Explain 2 ways to subtract two-digit numbers. "Subtraction of two-digit numbers (general case)". Counting on ice cream sticks
Good afternoon, dear readers! How much effort adults have to make to teach a child to count within 10 and 20. And not only count, but also solve examples, subtract and add! At the same time, this is not as difficult as it seems at first glance. We offer you non-standard game methods on how to teach a child to count examples within 20.
Where to begin?
Stage 2
If you have learned to count, get acquainted with the graphic representation of numbers. For this purpose, we use cubes with numerical images, cards.
Stage 3
The next step is very important: it prepares the basis for quick mental counting. This is the study of the composition of numbers. If the baby is firmly aware of how the numbers are laid out, he will easily solve examples for addition and subtraction.
The study of the composition of the number is traditionally carried out using the so-called "houses". Draw a house on a piece of paper. On one "floor" there are always 2 cell rooms. The number of storeys of the house is determined depending on the number of numerical pairs into which the figure can be decomposed.
For example, 4 can be decomposed into 3 and 1, 2 and 2. So the number 4 lives in a two-story house, and so on. We will write it on the roof. The example clearly shows how to correctly compose houses for the numbers 3, 4 and 5.
The resettlement of "tenants" on the floors of the child will have to memorize. Start with small numbers. Ask the baby to carefully look at who lives with which neighbor, and then “populate” the numbers on their own.
When the two and three are mastered, move on to more complex numbers. This technique gives the most solid results. Proven in my own experience.
Here you can download such a table and use it to master the technique of number composition: 
Stage 4
When the houses were completed, it was the turn of examples within 10. In the first grade, these examples will have to be solved in the first half, so it's better to prepare in advance. Now it remains only to put + or - signs between the “settlers”, having previously explained their purpose to the baby.
First, present addition or subtraction in the form of a game. For example, one left the floor from the four. Which of the neighbors will stay on the floor? Answer: three. Such exercises will help the crumbs quickly get used to mathematical examples. Gradually, the words “left”, “came” are changed to “plus” and “minus”.
So we mastered the count with the child within 10. As you can see, the technique is very simple, but it takes time and patience to work. Try to force the baby to first count in the mind: written exercises slow down thinking.
Along the way, train the concepts of “more-less” (first use the objects, spreading them on different sides, then compare the numbers), neighbors of the number (write a series of numbers with missing numbers and ask the baby to complete the series by correctly placing the neighbors).
Move on…
It's time to introduce the baby to the second ten. To overcome arithmetic difficulties, we propose the following lesson algorithm:
Part 1
We introduce the concept of ten. To do this, lay out 10 cubes in front of the child and add one more. We explain that it is eleven. We are talking about the fact that the end of the word "twenty" means "ten". To form a number from 11 to 19, you just need to add a number to the ending "twenty" and put the preposition "on" between them.
Part 2
Since the baby is already familiar with the concept of ten, we introduce the category of units and, when adding, we operate with these concepts. For example, 13+5. We add the units first: 3+5=8. Now add the remaining ten and get 18. 
Part 3
Now let's move on to the negative examples: we act in the same way. Subtract ones, then add ten.
Part 4
The most difficult stage is subtraction, in which the first unit is less than the second: 13-6. In this example, we cannot subtract six from 3. You have to deal with ten. One of the ways is to subtract three from six, subtract the remaining number from ten, i.e. 6-3=3, 10-3=7. After a few workouts, the kid will be able to subtract in his mind.
The child must clearly master the skills described: in grade 2, he will need this to solve examples with two-digit numbers.
To brighten up the learning process, you can attract various aids:
- cubes;
- magnets;
- pictures (training with pictures is especially diverse: you can simply count them, use coloring pages with examples to consolidate counting skills);
- any items at hand;
- counting sticks;
- abacus, etc.
The more you show imagination, the sooner you will interest the child in mathematics.
We have examined the sequence of teaching crumbs to solve examples within 20 in stages. If the article was useful to you, leave a comment or share the article with your friends on social networks. networks.
See you soon, dear friends!
The topic of this video lesson is “Written addition techniques two-digit numbers with a transition through a dozen of the form 37 + 48. Often you have to perform addition when both terms are from the first ten, and the sum is from the second ten. Such calculations are called action with the transition through the ten.
Lesson:Written tricks for adding two-digit numbers with a transition through a dozen of the form 37 + 48
We need to find the sum of two numbers 37 and 48. First, we will do it verbally, presenting the numbers in the form of models. (Fig. 1.)
There are 3 tens and 7 ones in the number 37. There are 4 tens and 8 ones in the number 48. When we execute , we concatenate both numbers.
Let's combine the units. We add 2 units to 8 units and we get a dozen. We can represent ten as a model of the number 10. (Fig. 2.)
What number did we get?
There are 8 tens and 5 ones in this number. This number is 85.
Let's use another way to add numbers. This method does not require the use of number models.
Look at the expressions:
Let's represent the second number as the sum of 40 and 8.
37 + 48 = 37 + (40 + 8)
Let's group the numbers differently. First we find the sum of the first two numbers, and then we add the third term.
37 + 48 = 37 + (40 + 8) = (37 + 40) + 8 = 77 + 8
In order to make it more convenient to add numbers, you can decompose the number 8 into a sum of terms, one of which will complement the number 77 to a round number. These are numbers 3 and 5.
37 + 48 = 37 + (40 + 8) = (37 + 40) + 8 = 77 + 8 = 77 + 3 + 5 = 80 + 5 = 85
Do you think there is a faster way to add numbers?
Let's use the column addition method.
When adding, the numbers are written one below the other. We start calculations in a column with the smallest digit - the digit of units.
We add 8 units to 7 units and get 15 units. Under the units place, we can only write units. To do this, we must find out how many ones are in the number 15. The number 15 consists of 1 ten and 5 ones. This means that we write the number 5 under the unit digit.
Ten we send to the category of tens.
Now let's count the tens. 3 + 4 = 7. And 1 more ten, 7 + 1 = 8. We write the number 8 under the tens place.
We added two numbers and got the number 85.
The little fox, the little squirrel and the kitten also learned to add numbers in a column. Let's see if they got it right. Look at the two numbers that the fox has stacked up. (Fig. 3.)
Let's check the correctness of his calculations. Let's find the sum of units. 5 + 7 = 12. Under the ones place, we write the number 2 and pass 1 tens to the tens place. The fox didn't show it. Let's see if he forgot to add it later ?.
Add up dozens. 3 + 2 = 5. We need to add another ten. 5 + 1 = 6. Therefore, you need to change the digit in the tens place. Therefore, let us remind Fox that we should not forget to give a dozen. (Fig. 4.)
Let's look at the calculations of the Kitten. (Fig. 5.)
First add the units. 7 + 6 = 13. The Kitten has the number 1 written, which means that a mistake was made. Now add up the tens. 4 + 1 = 5. And we also add the ten that we gave away from the category of units. 5 + 1 = 6. We see that the Kitten got the wrong answer. Did you guess what the Kitten made a mistake? He messed up the action. He subtracted the number 16 from the number 47. Therefore, we replace the sign and get the correct expression. (Fig. 6.)
Let's check the example of Belchonok. (Fig. 7.)
We add units. 8 + 5 = 13. We write down the number 3 and give 1 ten to the tens place. Now add up the tens. 2 + 1 = 3. And we also add 1 ten, which we gave away from the category of units. 3 + 1 = 4. We must not forget to write down the one, which we give from the discharge of units to the discharge of tens. (Fig. 8.)
do at home
1. Solve expressions:
a) 28 + 43 b) 34 + 17 c) 22 + 69
Solve expressions:
Solve expressions.
Organization of tasks for repetition.
In order to discover a new mathematical secret, it is necessary to conduct a mathematical warm-up. I suggest you play. Game conditions: the most attentive, observant one comes to the board; the student becomes with his back to the board, on which numerical expressions for subtractions within 20 are written without values; the guys in the class name the answers to the given numerical expressions; the student must quickly turn around to find a numerical expression for each answer and name it. Do you understand the rules of the game? Who can reproduce them? (You can call a student who repeated the rules.)
Be smart. What trick will help you quickly find the right numerical expressions, how will you act? (Strike through or underline already named numerical expressions.)
There are two interesting houses on the board. What task can you come up with for this drawing?
How to find this unknown number?
This game is called "We populate the houses." The houses will be populated by two teams, each with two participants. Who can complete this task faster?
Question to the teams: what needs to be done to become a winner?
Guys, did you cope with the task, how did you agree to act when completing the task? How were the calculations done?
And now I suggest you find the values of the following numerical expressions: 67-45, 38-27 and 67-39. Make notes in a notebook. What computational technique will help you do this?
Did everyone complete the task?
What is the difficulty? Why can't you count? Let's take a look at the board.
What new things will you learn today, what mathematical mystery will you discover?
What then is the purpose of the math lesson today?
How to act in this situation?
How many opinions in the class. (If among the proposed options there is no correct one, then the teacher himself names and shows the correct option, explains a new computational technique for subtracting two-digit numbers).
Which step should be added to our Path to Answer checklist. (Show memo)
And now you need to find the correct answer in numerical terms 67-39.
________________________________________
Want to test what you've learned today?
I propose to do calculations using a new computational technique, according to the textbook p. 75 No. 2.
The student is invited to the board.
Which of you can act as a teacher and help at the blackboard ... find the meaning of numerical expressions?
And now another "teacher" says out loud "The Way to the Answer", sitting at a desk, and the rest of the guys can check themselves and write down the calculations correctly.
For those who will cope with the task the fastest. A task with a secret from Athanasius, a brownie, who also studies at school number 9, but at night. Let's check if he learned to calculate correctly. How will you act?
43 - 26 \u003d 23 57 - 38 \u003d 29 69 - 43 \u003d 26 (calculations are written in a column)
How would you rate the work of the brownie Athanasius?
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 the transition occurs through a dozen. To teach a child to quickly count two-digit numbers, you should 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 positively affect the results.
Subtraction of two-digit numbers with the transition through the discharge
It is easier to explain to a child the subtraction of two-digit numbers using. This will allow you to focus on the process and improve the assimilation of the material covered. You should not immediately start with large numbers, it is better to start the first steps with the minimum numbers, gradually increasing.
Such a moment is important - the child will not be able to immediately count in his mind, even when it comes to small numbers. It is better to use a piece of paper, parts of the designer, a computer or other additional means where the baby can make the required notes. Attention should be paid to the study of 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 one ten. Having mastered the count within ten, you can proceed to the study of more complex actions, using one of the methods or combining them.
Separation of numbers when subtracting
When subtracting a single-digit number from a two-digit number with a transition through the discharge, division can be used. Explain to the child that it will be easier to subtract from a whole ten, and it is enough to divide a single-digit number in such a way that by subtracting one of its parts to get 10, and only then subtract the second part. As a result, the child will quickly master such an account, learning how to correctly divide 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 Visualize Numbers
A common option is when tens are indicated by triangles, and units 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 that allows you to carry out calculations quickly and clearly. However, it can be difficult to subtract an additional ten when subtracting (for example, 54-35=19). It is important to explain the subtlety of such a moment to the baby. Subtracting two-digit numbers in this way is better, avoiding such situations, or regularly showing examples to the child for better development.
Taking away with Lego
To apply this method, you can use Lego Duplo, designed for this purpose, or ordinary designer cubes, having previously numbered them. They can be used to solve challenging tasks, including those in which there is a transition through the ten.
It is enough to display the required numbers using the appropriate numbers (eg 25-19). In order 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 is further solved easily (10 and 5 - 5 and 4). It remains for the child to count 10-4, having received the final result.
Addition of two-digit numbers
It is usually easier to explain to a child the addition of two-digit numbers than the subtraction, even in cases where there is an addition of an additional ten after addition. There are enough ways to learn to choose the most suitable for your baby. Important - the occupation of all children preschool age should be played in a playful way.
Number separation
One of simple ways learning is the division of numbers into tens and ones. This also helps when adding ten after adding units. For example, 25 + 36 the child will write down as 10 + 10 + 10 + 10 + 10 + 6 + 5 and get the result 50 + 5 + 6. After that, the addition 5 + 6 = 11 takes place. Again, decomposing 11 by 10 + 1, we get 50 + 10 + 1 = 61. Children easily perceive this method and quickly learn to use it even when calculating in their minds.
Use the solution "in a column"
This will make the counting process much easier for your little one. So the child perceives tens and ones more easily, can make notes about additional tens and other necessary entries. Adding two-digit numbers in this way is easier and soon the child will be able to carry out the necessary operations in the mind.
This method can also be used to study the deduction.
Application of online games for learning
Today, there are many mini-games that are aimed at helping parents in teaching their child. Their use allows the baby to quickly and with interest learn the basic basics of counting, including cases when there is an addition of two-digit numbers with a transition through the discharge.
