Math lesson: "Adding and subtracting two-digit numbers" (2nd grade). How to explain to a child the subtraction and addition of two-digit numbers Using the example of subtracting two-digit numbers

At the age of 4, my son learned to find the patterns of the decimal system himself. What does nine subtract from a number when adding 1. That is, 11+9=20.
That 13+14 is easier to count as 3+4=7, and then +10 and +10 and = 27! And everything is in the mind.
How did I know that this is what he thinks? So I can hear what he says. And I know, as I think myself, I remember from my own childhood how I mastered numbers, however, I was already 8 years old. And it's the same! I naturally recognize the same train of thought.

Mastering counting turned out to be very useful for us. It’s easy to find an algorithm for using them on the Internet.
It was more difficult to find normal scores. Bought at Ikea.

I used a felt-tip pen to color the fifth and sixth dominoes in each row so that they would be different. It's more convenient. The son gradually began to move away from counting the dots on the board to manipulating numbers in his head.

Adding two-digit numbers
I used Excel again to make worksheets with tasks:

I also included subtraction here. And he deliberately made omissions in the place of the minuend and subtrahend. The son began to intuitively navigate the example. Then it will be easier to solve equations.

Column
A simple example is 25+64=89, when the numbers in each column do not go beyond ten. We started with these.
A complex example is 74-36=38, when you have to “occupy” and “keep in mind.”
For a long time, my son did not understand how numbers add up and especially how they are subtracted in a column. Confused. We took a break from math for two weeks. When we returned, everything began to work out on its own. “We need to give a pause,” as Zhvanetsky said, “otherwise it doesn’t reach the people.”

I’m thinking: as children, we were taught to add numbers up to ten in our heads. Double digits don’t require mental input - you can do it in a column. Three-digit and more - you can use a calculator.
What if you don’t tell the children what they can do on a calculator, but let them do the math in their heads? Something tells me that they will count :)

A person has learned to more or less add numbers within a hundred. There is no need to push it until such examples are 100% solvable. Move on to more complex ones. There he will definitely need this addition as a simple action. And he will train.

At first I sat, watched him count, tell me the answer, and I said whether it was correct or not. Now I'm leaving. Let him write the answer himself. I'll come and check. This is how a tiny amount of responsibility for one’s calculations appears. You need to make your own decision on what answer to write.
We have developed a reward system. I give ten examples on the board. If you solved an example correctly, you get +1, and if you solved it incorrectly, you get -1.

Problems
It's good to add numbers! What about the applied account? Pasha had five apples, but he lost two... Problems are needed so that the child himself can identify what is important. I found the problems online. And a lot of interesting tests. It’s very nice to know that at the age of five my son gets an A in first grade math.
But you still need to read the conditions of the problem, understand it and then just solve it. So we also practiced reading.

Textbooks
If you are teaching math to your child, check the school textbooks. There are a lot of little things that seem self-evident, such as measuring lengths with a ruler. Ignorance of such little things, if they had not been sorted out with the child, can unexpectedly emerge and remind you that the textbooks were not written in vain.
There is some kind of stupidity with modern mathematics textbooks. First of all, there are too many of them. Secondly, for some reason they are in two or three volumes for the academic year. Thirdly, they are impossible to understand. I, an adult with two higher educations, do not understand basic things: turtles and leaves are drawn, but in the next picture there are fewer turtles, and the leaves have become crossed out. I cannot explain in any way that I understand what happened between these pictures. The son also did not answer.


Through my mother-in-law we got a textbook from 1988. What a class! It lasts all year, and is the size of one of the modern volumes. The pictures in it are lively and intuitive. You can feel the flow of the school year: here is the first of September, here is the anniversary of the Revolution, New Year, February 23, March 8, May Day, Victory Day. Of course, the teacher must provide a reader for this textbook. I didn’t find it, but it seems to me that the Soviet version will win over the modern ones here too.

Add and subtract ten-digit numbers in a column. My son is just over 5 years old.
We'll be multiplying soon.

UMK "Perspective" Subject: Mathematics Textbook author: L.G. Peterson. Class: 2 Lesson type: ONZ Topic: “Subtraction of two-digit numbers with transition through place: 41 - 24” Main goals: 1) To consolidate knowledge of the structure of the first step of educational activity and the ability to perform the UUD included in its structure. 2) Construct an algorithm for subtracting two-digit numbers with transition through digits and develop the primary ability to apply it. 3) Fix the algorithm for subtracting two-digit numbers (general case), solving equations for finding an unknown summand, subtracting, reducing, solving problems on the relationship between a part and the whole. Mental operations necessary at the design stage: analysis, comparison, generalization, analogy. Demonstration material: 1) separate cards on which: The class got to work 2) standard of subtraction by parts with the transition through ten: ; 1 2 - 5 = 10 - 3 = 7 2 3 3) reference signal for subtracting two-digit numbers from a round number (from lesson 2-1-9): 4) standard for the general technique of adding and subtracting two-digit numbers (from lesson 2-1-0.1) : 5) reference signal for recognizing the type of example: m - B 6) card with the topic of the lesson: 41 - 24 7) graphic models; 8) an algorithm for subtracting two-digit numbers from a round number (from lesson 2-1-9): 9) cards to clarify the algorithm of lesson 2-1-9: 1 There are not enough units in the minuend. 10) card Subtract units from all received units: ... to replace zero in the reference signal of lesson 2-1-9. Handouts: 9 - 64 1) sheets with tasks for the updating stage: 7 - 54 5 - 44 3 - 34 41 - 24 ; 2) graphic models; 3) a notebook for supporting notes or the corresponding sheet from the “Build Your Own Mathematics” manual; 4) two halves (cut lengthwise) of a blank sheet of A-4 for the number of groups. Lesson progress: 1. Motivation for learning activities: - What was your goal during the trip in the last lesson? (Find a shortcut to the island. This turned out to be a convenient oral technique for adding two-digit numbers with moving through the place value - in parts.) - Today you will continue to study operations with two-digit numbers. Your familiar fairy-tale hero - Dunno - found out about how interesting you are in studying. How will you learn a new topic? (First, we repeat what is necessary, then we perform a trial action, fix our difficulty, and identify the cause of the difficulty.) - So, Dunno sent a telegram in verse. Do you want to read it and learn something new about operations with two-digit numbers? 2. Updating knowledge and fixing difficulties in a trial educational action. 1) Repetition of learned techniques for subtracting two-digit numbers. - But since Dunno is a great inventor, he encrypted his telegram. To read, you need to solve the examples. Open examples on the board. After the “=” sign, sheets with the words of the first line of the poem are attached with the white side. The sheets cover the written answers. 20 - You name the answers with examples, I take off the sheet so you can check yourself. The teacher writes down all the proposed answers on sheets of paper. If there are several of them, the correct answer is revealed on the basis of standards D-2 and D-3, which are displayed on the board. After agreeing on the answers, the teacher removes the sheets of paper, attaches them separately with the text down in the order of the examples, and the students compare the answers received with the numbers under the sheets. - You did a great job with Dunno’s examples, and you can read his telegram. The teacher turns over the sheets. - Read it in chorus. (The class got to work...) - What is this? (The telegram is not finished, it looks like the first line of the poem...) 2 - Probably, Dunno, due to his forgetfulness, did not send the second line. But nothing, but these examples will help you clarify what calculations will interest you today. - What do all the examples have in common? (They are all for subtraction; from a two-digit number you need to subtract a one-digit number.) - Which example is “extra”? (20 - 8 is an example for subtraction from a round number, and the rest are for subtraction with a transition through ten.) - What other examples of subtraction can you solve? (For subtraction of two-digit numbers according to the general rule.) Standard D-4 is placed on the board and the corresponding rule is pronounced. 2) Training of mental operations. Distribute worksheets. What is separated by a dotted line is wrapped. Children don't see this yet. Open the same on the board. 9 - 64 - 54 7 5 - 44 - 34 3 41 - 24 - Look at the task on your pieces of paper. It is also written on the board. What's interesting about the differences? (In the minuend, one digit is unknown, the unknown digits alternate; the known digits in the minuend are odd, in descending order; in the subtrahend, the number of tens is reduced by 1, but the number of ones does not change.) - Find the unknown digit of the minuend if it is known that the difference between numbers indicating tens and units is 3. One at a time with an explanation. The teacher writes numbers on the board, children - on pieces of paper. (In the first example 6 tens, 12 tens is not suitable, since it is a two-digit number; in the second example - 4 e, since 10 e are not suitable; in the third example - 8, since ...; in the fourth - 6..., in the fifth - 4...) - What technique will you need to solve these examples? (Subtraction of two-digit numbers according to the general rule.) - Do you know him? (Yes.) - Then solve these examples yourself. Execution time 1 minute. - Name the answer to the first (second, third, fourth) example. (5; 20; 41; 2.) The teacher writes down the results as the children answer. If different answers arise, the calculation method is clarified according to standard D-4. - What subtraction methods did I choose for repetition? (As a general rule, from a round one, with a transition through ten.) - Tell me, what will happen next? (Task for a trial action.) - What does “task for a trial action” mean? (This means that there is something new in it.) - Why am I offering it to you? (We try to complete it to understand what we don’t know.) 3) Task for a trial action. - Right. Turn over the bottom of the sheet and find the meaning of the expression written there. - State the result. (17; 23; 27, …) The teacher writes down all the children’s answer options. 3 - What do you see? (Opinions were divided, and someone could not find the result.) - Raise your hand those who did not receive an answer. -What couldn’t you do? (We were unable to solve example 41 - 24.) - Those who received the answer, prove, using the generally accepted rule, that you decided correctly. (We cannot prove that we solved example 41 - 24 correctly.) - Remind yourself and Dunno what to do when a person has identified a difficulty? (You need to stop and think.) 3. Identifying the location and cause of the difficulty. - Let's think. What numbers did you subtract? (Two-digit numbers.) - Remember the general rule for subtracting two-digit numbers. (When subtracting two-digit numbers, you need to subtract tens from tens, and ones from units.) - What prevented you from doing this? (Here there are not enough units in the minuend.) - What was new to you in this example? (We did not solve examples where the minuend has fewer units than the subtrahend.) Place a reference signal on the board to determine the type of example: m - B - Well done! You noticed an important feature of this example that distinguishes it from the previous ones: the minuend is missing units. - Where have you encountered such a case before? (When a one-digit number was subtracted from a two-digit number by passing through a ten.) - There are two-digit numbers here, so they say “with passing through a place.” - Tell us, how did you act, and where did you feel that you lacked knowledge? (…) - What is the reason for your difficulties? (There is no way to subtract two-digit numbers by moving through the digit.) 4. Constructing a project for getting out of the difficulty. - So, what goal should you set for yourself? (Construct a method for subtracting two-digit numbers with transition through place value.) - Name the topic of the lesson. (Subtraction of two-digit numbers with transition through the digit.) - For convenience, let’s write it briefly in the topic. Hang a card with the topic on the board: 41 - 24 - Let's first decide on the means. What tool do you need to visualize how the transition through the discharge occurs? (Graphic models.) - What recording method will be needed? (Write in a column.) - What standards do you know that can help? (The standard for subtracting a two-digit number from a round one.) - This means that you will refine this standard. - Now plan your work: in what order will you move towards achieving your goal. (First, we will solve the example using graphical models, then in a column, and then we will clarify the standard for subtracting a two-digit number from a round one.) It is advisable to record the plan on the board. 5. Implementation of the constructed project. - So, first... (Let's lay out a graphical model of the example.) One student is at the blackboard, the rest are at their desks: - Repeat again, how do you subtract two-digit numbers? (Tens are subtracted from tens, units are subtracted from units.) - What is stopping you from using this rule? (There are not enough units in the minuend.) 4 - Is the minuend less than the subtrahend? (No.) - Where are the few hidden? (In the top ten.) - How can this be? (Replace 1 ten with 10 ones. - Discovery!!!) - Well done! Continue subtraction. - So what is next? (We follow the general rule: from 3 d we subtract 2 d, we get 1 d; from 11 units we subtract 4 units, we get 7 units. Result: 1 d 7 e or 17.) - So, the correct answer is 17. - Well done, guys ! So, you have found a new method of calculation: if there are not enough units in the minuend, then... (You can split the ten and take the missing units from it). - What will you do next according to the plan? (Let’s solve the same example in a column.) - I think you can handle it without my help. One at the board with an explanation: (I write units under units, tens under tens. There are fewer units in the minuend, so I take 1 ten, divide it into 10 units and add them to the units of the minuend. I subtract the units: 11 - 4 = 7. I write the result under units. I reduce the number of tens by 1. I subtract the tens: 3 - 2 = 1. I write under the tens. Answer: 17.) - You did it really easily. What algorithm did you use? (There is no required algorithm; we used a similar algorithm for subtracting a two-digit number from a round one.) Open the algorithm for subtracting a two-digit number from a round number on the board (from lesson 2-1-9): - What’s next according to the plan? (This algorithm needs to be clarified.) Divide the children into groups of 4, as is customary in the class. - Meet in groups and make clarifications to this algorithm. Give each group two halves of an A-4 sheet (cut lengthwise). 1-2 minutes are allotted to complete the task. - Let's see what you got. Each group presents refinements to the algorithm and indicates the location of these refinements. During the discussions, a new option is agreed upon and placed on the board in the place indicated by the children. As a result, the algorithm should take approximately the following form: :... 5 - How do we change the reference signal for column addition? Open the reference signal for subtracting a two-digit number from a round number (from lesson 2-1-9): (You need to replace 0 with a card representing units.) The teacher makes changes to the reference signal of lesson 2-1-9 from the words of the children: - What do you think about What should you always remember when using this technique? Where is the error possible? (The number of tens is reduced by 1, ...) - Well done! You acted exactly according to plan. What can you say about achieving the goal? (We have achieved the goal, but we still need to practice.) 6. Primary consolidation with pronunciation in external speech. 1) No. 2, page 24. - Open in textbook No. 2 on page 24. - Read the task. Task: Solve examples according to the model. Write down and solve the following example: - Solve the first example. One from the spot with an explanation. (There are fewer units in the minuend, so I take 1 ten and divide it into 10 units: 10 + 1 = = 11. I subtract the units: 11 - 9 = 2. I reduce the number of tens by 1, subtract the tens: 7 - 2 = = 5. I write under tens. Answer: 52.) - We solve further. “Chain” from the spot with an explanation. Children solve examples until they notice a pattern: the minuend increases by 1, so the difference will increase by 1. When enough hands are raised, you can ask the children: - What happened? Is there a mistake somewhere? (No, you can simply write down the answers further without calculating.) - Why? (Here the minuend increases by 1, but the subtrahend does not change, so the difference will increase by 1.) - Great! List the answers next. (55, 56, 57.) - So that’s why mathematical laws are needed! They are always so helpful! Now make up your last example, taking into account the pattern. (87 - 29.) - Write down the answer without calculating. (58.) 2) No. 3, p. 24. - Well done! Now you can play! Guess game. The teacher distributes the columns into rows. - You will work in pairs. Write down examples of your column in a notebook. One person in the pair explains out loud the solution to the first example of the column. Then together you try 6 to guess the answer to the second example, understanding and explaining the pattern. Next, the second person from the pair checks the answer of the second example. The teacher provides assistance to individual students if necessary. The completion of the task is checked frontally. - Now everything is clear? (You must first work independently.) 7. Independent work with self-test according to the standard. - Well, try your hand at independent work: No. 4, p. 24. Assignment: Select and solve examples of subtraction with transition through place value. What's interesting about them? What is the next example? 98 - 19 47 + 38 95 - 20 54 - 17 50 + 30 29 - 9 76 - 18 68 + 23 - Read the task. a) - The task consists of several parts. What should you do first? (Select examples for a new computational technique.) - Complete this part of the task yourself, checking the boxes next to the examples you have chosen in the textbook. - Check it out. Open the standard for this part of the task on the board: m - B - What difficulties arose during completion? (You didn’t pay attention to the sign and didn’t compare the units to find out the type of example.) - How did you act when searching for examples of a new computational technique? (We looked at the sign first, then compared the units. If the number of units of the minuend was less, then we checked the box.) - Correct those who incorrectly found examples of a new type. - Who did it correctly? Put “+” in the margin of the textbook. b) - What needs to be done next? (Solve examples for a new computational technique.) - Solve all selected examples in your notebook yourself. - Check it out. Open the sample solution of examples on the board: - What difficulties arose when solving the examples? (Forgot to reduce the number of tens by 1, ...) - Who was not mistaken? Place another “+” in the margin of your notebook. - What interesting things did you notice in the examples? (The numbers in the minuends are written in order from 9 to 4; the subtrahends are in decreasing order, etc.) - What example will be next? (32 - 16.) - How to write down the answer without counting? (Trace the pattern in the answers: the number of tens decreases by 2, and the number of units - by 1, which means the answer to the next example is 16.) 7 8. Inclusion in the knowledge system and repetition. - Today in the lesson you showed that you can work alone, in pairs, and now work again in groups. Divide the class into groups. - What, in your opinion, is the main skill when working in a group? (The ability to listen, the ability to hear each other, etc.) - You will complete repetition tasks in groups: No. 6 (3rd column), p. 24; No. 9 (a, b - one task of your choice), p. 25. The task is written on the board. 3-4 minutes are given to work in groups. After this, sample recordings of solved equations and problems are displayed on the board. Task No. 6, page 24. Solve the equations and check: x - 9 = 14 x + 25 = 40 63 - x = 27 5 + x = 52 50 - x = 12 x - 48 = 24 - Check the solution using the sample. If there are mistakes, correct them and write down the correct solution. Solution (3rd column): 63 - x = 27 x = 63 - 27 x = 36 63 - 36 = 27 27 = 27 x - 48 = 24 x = 24 + 48 x = 72 72 - 48 = 24 24 = 24 Task No. 9 (a, b), page 25: Draw a diagram, pose questions to the problems and answer them: a) There are 5 horses, 4 camels and 2 elephants on the carousel. b) There are 30 dolls in the kindergarten, and 2 fewer trucks. - Evaluate your work in the group. Did everything work out? What were the difficulties? (It was difficult to agree on what we would decide...) 9. Reflection on learning activities in the lesson. - What goal did you set for the lesson? (Construct a method for subtracting two-digit numbers by moving through the digit.) - Have you achieved your goal? Prove it. (…) - What solution did you come up with? (…) - What did you like? (...) - You know, Dunno remembered that he sent us only half of the poem, and here is the following telegram: Open the note on the board: Everything will work out for you! - Was Dunno right? What did you get? (…) - What was difficult? - What else needs to be worked on? - Now let’s return to Dunno’s poem. Let's read it again. (If you get to work, everything will work out for you.) - Rework the second line so that it contains an assessment of the class’s work. (Everything worked out for us...) - Read the poem in full in chorus. - Tell me, what qualities helped you and what hindered you when working in pairs or in a group? (...) Homework:  No. 5 (come up with two examples), p. 24; No. 8, 9 (c), p. 25; ☺ No. 11, page 25. 8

Math is hard

But I will say with respect -

Math is needed

Everyone without exception!

12 d e To A blah.

TO la ss naya r A bot.

11 – 8

15 – 8

Exercise for the mind

70 ,

LESSON TOPIC:

ADDING AND SUBTRACTING TWO-DIGITS NUMBERS

help is needed

I doubt

I'm confident and can handle it

Remembering what is important for the lesson

50 – 7 = 80 + 5 =

43 – 21 = 34 + 45 =

60 – 4 = 76 – 6 =

We remember what is important for the lesson.

What do you know?

• Addition and subtraction table
• Names of addition action components
• Subtraction Action Component Names

An algorithm for adding two-digit numbers when the sum results in a round number.

• Algorithm for subtracting from a round two-digit number

• Have you considered all the ways to solve expressions?
• Are there any difficulties and what are they?
• Algorithm for solving expressions in a column for addition with transition through the digit.
• Algorithm for solving expressions in a column for subtraction with transition through the digit.

• Work in groups:
• 26+18=?
• 44-18=?

Adding up the units...

14 units is 1 ten and 4 units

I write 4 under the units, and write 1 ten above the tens.

Adding up tens...

I add 1 ten, which is obtained from adding units

In total it turned out...

I write under tens...

Reading...

I write tens under tens and ones under ones

I subtract units. 4

I borrow one ten. (I put a dot over the number)

I think 10 minus...

I write a number under the units...

I'll subtract tens. There were...dozens. They took one dozen. There are...dozens left. I count... tens minus... tens

I write under tens...

Reading...

Examination

Select and solve subtraction expressions with step-by-step transformation. What is the next expression?

Examination

I know

1.Addition and subtraction table.

I want to know

1. We have considered all cases of addition and subtraction.

Found out

2.Name of action components.

1. To find the value of the sum, you need to add the units, and if there are more than ten, then write down only the units, and remember the ten and add it when adding the tens.

3.Algorithm for adding two-digit numbers, when the sum results in a round number

2. Are there any difficulties in solving expressions, and what kind?

2. To find the value of a subtraction, you must first subtract the units from the units, but there are cases when the values ​​of the units of the minuend are less than the value of the units of the subtrahend, then you need to take one ten. And when subtracting, strictly know that the number of tens has become one less.

3.Algorithm for adding two-digit numbers into a column with transition through the digit

4. Algorithm for subtracting from a round two-digit number

4. Algorithm for subtraction into a column with transition through a digit

3. Column addition algorithm with transition through digit

4. Algorithm for subtraction into a column with transition through a digit

Teaching children simple arithmetic operations is a complex process divided into several stages. First, actions with single-digit numbers are studied, then cases with transitions through ten are studied. When the skill of counting within 10 and moving through tens is practiced to the point of automaticity, they begin to study the addition and subtraction of two-digit numbers. The use of various methods and conducting classes in a playful way will help the child understand the principle of action better and faster.

Preparatory work

Acquaintance with addition and subtraction of two-digit numbers occurs gradually:

1. First, children learn to add and then subtract round numbers.
2. Then solve examples in which the sum (difference) of units and tens does not exceed ten.
3. Finally, cases with transition through discharge are examined.

Before studying arithmetic operations, it is important to learn how to divide numbers into digit terms (25 = 20 + 5), determine which digit units the number consists of (25 - 2 tens and 5 ones).

When explaining the composition of numbers, you can use a practical method - laying out the number using counting sticks.

The essence of this method is as follows:

• It is explained that one vertical stick is a unit, two is the number 2, etc.
• 10 sticks is a ten. There are numbers consisting of several tens. To lay them out you need a lot of sticks, and it will be difficult to count. Therefore, a dozen will be denoted by a horizontal stick (if the sticks are of a standard size, then exactly 10 vertical ones will fit on the horizontal one).
• Any two-digit number is laid out, for example, “25”: put 2 sticks horizontally (tens) and 5 vertically (units).
• The skill is brought to automatism by repeated repetition.
• The ability to determine the composition of a number with the help of cards is consolidated: the child looks at the number and divides it into digit terms or determines its composition.

The sticks can be replaced with Lego parts or other construction sets: small ones will indicate units, large ones – tens. After practicing the skill, they begin to study addition and subtraction of round numbers.

Adding and subtracting round numbers

Explained in several ways:

• Based on knowledge of the composition of numbers: 10 + 20 = 1 ten + 2 tens = 3 tens, or 30.
• Using sticks or a construction set: lay out 1 horizontal stick, add 2 more, you get 3 - in total, 3 tens, or 30.

Subtraction is explained in the same way. Having solved several examples, move on to the next stage.

Addition and subtraction without jumping through digits

Actions are explained in a practical way. For example, you need to find the result of the expression “25+32” .

First, lay out the first number (2 horizontal and 5 vertical sticks), then the second (3 horizontal and 2 vertical). After this, count all the horizontal ones (add the tens - it turns out 5), then - the vertical ones (add the ones - it turns out 7).

Read the answer: 57. Based on the actions performed, they conclude that ones add with ones, tens with tens. After practicing the action, you can work without sticks.

If you skip the stage of illustrative explanation (and maybe even the “discovery” that can be made by solving an example with the help of sticks) and simply say that units of identical digits are added, the child may not understand why this is so. It will be difficult for him to remember how such examples are solved.

After explaining the meaning of the action, you can enter additions in the column.

It is important to explain that units are written under units (to make adding more convenient), and tens are written under tens. If the example is written incorrectly, you may come to an erroneous result.

It will be useful to first consider the incorrect entries, solve them in a column and check them by addition using sticks, and then draw conclusions.

Subtraction using sticks and in a column is introduced in the same way. If the child has successfully mastered the previous stage, then he will have no questions about this. And after a while it will be possible to move on to the last, most difficult stage.

Adding and subtracting two-digit numbers with place jumps

The difficulty in performing the actions is that you will need to “remember” numbers when adding and “borrow” when subtracting.

First, the example is solved using sticks (for example, 25+37):

1. They lay out numbers with sticks and add up digit units. This makes 5 horizontal and 12 vertical sticks.
2. They remember that 10 units are a ten, so they can be replaced with one horizontal stick.
3. It turns out 6 tens and 2 units. So, 25+37=62.
4. They conclude: when adding units, the result was a number greater than 10, so they divided it into tens and units, and then determined the number. It is more convenient to add the units first (if there are more than ten of them, then you can select the ten without any problems and add it to the existing ones).

After an illustrative example, we look at column addition and other ways of adding two-digit numbers:

• First, tens are added to the number, and then units: 25+37=(25+30)+7=62;
• The first term is brought to round (25 + 5 = 30), then the second is added to it (30 + 37 = 67) and as much is subtracted as was added in the first action (67-5 = 62);
• Units are added separately, tens are added separately, and then the results are added: 25+37=(20+30)+(5+7)=50+12=62.

It is also advisable to first show the essence of subtraction with transition of the discharge clearly (for example, 42-15):

1. Lay out the first number (4 tens and 2 ones).
2. It is determined that 5 cannot be subtracted from 2 units, so one ten must be “translated” into units (replaced with ten vertical sticks).
3. Further actions: subtract 5 from 12 units, you get 7, then subtract tens (it is advisable to say that there were 4, and after the transformation there are 3 left).
4. The result is 2 tens and 7 ones, or 27. You need to check the subtraction using addition to make sure that you solved the example correctly.

After the visual method, subtraction in a column and several other methods are considered:

• First, tens are subtracted, then units: 42-15 = 42-10-5 = 27;
• On the contrary, first - ones, then - tens: 42-15 = 42-5-10 = 37-10 = 27.

Abacus can be used to explain arithmetic operations. They have their own place for each digit, so it will be easy for children to “write” numbers on them and then perform actions.

Any method can be successful only if it is selected in accordance with the characteristics of the child. After all, it is enough for some to explain the principle of addition and subtraction using numbers, while others will not understand until they themselves “see” the solutions.

And, of course, systematization plays an important role in mastering any material: it is necessary regularly in the required volume.

Goals: secondary comprehension of already known knowledge, development of skills for their application.

Lesson type: lesson - fairy tale, consolidation of knowledge.

Lesson objectives:

1. Educational: repeat the learned technique of adding and subtracting two-digit numbers, based on digitwise addition and subtraction.

2. Developmental: develop students’ computing skills, creativity, development of logical thinking, attention, memory.

3. Educating: to cultivate interest and inquisitiveness in the learning process, to cultivate mutual assistance, support, and collectivism.

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Municipal educational institution "Krasnoyarsk secondary school No. 1"

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Primary school teacher

Municipal educational institution "Krasnoyarsk secondary school No. 1"

Tanatova Gulmira Salauatovna

year 2009.

Mathematics 2nd grade

Subject: Adding and subtracting two-digit numbers.

Goals: secondary comprehension of already known knowledge, development of skills for their application.

Lesson type: lesson - fairy tale, consolidation of knowledge.

Lesson objectives:

1. Educational: repeat the learned technique of adding and subtracting two-digit numbers, based on bitwise addition and subtraction.

2. Developmental: develop students' computing skills, creativity, development of logical thinking, attention, memory.

3. Educating:cultivate interest and inquisitiveness in the learning process, cultivate mutual assistance, support, and collectivism.

Equipment: boxes with numbers, drawings depicting a stone, Gorynych the Snake, the evil witch Karchena, textbook “Mathematics” 2nd grade.

During the classes.

1. Organizational moment.

Hello guys!

Today I, Gulmira Salavatovna, will teach you a math lesson.

Check if you have everything ready for the lesson. Before you and I begin our lesson, I want us to smile: you at me, and I at you; and you to each other and to our guests. Well, are you ready to start the lesson? Well, that's great.

You are a good friendly class.

Everything will work out for us.

2. Calligraphy.

U. Guys, do you like fairy tales?

Today in the lesson we will find ourselves in a fairy tale. Let's get there using the magic number. What number is most common in fairy tales?

D. Number 3.

U. Where is it found?

D. The fish has three wishes, thirty-three heroes, three inscriptions on a stone, three sisters, and so on.

U. Tell me two-digit numbers that have 3 ones and let’s write these numbers down.

We sit down correctly and write beautifully.

D. 13,53,73,83, etc.

U. From a series of numbers, tell me the smallest number and underline it with one line, and name the largest number, underline it with two lines.

Slide No. 1 (topic)

3.Message of the topic of the lesson.

U. Since our fairy tale is not simple, but mathematical, we will not only travel, but also repeat the method of adding and subtracting numbers, and wrestle with tricky problems.

4. Oral counting.

Now we will solve fairytale problems orally.

Slide No. 2

No. 1 Baba Yaga asked Ivan Tsarevich 10 easy riddles, and 5 more difficult ones. How many difficult riddles did Baba Yaga tell Ivan Tsarevich? (15)

Slide No. 3

No. 2 The squirrel gave the Hedgehog 18 large mushrooms, and 5 less small ones. How many small mushrooms did the Squirrel give to the Hedgehog?

Slide No. 4

No. 3 Santa Claus has 8 toy bears and 20 bunnies in his bag. How many fewer bears than bunnies are there in Santa Claus's bag?

What fairy-tale characters have you met?

Guys! What other fairy-tale characters do you know?

Well done! And today we will meet some heroes?

Slide No. 5

W. Once upon a time there was a large, strong kingdom in the world. Beautiful, brave people lived in it. They were not afraid of anyone, but they themselves never quarreled with anyone. And all because Elena the Wise ruled them. The evil witch Karchena was very jealous of their happiness. So she decided to destroy Elena. Lured her to me

cast a spell.

Slide No. 6

And she threw boxes to her faithful servants, and above them were mysterious signs.

What are these signs? (these are numbers)

U. – What numbers are these?

D. Two-digit numbers.

U. We will have to work verbally with two-digit numbers and help open the desired box. Read the numbers written above the caps

D. 35, 33, 73, 40, 13, 23.

U. Which number is the odd one out? Why?

D. The number is 40, since this number only contains round tens. All other numbers have tens and ones.

W. The box with the number 40 opened, and there was a letter.

You won’t find Elena, no matter how hard you try!

A magic flower can cast a spell on her,

And who I hid it with, you will understand if you go from large to small. Karchena.

Slide No. 7

You need to try to arrange the numbers that are written above the boxes in descending order and, accordingly, write down the letters that are given with these numbers.

Write down the numbers in your notebook on a line across the square.

Landing.

On the board: 73, 35,33,23,13. (student leaves)

Read the word that came out.

Who has the magic flower hidden?

D. The word “Koshchey” came out, which means he has a flower.

U. The faithful servant of Elena the Wise Bulat, the knight, got ready for the road and went to get a flower. Whether long or short, the knight arrived at the fork of three roads, and there lay a stone and the inscription:

Who will read it?

“If you go through three roads, you will find the way to Koshchei.”

Bulat thought:

“To walk along every road, you will lose time, but here every minute is precious, and without Elena, wisdom and beauty on earth will be lost.”

5. Consolidation of the material covered.

U. Now we will need all your knowledge, skills, and what you learned in your last lessons. Let's test how well you can add and subtract two-digit numbers.

There are three roads in front of Bulat. In our classroom, the desks are in three rows.

Let us help the knight travel along all roads at once.

Landing

The first row will go along the first road, collect all the pebbles, and count the examples written on them.

Write the examples down in your notebook, line by line, and then check with each other. (One works at the board, give a rating)

The third row has a difficult path - winding and steep. Make sure you don't make a mistake and don't fall into the abyss. (One at the board is working on the assessment)

And the second row and I will follow the middle path and do our task.

Review the recording carefully.

Find the pattern according to which the numbers are located in the row from the stone.

D. Numbers decrease, decrease by 3

U. Write down the entire series of numbers. (one at the board)

Children complete tasks. – What did you do?

D. 20, 17, 14, 11, 8, 5.

U. Can we also reduce the series of numbers by 3?

D.Yes.

U. What number will you get? (2) complete.

And I'll see how the first and third rows are doing. Let's check if anyone has tripped on the path.

Records of students working at the board open.

We check that all roads have been passed.

Well done guys, you all completed the task.

And I suggest you get some rest.

6. Physical exercise.

Slide No. 8

U. And here Koschey and his friend Zmey Gorynych meet us, hissing in unison with anger. Koschey says: “Since you were able to get to me, Bulat, you can solve my problem.

Let's read the problem.

On the desk: In my garden the apple tree grows with golden and silver apples. There are 25 gold ones, and 12 less silver ones. How many apples are there in total?

Let's help Bulat solve this problem.

The solution is written down on the board with comments.

Z. – 25ab.

WITH. - ? 25 less.

Total - ?

1. 25-12=13 (Yab) – silver
2. 25+13=38 (Yab) - total

Answer: 38 apples. Student grade

Are there golden and silver apples in life?

What benefits do apples bring in real life?

Slide No. 9

We haven't solved all the problems yet. The three heads of the Serpent Gorynych have prepared tasks for us.

Task No. 1. Karchena has 28 bats in his service, and 8 fewer snakes. How many snakes does Karchena have?

Task No. 2. Along the road from Karchena to Koshchei, 9 of her faithful dwarf servants ran. How many dwarfs fled to Koshchei?

Task No. 3. And the third head offers a task from the textbook: “Do the task and you’ll get a flower!” p.5 No. 5

7. Independent work. (additionally) Slide 2

Task 1. Baba Yaga asked Ivan the Tsarevich 10 easy riddles, and 5 more difficult ones. How many difficult riddles did Baba Yaga tell Ivan Tsarevich?

Task 2. The squirrel gave the Hedgehog 18 large mushrooms, and 5 less small ones. How many small mushrooms did the Squirrel give to the Hedgehog?

Problem 3. Santa Claus has 8 toy bears and 20 bunnies in his bag. How many fewer bears are there than bunnies in Santa Claus's bag?

You won’t find Elena, no matter how hard you try! A magic flower can disenchant it, and who I hid it with, you will understand if you go from larger to smaller. Karchena. 23 33 73 40 13 35

23 33 73 13 35 35 - O 33 - SC 73 - K 13 - J 23 - E

Task. “In my garden the apple tree grows with golden and silver apples. There are 25 gold apples, and 12 less silver apples. How many apples are there in total?

Task 1. Karchena has 28 bats in her service, and 8 fewer snakes. How many snakes does Karchena have? Task 2. Along the road from Karchena to Koshchei, 9 of her faithful dwarf servants ran. How many dwarfs fled to Koshchei? Task 3. Textbook page 5 No. 5.