When learning addition and subtraction V within 100 obl. all the requirements that apply to learning to understand actions within 20.
Many of the difficulties that schoolchildren with intellectual disabilities experience when performing addition and subtraction actions within 20 are not removed when performing the same deist! within 100. As experience and special studies show, students still experience great difficulties in performing the subtraction action. The largest number errors (occurs when solving examples of addition and subtraction by passing through a discharge. A characteristic error in subtraction, units of the subtrahend subtract units of the reduced. For example, 35-17 = 22. There is also a tendency to replace one dej "wii with another. For example: 64-16 \u003d 80 , 17+2=15 (instead of subtraction, addition was performed and vice versa). < In two-digit numbers, students often take into account only units of one category, units of another category (the first or second components) are rewritten without change (36 + 11 = 46, 85-24 = 64). The following mistakes are also allowed: 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 decision difficult examples perform only one action (12+14-8=26).
It is characteristic that students of the VIII type school do not master rational methods of calculation for a long time, lingering on the methods of counting specific objects, counting by unit.
The reasons for the errors are insufficient knowledge of the addition and subtraction tables within 10 and 20 (39-7 = 31, 42 + 7 = 48), insufficient knowledge and understanding of the positional meaning of numbers 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 knowing the numbering of round tens).
2. Addition and subtraction without crossing the discharge.
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. Addition of a two-digit number with a one-digit number, when round tens are added to the sum. Subtraction from round tens of a single-digit and two-digit number:
4. Addition and subtraction with transition through the category.
D All actions with examples of the 1st, 2nd and 3rd groups are performed by methods of oral calculations, that is, calculations must begin with units of higher digits (tens). Examples are written in a line. Calculation techniques are based on students' knowledge of numbering, the decimal composition of numbers, addition and subtraction tables 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 cases of addition 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 within 100:
1) 30+20= 50-30=
Reasoning is carried out as follows: 30 is 3 tens (3 bunches of sticks). 20 is 2 tens (2 bunches of sticks). We add 2 bunches to 3 bunches of sticks, in total we got 5 bunches of sticks, or 5 tens. 5 tens is 50. So 30+20=50.
The same reasoning is carried out when subtracting the circle / and tens of tens.
A detailed record at first allows you to fix the sequence and consistency of reasoning:
3 dec.+2 dec.=50 dec.=50,._. _ ^^.-^ ds1..=oi
To solve the examples, all manuals are involved, which<
used in the study of numbering. Actions are performed o6>
especially on the accounts.
2) 30+26 26+30 „„ „„
An explanation of the solution of examples of this type is also carried out on manuals (abacus, arithmetic box, abacus). It is useful to show students a detailed record of the action being performed:
56=50+ 6 50-30=20 20+ 6=26
or 30+26=30+20+6=50+6=56.
The teacher uses this record only when explaining. Students need to be shown a short form of recording, but require verbal commenting when performing actions, while recording - underlining tens:
The above cases of addition, as well as subtraction, are solved responsibly by the same methods. However, they are not clear in terms of difficulty. 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 | and more hard case tabular subtraction. All this suggests that, while observing the requirement of a gradual increase in difficulties (fi solving examples, it is necessary to take into account not only the methods of exchanging, but also the numbers on which actions are performed. Explanation:
“In the number 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 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 appropriate because when subtracting with a transition through a discharge, the use of the decomposition into bit terms of two components will lead to subtraction from a smaller number of units of the reduced larger number of units of the subtrahend (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 how to reason when solving examples, but they can easily cope with their solution on the accounts, they do not mix discharges. These students may be allowed to use the abacus.
For greater clarity, a better understanding of the positional meaning of numbers in a number, writing units and tens on the board and in notebooks for some time can be done in different colors. This is important for those students who do not distinguish between categories well.
| 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 in solving these addition examples is no different from the reasoning in solving the two previous types of addition examples, although the latter are more difficult for students.
When considering cases of the form 50-5, it is necessary to indicate that it is necessary to take one ten, since the number of units in the number 50 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 methods, we have considered each new case in isolation. 1 learning process of students oral computing reception! it is necessary to look at each new case of addition or subtraction in an inextricable connection with the previous ones, post-learning including new knowledge into existing ones, constantly comparing them. For example, 45+2, 45+5, 45+32, 45+35. Compare the examples find general and different. Write examples of this kind.
Such tasks will allow you to see the similarities and differences in examples, make students think, consider each addition tea not in isolation, but in connection and interdependence. This will make it possible to develop a generalized method 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 the category (2nd group of examples) are performed by methods of written calculations, i.e., calculations begin with units of the lowest digits (from units), with the exception of division, and the entry is given in a column.
Students become familiar with notation and written addition and subtraction algorithms and learn to comment on their activities. It is necessary to compare different cases of first addition, then subtraction, to establish similarities and differences, to include students in the process of compiling similar examples, to teach them to reason. Only such techniques can give a corrective effect.
When students learn how to perform addition and subtraction operations with the transition through the discharge to the column, they are introduced to the performance of these actions by the methods of oral calculations.
t t
The explanation is usually carried out on an abacus, sticks, bars or cubes of an arithmetic box, accounts. 158
the shtel suggests reading the example, putting aside 38 on the abacus, having previously found out 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 iiis are replaced by one dozen, it turns out 4 dozens. To 4 Gntkam, 1 more unit is added.
When subtracting a single-digit number from a two-digit number with a transition through the discharge, all units of the reduced number 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 sum to be added or reduced into two numbers. When adding, the second term is decomposed into two numbers such that the first one adds the number of units of a two-digit number to a round ten.
When subtracting, the subtracted is decomposed into such two Numbers so that one is equal to the number of units of the reduced, 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 a sequence of necessary operations, remember and add or subtract the remaining units.
For example, performing the action 54 + 8, the student can correctly complete 54 to 60. The difficulty is the decomposition of 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 round tens (to 60), he forgets.
Given this, it is necessary, before considering cases of this type, to repeat the composition of the numbers of the first ten again and again, to carry out exercises to complete numbers up to round tens, for example: “How many units are missing from 50 in the numbers 42, 45, 48, 43, 4? What number must be added to the number 78 to get 80? It is necessary to consider cases of the form 37+3+2=40+2=42 and seek an answer to the question: “How many units were added to the number (37)?”
“What is the total number of units subtracted from the number 43?” This means that 43-5 = i For some students of the VIII type school, when solving a specific type of examples, partial clarity is used, for example 38 + 7. The student puts 7 bones on the accounts or draws sticks and argues like this: “I’ll add 2 to 38, it will turn out 40 (and removes or crosses out 2 sticks), now add 5 more sticks to 40.”
Another example: 45-8. The student puts aside 8 sticks and I will reason
em like this: “First, we subtract 5 from 45, it will be 40 (removes 5 sticks ^
it remains to subtract 3. Subtract 3 from forty, 37 remains. 45-8=3?
The solution of examples of this type is based on the solutions already known to students:
38+24 24=20+ 4 38+20=58 58+ 4=62
The solution of these examples is based on the decomposition of the second! term and subtrahend into bit terms and successor | nominal addition and subtraction from the first component of the action.
Schoolchildren with intellectual disabilities due to unstable!
attention, inability to concentrate often make mistakes
of this nature: they add or subtract tens, but forget
twist or subtract units. I
Firmly not having mastered the reception of calculations, positional value | digits in a number, students add tens with ones, subtract from the units of the reduced tens of the subtrahend: 54-18 = 43. I
Addition and subtraction with the transition through the category students ^ should be able to perform on the accounts.
For example: 56+27. First, set aside the number 56. Add 20. It turned out 76. Add 7. Add 76 to 80, replace 10 units with one ten, add 3 more units to 8 tens.
Let's subtract on the accounts (Fig. 11): 41-24.
In order for students to acquire skills and abilities in solving the application of addition and subtraction with the transition through the category, 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 puffing. The following examples are also solved: 48+(39-30).
The arrangement of the material with a gradually increasing degree of Fudnost allows students to master the necessary techniques when performing addition and subtraction. The success of mastering computational techniques largely depends on the activity | many students.
In a school of type VIII there will always be a group of children who find it impossible to master an oral computational technique when solving examples with a transition through a category (27 + 38, 65-28). Such students will solve examples using written calculations (in a column).
When studying hundreds, the name of the components and results of addition and subtraction is fixed. In order for the names of the components to be included in the active dictionary 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. Decreasing 80, subtracting 32. Find the difference. Find the sum of three numbers: 30, 18, 42. What are the numbers called when adding? Subtract 40 from the sum of the numbers 20 and 35, etc.
When studying hundreds, students are introduced 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 indicated by a letter and students get acquainted with the rule for finding unknown components.
Before acquainting students with solving examples containing an unknown component, it is necessary to create a situation, come up with such a vital and practical task 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. 3 more pencils lived. There are 8 pencils in the box. How many pencils were in the box?
This task should be dramatized. The student takes a box of pencils (the number of pencils in it is unknown), kla; there are 3 pencils. Counts all the pencils in the box. I turns out to be 8. The teacher offers the number of pencils, which 1 swarm was (i.e., unknown), denoted by the letter X. and recording x+3=8. If we subtract 3 pencils from 8 pencils that we added, then 5 pencils will remain: * + 3 = 8, x=8- 3, x=5.
Examination. 5+3=8 8=8
After solving a few more problems with real objects, we can conclude: “To find the unknown term! subtract the known term from the sum.
Finding an unknown reduced is also best, as experience shows, to show on the solution of a vital practical problem, for example: “There are several mushrooms in a basket (X), 5 mushrooms were taken from her (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 X and write: X- 5=4. “What action can you find out how many mushrooms there were?” (Addition.)
Examination. 9-5=4 4=4
Questions and tasks
1.Compose thematic plan learning the numbering of the numbers of the first hundred
in the 3rd grade of the VIII type school.
2. Name the stages of studying the numbering of the numbers of the first hundred.
3. What is the sequence of studying addition and subtraction within
100?
4. Make a summary of the lesson, the purpose of which is to familiarize the student
using a written addition or subtraction algorithm within 100.
5. Write out 3-5 types from the math textbook for the 3rd grade
exercises for development and correction analysis and synthesis, comparison. So
put on 5 exercises aimed at solving similar problems.
Chapter 11
The manual contains 3000 examples in mathematics. The topic "Hundred" is one of the basic topics studied in the second grade. Like any other, it requires good fixing. The guide can be used as additional material in the classroom, 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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Publication date: 03/20/2013 08:52 UTC
- 500 tasks in mathematics, All types of tasks of the elementary school course, Learning to count money, grades 1-4, Uzorova O.V., Nefedova O.V.
- 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 elementary school course, Uzorova O.V., Nefedova E.A., 2010
- 500 tasks in mathematics with explanation, step-by-step solution and correct design, Grade 2, Uzorova O.V., Nefedova E.A., 2008
The following tutorials and books:
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 in math exams are due to incorrect calculation 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 work out mathematical skills and abilities and bring them to automatism. The simulators are diverse, it is not necessary to download them all, just one or two you like. The guides can be used with younger students regardless of the program under which the training is conducted.
Mathematics. We solve examples with the transition through a dozen.
Notebook for practicing addition and subtraction skills with the transition through a dozen. Not just examples, but interesting games and tasks.
Task cards. Mathematics. Addition and subtraction. Grade 2
Handy cards for second grade teachers. 2 options for addition and subtraction of the same kind. Suitable for organization independent work in mathematics, depending on the 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 grade 1 or at the beginning of grade 2. 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 a kind of hints. In the course of independent work with a notebook, the child is guided by a sample of execution and algorithmic instructions. The ability to use such hints in studies will allow the student not only to find and use the necessary information in the course of the task, but also to carry out self-examination.
The notebook begins with practicing addition and subtraction within 10, this part is also suitable for first-graders.
Mathematics exercise book for grade 2
The notebook contains not only examples of addition and subtraction, but also the conversion of units into each other, and the comparison of calculation results (more-less).
3000 math examples (counting within 100 part 1)
Trainer with an account for time. Time to mark the solution of one column of examples 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 the transition through a dozen, addition and subtraction of tens, manipulations within a hundred.
Score from 0 to 100
This recipe gives many examples of addition and subtraction to reinforce the skills of mental counting within 100.
We think it's right. Mathematics workbook. G.V. Belykh
The notebook is also made in the form of a simulator, solid examples and equations. It starts with a count within ten, then within a hundred (addition, subtraction, multiplication and division), ends with a comparison of equations (examples with greater than, less than, equal signs).
Helpful for teachers too primary school in their work, and for parents to work at home with children, in particular, in summer holidays. Tasks different levels 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 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
puzzles
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?
Long 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. They fed on the leaves, fruits and roots of various plants. Sometimes they fished, collected shells or hunted. They dressed in the skins of dead animals.
The life of primitive people was not much different from the life of animals. And the 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, as well as modern small children, did not know the account. But now children are taught to count by parents and teachers, older brothers and sisters, 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 from many different objects individual items. 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 concept of number. Our distant ancestor, talking about seeing two ducks, compared them with a pair of eyes. And if he saw more of them, he said: "Many." Only gradually did a person learn to single out three objects, and then four, five, six, etc.
Learning to count required life. Getting food, people had to hunt large animals: elk, bear, bison. Our ancestors hunted in large groups, sometimes the whole tribe. For the hunt to be successful, it was necessary to be able to surround the beast. 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 of 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 made by him with a stone tip for five skins for clothes, a person 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 the hands were not enough, the legs were also used. Two arms and one leg - 15, two arms and two legs - 20.
Traces of counting on the fingers have been preserved in many countries.
So, in China and Japan, household items (cups, plates, etc.) are counted not in dozens and half dozens, but in fives and tens. In France and England, counting by twenty is still in use.
At first there were special names for numbers only for one and two. Numbers greater 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 nations indicate their origin.
So, the Indians have two - eyes, the Tibetans - wings, other peoples have one - the moon, five - the hand, etc.
HOW PEOPLE LEARNED TO WRITE NUMBERS
In different countries and different times it was done differently. When people did not yet know how to make paper, records appeared in the form of notches 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 in the air. He had something to be surprised about. After all, he meant a whole million. And it's not a joke. The ancient Egyptians drew such a little man when they wanted to portray a million. The man performed the duties of the number.
Now we, accustomed to the inscription of numbers, can’t even believe that there was some other system for writing numbers. These “numbers” were very different and sometimes even funny 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 form of a horseshoe. To write 15, it was necessary to put 5 sticks and 1 horseshoe. And so on up to a hundred. For a hundred, a hook was invented, for a thousand - a badge 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 in this way big numbers and it was quite inconvenient to add, subtract, multiply, divide them. There was a lot of fuss with these hieroglyphic icons!
The Babylonians were different. They wrote down the numbers, squeezing the icons with a stick on a clay tablet. And therefore, all their numbers were made up of combinations of wedges. If it was necessary to record a unit, they put one wedge, if two, they put two wedges side by side, five - five.
Much later, the figures began to be depicted differently. Look at the Roman numbering: I - one, II - two, III - three. There are five fingers on the human hand. In order not to write five sticks, they began to depict a hand. However, the drawing of the hand was made very simple. Instead of drawing the whole hand, it was depicted with a V sign, and this icon began to denote the number 5. Then one was added to five and got six. Like this: six - VI, seven - VII.
And how many are written here: VIII? That's right, eight. Well, what's the shortest way to write four? It takes a long time to count four sticks, so one was taken away from five and written like this: IV is five without one.
How about ten?
You know that ten consists of two fives, so in Roman numeration 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 you write one stick next to X on the right - XI, then it 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, and 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. 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 the clock face; in books, they often indicate the number of a volume or chapter.
Solve these examples:
V+II= V+I=
IIX+I=X-II=
VI+II= VIII-III=
X-I= IX+I=
Roman numbering was a great invention for its time. And yet, for recording and performing arithmetic operations, it was not very convenient.
After people created the alphabet, in many countries they began to write numbers using letters.
The Greeks and Slavs added special signs to the letters so as not to be confused with ordinary letters. IN Ancient Rus' the letter "a" denoted one, "c" - two, "g" - 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 sign on the left meant a thousand, and circled - ten thousand, or "darkness", as such a number was then called.
However, the alphabetic numbering was also inconvenient for indicating a large number. At that time, people did not even think of the fact that the same number could mean different numbers depending on its position in a series of other figures, as we now have. A great achievement was the introduction of zero into the account, which made it possible to indicate the missing bit when writing numbers. (More on zero in a moment.)
A way to write numbers with 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 (in contrast to the Roman numerals sometimes used). 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 5
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 magazine and tell my classmates who got what mark. But you can’t speak during the lesson, so I had to resort to the help of my fingers.
They gave Favorsky five - I, spreading my fingers, show five. They put Korolkov's four - I raise four fingers. If it was necessary to report a three, three fingers were used, and two - two, a one - one.
I was terribly proud that I had come up with such an ingenious way. The fact that it is the oldest one that can be, did not occur to me then.
It turns out in. In the old days, among all peoples, only such a manual account existed - there was no other. It was necessary to write down the numbers - the fingers were replaced by 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 in this way - standing up. And in our current figures that came to us from the Arabs, there is only one, like an outstretched finger. The rest lay down on the side. Two - two lying sticks, only from a quick letter connected to each other with an oblique stroke; three - three sticks lying on their side with two oblique strokes. The five is, as it were, the outline of a five with the thumb set aside and the rest bent. It is not without reason that our words “five” and “past”, which in Old Russian means “hand”, are so similar to each other.
And the four, doesn't it look like four sticks lying side by side?
It doesn’t look like those lying in a row, but it looks very much like a broken cross, where each stick is connected to another with a cursive stroke.
These first five digits are the most important, because all the rest are made up of them.
The fact that for most peoples the numbers were depicted with sticks is best told by a unit. It was spelled differently in different countries. But everywhere it was similar to the current unit.
Soon you will learn in more detail about each figure and understand that it is impossible to do without knowledge of mathematics. How, for example, to 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? Therefore, mathematics is called the queen of all sciences. Learn it better - you will become "kings"!
So, we begin our unusual journey to the fabulous 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, go!
Without an account, there will be no light on the street.
Without an account, a rocket will not be able to rise.
Without an account, a letter will not find an addressee
And the guys will not be able to play hide and seek.
Our arithmetic flies above the stars
Goes to the seas, builds buildings, plows,
Plants trees, forges turbines,
Reaches the very sky.
Count guys, count more precisely
Feel free to add a good deed
Subtract bad deeds as soon as possible
The textbook will teach you accurate counting,
Get to work, get 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 verbal counting:
Decrease 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? What about 4?
How much do you need to add to 90 to make 99? What about 100?
* * *
* * *
* * *
12 decrease by 6.
Find the sum of numbers 8 and 7
60 decrease by 2.
What number must be increased by 9 to get 17?
Find the difference between the numbers 12 and 8.
From what number must 4 be subtracted to get 7?
How many tens and how many units in numbers: 42, 51, 60, 94, 8.
What is 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 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 in which 9 units.
8. Name the number in which there are 9 tens and 4 units.
9. Name the number in which there are 5 tens and 6 units.
4) Counting begins with an arrow.
Oral counting (tasks in verse)
1)
The squirrel was returning from the market and met the fox.
- What are you, squirrel, carrying? the fox asked 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 counted.
- Oh, you, Red-haired cheat, cleverly deceived the squirrel!
“You guys don’t believe her and check her answer!”
2)
The mushrooms dried on the trees.
Well, they got wet in the rain.
Forty yellow butterflies,
Eight thin mushrooms
Yes, three red foxes -
Very cute sisters.
You guys don't be silent.
How many mushrooms can you tell me.
3) -reduced - 80, subtracted - 25, what is the difference?
1st term - 15, 2nd term - 15, sum = ?
Added 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 did I think?
The number 60 was reduced by 8, how much did it turn out?
What number comes before 57? Follows the number 57?
4)
On branches adorned with snow fringe,
Ruddy apples grew in winter.
Bullfinches sat on an apple tree, look!
Three dozen of them merrily flew in.
Look here, they're flying.
There are now fifty of them.
You think about
How many birds came after?
5)
The sea lion - the billhook spoke, reasoning:
My family is quite small,
Me, seven wives, and six children...
How many suits do you need for the summer
6) Tasks for ingenuity:
Lena is Anna's daughter, and Anna is Natalia's daughter. Who is Lena Natalia related to? (Granddaughter.)
The assembly shop received 70 cans and 80 handles for them. How many finished cans can be assembled from them? (70 cans.)
From the forest you need to bring 9 logs. You can put no more than 4 logs on the car. 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 on eight hands.
"How many girls are in our class?" Yasha asked Gali. Galya, thinking a little, answered: “If we subtract the number written by two eights from the largest two-digit number, and add the smallest two-digit number to the resulting number, then the number of girls in our class will turn out exactly.” How many girls were 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 in one row. In how many ways can they do it? (6)
The ladder to the ship consists of 13 steps. What step do you need to 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 tallest? Who is below?
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 in total?
Nina is shorter than Roma, Masha is shorter than Tolya, but taller than Roma. Who is the tallest?
7) 1. The California cuckoo can run 40 km in 1 hour, and the ostrich can run 30 km more. How many kilometers can an ostrich run in 1 hour?
2. A small hummingbird makes 30 flaps per second with its wings, and an eagle only 1 flap. How many strokes does a hummingbird make 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 brings 60 more. How many caterpillars do starlings bring in 1 hour?
8)
The sun sheds light on the earth
Ryzhik hides in the grass.
Nearby, right there in yellow dresses,
There are 12 other brothers.
I hid them all in a box,
Suddenly I look - butterflies in the grass.
And 15 of those butter
They are already in the box.
And your answer is ready:
How many fungi did I find?
9) Entertaining tasks
1. There is a cat in each of the 4 corners of the room. Opposite each of these cats sit three cats. How many cats are in this room?
2. A father has six sons. Every son has a sister. How many children does this father have?
3. In a tailoring workshop, 20 meters were cut off from a piece of cloth 200 meters daily, starting from March 1. When was the last piece cut?
4. There are 3 rabbits in the cage. Three girls asked for one rabbit each. Each girl was given a rabbit. And yet there was only one rabbit left in the cage. How did it happen?
5. 6 fishermen ate 6 zander in 6 days. In how many days will 10 fishermen eat 10 zander?
6. There were 40 magpies on one tree. A hunter passed, 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 shared 3 oranges among themselves so that each got one orange. How could this happen?
9. A caterpillar crawls along the stem of a plant whose height is 1 m. During the day it rises by 3 dm, and at night it falls by 2 dm. In 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 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: the number 27 containsseven tens and two units;
two tens and seven ones.
6. Find the wrong entries and circle:
7 tens is equal to 17 units;
the number 80 is greater than 70 by 1;
If the number 50 is reduced by 1, it will be 48.
2) Find the values 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+50e) 40+28+2 f) 30+26+4
g) 63+7+20
3) Read the entries using the words "greater than" and "less than" so that the entries are correct and put a sign (<,>).
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) Write the correct answer.
a) How many centimeters are there in 1 metre? In 1 m =
b) How many decimeters are in 1 meter? In 1 m =c) How can a word be abbreviated with a numbermeter ?
d) Write down abbreviated 10 meters, 12 meters, 7 meters.
e) Express in decimeters:1) 8 m 1 dm; 2) 3 m 9 dm; 3) 6 m.
e) Express in meters and decimeters:
a) 54 dm; b) 77 dm.
6) Decipher the record.
- 7) Help the squirrel collect the 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? Say 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 in each picture?
4. There are twenty-nine sticks in the picture. Let's put one more. How many sticks were there?
5. Name all the numbers from 20 -39; 65-78; 76-81; 34-56; 55-67.
6. Decide verbally.
15 willows grew by the pond. 6 old willows were cut down, and 9 young ones were planted. How many willows are by the pond?
For dinner, my mother served 3 cucumbers, and 6 more tomatoes. At dinner we ate 4 tomatoes. How many tomatoes are left?
There were 15 buckets of water in the barrel. 6 buckets were used for watering the trees, but then 9 buckets of water were added to the barrel. How many buckets of water were in the barrel?
There were 14 students in the class doing homework. Then 6 children left and 9 came. How many children were in the class?
