Lesson summary "adding sum to sum." The rule for adding a sum to a sum to form a new digit unit

21.09.2019 -

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Parents of modern children watch with envy the child prodigies - participants in the television shows “Best of All” and “ Amazing people“- and they worry that their children are not distinguished by their outstanding intelligence and super-smartness: they do not learn the elementary school curriculum well, do not like to strain their brains, and are afraid of mathematics lessons.

From the first grade they count on fingers and sticks, they don’t know the tricks oral counting, therefore they experience great problems in all subjects of the school course.

The techniques of quick mental counting are simple and easy to learn, but one must remember that successful mastery of them presupposes not mechanical, but quite conscious use of the techniques and, in addition, more or less long training.

Having mastered the elementary techniques of mental calculation, those who use them will be able to correctly and quickly perform instant calculations in their heads with the same accuracy as in written calculations.

Peculiarities

There are many techniques that help you learn quick mental arithmetic. Despite all the visible differences, they have an important similarity - they are based on three “pillars”:

Training and gaining experience. Regular practice and solving tasks from simple to complex qualitatively and quantitatively change the skill of mental calculations.
Algorithm. Knowledge and application of “secret” techniques and laws greatly simplifies the counting process.
Abilities and natural talent. Developed short-term memory and its considerable volume, as well as a high concentration of attention, are a great help in practicing quick mental arithmetic. A definite plus is the presence of a mathematical mind and a predisposition to logical thinking.

The benefits of mental counting

People are not iron robots, but the fact that they create smart machines speaks of their intellectual superiority. A person needs to constantly keep his brain in good shape, which is actively facilitated by training the skill of mental arithmetic.

For everyday life:

successful mental arithmetic is an indicator of an analytical mindset;
regular mental arithmetic will protect you from early dementia and senile insanity;
your ability to add and subtract well will not allow you to be deceived in the store.

For successful studies:

mental activity is activated;
memory, speech, attention, the ability to perceive what is said by ear, speed of reaction, quick wits, and the ability to find the most rational ways to solve a given problem develop;
Confidence in one's capabilities is strengthened.

When should you start training?

According to scientists (psychologists and teachers), by the age of 4 a child is already able to add and subtract. And by the age of 5, the baby can freely solve examples and simple problems. But these are statistics, and children do not always adapt to them. That's why Everything here is purely individual.

Rules

The queen of sciences - mathematics - took care of schoolchildren and compiled a set of laws, algorithms and rules, which, having mastered and skillfully used, children will love mathematics and mental work:

Commutative property of addition: swapping the components of the action, we get the same result.
Combinative property of addition: When adding three or more numbers, any two (or more) numeric values can be replaced by their sum.
Addition and subtraction with passing by ten: complete the larger component
To round tens, and then add the remainder from the other component.

First, we subtract individual units from the number up to the action sign, and then subtract the remainder of the subtrahend from the round tens.
Having represented the minuend as a sum of tens and ones, we will remove the smaller from the tens of the larger and add the units of the minuend to the answer.
When adding and subtracting round tens (they are also called “round” numbers), tens can be counted in the same way as ones.
Adding and subtracting tens and ones. It is more convenient to add tens to tens, and ones to ones.

Adding a number to a sum

The methods are as follows:

We calculate its value, and then add this value to it.
We add it to the first term, and then add the second term to the result.
We add the number to the second term, and then add the first term to the answer.

Adding a sum to a number

The methods are as follows:

Let's calculate its reading and then add it to the number.
We add the first term to the number, and then add the second term to the result.
We add the second term to the number, and then add the first term to the result.

Addition of two sums. By adding two sums, we choose the most convenient calculation method.

Using the main properties of multiplication

The methods are:

Commutative property of multiplication. If you swap the factors, their product does not change.
Combinative property of multiplication. When multiplying three or more numbers, any two (or more) numbers can be replaced by their product.
Distributive property of multiplication. To multiply a sum by a number, you need to multiply each of its components by this number and add the resulting products.

Multiplying and dividing numbers by 10 and 100

To increase any number by 10 times, you need to add one zero to its right.
To do the same thing 100 times, you need to add two zeros to the right.
To reduce a number by 10 times, you need to discard one zero on the right, and to divide by 100, you need to remove two zeros.

Multiplying a sum by a number

1st method. Let's calculate the amount and multiply it by this value.
2nd method. Let's multiply the number with each of the terms and add the resulting answers.

Multiplying a number by a sum

1st method. Let's find the sum and multiply the number by what we get.
2nd method. Let's multiply the number by each of the terms and add the resulting products.

Dividing a sum by a number

1st method. Let's calculate the sum and divide it by the number.
2nd method. Divide each term by a number and add the resulting quotients.

Dividing a number by a product

Options:

1st method. Divide the number by the first factor, and then divide the resulting result by the second factor.
2nd method. Divide the number by the second factor, and then divide the resulting result by the first factor.

Species

During the lessons, a scant amount of time is allocated for oral arithmetic, but this does not detract from its importance for the development of children’s mental activity. Mental calculation skills are developed in mathematics lessons in elementary school when performing various types of tasks and exercises.

Find the value of a mathematical expression

Compare Math Expressions

Such tasks differ in variability:

determine the equality or inequality of two given expressions (by first finding and comparing their values);
to the given relation sign and one of the expressions, compose a second expression or complete an unfinished proposal;
in such exercises, single-digit, two-digit, three-digit numbers and quantities and all four arithmetic operations can be used in expressions. The main purpose of such assignments is a solid assimilation of theoretical material and the development of computational skills.

Solve equations. They help to understand the connections between the components and results of arithmetic operations.
Solve the problem. These can be simple or complex tasks. With their help, theoretical knowledge is strengthened, computational skills are developed, and the mental activity of children is activated.

Mental counting techniques

Signs of divisibility of numbers:

by 2: everything that exceeds it, and in number series go through one;
for 3 and 9: if the sum of the digits is a multiple of these indicators without a remainder;
by 4: if the last two digits in the entry successively form a number that is divided by 4;
on 5: round tens and those with a 5 at the end;
by 6: numbers that are multiples of two and three are divided;
by 10: numeric values ending in 0;
by 12: numbers that can be divided into three and four at the same time are divided;
by 15: numbers that are simultaneously divisible into whole single-digit components of this number factors.

Forms of counting in elementary school

It is well known that the main activity of preschoolers and junior schoolchildren is a game that is useful to include at all stages of the lesson. Below are some forms of oral counting.

Game "Silence"

Helps develop attention and discipline. Silence can consist of examples in one action, two or more. It is played in all primary school classes with both abstract integers and named numbers.

Students count in their heads and silently, when called by the teacher, write answers to the examples given to them on the board. Correct answers are met with light clapping, and incorrect answers are met with silence.

Lotto game

There may be several types corresponding to those sections of mathematics that have been studied and need to be consolidated. For example, lotto with examples of multiplication and division within “hundreds”.

To make the game more interesting, tires with answers can be made from a cut picture. If all the examples are solved correctly, a picture is made from the tires.

Arithmetic Mazes Game

They look like concentric circles with gates with numbers on them. To get to the center, you need to dial the number in the center. Labyrinths may require either one action (addition) or several to solve. It should be taken into account that these problems have several solutions.

Game “Catch the pilot” (variation of “Ladders”)

There is a drawing on the board: an airplane with loops with examples. Two students are called to write down the answers to the left and right of the loops. Whoever decides correctly and quickly will catch up with the pilot.

Game "Circle Examples"

Didactic material is a set of cards arranged in envelopes; each of them has 8 cards, each of which has one example written on it.

The numerical examples in each envelope are different in content and are selected according to the principle of self-control: when solving them, the result of one example will be the beginning of the next.

Circular examples can be offered in the form of ladders.

Development methods and techniques

Considering ways to teach 6-year-old children quick mental arithmetic, it is impossible not to note the uniqueness and simplicity of the Japanese “Soroban” counting method. The Soroban method allows you to teach children aged 4 to 11 years, developing them mental abilities and expanding the range of intellectual capabilities of children. It is easy to teach any schoolchild to count math examples in their head using the Japanese method of counting on the soroban. By practicing mental mental arithmetic, we engage the whole brain in our work., thereby unloading left hemisphere, which is responsible for solving mathematical problems.

Mental arithmetic makes it possible to interest even the “figurative” hemisphere in computational operations, which increases the efficiency of the brain.

Large numbers require written calculation techniques, although there are individuals who hone their skills in working with them.

Counting examples in mathematics in your head is a vital necessity, since exams at school are now held without the use of calculators, and the ability to count in one’s head is included in the list of required skills for graduates of grades 9 and 11.

Basic rule for mental addition:

Features of subtraction: reduction to round numbers

Single-digit subtractions are rounded to 10, double-digit subtractions are rounded to 100. Subtract 10 or 100 and add the correction. The technique is relevant for small amendments.

Subtract three-digit numbers in your head

Based on good knowledge composition of the numbers of the 1st ten, can be subtracted in parts in this order: hundreds, tens, units.

You can multiply and divide without problems if you know the multiplication table - a “magic wand” for quickly mastering mental arithmetic. It is noteworthy that the village children of pre-revolutionary Russia knew the continuation of the so-called Pythagorean table - from 11 to 19, and modern schoolchildren would do well to know the table up to 19 * 9 from memory.

To get kids interested in math and make difficult moments easier school curriculum closer and more accessible, there are ways and methodological techniques turning complexity into fun and interesting:

To multiply any single-digit number by 9, let's show everyone our empty palms. Bend the finger corresponding in order (counting from thumb left hand) to the number of the first factor. We look at how many fingers are to the left of the curved one - these will be tens of the desired product, and to the right - its own units.
Multiplying by 11 any two-digit number, the sum of the digits of which does not reach 10, is carried out in a fun and simple way: mentally separate the digits of this number and put their sum between them - the answer is ready.
If the sum of the digits of the number multiplied by 11 turns out to be equal to 10 or more than 10, then between the mentally expanded digits of this number you should put their sum and add the first two digits on the left, leaving the other two unchanged - you get the product.

It is the next most complex type of sum, since a sum is formed in which, when adding units of any digit, a unit of the highest digit is formed.

When adding single-digit numbers, for example 5 and 8, a two-digit number is obtained, i.e. a unit of the highest digit is formed - the tens place. This unit is written in the appropriate place.

When adding the numbers 25 and 8. When adding 5 and 8, a new ten is obtained, which is added to the existing two tens.

The operation being performed is commented as follows:

Add 4 to 6, you get 10. I write zero in the ones place, and remember one ten. Add 3 to 5, you get 8, and one more ten - you get 9. In the tens place I write 9. Add 2 to 3 hundreds, you get 5 hundreds. In the hundreds place I write 5. The answer is 590.

In the future, students pronounce intermediate operations more briefly.

354+237=591

When calculating sums in which tens are added to form a hundred.

354+462=816

Addition of three-digit numbers, when both ten and hundred are formed.

First, addition is performed on the abacus. The replacement of 10 units with a ten, and then 10 tens with a hundred is consistently explained. 354+246=600

To 4 add 7 – 11. I write one, I remember one. To 5 add 6 - 11 and one more - 12, I write two, I remember one. To 3 add 2 – 5 and another 1 – 6. The sum is 621.

The teacher explains in specific example, why column addition begins with the least significant units. If you start adding the numbers 367 and 594 from the hundreds place, you will have to make adjustments to the sum twice.

When studying the technique of written subtraction, as well as addition, cases of different complexity are sequentially considered: 382-261

Actions are illustrated using an abacus and written in mathematical language:

382-261=(300-200)+(80-60)+(2-1)=100+20+1=121

By analogy with addition in a column, it is clear that it is more economical to write the subtraction operation in a column.

The subtrahend is written under the minuend. Subtraction, like addition, begins with the ones place.

One of the minuend digits has fewer units than the corresponding subtrahend digit: 583-277

277 is subtracted from 583. You cannot subtract 7 from 3. The solution is to use the rule of replacing 10 units with tens in the reverse order. Now ten is replaced by 10 units. On the units knitting needle there are 13 bones, but on the tens knitting needle there are 1 less bones. First, the intermediate transformation of the minuend can be written down. Subsequently, it is performed in the mind. In order not to forget that a unit was occupied in the most significant digit, a dot is placed above this digit.

Then we study the case when the minuend contains a unit from the hundreds place: 836-354

354 is subtracted from 836. Subtract 4 from 6, you get 2, I write 2 in the ones category. You cannot subtract 5 from 3. I borrow from 8 one hundred. I put a dot over 8 - this means that there are 7 hundred left. I divide a hundred into 10 tens. Subtract 5 from 13 tens, you get 8. I write 8 in the tens place. Subtract 3 from 7 hundreds to get 4 hundreds. I write 4 in the hundreds place. The answer is 482.

The case is considered in detail when two digits of the minuend have fewer units than the corresponding digits of the subtrahend: 564-267

267 is subtracted from 564. You cannot subtract 7 from 4. Let's take one ten and split it into 10 units. There are 14 units in total. Subtract 7 from 14, you get 7. Subtract the tens. You cannot subtract 6 from 5. Let's take one hundred and split it into 10 tens. There are 15 tens in total. Subtract 6 from 15, we get 9. Subtract 2 hundreds from 4 hundreds, we get 2 hundreds. Answer 297.

Another case of subtraction, when the missing units in the minuend cannot be taken from the adjacent digit: 307-189

Students are also encouraged to check the calculated result using the reverse action.

The values of expressions containing several addition and subtraction operations are calculated: 123+256+587

Various tasks are offered:

“Find an error in calculations”

"Fill in the missing numbers"

Exercises on addition and subtraction in a column of composite named numbers are considered: 2r.36k.+3r.57k.

Operations on named numbers are performed after converting both components to smaller units.

Methods for studying the numbering of multi-digit numbers.

While studying the material from the concentrations “Ten”, “Hundred”, “Thousand”, students became familiar with the numbers of the decimal number system, the digits of units, tens, hundreds. Later they will become familiar with the concept of number classes. Multi-digit numbers – having more than three numbers.

Units class, thousands class, millions class: units place, tens place, hundreds place.

When studying the numbering of multi-digit numbers, two stages can be distinguished. First, students learn to name and write multi-digit numbers that do not have ones in the digits of the unit class, that is, numbers ending with three zeros.

The first numbers of the thousands class are formed as a result of counting by thousands: one thousand, two thousand. When you receive 10 thousand, according to the rule of working with abacus, 10 bones on the knitting needle are replaced by one bone on the knitting needle of a higher category - tens of thousands. Then the counting continues in tens. When there are 10 of them, they are replaced by one bone, which is strung on a knitting needle of a higher grade - hundreds of thousands. The count continues in the hundreds of thousands. When there are 10 bones, they are all replaced by one bone on the next knitting needle - a million.

On the knitting needles of units, tens and hundreds of thousands of abacus, 5, 3 and 7 seeds are strung, respectively. The question is what number is depicted on the abacus. Students reason: this number includes 7 hundred thousand, 3 ten thousand and 5 thousand. The teacher announces that this number is called seven hundred thirty-five thousand.

In the process of such work, students should see the similarity in the formation of the names of numbers of the first and second classes: there are no special names for units of thousands; they are called the same as units of the first class, but with the addition of the word “thousand”.

Simultaneously with the study of numbering, you can consider the techniques of oral addition and subtraction of multi-digit numbers.

600000-400000, 342000-42000

Students become familiar with the numbering of other multi-digit numbers by adding first-grade numbers to multi-digit numbers ending in three zeros.

A multi-digit number is deposited on the abacus: 315000. And the bones are strung on the knitting needles of the first class digits: 876. The teacher asks how to write the number resulting from the addition of 315000 and 876. Students learn to name similar numbers: first the number of units of the second class is called, and then the number of the first class.

In connection with the introduction of the concept of class into the system of exercises for developing oral and written numbering skills, it is advisable to include exercises that require the use of this concept.

“Write down a number in which there are 200 units of the first class and 60 units of the second class.”

“Tell what class and category each digit of the number 356789 belongs to.” Students learn to compare multi-digit numbers. (The number is larger, which has more units of the second class; if their number is the same, then the number of units of the first class is compared).

Additional questions:

3 units in the ones digit (3 units in the first digit) The number 3 indicates the number of units

0 ones in the tens place

1 unit in the hundreds place

103 units per unit class

70 units in thousand class

Development of a mathematics lesson in 1st grade on the topic

"Adding Sum to Sum"

UMK "Perspective primary school»

Sidorenko Irina Viktorovna –

teacher primary classes MBOU secondary school No. 25

Lesson type: lesson in discovering new knowledge

Goals of the teacher: create conditions for familiarization with ways of adding sums to sums; learn to apply the rule of adding sum to sum; continue to develop problem-solving skills; develop speech skills, logical thinking.

Planned results(metasubject universal learning activities) :

Regulatory: realize the need to monitor the result (retrospective), control the result at the request of the teacher; distinguish a correctly completed task from an incorrect one.

Cognitive: use (build) tables, check against a table; carry out comparison, series, classification, choosing the most effective way decisions or correct decision (correct answer); build an explanation orally according to the proposed plan; search for the necessary information to complete educational tasks using reference materials textbook; apply logical thinking techniques (analysis, comparison, classification, generalization) at an accessible level.

Communicative: engage in dialogue (answer questions, ask questions, clarify what is unclear); negotiate and come to general decision, working in pairs; participate in a collective discussion of an educational problem; build productive interaction and cooperation with peers and adults to implement project activities(under the guidance of the teacher).

Personal: establish connections between goals educational activities and its motive, in other words, between the result of the teaching and what motivates the activity, for the sake of which it is carried out; The student must ask himself the question “what is the significance and meaning of the teaching for me?” and be able to answer it.

Equipment:

Chekin A.L. Mathematics. 1st grade: Textbook. At 2 o'clock - M.: Akademkniga/Textbook, 2014

Zakharova O.A., Yudina E.P. Mathematics in questions and tasks: Notebook for

independent work 1st grade (in 2 parts) - M.: Akademkniga/Textbook, 2014.

Cards with tasks for pair work (Appendix 2)

Cards with tasks for groups (Appendix 3)

Presentation (Appendix 1)

TSO (wall screen, laptop, multimedia projector, speakers)

Lesson script.

Motivation for learning activities.

Checking readiness for the lesson. Having a general attitude towards the lesson. Greeting students.

- Let's check your readiness for the lesson. (Slide 2. Presentation –Appendix 1 )

Emotional mood.Slides 3-4.

Smile at me, smile at each other.

Updating and trial learning activities.

Oral counting.Slide 5

Work in pairs. Slide 6 .

1) Game “Cryptor”Envelopes with assignments on the tables(appendix 2).

- You will work in pairs. The assignment is in an envelope. You must solve the expression together and write down the answer next to it. When all the expressions have been solved, you need to enter the answers in the table in ascending order and write the letter under the answer. You will get a word.

Before you begin the task, let's remember the rules for working in pairs.

What rules do you know? Let's read those rules that you didn't mention. Slide 7.

Get to work.

10 + 7 = ____ t

Which of the proposed expressions is redundant? Why? (9-4, because this is the difference, and all other amounts)

In what order did you put the answers? (ascending)

What does "ascending" mean? (From the small number to the biggest)

Let's check your answers. Slide 8.

What word did you get? Slide 9

Zero comes after one -

Number 10 on the page.

What can you tell us about this number?

( A person has TEN fingers on both hands. This was the reason for the creation of the decimal number system. TEN is the smallest multi-digit number.)

The number 10 is the sum of the first four natural numbers. Slide 10.

There are ten commandments in the bible.

In international (hundred-cell) checkers, the size of the board is 10x10 squares.

Chervonets is a monetary unit in Russian Empire and the USSR. Chervonets, since the beginning of the 20th century, have traditionally been called banknotes with a face value of TEN units.

Diving is one of the water sports. The highest height from which these jumps are made is 10 meters.

2) Composition of the number 10.

- Let's remember the composition of the number 10? (table) Slide 11

Where can this knowledge be useful to you? Why do we need to know the composition of a number?

(Students' answers)

- Let's check how you can solve problems.

I read the texts of the tasks. Children work in pairs and name the answer.

Here are eight bunnies walking along the path.

Two people run after them.

So how much is there along the forest path?

Are the bunnies in a hurry to go to school in winter? (10)

Slide 12.

The hen went for a walk and gathered her chickens.

Seven ran ahead, three remained behind.

Count it, guys, how many chickens there were. (10)

Who did I read the problem to you about? State the answer. Let's check it on the slide. Slide 12 (click)

We had fun and danced and frolicked at the Christmas tree.

Afterwards, kind Santa Claus brought us gifts.

He gave me huge bags with delicious items in them.

2 candies in blue pieces of paper, 5 nuts next to them,

Pear with apple, 1 golden tangerine.

Everything is in this bag, count all the items. Answer: 2+5+1+1+1=10.

Who did I read the problem to you about? State the answer. Let's check it on the slide. Slide 12 (click)

Work in groups.Slide 13.

- I have given you sheets of work to complete while working in groups.

(appendix 3).

Consider the expressions. Find their meaning. Write the answer on a piece of paper and attach it to the board.

(6 + 2) + (4 + 3) =

III. Identifying the location and cause of the problem. Lesson topic message.

Checking (sheets on the board)

Review the results of your work.

Why didn't all groups find the meaning of the expressions? (Children's answers).

Which expressions were solved easily? Why were you able to solve them? (Such expressions were solved).

What knowledge helped you cope with the task? (Adding a number to a sum, adding a sum to a number).

What was the difficulty? (We don’t know how to add two sums). Slide14.

What is the topic of the lesson? (Adding sum to sum). Slide 15.

What is the purpose of the lesson? What should you learn in class? Slide16 ( I correct the children’s answers).

IV. Building a project for getting out of a problem. Slide 17.

(There are plates of fruit on the board).

Yellow apples – 6 Yellow pears – 3

Green apples -4 Green pears - 2

What do you see on the board? (plates with apples, pears) How to call the depicted objects in one word? (Fruits).

On what basis were the fruits placed on plates? (By color and shape).

Make up different questions about this picture. Lead to the answer. (How many fruits are there on 4 plates).

Misha answered this question like this. Appears Slide 18.

Read the expression correctly.

By what criteria did Misha add the numbers? (by color). How did he find the number of all the fruits? Explanation. Misha found the number of green fruits (6+3), and then found the number of yellow fruits (4+2). Then he added up the results.

Masha thought so. Slide 18 (click)

Read mathematical expression.

On what basis did Masha count? (by type of fruit) . How did Masha find the number of all the fruits? Explanation. Masha found the number of apples (6+4), then found the number of pears (3+2). Then I added up the results.

Why were the amounts equal? Whose method do you like better? Why?

What is the best way to add a sum to a sum? (first add to 10, then the remaining numbers)

Do you remember how Misha and Masha stacked the fruits? Do you think the attribute is important in answering the question? Should you pay attention to the signs? Fine.

Let's return to the expression. An expression appears. Slide 19.

(6+2)+(4+3)

How will we solve this expression? How can we solve this expression? Is the attribute important in the decision? (Not important).

Why are these amounts equal? Explain.

Whose method do you like better? Why do you think so?

Shall we draw a conclusion? (To add the sums, we must add the number to 10. First add the first terms, and then the second)

Now could you solve the expression? In what way?

Physical education minute.Slide 20.

V. Implementation of the constructed project.

Work from the textbook (pp. 56–57).Slide 21.

Open the textbook at p. 56, no. 2Slide 22.

Read the entry on the left. Select the entry on the right that shows a convenient way to solve this expression.

Why did you choose this method? How do we add two sums?

Task No. 1.

– Look at the illustration for the problem.

– State the condition of this problem. (On four plates there were 3 green apples and 7 yellow apples, 4 green pears and 6 yellow pears.)

– Formulate the requirement of this task. (How many fruits are there on four plates?)

– Explain how Misha solved the problem.

(7 + 6) + (3 + 4).

Explanation. Misha found the number of yellow fruits (7 + 6), then found the number of green fruits (3 + 4). Then he added up the results.

– Explain how Masha solved the problem.

(7 + 3) + (6 + 4).

Explanation. Masha found the number of apples (7 + 3), then found the number of pears (6 + 4). Then I added up the results.

– Why do you think these amounts have equal values?

– Whose addition method do you like better? Why? (The machine method is more convenient.)

Task No. 2.

– Analyze these amounts.

– What unites them? (In these sums, each term is represented as the sum of two numbers.)

– Without doing the calculations for the sum on the left, find the sum on the right with the same value and underline it.

– Will you pay attention to the order of the terms? (No.)

Entry: (8 + 5) + (2 + 5) = (8 + 2) + (5 + 5).

– Underline that part of the equation from which it is more convenient to calculate the value of the sum.

– Find the value of this sum using the rule of adding sum to sum.

VΙ.Primary consolidation with pronunciation in inner speech.

Task No. 3. Work in TVET p. 76, no. 1Slide 23.

Open your notebook p. 76, no. 1(commenting)

Read the expression. How are we going to do it? Why?

Let's execute 2 expressions using new trick. Find the value of the sums using Masha's experience.