbers in this way, and it was completely inconvenient to add them, subtract, multiply, divide them. There was a lot of fuss with these hieroglyphic icons!
It was different with the Babylonians. They wrote down the numbers by squeezing the signs 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 down one, they put one wedge, if two, they put two wedges next to each other, five - five.
Much later, figures began to be depicted differently. Here's a look at the Roman numbering: I - one, II - two, III - three. There are five fingers on the man'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 icon began to represent the number 5. Then one was added to five and received six. Like this: six - VI, seven - VII.
And how many is written here: VIII? That's right, eight. Well, what's the shortest way to write down four? It takes a long time to count four sticks, so they took one away from five and wrote it down like this: IV is five without one.
How do you write ten?
You know that ten consists of two fives, so in Roman numbering, 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 write one stick on the right - XI, then there will be eleven, and if on the left - IX - nine.
Remember the peculiarity of the Roman notation: the smaller number to the right of the larger one is added to it, the one to the left is subtracted. Therefore, the sign VI means 5 + 1, that is 6, and the sign IV means 5-1, that is 4. It is not difficult to learn to read the numbers written in the Roman numbering, and we advise you to do it without fail.
Roman numerals are used quite often these days. For example, on the hour dial sometimes designations are made in Roman numerals; in books, they often indicate the number of a volume or chapter.
Solve these examples:
V + II \u003d V + I \u003d
IIX+ I \u003d X-II \u003d
VI + II \u003d VIII-III \u003d
X-I \u003d IX + I \u003d
Roman numbering was a great invention for its day. And yet it was not very convenient for recording and performing arithmetic operations.
After people created the alphabet, in many countries, numbers began to be written using letters.
The Greeks and Slavs added special signs to the letters so as not to be confused with ordinary letters. In ancient Russia, the letter "a" denoted one, "c" - two, "g" - three. Etc. A special dash above a letter (titlo) indicates that it is not a letter, but a number. Also, the letter "a" with a special sign on the left denoted a thousand, and the one circled - ten thousand, or "darkness", as this number was then called.
However, letter numbering was also inconvenient for denoting a large number. At that time, people had not yet come up with the idea that the same number can mean different numbers depending on its position in a number 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 later.)
A way of writing numbers with just a few characters (ten); which is now accepted all over the world, was created in ancient India. The Indian counting system then spread throughout Europe, and the numbers were called Arabic (in contrast to the sometimes used Roman numerals). But it would be more correct to call them Indian.
And now, I think it will be interesting for you to listen to the story ...
IT ALL STARTED WITH FIVE
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 into the class magazine and tell my classmates who got what grade. But you cannot speak during the lesson, so I had to use my fingers.
We gave Favorsky a five - I, spreading my fingers, show the five. We gave Korolkov a four - I raise four fingers. If it was necessary to report a three, three fingers were used, and a two was two, and one was one.
I was terribly proud to have come up with such an ingenious way. The fact that he is the most ancient, which only can be, did not even occur to me then.
It turns out that in. In the old days, all peoples only had such manual counting - there was no other. It was necessary to write down the 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 hand, stick, counting, and were written - standing. And in our current figures, which came to us from the Arabs, there is, like an extended finger, only one. The rest lay down on one side. Two - two lying sticks, only from a quick letter connected by an oblique stroke; three - three sticks lying on the side with two oblique strokes. The five is, as it were, the outlines of a hand with the thumb set aside and the rest bent. It is not for nothing that our words "five" and "metacarp", 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 it?
It does not look like those lying in a row, but very much like a broken cross, where each stick is connected to another by a cursive stroke.
These first five digits are the most important, because all the rest are composed of them.
The fact that the majority of peoples depicted numbers with sticks is best told by a unit. It was written differently in different countries. But everywhere it looked like the current unit.
Soon you will learn more 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 for a ship, or how much wood for a children's cube? Therefore, mathematics is called the queen of all sciences. Learn it better - you will become "kings"!
So, we begin our unusual journey into the fabulous kingdom of mathematics, where all ten numbers live cheerfully. 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 an account, the rocket will not be able to rise.
Without an account, the letter will not find the addressee
And the guys 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,
He reaches up to the sky with his hand.
Count the guys, or rather count
Add a good deed boldly,
Subtract bad deeds as soon as possible,
The tutorial will teach you accurate counting,
Get to work, get to work!
(Yuri Yakovlev)
Examples of
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:
Decrease the number 73 by 70.
Find the difference between 57 and 7.
Increase the number 50 by 8.
Find the sum of the numbers 49 and 1.
How much do you need to subtract from 64 to make 60? And to make it 4?
How much do you need to add to 90 to make 99? And to become 100?
* * *
* * *
* * *
12 decrease by 6.
Find the sum of the numbers 8 and 7
60 decrease by 2.
What number should be increased by 9 to get 17?
Find the difference between the numbers 12 and 8.
From what number should 4 be subtracted to get 7?
How many tens and how many units are in numbers: 42, 51, 60, 94, 8.
What is the number in which: 6 dess. 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 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 row of numbers: 27, 18, 54, 9, 10, 90, 36, 50, 70. What two groups can these numbers be divided into?
6. Name the number in which there are 7 tens.
7. Name the number with 9 units.
8. Name the number in which there are 9 tens and 4 ones.
9. Name the number in which there are 5 tens and 6 units.
4) The counting starts in the direction of the arrow.
Verbal counting (tasks in verse)
1)
The squirrel was returning from the market and met the fox.
- What are you, squirrel, are you talking about? - asked the fox a question.
- I bring my kids 3 nuts and 7 cones.
- You, fox, tell me: how much is 7 + 3?
The fox quickly counted, exactly eight.
- Oh, you, Red cheat, deceived the squirrel cleverly!
- You guys, don't believe her and check her answer!
2)
The mushrooms were drying up on the trees.
Well, they got wet in the rain.
Forty yellow butter,
Eight thin honey agarics,
Yes, three red chanterelles -
Very cute sisters.
You guys are not silent.
How many mushrooms tell me.
3) -reduced - 80, subtracted - 25, what is the difference?
1st term - 15, 2nd term - 15, sum \u003d?
Add 4 numbers, each of which is 25, how much in total? How to calculate in a convenient way?
I thought of a number, added 70 to it and got 100. What number was I thinking?
The number 60 was reduced by 8, how much was it?
Which number precedes 57? Follows the number 57?
4)
On branches adorned with snow fringes
Ruddy apples grew in winter.
Bullfinches sat on an apple tree, look!
Three dozen of them flew merrily.
Look here again, they fly.
There are fifty of them now.
You think about
How many birds flew in afterwards?
5)
Steller sea lion - chopper spoke, reasoning:
My family is very small, -
I, yes, seven wives, and six children ...
How many suits do you need for the summer
6) Tricky Tasks:
Lena is Anna's daughter, and Anna is Natalia's daughter. Who is Lena Natalia? (Granddaughter.)
The assembly shop received 70 cans and 80 pens for them. How many ready-made cans can you collect from them? (70 cans.)
You need to bring 9 logs from the forest. You can put up to 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 the 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 in our class?" - Yasha asked Gali. Galya, after thinking a little, answered: "If you subtract the number written in two eights from the largest two-digit number, and add the smallest two-digit number to the resulting number, then you will get the number of girls in our class." How many girls were in this class. (21, 99-88 \u003d 11, 11 + 10 \u003d 21).
One rooster woke up 2 sleeping people. How many roosters do you need to wake up 10 people?
The hares (2) and the squirrel got tired of playing with the burners and sat in one row. How many ways can they do this? (6)
The staircase to the ship consists of 13 steps. What step should you take to be in the middle? (7)
Of the three brothers, December was higher than January, and January was higher than February. Which of the brothers is the highest? Who is lower?
There are 4 apples on the table. One was cut in half. How many apples are on the table?
Two collective farmers went to the garden and met three more collective farmers on the way. How many collective farmers went to the garden?
Nina is below Roma, Masha is below Tolya, but above 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 hummingbird with its wings makes 30 beats per second, and the eagle only 1 beat. How many swings does a hummingbird do more than an eagle?
3. It is estimated that one pair of woodpeckers brings 90 caterpillars to chicks in 1 hour, and a pair of starlings more. How many caterpillars do starlings bring in 1 hour?
8)
The sun pours light on the earth
Ginger hides in the grass.
Nearby, right there in yellow dresses,
There are 12 more brothers.
I hid them all in the box,
Suddenly I looked - boletus in the grass.
And 15 of those butter,
They are already in the box.
And you have the answer:
How many fungi have I found?
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?
3. In a sewing workshop, from a piece of cloth 200 meters long every day, starting from March 1, 20 meters were cut off. When was the last piece cut off?
4. There are 3 rabbits in the cage. Three girls asked for one rabbit each. Each girl was given a rabbit. And yet only one rabbit remained in the cage. How did it happen?
5. 6 fishermen ate 6 pike perch in 6 days. How many days will 10 fishermen eat 10 pike perch?
6. On one tree there were 40 forty. A hunter passed, shot and killed 6 forty. How many forty are left on the tree?
7. Two excavators will dig 2 m of ditches in 2 hours of work. How many diggers do you need 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 have happened?
9. A caterpillar creeps from the ground along the stem of a plant, which is 1 m high. During the day, it rises by 3 inches, and at night it drops by 2 inches. How many days will the caterpillar 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 the neighbors of the number 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 containsseven tens and two units;
two tens and seven units.
6. Find the incorrect entries and circle:
7 tens is equal to 17 units;
the number 80 is more than 70 by 1;
if you reduce the number 50 by 1, you get 48.
2) Find the values \u200b\u200bof the expressions using the moveable addition property:
a) 20 + 2 + 8 + 40 b) 17 + 5 + 5 + 3
c) 18 + 11 + 2 + 9 d) 40 + 1 + 9 + 50e) 40 + 28 + 2 f) 30 + 26 + 4
g) 63 + 7 + 20
3) Read the entries using the words "more" and "less" so that the entries are correct and put a (<,>).
15…17 17…7121…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 old Russian measure of length, putting the answers in decreasing order.5) Enter the correct answer.
a) How many centimeters are there in 1 meter? 1 m \u003d
b) How many decimeters are there in 1 meter? 1 m \u003dc) How can a word be written in shorthand for a numbermeter ?
d) Record in abbreviated form 10 meters, 12 meters, 7 meters.
e) Express in decimetres: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) Decrypt the entry.
- 7) Help the squirrel collect mushrooms in the basket. To do this, you need to solve the examples and connect the card with the correct answer with lines.
8)
Addition and subtraction problems within 100
Tasks:
1 What numbers are missing? What is the number following each missing number?
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 in each drawing?
4. The figure shows twenty-nine sticks. Let's put one more. How many sticks have become?
5. Name all 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, and 9 young ones were planted. How many willows are there by the pond?
Mom served 3 cucumbers for lunch, and 6 more tomatoes. We ate 4 tomatoes at lunch. How many tomatoes are left?
The barrel contained 15 buckets of water. We used 6 buckets to water the trees, but then 9 buckets of water were poured into the barrel. How many buckets of water are in the barrel?
In the classroom, 14 students did their homework. Then 6 children left and 9 came. How many children are there in the class?
The manual contains 3000 examples in mathematics. The topic "One Hundred" is one of the basic topics taught in the second grade. Like any other, it requires good anchorage. The manual can be used as additional material in the lesson, as well as for work at home.
Addition and subtraction of the form 40 + 16, 40-16.
30+66 = 60+39 = 50+16 = 50-12 =
30-36 = 40-22 = 40+37 = 40+36 =
70+24 = 50-14 = 80-75 = 80-57 =
50-38 = 70-14 = 50-49 = 70-33 =
100-83 = 90-77 = 50-26 = 60+28 =
90-46 = 30+56 = 30+63 = 90-72 =
80-45 = 70+21 = 80-56 = 30+54 =
70-28 = 70-32 = 50+28 = 30+58 =
30+53 = 50+24 = 80-53 = 70-37 =
90-68 = 50-24 = 60-34 = 90-44 =
100-86 = 80+13 = 100-71 = 60+24 =
10+83 = 80-23 = 20+65 = 80-58 =
40-24 = 40+21 = 40+47 = 50-13 =
100-68 = 40-21 = 30-15 = 90-77 =
70+27 = 50+36 = 30+23 = 40+54 =
90-53 = 50-36 = 90-62 = 30-11 =
70-16 = 70+26 = 70-55 = 70+17 =
80+14 = 50-14 = 40+16 = 70-36 =
30+19 = 80+19 = 40-16 = 70+13 =
50-37 = 60-13 = 50+15 = 80-59 =
20+74 = 40-22 = 50-15 = 90-78 =
70-25 = 30-18 = 40+14 = 40+45 =
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Date of publication: 20.03.2013 08:52 UTC
- 500 problems in mathematics, All types of problems in the course of elementary school, Learning to count money, grades 1-4, Uzorova OV, Nefedova OV
- Summer assignments in mathematics for repetition and consolidation, grade 2, Uzorova O.V., Nefedova E.A., 2017
- Mathematics, grades 1-4, Big book of examples and assignments on all topics of the primary school course, Uzorova O.V., Nefedova E.A., 2010
- 500 problems in mathematics with an explanation, step-by-step solution and correct design, grade 2, Uzorova O.V., Nefedova E.A., 2008
The following tutorials and books:
When learning addition and subtraction atwithin 100 obl. all the requirements for learning to understand actions within 20 are met.
Many difficulties that schoolchildren with intellectual disabilities experience when performing addition and subtraction actions within 20 are not removed even when performing the same deist! within 100. As experience and special studies show, students still experience great difficulties in performing the subtraction action. The greatest number of errors (arises when solving examples of addition and subtraction by passing through the discharge. A typical error in subtraction, the units of the subtracted subtract the units of the reduced. For example, 35-17 \u003d 22. There is also a tendency to replace one bowl with another. For example: 64-16 \u003d 80, 17 + 2 \u003d 15 (addition is performed instead of subtraction and vice versa). < in two-digit numbers, students often take into account only units of one category, units of another category (first or second components) are rewritten without change (36 + 11 \u003d 46, 85-24 \u003d 64). The following mistakes are also allowed: students add or subtract without paying attention to the digits: units are added with tens (37 + 2 \u003d 57, 38-20 \u003d 36), a larger number is subtracted from a smaller number (17-38 \u003d 21), with solving complex examples, perform only one action (12 + 14-8 \u003d 26).
It is characteristic that students of the VIII type school for a long time do not master the rational methods of calculation, lingering on the methods of counting specific objects, counting by one.
The reasons for the errors are insufficient knowledge of the tables of addition and subtraction within 10 and 20 (39-7 \u003d 31, 42 + 7 \u003d 48), insufficient knowledge and understanding of the positional meaning of digits in a number or inability to use their knowledge in practice, as well as in the peculiarities of thinking of schoolchildren with intellectual underdevelopment.
The sequence of studying the actions of addition and subtraction is due to the increase in the degree of difficulty when considering various cases.
1.Addition and subtraction of round tens (30 + 20, 50-20,
the solution is based on the knowledge of the numbering of the round tens).
2. Addition and subtraction without passing through the digit.
154
B + 5 35-5 \u003d 30 41-2 \u003d 45
| B + 30 3.5-20 \u003d 5 47-32 \u003d 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. Addition of a two-digit number with a one-digit number when the total is in the tens. Subtraction from round tens of No and two-digit numbers:
4. Addition and subtraction with a transition through the discharge.
D All actions with examples of groups 1, 2 and 3 are performed by means of oral calculations, ie, calculations must be started with units of the highest digits (tens). Examples are written in a line. Calculation techniques are based on students' knowledge of numbering, decimal composition of numbers, addition and subtraction tables within 10.
Addition and subtraction are learned 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.
The explanation of each new case of addition and subtraction is carried out on visual aids and didactic material, with which all students of the class work.
Consider the techniques for performing addition and subtraction actions within 100:
1) 30+20= 50-30=
The reasoning is as follows: 30 is 3 dozen (3 bundles of sticks). 20 is 2 dozen (2 bundles of sticks). We add 2 beams to 3 bundles of sticks, in total we got 5 bundles of sticks, or 5 dozen. 5 tens is 50. So, 30 + 20 \u003d 50.
The same reasoning is carried out for the subtraction of the circle / u.r tens.
A detailed note at first allows you to consolidate the sequence of reasoning:
3 dec. + 2 dec. \u003d 50 dec. \u003d 50, ._. _ ^^ .- ^ ds1 .. \u003d oi
All the manuals are involved in solving the examples, which and<
use when studying numbering. Actions are performed o6\u003e
especially on the accounts.
2) 30+26 26+30 „„ „„
The explanation of the solution of examples of this type is also carried out on manuals (abacus, arithmetic box, abacus). It is helpful to show students a detailed record of how an action was performed:
56=50+ 6 50-30=20 20+ 6=26
or 30 + 26 \u003d 30 + 20 + 6 \u003d 50 + 6 \u003d 56.
The teacher uses this record only when explaining. Students need to be shown a short form of recording, but require oral commentary when performing actions, while recording - underscore tens:
The above cases of addition and subtraction are solved responsibly by the same methods. However, in terms of difficulty, they are ambiguous. For a student with intellectual disabilities, it is much more difficult to add more to a smaller number. (2 + 7) -9-7 is | the more difficult case of table subtraction. All this suggests that, observing the requirement for the gradual increase of difficulties (fi solving examples, it is necessary to take into account not only the methods of elevation, but also the numbers on which the actions are performed. Explanation:
“Among 45 there are 4 tens and 5 units. Let's put the number on the abacus. [Add 2 units. We get 4 tens and 7 units, 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 subtraction with a transition through the discharge, the use of the method of decomposition into bit terms of two components will result in the subtraction from a smaller number of units of the reduced number of units of the subtracted (43-17, 43 \u003d 40 + 3, 17 \u003d 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 conduct reasoning when solving examples, but they can easily cope with their solution on abacus, they do not mix the categories. These students can be allowed to use the accounts.
For greater clarity, a better understanding of the positional meaning of numbers in the number, the recording of 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 between categories.
| 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 for solving these examples for addition is no different from the reasoning for solving examples for addition of the two previous types, although the latter are more difficult for students.
When considering cases of the type 50-5, it is necessary to indicate that it is necessary to take one ten, since in the number 50 the number of units is 0, split ten into ones, subtract 5 from ten, and add the remaining tens with the difference.
For convenience and clarity of the presentation of computational techniques, we considered each new case in isolation. 1 teaching students oral computational reception! it is necessary to consider each new case of addition or subtraction of a row in an inextricable connection with the previous ones, post-patch including new knowledge into existing ones, constantly comparing them. For example, 45 + 2, 45 + 5, 45 + 32, 45 + 35. Compare examples, to findgeneral and different. Create examples of this kind.
Such tasks will allow you to see the similarities and differences in examples, make students think, consider each tea of \u200b\u200baddition not in isolation, but in connection and interdependent. This will allow you to develop a generalized way of oral calculations. (Solve, compare calculations, and make similar examples: 40-6, 40-26, 40-36, 40-30.)
4) Addition and subtraction with a transition through a digit (2nd corpse of examples) are performed by methods of written calculations, i.e. calculations begin with units of the lowest digits (from ones), with the exception of division, and the record is given in a column.
Students become familiar with writing and algorithms for written addition and subtraction and learn to comment on their activities. It is necessary to compare various cases, first addition, then subtraction, establish similarities and differences, include students in the process of compiling similar examples, teach them to reason. Only such techniques can give a corrective effect.
When students learn how to perform addition and subtraction through the column digit, they are introduced to performing these actions using oral computation techniques.
t t
The explanation is usually carried out on an abacus, sticks, bars or cubes of an arithmetic box, abacus. 158
shtel suggests reading an example, postponing 38 on abacus, having previously clarified its decimal composition. First-I units need to add 3 units: the number 8 is added: yatka, that is, 2 units are added; the resulting ten Iiits are replaced by one ten, it turns out 4 dozen. One more unit is added to 4 Gnts.
When subtracting a single-digit number from a two-digit number with a transition through a discharge, all the units of the reduced are first subtracted, I then the remaining units of the Count are subtracted from the round tens.
Detailed 38+3=41 38+2=40 40+1=41
Both in addition and in subtraction, it is necessary to decompose the second lagged or reduced into two numbers. When adding, the second lagged one is decomposed into two numbers such that the first adds the number of units of a two-digit number to a round ten.
When subtracting, the subtracted is decomposed into two numbers so that one is equal to the number of units of the reduced, that is, I so that when subtracted, a round number is obtained.
When performing actions, the difficulty for students is the ability to correctly decompose a number, perform a sequence of necessary operations, remember and add or subtract the remaining units.
For example, performing action 54 + 8, the student can correctly add 54 to 60. It is difficult to decompose 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 first ten numbers, to carry out exercises to add numbers to round tens, for example: “How many units are missing to 50 in the numbers 42, 45, 48, 43, 4? What number should you add to 78 to get 80? " It is necessary to consider cases of the form 37 + 3 + 2 \u003d 40 + 2 \u003d 42 and seek an answer to the question: "How many units have been added to the number (37)?"
"How many units have you subtracted from 43?" So, 43-5 \u003d 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 lays 7 dice on the abacus or draws sticks and thinks like this: "By 38 I will add 2, it will turn out to be 40 (and removes or crosses out 2 sticks), now about 40 more sticks".
Another example: 45-8. The disciple puts aside 8 sticks and thinks
em like this: “First we subtract 5 from 45, it will be 40 (removes 5 sticks ^
left to subtract 3. From forty, subtract 3, will remain 37. 45-8 \u003d 3?
The solution of examples of this type is based on already informing students of the solution techniques:
38+24 24=20+ 4 38+20=58 58+ 4=62
The solution to these examples is based on the decomposition of the second! term and subtracted by bit terms and successor | adding and subtracting them from the first component of the action.
Schoolchildren with intellectual disabilities due to erratic!
attention, inability to concentrate often make mistakes
of this nature: add or subtract tens, but forget
add or subtract units. I
Without firmly mastering the technique of calculations, positional meaning | digits in a number, students add tens with ones, subtract tens of the subtracted from the units of the reduced: 54-18 \u003d 43. I
Addition and subtraction with the transition through the category of students ^ should be able to perform on the accounts.
For example: 56 + 27. First, put aside the number 56. Add 20. It turns out 76. Add 7. 76 add up to 80, replace 10 units with one ten, add 3 more units to 8 tens.
Let's perform subtraction on accounts (fig. 11): 41-24.
For students to acquire the skills and abilities in solving the application of addition and subtraction with a transition through the discharge, it is necessary to complete a lot of exercises. Examples can be given
with two and with three components, alternating the actions of addition and whine. The following examples are also solved: 48+ (39-30).
The arrangement of the material with a gradually increasing degree of Efficiency allows students to master the necessary techniques when performing addition and subtraction actions. The success of mastering computational techniques largely depends on activity | lmikh students.
In a school of the VIII type, there will always be a group of children who find it impossible to master the oral computational technique when solving examples with a transition through the category (27 + 38, 65-28). These students will solve the examples using written (columnar) techniques.
When studying hundreds, the names of the components and the results of addition and subtraction actions are fixed. In order for the names of the components to enter 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. Decreased 80, subtracted 32. Find the difference. Find the sum of three numbers: 30, 18, 42. What are the names of the numbers when adding? Subtract 40 from the sum of numbers 20 and 35 ", etc.
As they study hundreds, students become familiar with finding the unknown components of addition and subtraction.
When studying the actions of addition and subtraction within 10 and 20, students solved examples with unknown components using the selection technique, for example: P + 3 \u003d 10, 4 + P \u003d 7, P-4 \u003d 6, 10-P \u003d 4.
When studying hundreds of unknown components, a letter is designated and students are introduced to the rule for finding unknown components.
Before acquainting students with the solution of examples containing an unknown component, it is necessary to create a situation, to come up with a life-practical problem that would give students the opportunity to understand that this third unknown component can be found from two known components and one unknown.
6 Perova M.N.
For example: “There are several pencils in the box, but there. lived 3 more pencils. The box now contains 8 pencils. Chipped) pencils were in the box? "
This task should be dramatized. The student takes the box with pencils (the number of pencils in it is unknown), kla; there 3 pencils. Counts all the pencils in the box. I turns out to be 8. The teacher suggests the number of pencils, to which 1 swarm was (ie, unknown), denote by the letter x.and recording x + 3 \u003d 8.If we subtract 3 added pencils from 8 pencils, then 5 pencils will remain: * + 3 \u003d 8, x \u003d 8-3, x \u003d 5.
Checking. 5 + 3 \u003d 8 8 \u003d 8
After solving a few more problems with real objects, we can conclude: “To find the unknown summand! you need to subtract the known term from the sum. "
Finding an unknown diminished is also best, as experience shows, to show on solving a life-practical problem, for example: “There are several mushrooms in the basket (x),5 mushrooms were taken from it (we take), 4 mushrooms remained in the basket (count 1 li). How many mushrooms were in the basket? "
The task is played out. Let's denote the mushrooms that were in the basket with the letter xand write: x-5 \u003d 4. "What action can you find out how many mushrooms there were?" (By folding.)
Checking. 9-5 \u003d 4 4 \u003d 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 learning the numbering of the first hundred.
3. What is the sequence of learning addition and subtraction within
100?
4. Make a summary of the lesson that aims to familiarize
with the algorithm of written addition or subtraction within 100.
5.Write out from the textbook on mathematics for the 3rd grade 3-5 types
development and correction exercises analysisand synthesis, comparison. Co
put on 5-b exercises aimed at solving similar problems.
Chapter 11