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The national project “Digital Educational Environment” is coming to Russian regions: equipment will be supplied to schools and Internet access will be improved. But let's not forget about the content: what will the teacher do with new but empty computers? A digital classroom is not only computers and the Internet; an important component of the digital environment are tools and services that allow organizing the educational process at school using electronic educational resources.
Adding and subtracting round tens (two-digit place numbers) comes down to adding and subtracting single-digit numbers that express the number of tens. For example, to add 30 to 50, it is enough to add 3 tens to 5 tens, you get 8 tens, or 80, and to subtract 30 from 50, it is enough to subtract 3 tens from 5 tens, you get 2 tens, or 20. On the next 2-3 lessons, students say the explanation out loud and then silently. As a result of exercises, students gradually develop a skill.
The sequence of studying the operations of addition and subtraction is determined by the increasing level of difficulty when considering various cases. There are:
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.
All actions with examples of groups 1 and 2 are performed using methods of mental calculations, that is, calculations must begin with units of higher ranks. Examples are recorded in numbering, decimal composition of numbers, tables of addition and subtraction within 10. The actions of addition and subtraction are studied in parallel.
14) Methodology for studying arithmetic operations. Addition and subtraction of numbers within the first hundred (tasks for studying the topic, ranking techniques from the simplest to the most complex, methods for studying addition and subtraction techniques with transition through rank).
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 units), 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.
For example:
The explanation is usually carried out on an abacus, sticks, bars or cubes of an arithmetic box, and an abacus.
When subtracting a single-digit number from a two-digit number with a transition through the digit, first all units of the minuend are subtracted, I then the remaining units of the Counted are subtracted from the round tens.
record. 41-3=38 41-1=40 40-2=38
Detailed 38+3=41 38+2=40 40+1=41
Both when adding and when subtracting, you need to decompose the second addend or minuend into two numbers. When adding, the second addend 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 aside 8 sticks and reasons as follows: “First, subtract 5 from 45, there will be 40 (removes 5 sticks, 3 remains to be subtracted. Subtract 3 from forty, 37 remains. 45-8 = 3?
Solving examples of this type is based on the solution techniques already known to students:
The solution to these examples is based on decomposing the second term and the subtracted term into bit terms and sequentially adding and subtracting them from the first component of the action.
Methods for studying arithmetic operations. Addition and subtraction of numbers within the first thousand (tasks for studying the topic, methods of familiarization with oral addition and subtraction techniques).
The main objective of the topic is to develop oral and written calculation skills.
In the “thousand” concentration, first oral and then written addition and subtraction techniques are studied.
Oral methods of addition and subtraction (260+120, 570+280), as well as within 100, are based on the properties of adding a number to a sum, a sum to a number, a sum to a sum, as well as the corresponding cases of subtraction.
When studying addition and subtraction within 1000, they widely rely on the knowledge and skills of children formed while studying the topic “hundred”; they often use comparison and analogy techniques.
Oral addition and subtraction techniques within 1000.
They are studied simultaneously and considered in the following order. At the preparatory stage, the simplest cases are considered, directly related to the application of knowledge on numbering of the form: a) 700+40, 820+8, 948-8 b) 789+1, 870-1, 699+1 c) 400+200, 800- 200.
At stage 1, cases are revealed where addition is performed based on the rule of adding a sum to a number, and subtraction is performed based on the rule of subtracting a sum from a number.
Techniques of addition and subtraction, directly related to the application of knowledge of numbering, serve to consolidate this knowledge and are considered mainly when studying numbering. The cases of 400+200 come down to actions on different numbers (4 hundred + 2 hundred). These calculations reinforce numbering knowledge and prepare children to learn more complex addition and subtraction.
At the first stage, children become familiar with addition and subtraction techniques of the form 540 + 300 (54 dec. + 30 dec. = 57 dec.)
Using this technique prepares children to learn techniques for multiplying and dividing within 1000, as well as written techniques for these operations with multi-digit numbers.
At the second stage, cases of addition and subtraction are considered, based on the use of the rules for adding a sum to a number and subtracting a sum from a number.
Methods for studying arithmetic operations. Addition and subtraction of numbers within the first thousand (which cases relate to written techniques, rules for writing in a column, possible errors during recording, algorithms).
Written addition and subtraction techniques within 1000.
These techniques are revealed following oral techniques. Mastering written techniques for adding and subtracting three-digit numbers is a prerequisite for successfully applying them to numbers of any size.
Written addition and then subtraction are learned first.
Written calculations use written addition and subtraction algorithms—certain rules that strictly determine the content and order of operations performed. Conscious application of the algorithm requires knowledge of the bit composition of a number, mastering the relationship of bit units, as well as a solid knowledge of tabular cases of addition and subtraction.
Consideration of cases of written addition and subtraction is based on the principle “from simple to complex.” First, the addition algorithm is applied for cases of addition without passing through a digit, then with a transition through 1 digit, through 2 digits (234+425, 235+425, 237+526, 453+371).
A similar principle is observed when using the subtraction algorithm (469-246, 540-126, 542-126, 909-714).
An algorithm is an exact prescription, a rule about performing a certain system of operations in a certain order.
Lesson topic: “Adding and subtracting round tens. Procedure in examples with brackets.”
Lesson type: combined.
Goal: to introduce children to the use of parentheses when solving examples.
1. Educational:
teach children to indicate the order of actions when solving examples with brackets;
consolidate the skill of solving compound problems;
teach how to solve a given problem based on constructing a hypothesis.
2. Developmental:
development of perception based on recognition of geometric shapes;
development of attention;
Correction of thinking based on the “match the letter and number” exercise.
3. Health-saving:
develop fine motor skills of the hand;
strengthening the correct posture when writing;
spend moments of emotional relief;
4. Educational:
cultivate motivation to study;
cultivate emotional adequacy of behavior.
Equipment:
slides with letters (Aibolit);
cards with an individual geometric task;
a disc with a recording of a musical composition for a physical education minute.
Expected Result:
children’s understanding of the concept of “brackets”;
children's acquisition of knowledge about solving examples with brackets.
Math lesson 2nd grade.
Lesson topic: “Adding and subtracting round tens. Procedure in examples with brackets.”
During the classes.
I. Organizational moment:
The bell has rung, friends,
The lesson begins.
II. Verbal counting:
Guys, do you like fairy tales? What fairy tales do you know? Today we will also get into a fairy tale and help its main character. And which one you will find out by unraveling the encrypted entry.
Here is a table, the first column is a letter, the second is an example. After solving the example, you will find out the code of the letter. And then substitute it into this number series.
Example: Answer:
Of course, this is the fairy tale “Aibolit”. Who wrote it?
Aibolit wrote us a letter, and it contains a riddle. Before we guess it, let's remember who was the first to help Aibolit go to Africa?
That's right, these are wolves. Let's guess how many wolves there were by listening to Aibolit's riddle:
On the path by the bush,
I saw three tails.
How many legs were there?
I couldn't understand it at all.
Guys, what example can you use to solve this riddle?
Additional questions:
Guys, how many wolves were there if three tails peeked out of the bushes?
How many legs does each wolf have? This riddle can be solved correctly with the following example:
4+4+4=12
What action can replace the addition of identical terms?
III. Work in notebooks.
Write down the number, great job.
2 17 0 4 16 11 9 18 20
Strong waves prevented the whale from swimming, they mixed up all the numbers, write down the numbers correctly, placing them in order: from the smallest number to the largest. Then Aibolit will be able to travel further.
Correct answer:
0 2 4 9 11 16 17 18 20
Compose and write two inequalities using this number series:
IV. Statement of educational problem.
Let's help Aibolit get to the top of the mountain faster so that the eagles can catch him. In order for Aibolit to reach the highest point where eagles live, we must solve the problem.
Guys, there are two entries in front of you.
- The examples are the same, but the answers are different.
If the right sides are different, then...finish my thought.
- So the left parts should also be different.
- So what question should we think about?
- How are the left parts different?
So, how are the left parts different?
- Procedure.
What is the procedure in the first example?
- First subtraction, then addition
And in the second?
- First addition, and then subtraction.
In which example did we follow the rules when making calculations?
- In the first.
And in the second?
- We broke the rule.
Teacher:
How can we guess that in the example there must be addition first?
- There must be some other sign.
Wonderful, there really should be such a sign. It's called a parenthesis. So what is the topic of today's lesson?
- Brackets.
(slide)
Brackets
Teacher: So what do the brackets mean? The parentheses indicate that the action is performed first. Conclusion:
(slide)
The action in parentheses is executed first.
That's right, guys, we solved this difficult problem and helped Aibolit get to Africa.
V. Physical moment. (Dynamic music break)
VI. Consolidation of new material.
Where did the eagles fly with Aibolit? (To Africa)
On Aibolit’s path he encountered impenetrable jungles with examples and tasks. Let's help our hero get to the poor sick animals.
Guys, there are 4 examples on the board, solve them and arrange the order of actions.
90-(30+40)= 80-40-20=
90-30+40= 80-(40-20)=
VII. The solution of the problem.
Aibolit had 40 chocolates. He prepared 20 chocolates for tiger cubs, 10 for ostrich cubs. Need to find out how many chocolates are left for other sick animals?
Repeat the problem statement.
Can we answer the question right away?
What should we know first?
How many actions are there in a task?
What will we learn as the first step?
What do we learn in the second step?
Write down a brief condition and solution to the problem in your notebook.
(Students solve problems under commented guidance.)
Well done guys, we completed all the tasks. Now let's take a break.
Tilt your head down
Turn right smartly
Return slowly to the left
And put it down on your desk.
We sometimes need moments of silence.
VIII A minute of relaxation.
IX. Working with geometric material.
Guys, what do you think are the tallest animals in Africa? They were probably the first to see Aibolit?
We also received an unusual African giraffe - it is made of geometric shapes.
Count them and write the answer on individual cards.
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X. Evaluation of own activities. Reflection.
Guys, each of you has cards with tiger cubs that Aibolit cured. If you were interested in the lesson and everything was clear, then place the card in first place; if there were minor difficulties, then place the card in second place; if there was a lot that was unclear to you, then place the card in third place.
XI. Evaluating students' work in class by the teacher.
Guys, I am very pleased that not a single tiger cub ended up in third place.
XII. Homework and lesson summary.
Guys, tell us what you met today. What are parentheses and what are they for?
Make four examples with the same numbers and signs, but with different
Open lesson summary
in third grade math
on the topic of:
“Adding and subtracting round tens. Procedure in examples with brackets.”
Compiled and conducted
Primary school teacher
Mustakimova E.Sh.
MATH LESSON
"Adding and subtracting round tens"
Target:
1. Strengthen the skills of adding and subtracting round tens within 100.
2 .Develop the ability to solve problems of the types studied, logical thinking skills.
3. Arouse interest in the subject through didactic games and logical tasks.
Equipment:
Drawings depicting Ivan Tsarevich, Serpent Gorynych, Vasilisa the Beautiful and Koshchei;
Cards with numbers and letters;
Number sheets for group work;
Key words for briefly recording tasks, etc.
During the classes.
1. Organizational moment.
- Guys, get ready for your math lesson.
Math is hard
But I will say with respect -
Math is needed
Everyone without exception!
- Do you love mathematics? (Address to children.)
It can be very difficult, but no less interesting. And I also know for sure that you love fairy tales. That's why I have prepared a surprise for you. Our lesson today will be fabulous!
There are traffic lights on your desks, show your mood. Green - a joyful mood, yellow - you are calm and confident,
Red - I'm a little worried.
What will we take with us to math class? (knowledge, ingenuity, attention)
Well, our assistants in the lesson will be ingenuity, attention, and resourcefulness. Now we will check how attentive you are.
2. Report the topic of the lesson.
- Today the topic of the lesson is not new, but repetition. But what topic? We will find out if we remember how fairy tales usually begin. Key words will help us:
In a certain kingdom, in the Far Far Away State, they lived - they were...
B…………………Addition
some………and
kingdom,………….subtraction
in…………………..round
Far away……..dozens
state……..in
lived…………….within
were………….100
3. Calligraphy minute.
- We opened the notebooks, wrote down the number, great job. We wrote down the numbers in the notebook. (The teacher comments on the writing.)
Open your notebooks, write down the date –….
What date was yesterday? (...), what date will it be tomorrow? (...)
What number will we write today in penmanship? (39)
What numbers does a word consist of? THIRTEENTH state?
- 3 and 9.
Name the neighbors of this number (38 and 40)
What number will you get if the numbers are swapped? (93)
4. Oral counting:
Let's start our journey with a warm-up - mathematical dictation:
Write down a number consisting of 1 dec. 3 units, 13
Write down a number less than 16 but greater than 14 15
- The 1st term is 3, the 2nd term is 4. What is the sum? (7)
Find the sum of numbers 4 and 5. ( 9)
The minuend is 7, the subtrahend is 5. Find the difference. ( 2 )
Find the difference between the numbers 9 and 6. (3 )
How much more is 6 than 4? (2)
How much is 5 less than 8? (3 )
What number add 9 to and get 9? (0)
Add the same amount to 4. What is the amount? ( 8 )
Five increase by 3. ( 8 )
9 decrease by 4. (5 )
-Mutual verification 13 15 7 9 2 3 2 3 0 8 8 5
Who can praise his neighbor?
5. Lesson material.
- And we continue that in a certain kingdom, in a distant state, there lived Ivan Tsarevich and Vasilisa the Beautiful (drawings on the board). One day Vasilisa disappeared. Ivan Tsarevich grieved, grieved and went in search. Who kidnapped Vasilisa?
1) Find the “extra” number.
- And we will know this if we find the “extra” number:
35, 73, 33, 40, 13, 23
and correctly arrange the numbers in descending order. Let's write down the correct order in your notebook:
73 35 33 23 13
- If we turn the cards over, we will find out who kidnapped Vasilisa the Beautiful:
K O SCH E
Ivan Tsarevich set off on his journey. But the Serpent Gorynych, sent by Koshchei, is already waiting for him. And the Serpent has three heads. And each one must be overcome. (Drawing on the board.)
2) Group task in rows.
If we find the correct solution to numerical expressions, we will help Ivan Tsarevich and overcome his head. Everyone finds only one solution and passes it on to their neighbor on the desk and on. The last one quickly brings me a sheet with the completed task. We will also see which series will quickly and correctly cope with this task. This will help us in further work:
38+2= 68+2= 28+2=
40+60= 80-30= 30+60=
40+40= 80+10= 30+30=
80+20= 50+40= 70+7=
100-20= 100-30= 100-40=
75-5= 64-4= 83-3=
50-30= 70-40= 60-30=
50-10= 70+20= 60-40=
20+40= 30+40= 40+30=
60+8= 70+5= 80-60=
- How Ivan Tsarevich defeated the Serpent Gorynych with our help, our expert commission will test your knowledge. And we will perform the following task:
3) "Labyrinth".
Ivan Tsarevich found himself in a dense forest, and it was very difficult for him to get out. But what do you think, with the help of what magical object will Ivan Tsarevich get out of the forest?
That's right, a magic ball! Imagine we have in our hands a magic little ball that must find the correct path among two-digit numbers from the smallest to the largest. While one student leads the way, the rest write down two-digit numbers in increasing order:
30 36 38 42 45 49 50 54 58 61 68 70
Our little ball led us out of the dense forest right at the crossroads. Three roads in front of Ivan Tsarevich, which one should we take next in search of Vasilisa?
Who was the first to win the battle with the heads of the Serpent Gorynych and correctly found all the solutions? (Row 1 means we’ll go along the first path.)
4) “Find a pattern, continue the series...”.
And a new task is on our way. Look at these numbers, guys, find a pattern in them and continue the series with other numbers. Who found the solution?
20, 17, 14,….. (11, 8, 5, 2)
2, 4, 6, 8,….. (10, 12, 14,…)
(Students work at the board, everyone writes down the correct solution in a notebook.)
The road led us to an oak tree on which a huge chest hung. What's in the chest, kids? (Children's answers.)
5) Turn false equalities and inequalities into correct ones.
Yes, the chest is not easy, it is closed with three locks, which these numerical expressions will help us open. But what is it? There are errors in the numerical expressions! This is the witchcraft of Koshchei the Immortal! Are we capable of correcting these mistakes?
40=50 28+1=30 60 70
(Students perform different solutions at the board, write the rest in a notebook:
40+10=50 1+28+1=30 60 70-20
40=50-10 28+1=30-1 60 70-50
Yes, indeed, there is an egg in the chest, and in the egg is Koshcheev’s death. Koschey appeared before Ivan Tsarevich and asked him:
“Spare me, Ivan Tsarevich, I’ll give you my rejuvenating apples, take them to your father. And if you kill me, they will lose their rejuvenating power. I just forgot how many of them I had left.
6) Solving the problem.
Rejuvenating apples grew in the Koshcheev Garden. Total 30. Koschey picked 10 apples. How many rejuvenating apples are left?
There were 30 apples
Picked - 10 apples
Left - ?
30-10=20(January)
Answer: Koshchei has 20 apples left.
Create an equation for the problem and solve it.
7) Logical task “Towers”.
- But Koschey is cunning. Ivan Tsarevich took pity on him, so he decided to give him a new problem.
“Well, Ivan, take Vasilisa,- said Koschey. - Just guess where she is first. I have 4 towers. The first tower is empty. Vasilisa is not in the highest tower. Where is she?
