Teaching children simple arithmetic operations is a complex process divided into several stages. First, actions with single-digit numbers are studied, then cases with a transition through a dozen are investigated. When the skill of counting within 10 and with the transition through a dozen is worked out to automatism, they begin to study the addition and subtraction of two-digit numbers. The use of various methods, conducting classes in a playful way will help the kid understand the principle of action better and faster.
Preparatory work
The introduction to the addition and subtraction of two-digit numbers occurs gradually:
- Children first learn to add and then subtract round numbers.
- Then they solve examples in which the sum (difference) of units and tens does not go beyond ten.
- Finally, the cases with the transition through the discharge are investigated.
Before studying arithmetic operations, it is important to learn how to divide numbers into bit terms (25 = 20 + 5), to determine which bit units the number consists of (25 - 2 tens and 5 units).
When explaining the composition of numbers, you can use a practical method - laying out the number with the help of counting sticks.
The essence of this method is as follows:
- It is explained that one vertical stick is one, two is the number 2, and so on.
- 10 sticks is a dozen. 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 denote a horizontally located 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 the method of repeated repetition.
- The ability to determine the composition of a number with the help of cards is strengthened: the child looks at the number and divides it into bit terms or determines its composition.
Sticks can be replaced with Lego parts or other constructors: small ones will denote units, large ones - tens. After practicing the skill, they begin to study the 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 dozen + 2 dozen = 3 dozen, or 30.
- With the help of sticks or a constructor: lay out 1 horizontal stick, add 2 more, it turns out 3 - in total, 3 dozen, or 30.
Subtraction is explained in a similar way. Having solved a few examples, proceed to the next stage.
Addition and subtraction without passing through the digit
The 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 that, they count all horizontal (add tens - it turned out 5), then - vertical (add units - it turns out 7).
Read the answer: 57. On the basis of the actions performed, it is concluded that units are added with units, tens - with tens. After completing the action, you can work without sticks.
If you skip the stage of illustrative explanation (and maybe even “discoveries” that can be made by solving the example with the help of sticks) and just say that units of the same 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 column addition.
It is important to explain that units are written under units (to make it easier to add), and tens - under tens. If the example is written incorrectly, then you can come to an erroneous result.
It will be useful to first consider the incorrect entries, solve them in a column and check the addition with the help of sticks, and then draw conclusions.
Similarly, subtraction is introduced using sticks and in a column. If the child has successfully mastered the previous stage, then he will not have any questions about this. And after a while it will be possible to move on to the last, most difficult stage.
Addition and subtraction of two-digit numbers with a transition through the digit
The complexity of performing actions lies in the fact that you will need to "memorize" numbers when adding and "borrowing" when subtracting.
First, the example is solved using sticks (for example, 25 + 37):
- Lay out the numbers with sticks, add bit units. It turns out 5 horizontal and 12 vertical sticks.
- They remember that 10 units is a dozen, so they can be replaced with one horizontal stick.
- It turns out 6 tens and 2 units. Hence, 25 + 37 = 62.
- They draw a conclusion: when the units were added, the number was greater than 10, so we divided it into ten and ones, and then determined the number. It is more convenient to first add the units (if there are more than ten, then you can select a dozen without any problems and add it to the existing ones).
After an illustrative example, consider adding in a column and other ways of adding two-digit numbers:
- First, tens are added to the number, and then ones: 25 + 37 = (25 + 30) + 7 = 62;
- The first term is brought to a round one (25 + 5 = 30), then the second is added to it (30 + 37 = 67) and as much as was added in the first action (67-5 = 62);
- Units are added separately, tens separately, and then - the results: 25 + 37 = (20 + 30) + (5 + 7) = 50 + 12 = 62.
It is also advisable to first show the essence of subtraction with the transition of a digit clearly (for example, 42-15):
- Spread out the first number (4 tens and 2 units).
- It is determined that 5 cannot be subtracted from 2 units, so one ten must be "converted" into units (replaced with ten vertical sticks).
- Further actions: subtract 5 from 12 units, it turns out 7, then dozens are subtracted (it is advisable to say that there were 4, and after the transformation there are 3 left).
- The result is 2 tens and 7 units, or 27. You need to check the subtraction using addition to make sure that you solved the example correctly.
After the visual method, column subtraction and several other methods are considered:
- First, dozens are subtracted, then - units: 42-15 = 42-10-5 = 27;
- On the contrary, first - units, then - tens: 42-15 = 42-5-10 = 37-10 = 27.
Abacus can be used to explain arithmetic operations. There is a place for each category on them, so it will be easy for children to “write down” 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 with the help of numbers, others will not understand until they themselves "see" the solution.
And, of course, systematization plays an important role in mastering any material: you need to regularly in the required amount.
This is finding one of the summands in terms of the sum and the other summand.
The original amount is called diminished, the known term - deductible, and the result (i.e., the required term) is called difference.
Subtraction properties of numbers
1. a - (b + c) = (a - b) - c = (a - c) - b ;
2. (a + b) - c = (a - c) + b = a + (b - c) ;
3. a - (b - c) = (a - b) + c .
For a visual representation of arithmetic operations (both addition and subtraction), you can use number line- this is a straight line, which consists of a point of origin (this point corresponds to zero) and two rays propagating from it, one of which corresponds to positive numbers, and the other to negative ones.
An example of subtraction on the number line
On this number line, you can see that the numbers to the left of 0 have a negative value. Subtracting one from a negative number (in this case -1) three times, we get the number -1.
Subtracting from positive number 4, positive number 3 (or negative number -1 three times), we get one
Example
| 4 - 3 = 1 ; | 3 - 4 = - 1 ; |
| -1 -3 = - 4 ; |
Column subtraction of numbers
Units are subtracted first, then tens, hundreds, etc. The difference for each column is recorded below it. If necessary, from the adjacent left column (i.e. from the most significant bit) 1 .
Let's look at a few examples of column subtraction below.
Example of subtracting two-digit numbers in a column
Example of subtracting three-digit numbers in a column
The principle of subtracting three-digit numbers is similar to the method of subtracting two-digit numbers, in this case the numbers are no longer tens, but hundreds.
Example of subtracting four-digit numbers in a column
The principle of subtracting four-digit numbers is similar to the method of subtracting three-digit numbers, in this case the numbers are no longer hundreds, but thousands.
Subject: Mathematics
Grade: Grade 3
Teacher: Antonova Tatiana Gennadievna
Lesson type: Learning new material
Lesson topic: Subtracting two-digit numbers without
transition through a dozen.
The purpose of the lesson: Creating comfortable conditions for
development of students' skills, to solve
examples of the type: 58-27.
Tasks:
1. Formation of skills to solve
double-digit subtraction examples
numbers without going through a dozen.
2. Correction of logical thinking
based on inference and analysis.
3. Development of students' skills
cooperation with peers.
4. Continue education of communicative
ability and understanding through
organization of joint activities.
During the classes
“Hello,” you say to the person.“Hello,” he will smile back.
And probably won't go to the pharmacy
And the whole century will be healthy.
- I am glad to see you and really want to start working with you!
Let the one who says a two-digit number, in which there are 4 ones, sit down.
Stage 2. 3 minutes
Homework check
Check the correctness of homework.
Home notebooks
Without opening your notebook, say:
-What numbers are we working with now? (two-digit)
- What action were the examples given? (+)
P. 130 No. 1 (1,2)
- Name an example that is located:
…in 1 column the second ...
… in the 2nd column, the last ... andetc.
- Who had difficulties in solving these examples?
- Let's see how you learned to solve them.
-Now there will be an opportunity to practice more.
Stage 3. 5 minutes
Verbal counting
Form the ability to add two-digit numbers.
Develop spatial representations.
Develop communication skills.
Numbers
On the chalkboard examples
Z3 + 22 Kirill
54 + 24 Masha
52 + 16 Danil
25 + 43 Masha
27 + 31 Vitaly
53 + 45 Nastya
11 + 67 Danil
64 + 34 Alina
The first example - Kirill will go to the left small board and solve, Danil Kostenko - to the right small board, Vitaly to the large one on the right, Danil Evsikov - to the large one on the left.
- The second example is decided by:
On the large board on the left - Masha Taratukhina, on the small one on the right - Alina, on the large one on the right - Nastya, on the small one on the left - Masha Boykova.
- Let's check. 1 pair, 2 pair, 3 pair, 4 pair.
- What do the answers have in common? (units - 8)
- We must clearly understand where there are units in the number, where are tens, for we will play.
Make a Number Game
- Let's play with the same pairs and check each other
Set three numbers differently.
1 pair - on the desk in the playroom
2 pair - on the teacher's desk
3 pair - on the blue table in the playroom
4 pair - on a free student table.
"Vasya knows tens of units well"
"Tanya needs to work on ones and tens"
Stage 4. 3 minutes
A minute of calligraphy
Education of the ability to accurately draw up work in notebooks. Connection with life.
Workbooks
Open notebooks, write down the number, great work.
- What number are we working with? (24)
- What do you know about him? (even, two-digit, it contains 2 decimal places, 4 units, consists of the numbers 2 and 4, the previous 23, the next 25).
- Call with this number : measure of length
measure of value
measure of time
measure of capacity
measure of mass
- Where can we use different measures?
Stage 5 ... 1 minute
Gymnastics for the eyes
Stage 6. 10 minutes
Preparation for the main stage
Prepare children to learn a new type of example.
30 + 7=
78 – 8 =
81 – 80 =
25 + 2 =
67 – 3 =
43 + 20=
56 – 30 =
37 + 42=
58 – 27=
While preparing for the lesson, I was worried and scattered examples. I can't figure out which ones we have already decided. Will you help me?
Find the studied example game.
Find an example and solve it.
Stage 7. 3 minutes
Assimilation of new knowledge
To acquaint students with a way to solve new examples.
58 – 27 =
- Guys, look closely at the example, how does it differ from the previous ones?
- Maybe someone knows how to solve it.
- Let's decide in color.
- How do we start work? From units.
- What color units? Red.
- How many units are in the first number? 8
- How many units are in the second number? 7
- 8 - 7 we get 1.
- I work with dozens.
- What color do we designate dozens? Blue.
- How many tens in the first number? 5
- How many tens are in the second number? 2
- 5 - 2 we get 3.
- Answer 31.
- What kind of example did you get? (to subtract two-digit numbers).
- What example will appear on the tape?
Stage 8. 2 minutes
Physical education minute
Develop auditory attention while playing.
Game "Be attentive"
I say a single-digit number - you clap.
I say a two-digit number - you stomp.
I say a round number - you jump.
I call 100 - keep quiet.
Step 9. 15 minutes
Primary anchoring
Continue to develop the ability to solve examples and solve problems to reduce the number by several units.
1p. - 37 K.
2p. -? 16 k. less
- Name the kind of examples that we will solve.
Who can come up with an example. Let me start. The first number must contain tens and more ones than the second. 85 - 63 =
Making examples
Or p. 130, no. 4.
- Where can such examples be found?
- Let's solve the problem p. 130, No. 5 (a).
1. Read it.
2. I will read it, and you think, in order to solve the problem, which is more convenient to do?
3. Read the condition and find the main words for a short note.
4. What are the main words?
5. What do we know about the 1st shelf?
6. What do we know about the 2nd regiment?
7. Read the main question.
- Look at the short entry, does it fit the task? Why doesn't it fit?
1. Can we immediately answer the main question?
2. What we don’t know?
3. Can we find out how much is on the 2nd shelf?
4. What action? (-) Why?
5. And then we can answer the main question? (Yes)
6. What action? (+) Why?
- Who is confident and can solve the problem on their own? Decide.
- Who is not sure go to the board.
Answers 21k., 58k.
Step 9. 2 minutes
Control and self-test of knowledge
Study the state of knowledge of each student on the topic.
Individual
cards
- Do you want to test yourself, can you solve examples of subtraction of two-digit numbers?
- I offer you tasks. (There is a card in the notebook on the back side, solve examples)
Step 10. 2 minutes
Outcome
Summarize the lesson.
Let's summarize now,
Maybe the lesson was wasted?
For oral work in the lesson, we received marks ... .., work in notebooks and on cards must be checked, then we can put the mark in the journal.
Step 11.
1 minute
Additional task Describe:
58 =… dec. … Unit
6 dec. 2 units = ...
Teaching a child to subtract and add is a complex, multi-stage process, starting with the study of single-digit numbers and turning into two-digit ones, with a gradual study of the moments when there is a transition through a dozen. To teach a child to quickly count two-digit numbers, you must go through each stage sequentially. The use of different learning methods, mainly in a playful way, makes it possible to make the whole process interesting for the baby, which will have a positive effect on the results.
Subtraction of two-digit numbers with a transition through the digit
Explaining the subtraction of two-digit numbers to a child is easier using. This will allow you to focus on the process and improve the assimilation of the passed material. You should not start with large numbers right away, it is better to start the first steps with minimum numbers, gradually increasing.
An important point is that the child will not be able to immediately count in his head, even when it comes to small numbers. It is better to use a piece of paper, parts of the construction kit, a computer or other additional means where the kid can make the required notes. Attention should be paid to studying the order of formation of tens, up to a hundred. This will help when learning addition and subtraction with the transition through the digit, and not just within the limits of one ten. Having mastered the counting within ten, you can proceed to the study of more complex actions, using one of the techniques or a combination of them.
Separating numbers by subtracting
When subtracting a single digit from a two-digit number with a transition through the digit, you can use division. Explain to your child that it will be easier to subtract from a whole ten, and it is enough to divide a single number in such a way that by subtracting one of its parts you get 10, and only then subtract the second part. As a result, the child will quickly master such an account, having learned how to correctly divide the numbers and get the final result.
This method is well suited in cases where a count of up to 10 has been mastered, and the baby is also familiar with numbers up to at least 20. Classes should be conducted in a playful way, using consumables or special ones.
Using geometric shapes to render numbers
A common variant when tens are denoted by triangles and ones by dots. It is enough to explain to the child the meaning of the figures and give a few examples. After that, you can start training, starting with simple tasks, using numbers up to 20, gradually complicating them.
For the entry-level, this is a suitable option, allowing you to make calculations quickly and clearly. However, it can be difficult when the additional ten must be subtracted when deducting (for example, 54-35 = 19). It is important to explain to the kid the subtlety of such a moment. It is better to subtract two-digit numbers in this way, avoiding such situations, or regularly show examples to the child for better mastery.
Taking away with Lego
To apply this method, you can use Lego Duplo, calculated for these purposes, or ordinary construction blocks, having previously numbered them. With their help, you can solve complex problems, including those in which there is a transition through a dozen.
It is enough to display the required numbers using the appropriate digits (for example 25-19). To explain the subtlety more clearly to the child, it is enough to divide them into smaller ones (10, 10, 5 and 10, 5, 4). The child easily learns that 10-10 = 0, and will be able to remove the extra tens. The remaining equation can be easily solved in the future (10 and 5 - 5 and 4). The child only has to count 10-4, having received the final result.
Adding two-digit numbers
It is usually easier to explain to a child the addition of two-digit numbers than a deduction, even in cases where there is an additional ten being added after the addition. There are enough teaching methods to choose the most suitable one for your little one. It is important that all preschool children should be entertained in a playful way.
Splitting numbers
One easy way to learn is to divide numbers into tens and ones. This also helps in the case when the ten is added after adding the units. For example 25 + 36 the child will write as 10 + 10 + 10 + 10 + 10 + 6 + 5 and get the result 50 + 5 + 6. After that, the addition takes place 5 + 6 = 11. Expanding 11 by 10 + 1 again gives 50 + 10 + 1 = 61. Children easily perceive this method and quickly learn to use it even with mental calculations.
Use a stacked solution
This will greatly simplify the counting process for your little one. So the child perceives tens and ones more easily, can make notes about additional tens and other necessary entries. It is easier to add two-digit numbers in this way and soon the child will be able to carry out the necessary operations in the mind.
It is possible to use this method to study the deduction.
Application of online games for learning
Today there are many mini-games that are aimed at helping parents to educate their child. Their use makes it possible for the kid to quickly and with interest to master the basic basics of counting, including cases when two-digit numbers are added with a transition through the category.