Teaching a child to subtract and add is a complex, multi-stage process, starting with the study of single-digit numbers and moving to two-digit ones, with a gradual study of the moments when the transition occurs through ten. To teach a child to quickly count two-digit numbers, you should go through each stage sequentially. Using different learning methods, mainly in a playful way, makes it possible to make the whole process interesting for the child, which will have a positive impact on the results.
Subtracting two-digit numbers with place jumps
It is easier to explain to a child the subtraction of two-digit numbers using. This will allow you to concentrate 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 minimal numbers, gradually increasing.
This point is important - 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 a construction set, a computer or other additional means where the child 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 by moving through place value, and not just within one ten. Having mastered counting within ten, you can move on to studying more complex actions, using one of the techniques or combining them.
Dividing numbers when subtracting
When subtracting a one-digit number from a two-digit number and moving 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-digit 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 this kind of counting, learning to correctly divide numbers and get the final result.
This method is well suited in cases where the child has mastered counting up to 10, and the child 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 this, 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 get tricky when subtracting an extra ten (for example, 54-35=19). It is important to explain to the child the subtlety of such a moment. It is better to subtract double-digit numbers in this way, avoiding such situations, or regularly show examples to the child for better mastery.
Taking away with Lego
To use this method, you can use Lego Duplo, designed for these purposes, or ordinary construction bricks, having previously numbered them. With their help, you can solve complex problems, including those in which there is a transition through ten.
It is enough to display the required numbers using the appropriate numbers (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 just has to count 10-4 to get the final result.
Adding two-digit numbers
Explaining addition of two-digit numbers to a child is usually easier than subtraction, even in cases where an additional ten is added after addition. There are enough teaching methods to choose the most suitable one for your baby. It is important that all preschool children should be taught in a playful way.
Dividing numbers
One simple way to learn is to divide numbers into tens and ones. This also helps when adding tens after adding units. For example, a child will write 25+36 as 10+10+10+10+10+6+5 and get the result 50+5+6. After this, the addition 5+6=11 occurs. Dividing 11 into 10+1 again, we get 50+10+1=61. Children easily perceive this method and quickly learn to use it even when doing mental calculations.
Use the columnar solution
This will greatly simplify the counting process for your baby. This makes it easier for the child to perceive tens and ones, and can make notes about additional tens and other necessary notes. Adding two-digit numbers is easier this way and soon the child will be able to carry out the necessary operations in his mind.
This method can also be used to study deductions.
Application of online games for learning
Today there are many mini-games that are aimed at helping parents educate their children. Their use allows the child to quickly and with interest master the basic basics of counting, including cases when two-digit numbers are added with a transition through place value.
This is finding one of the terms by the sum and the other term.
The original amount is called reducible, the known term is deductible, and the result (i.e. the required term) is called difference.
Properties of number subtraction
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 is a straight line that consists of the origin point (this point corresponds to zero) and two rays extending from it, one of which corresponds to positive numbers and the other to negative ones.
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 the positive number 4, the positive number 3 (or the negative number -1 three times), we get one
Example
| 4 - 3 = 1 ; | 3 - 4 = - 1 ; |
| -1 -3 = - 4 ; |
Subtracting numbers in a column
Units are subtracted first, then tens, hundreds, etc. The difference of each column is written below it. If necessary, it is taken from the adjacent left column (i.e. from the highest digit) 1 .
Let's look at some examples of columnar subtraction below.
An example of subtracting two-digit numbers in a column
An 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.
An 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
Class: 3rd grade
Teacher: Antonova Tatyana Gennadievna
Lesson type: Learning new material
Lesson topic: Subtracting two-digit numbers without
moving through ten.
Purpose of the lesson: Creating comfortable conditions for
developing students' skills, solving
examples of the form: 58-27.
Tasks:
1. Formation of decision-making skills
examples for subtracting two digits
numbers without going through ten.
2. Correction of logical thinking
based on inference and analysis.
3. Development of students' skills
collaboration with peers.
4. Continue to develop communication skills
abilities and mutual understanding through
organization of joint activities.
During the classes
“Hello,” you say to the person.“Hello,” he will smile in response.
And probably won't go to the pharmacy
And you will be healthy for a whole century.
- I'm glad to see you and really want to start working with you!
Let the one who can name a two-digit number with 4 units sit down.
Stage 2. 3 minutes
Checking homework
Check that your homework is completed correctly.
Homework books
Without opening your notebook, say:
-What numbers are we working with now? (two digits)
- What action were the examples given for? (+)
Page 130 No. 1 (1.2)
- Name an example that is:
…in the 1st column the second...
… in column 2 the last one... Andetc.
- Who had difficulties 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
Develop the ability to add two-digit numbers.
Develop spatial concepts.
Develop communication skills.
Numbers
Examples on the board
Z3 + 22 Kirill
54 + 24 Masha
52 + 16 Danil
25 + 43 Masha
27 + 31 Vitaly
53 + 45 Nastya
11 + 67 Danil
64 + 34 Alina
Kirill will go to the small left board and solve the first example, Danil Kostenko will go to the small right board, Vitaly will go to the big right board, Danil Evsikov will go to the big left board.
- The second example is solved:
On the large board on the left is Masha Taratukhina, on the small board on the right is Alina, on the large board on the right is Nastya, on the small board on the left is 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 in the number there are ones and where there are tens, so let’s play.
Game "Make a Number"
- Let's play in the same pairs and test each other
Specify three numbers differently.
1 pair – on a desk in the playroom
2 pair – on the teacher’s desk
3 pairs - on the blue table in the gaming room
4 pairs - on a free student table.
“Vasya knows tens well”
“Tanya needs to work on ones and tens”
Stage 4. 3 minutes
A minute of penmanship
Developing the ability to accurately format work in notebooks. Connection with life.
Workbooks
Open your notebooks, write down the number, great job.
- What number are we working with? (24)
- What do you know about him? (even, two-digit, it has 2 dec., 4 units, consists of the numbers 2 and 4, the previous one is 23, the next one is 25).
- Name 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 study a new type of examples.
30 + 7=
78 – 8 =
81 – 80 =
25 + 2 =
67 – 3 =
43 + 20=
56 – 30 =
37 + 42=
58 – 27=
While I was preparing for the lesson, I was worried and scattered examples. I can’t figure out which ones we’ve already solved. Can you help?
Game "Find the studied example."
Find an example and solve it.
Stage 7. 3 minutes
Learning new knowledge
Introduce students to how to solve new examples.
58 – 27 =
- Guys, look carefully at the example, how does it differ from the previous ones?
- Maybe someone knows how to solve it.
- Let's decide in color.
- Where do we start working? From units.
- What color are the units? Red.
- How many units are in the first number? 8
- How many units are in the second number? 7
- 8 – 7 gets 1.
- I work with dozens.
- What color do we designate tens? Blue.
- How many tens are in the first number? 5
- How many tens are in the second number? 2
- 5 – 2 we get 3.
- Answer 31.
- What type of example did you get? (for subtracting two-digit numbers).
- What example will appear on the tape?
Stage 8. 2 minutes
Physical education moment
Develop auditory attention during the game.
Game "Be careful"
I call a single digit number and you clap.
When I call a two-digit number, you stomp.
I call a round number and you jump.
I call 100 - be silent.
Stage 9. 15 minutes
Primary consolidation
Continue to develop the ability to solve examples and solve problems involving reducing a number by several units.
1p. – 37 k.
2p. - ? 16 k. less
- Name the type of examples that we will solve.
Who can come up with an example themselves. Let me start. The first number must have more tens and ones than the second. 85 – 63 =
Making up examples
Or p. 130, no. 4.
- Where can examples of this type be found?
- Let's solve the problem p. 130, no. 5 (a).
1. Read.
2. I will read, and you think, to solve the problem, what is more convenient to do?
3.Read the condition and find the main words for a short entry.
4. What are the main words?
5. What do we know about 1 shelf?
6. What do we know about the 2nd shelf?
7. Read the main question.
- Look at the short note, does it fit the task? Why doesn't it fit?
1. Can we immediately answer the main question?
2. What don’t we 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.
- Those who are not sure go to the board.
Answers 21k., 58k.
Stage 9. 2 minutes
Control and self-test of knowledge
Examine the state of knowledge of each student on the topic.
Individual
cards
- Do you want to test yourself, can you solve examples of subtracting two-digit numbers?
- I offer you tasks. (There is a card on the back of the notebook, solve the examples)
Stage 10. 2 minutes
Bottom line
Summarize the lesson.
Let's sum it up now,
Maybe the lesson was wasted?
We received grades for oral work in class….., we need to check the work in notebooks and on cards, then we can put a grade in the journal.
Stage 11.
1 minute
Additional task Write down:
58 =... dec. ... units
6 dec. 2 units = ...
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. Using 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:
- First, children learn to add and then subtract round numbers.
- Then solve examples in which the sum (difference) of units and tens does not exceed ten.
- 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 a similar 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 ones (to make adding more convenient), and tens are written under tens. If the example is written incorrectly, you may arrive at 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 lies in the fact that you will need to “remember” numbers when adding and “borrow” when subtracting.
First, the example is solved using sticks (for example, 25+37):
- They lay out numbers with sticks and add up digit units. This makes 5 horizontal and 12 vertical sticks.
- They remember that 10 units are a ten, so they can be replaced with one horizontal stick.
- It turns out 6 tens and 2 ones. So, 25+37=62.
- 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):
- Lay out the first number (4 tens and 2 ones).
- It is determined that 5 cannot be subtracted from 2 units, so one ten must be “translated” into units (replaced with ten vertical sticks).
- 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).
- 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.
