Algebraic sum and calculation rules independent work. Methodological development in algebra (6th grade) on the topic: the rule for calculating the value of the algebraic sum of two numbers

Balabanova Irina Georgievna

mathematic teacher

Lesson topic: “The rule for calculating the value of the algebraic sum of two numbers”

Lesson objectives:
- updating and systematization of knowledge on the topic “The rule for calculating the algebraic sum of two numbers”, - training memory, attention, logical thinking, - fostering accuracy and the ability to take notes in a notebook, fostering a culture of behavior in the classroom, the ability to listen, - developing cognitive interests. Lesson type: combined Material for the lesson: Didactic material for completing tasks in groups. Cards for mental calculation (work in pairs). Cards with multiple choice answers. Tasks for "Math Football" on the board.

During the classes:

Lesson steps

Part 2

1) 3,4 – (- 5,7) 2) -14 – 1,8 3) 1,9 – 3,4 4) - 21 + 11 5) - 1,8 + (-4,7) 6) – 4,5 + 4,5
7) – 0,2 + 6,9 + (- 5,9) – (- 2,3) 8) - + 9) - - 10) - 6 - - 1 11) 2+ (- 7)Answers to part 2: 0; -10; -1.5; ; - 4; - 7; 9,1; - 6,5; 3,1; - ; - 15,8.

Balabanova Irina Georgievna

Municipal educational institution

Drovninskaya secondary school

mathematic teacher

Mozhaisky district, Tsvetkovsky village

The motto of the lesson: “To everyone’s surprise, we do addition.”

Lesson objectives:

• 
  educational: consolidation of skills in adding numbers with the same and different signs, the ability to apply and transfer your knowledge to a new, non-standard situation, development of computational skills, competent oral mathematical speech.
• 
  developing: help master mathematical terminology, develop creative, speech, and mental activity using various forms of work; develop interest in the subject.
• 
  educational: fostering attentiveness, activity, independence in work

• 
  computer, projector;
• 
  presentation (see Annex 1 );
• 
  Appendix 2 :

• 
  self-esteem cards;
• 
  worksheets;
• 
  tests

During the classes

I. Organizing time.(Slide 1) Guys, we continue to work on positive and negative numbers. . Have you ever wondered why we need negative numbers? After all, we have been studying mathematics for several years and managed without them. Maybe we could continue to live without knowing about the existence of negative numbers? Where are positive and negative numbers found in life? (student survey)

That's right, they are needed to measure temperature; when measuring the depths of seas and oceans; to record debts, profits, and during games (when you lose, record points), etc., as well as when studying school subjects geography and physics. Therefore, it is necessary to be able to perform operations with positive and negative numbers.

So, your goal is to learn how to correctly apply the rule for calculating the value of the algebraic sum of two numbers when calculating the values ​​of expressions, solving equations, problems. (recording the number and topic of the lesson) (slide 2)

Today's lesson will be unusual. You and I will go on a trip in a time machine, (slide 3) we will learn the history of the development of negative numbers. Moreover, we will calculate the flight route ourselves, for this we will divide into crews. (Three crews: basic level, advanced level and high level) Where did information about positive and negative numbers first appear?

There will be our first stop. Let's determine the route.

II. Updating knowledge.

Verbal counting

1 Find the error (slide 4)

a)17-19 =2

b) -6 +3 = 3

c) -2.2 – 7.4 = - 9.6

Place + or – next to the number of each example on the self-assessment sheet. .

Self-test.(slide 5)

So we found ourselves in 2nd century BC in China by the scientist Li E. (slide6)

Historical reference : “Chinese scientists approached the creation of the concept of a negative number earlier than mathematicians of other nations, in the 2nd century. BC e. In Chinese mathematics, positive quantities were called “zheng”, negative quantities were called “fu”. They were depicted in different colors: “zheng” - red, “fu” - black. This method of depiction was used in China until the middle of the 12th century, until Li Ye proposed a more convenient designation for negative numbers - the numbers that represented negative numbers were crossed out with a dash from right to left. The introduction of negative numbers and the rules for their addition and subtraction can be considered one of the largest discoveries of Chinese scientists.

Let's calculate the next stop. To do this, let’s complete the task orally. (slide 7)

1. 
   x+(-2)=0
2. 
   (-15)+ x=5
3. 
   -7.5+x=-4.3

Historical reference : “In Indian mathematics, negative numbers were first encountered by the mathematician and astronomer Brahmagupta in the 7th century. The scientist uses the interpretation of positive and negative numbers as property, and negative numbers as debt. He was the first to formulate rules for dealing with negative numbers. This was in 628. Rule one says: The sum of two debts is a debt.

By arranging the numbers in ascending order, we will determine where we will stop next.

I. 0.5 4 -3 -6.5

WHETHER I'M THAT AND

II. 6 -7 -1.5 -4.5 2

K B ⃓⃓⃓ E

III. 2.3 -4.9 -1 -5.5 -3.1;

Y ZA K I PI NS

Write your answer on the self-assessment sheet. Peer review. (slide 10)

Historical reference : “ In Europe, the Italian mathematician Leonardo of Pisa came quite close to the introduction of negative numbers. In Italy, moneylenders, when lending money, put the amount of the debt and a dash in front of the debtor's name, like our minus, and when the debtor returned the money, they crossed it out, it turned out something like our plus. A thrifty owner must know well both the size of his property and his debts.

Each crew does the work in writing in a notebook.

III. Work in groups followed by testing.(Slide 12)

1. Solve the problem by composing the expression: A thrifty owner must know both the size of his property and his debts. And then one day the moneylender decided to calculate whether he lived this month with a profit or a loss?

Icrew. 1) the last transaction brought him an income of 30.8 lira;

2) he donated 20.2 liras to charity;

3) lent 10 liras.

IIcrew. 1) the last transaction brought him an income of 20.6 lira;

2) he donated 18.2 liras for the construction of the tower:

3) lent 4.8 lira

4)repaid him the debt of 10 liras.

IIIcrew. 1) the first person gave him 32.4 liras;

2) he lent the second person 50% of this money;

3) he donated 30.8 liras for the construction of the tower;

4) the third returned 17.6 liras.

(slide 13)

We found ourselves in France in 1484 with the mathematician Nicolas Chuquet. (Slide 14)

Historical reference : “In Europe, with the consciousness of confidence in the validity of his calculations, the French mathematician Nicolas Chuquet began to operate with negative numbers. In his writings in 1484, he considered problems leading to equations with negative roots. Schuke states that “this calculation, which others consider impossible, is correct.”

The root of the first equation will tell us the next stop. (slide 15)

2. Solve the equations:

Icrew. a) 4x=16;

b) x + 3 = -8.1.

IIcrew. a) 4.31 – x = 5.18;

b) x -2.9 = - 7.8.

IIIcrew. a) ⃓х+1⃓=2;

b) ⃓х-2⃓=5.(slide 16)

Our stop is Czech Republic 1489. Scientist mathematician Jan Widman. (slide 17)

Historical reference : Czech Jan Widman introduced the signs “+” and “-” to denote positive and negative numbers and outlined this in his book in 1489, which was called “Quick and Beautiful Counting”.

Physical education minute.

Our car overheated.

We will also rest and do exercises.

The teacher calls a positive number - hands up, a negative number - jump in place.

Our journey is coming to an end. The answers to the next task will help determine the place of our last stay. (Slide 18)

3. Find the meaning of the expression:

I
. x+y+16, if x= -5.7; y= -2.9

I


I. ( x+y)-z,if x= ; y= ; z= -5

III. (x+y)+(z+c),if x = ; y= ; z= ; c=

Historical reference : The German scientist Michel Stofel wrote “Complete Arithmetic”, which was published in 1544. It contains the following entries for numbers: 0 – 2; 0 + 2; 0 – 5; 0 + 7. Negative numbers received general recognition in the first half of the 19th century, when a rigorous theory of positive and negative numbers was developed.

I. Performing test tasks

To return home safely, you must complete the test. (Appendix)

Self-test.

(A test and a self-assessment sheet are given)

Answers:

. Summarizing. Homework assignment.(slide 21)

No. 283.321 (a;b), 328 (c;d)

Compose 5 examples on the application of the rule for calculating the value of the algebraic sum of two numbers.

Self-assessment sheet.

Oral work.

2. Write down the root of the equation: ___________

3. Arrange the numbers in ascending order:⃓.

Municipal educational institution Tsninskaya secondary school No. 2

Lesson topic:

The rule for calculating the value of the algebraic sum of two numbers.

6th grade.

Math lesson in 6th grade.

Plotnikova Lyudmila Vasilievna

Topic: “The rule for calculating the value of the algebraic sum of two numbers.”

Target: 1. Lead students to independently deduce calculation rules

values ​​of the algebraic sum of 2 numbers.

2. Development of students’ logical thinking and computational skills

Equipment: drawings, screen, interactive whiteboard, music, tables.

During the classes

1. Statement of the topic and purpose of the lesson.

ITeacher: Guys! You have learned to add numbers by moving a point along a coordinate line. We examined the algebraic sum and its properties using the laws of arithmetic operations. But using such methods is not always convenient. We were convinced of this when we encountered such examples -5, 125 + 2, 36; - 87 + (- 26)

Therefore, it will be nice if today, with the help of new rules, we learn how to do this without a number line.

Well - ka! Pencils aside!

No knuckles, no pens, no chalk.

Verbal counting, we are doing this thing.

Only by the power of mind and soul.

The numbers converge somewhere in the darkness,

And the eyes begin to glow

And there are only smart faces around

Because he does the math in his head!

Imagine: a hamster runs along a coordinate line and digs holes. In what places on the coordinate line will burrows appear? Each hole corresponds to a number on the line. We will find the answer by solving the examples orally.

9 + 6 = -3 5) 5 + (-4) = 1

6 + (-2) = -8 6) -8 + 8 = 0

13 + (-4) = 9 7) 0 +(-7) = - 7

3 + (-3) = 0 8) -12 + 10 = - 2

Let's check where the minks have appeared. We check the answers on the screen. Numbers are read from left to right. Children, what are all these numbers called? (whole)

2) On the coordinate line of the numbermAndnopposite

a) Where is the origin of coordinates?

b) Compare all numbers: m o

IILearning new material.

Now let's learn how to add numbers without using a coordinate line.

A) When one of the terms is “0”, then everything is very simple:

0 + a = a, 0 + a = a, for any value of a.

B) The second case is when both terms are positive numbers

5 +8 = 13 7 + 12 = 19

C) There are only 2 cases left to consider:

1) both terms are negative

2) the terms have different signs.

"A fun moment"

How are you?

How are you going?

Are you running?

Do you sleep at night?

How do you take it?

Will you give it?

How are you being naughty?

Are you threatening?

B) 1. Add -2 and -6

Let's find the modulus of the sum and the sum of the moduli of the terms.

The sum has the same sign as the terms.

add the modules of the terms;

put “-” before the answer

c) 2. The terms have different signs: - 4 + 6. = 2.

1) Find the difference between the modules, (subtract the smaller from the larger),

2) Before the resulting number we put the sign of the term whose modulus is greater.

3) Sum of opposite numbers = 0

Listen to the song that contains the rule(to the music of “Island of Bad Luck”)

Numbers are negative

New to us

Only very recently

Studied our class

Immediately more

Everyone is in trouble now

They teach, they teach the rule

The children have all their lessons.

If you really want to

Very good for you

Numbers are negative

There's no need to bother

You need the sum of modules

Find out quickly

Then a sign to her -

Take and attribute

If numbers with different

They will give signs

To find their sum

We are all right here

Larger module quickly

Choose very much

From it you subtract the smaller module

The most important thing

Sign not to forget

“Which one will you put?”

We want to ask

We'll tell you a secret

There's nothing simpler

Sign where the module is greater

Write back

IIISolving problems on the topic of the lesson

Textbook page 59

Orally: No. 259 (a, b.) a) 3 + 6 = 9

No. 262 a) 5.3 + (- 5.3) = 0 c) 3.2 + (-3.2) = 0

b) 3 + (-1) = 2 d) -2.5 + 2.5 = 0

No. 263. Find a rational solution

A) -25 – 34 +25 - 66 = -100

B) -18 +3 +15- 17 = - 17

No. 270, No. 268 (a, b)

Independent work No. 258 (8). (1, 2 tables.)

IVHomework.

$8, No. 258(8) (3.4 table), 264(c, d)

Come up with 5 examples for the algebraic sum of 2 numbers.

VLesson summary. Grading.

We hear the call

The lesson is over,

Only in labor

Knowledge comes to you.

Thank you for the lesson.

Additional material

1) Calculate

2) Indicate all natural numbers x for which the inequality is true.

3) Solve the equation

Lesson 32 “RULE FOR CALCULATING THE VALUE OF THE ALGEBRAIC SUMM OF TWO NUMBERS”

The purpose of the lesson: derivation of the rule for calculating the value of the algebraic sum of two numbers.

Tasks: developing the skills to apply this rule when calculating the values ​​of an algebraic sum

Educational: develop observation, attention, memory, logical and mathematical speech.

Educational: cultivate accuracy and mutual respect.

Type: lesson explanation of new material.

DURING THE CLASSES:

1.Organizational moment

Hello guys! I'm glad to see you. We are starting our lesson.

2.Lesson motivation

I hope that our collaboration in the lesson will be successful. And I want this lesson to bring you new discoveries, and you will successfully apply your existing knowledge in solving practical problems.

What main topic did we start studying in 6th grade?

What did we study in previous lessons?

What techniques for calculating an algebraic sum do you know?

You have learned to add numbers by moving a point along a coordinate line. We examined the algebraic sum and its properties using the laws of arithmetic operations.

You have route sheets, we fill them out during the lesson.

3.Checking d/z.

Checking homework (using flashcards)

№ 244

A)a + b + (-18) = 15 – 17 -18 = - 20 c) - 40 + 25 – 18 = - 33

№ 248

a) 4 2 / 9 + 3 5 / 9 = 7 7 / 9 b) - 4 2 / 9 - 3 5 / 9 = -7 7 / 9

№ 249

A) - 7 / 15 + 13 / 30 = - 1 / 30 V) 5 / 6 - 3 / 8 = 11 / 24

4. Oral work

Imagine: a hamster runs along a coordinate line and digs holes. In what places on the coordinate line will burrows appear?

1) Calculate verbally: (slide 1)

9 + 6 = -3 5) 5 + (-4) = 1

6 + (-2) = -8 6) -8 + 8 = 0

13 + (-4) = 9 7) 0 +(-7) = - 7

3 + (-3) = 0 8) -12 + 10 = - 2

Let's check where the minks have appeared.

We check the answers on the screen.

Read the numbers from left to right (-8, -7, -3, -2, 0, 1.9)

Guys, what are the names of all the numbers you listed? (whole)

5. Search - heuristic activity

Compute the following assignment:

TASK No. 1. (slide 2) (on your own, then check)

1) 3714+226=? (3940)

2) 23,5+0,3=? (23,8)

3)357+(-3299)=? (-2942)

There is no answer to the last example. YouBye you can't complete it. Is this a problem for you?

Let's fix this problem (we emphasize this example)

What is the difficulty? What can't you do?

So what will we do in class?

Write down the topic of the lesson

LESSON TOPIC

“RULE FOR CALCULATING THE VALUE OF THE ALGEBRAIC SUMM OF TWO NUMBERS”

6.Learning new material .

Now let's learn how to add numbers without the help of a coordinate line. (Slide 4)

A) When one of the terms is “0”, then everything is very simple:

0 + a = a, 0 + (-a) = -a, for any value of a.

B) There are only 2 cases left to consider:

1) both terms are positive or negative

2) the terms have different signs.

– 6 – 8 = - 14

6 + 8 = 2

6 + 8 = 14

6 – 8 = -2

2 – 11 = -13

2 + 11 = 9

11 + 2 = 13

11 + 2 = -9

– 6 – 8 = (– 6) + (– 8) = - 14

6 + 8 = (-6) + (+8) = 2

6 + 8 = (+6) + (8) = 14

6 – 8 = (+6) + (-8) = -2

2 – 11 = (-2) + (-11) = -13

2 + 11 = (-2) + (+11) = 9

11 + 2 = (+11) + (+2) = 13

11 + 2 = (-11) + (+2) = -9

The signs of the terms are the same

The signs of the terms are different

The sign of the sum coincides with the signs of the terms

The sign of the sum has the sign of the term with a large modulus

│(- 6) + (-8)│ = │-14 │ = 14

│– 6│ +│ – 8│= 6+8 = 14

│(-6) + (+8)│ = │2│ = 2

│8│ – │-6│ = 8-6 = 2

│(-8) + (+6) │ = │-2│ = 2

│-8│ – │6│ = 8 – 6 = 2

│(-2) + (+11)│ = I9I = 9

│11│ – │2│ = 11 - 2 = 9

│ (+2) + (-11) │ = │-9│ = 9

│-11│ – │2│ = 11- 2 = 9

Conclusion: the module of the sum is equal to the difference of the modules

│ 6 + 8│ = │14│ = 14

│6│ + │8│ 6+8 = 14

│ (-2) + (-11) │ = │-13│ = 13

│- 2│+│ – 11│ = 2 + 11 = 13

│11 + 2│ = │13I│ = 13

│11│ + │2│ = 2 + 11 = 13

Conclusion: the module of the sum is equal to the sum of the modules

If the terms have the same signs, then the sum has the same sign as the terms, and the module of the sum is equal to the sum of the modules of the terms

If the terms have different signs, then the sum has the same sign as the term with a larger module, and the module of the sum is equal to the difference of the terms, provided that the smaller module is subtracted from the larger module.

7. Consolidation of new material

A poster is posted on the board:

Using the rule, we find the meanings of the expressions; next to the answer we put the corresponding letter:

(+16) + (+4) =

(+16) + (-4) =

(+8) + (+2) =

(-7) + (-12) =

(-16)+ (+4) =

(-16) + (-4) =

(-8) + (-2) =

(-8) + (+2) =

(+8) + (-2) =

(+7) + (+12) =

(+7) + (-12) =

Students say the rule in each example:

(+16) + (+4). Both terms have the same sign - “+”, which means the sum has the same sign “+”, then we add the modules 16 + 4 = 20, as a result we get +20, letter B;

(+16) +(-4) The terms have different signs, and the term with a larger module has a “+” sign, therefore the sum has a “+” sign, then we subtract the smaller one from the larger module (or find the difference in modules) 16 – 4 = 12, we get +12, the letter P, etc.

What word did you get?

(Slide 5) BRAHMAGUPTA - an Indian mathematician who lived in the 20th century, used negative numbers. He represented positive numbers as “properties”, negative numbers as “debts”. The rules for adding “+” and “-” numbers were expressed as follows:

“The sum of two properties is property” “+” + “+” = “+”

“The sum of two debts is debt” “ - ” + “ - ” = “ - ”

8. Physical education minute

Are you probably tired? Let `s have some rest!

Have a physical education session!

Now let's go back to our first task and solve it

357+(-3299)=? (-2942)

To add two numbers with different signs, you need to:

Put the sign of the term with a large module,(-)

Subtract the smaller one from the larger module 3299-357=2942

ANSWER:-2942

9. Solving problems on the topic of the lesson

10.Independent work (mutual testing in pairs)

Students do independent work on the assignment on cards. Works are checked against a standard (by your desk neighbor). Errors are analyzed and corrected.

1 option

№

16-18; -9+24; -9-24; -16-18; -47+52; 3+13; 5-87.

№2. Calculate:

a) -34-72+34-18;

b) 96-45-26+15.

Option 2

№1. Write expressions whose values ​​are positive in the right column, and expressions whose values ​​are negative in the left column

15-24; -8+32; -6-27; -15-24; -39+81; -39-81; 9-19; 6+27.

№2. Calculate:

a) -72-65+72-15;

b) 86-38-52+44.

11. Homework.

Level 1: $8, No. 258 (3.4 table), 264 (c, d)

Level 2: come up with 5 examples for the algebraic sum of 2 numbers.

Let me remind you that level 1 is mandatory for everyone, and level 2 is optional.

12. Reflection. (slide)

Compose a syncwine for the word RULE

13. Lesson summary. Grading.

Today in class we formulated a rule for calculating the value of the algebraic sum of two numbers and applied it to solve examples. While completing the tasks, we repeated the concept of opposite numbers. You have demonstrated the ability to think independently, draw conclusions, and correctly formulate solutions to examples. Today you receive the following grades for the lesson:………………Thanks for the lesson!

Class: 6

Teacher Shirshitskaya L.I.

Lesson topic

“RULE FOR CALCULATING THE VALUE OF THE ALGEBRAIC SUMM OF TWO NUMBERS”

The purpose of the lesson: Deduce a rule for calculating the value of the algebraic sum of two numbers and teach how to apply this rule when finding the values ​​of expressions.

Tasks

Educational:

• develop the ability to apply this rule when calculating the values ​​of an algebraic sum;
• achieve conscious assimilation of the material;
• activate thinking through interesting and non-standard forms of work;

Educational:

• develop observation, attention, memory, logical and mathematical speech.
• develop students’ abilities to analyze, draw conclusions, determine the relationship and sequence of thoughts;

Educational:

• cultivate accuracy and mutual respect;
• cultivate interest in studying the subject;
• develop a positive attitude towards goodness.

Lesson type: lesson explaining new material.

Equipment: computer, multimedia projector, screen, demonstration materials, task cards.

Teaching methods used:

• search engines;
• research;
• explanatory and illustrative;
• reproductive.

Didactic techniques:using the search method.

Forms of work in the lesson:

1. Frontal.

2. Group.

3. Steam room.

4. Individual.

Lesson structure:1. Organizational moment 1 min

2. Lesson motivation 2 min

3. Checking the d/z. 2 minutes

4. Oral work 3 min

5. Search and heuristic activity 3 min

6. Learning new material 7 min

7. Physical education minute 1 min

8. Consolidating new material 6 min

9. Solving problems according to the textbook 7 min

10. Independent work 6 min

11. Homework 2 min

12. Reflection 3 min

13. Lesson summary 2 min

DURING THE CLASSES:

1.Organizational moment

(greeting, preparing students for the lesson).

Hello guys! I'm glad to see you. We are starting our lesson.

Guys, today we have important and responsible work ahead of us. I wish you all hard work and success in your work.

So, friends, let's get to work!

The call has already been given, the work is waiting.

And we will be decisive and brave,

After all, mathematics is calling us on our journey.

2.Lesson motivation

I hope that our collaboration in the lesson will be successful. And I want this lesson to bring you new discoveries, and you will successfully apply your existing knowledge in solving practical problems.

• What main topic did we start studying in 6th grade?
• What did we study in previous lessons?
• What techniques for calculating an algebraic sum do you know?

You have learned to add numbers by moving a point along a coordinate line. We examined the algebraic sum and its properties using the laws of arithmetic operations.

3.Checking d/z.

We check homework (correct/incorrect using signal cards).

Communication on issues that arose while doing homework. Discussion of difficulties.

You have signal cards where GREEN is correct, YELLOW is doubtful, RED is incorrect.

№ 244

a) a + b + (-18) = 15 – 17 -18 = - 20 c) - 40 + 25 – 18 = - 33

№ 248

a) 4 2/9 + 3 5/9 = 7 7/9 b) - 4 2/9 - 3 5/9 = -7 7/9

№ 249

a) - 7/15 + 13/30 = - 1/30 c) 5/6 - 3/8 = 11/24

4. Oral work.

1) Calculate verbally:

1. -8 + 6 = -2 5) 8 + (-3) = 5
2. -5 + (-3) = -8 6) -11+ 11 = 0
3. 24 + (-4) = 20 7) 0 +(-9) = - 9
4. 5 + (-5) = 0 8) -14 + 10 = - 4

We check the answers on the screen.

2) Read the numbers from left to right (-8, -7, -3, -2, 0, 1.9)

Guys, what are the names of all the numbers you listed? (whole)

3) Given numbers: -15; -2; -17; -9

8; -16; -26; 28

3,2; -1,9; -3,9; 0

a) name the modulus of each number;

b) name in each line the number whose modulus is greater;

c) name in each line the sign of the number whose modulus is greater.

Okay, open your notebooks and write down the number.

5. Search - heuristic activity

Compute the following assignment:(on your own, then check)

1) 3714+226=? (3940)

2) 23,5+0,3=? (23,8)

3)357+(-3299)=? (-2942)

The third example was problematic. You are still finding it difficult to complete it. Is this a problem for you?

Let's fix this problem (we emphasize this example).

What is the difficulty? What can't you do?

So what will we do in class? (We need to find a rule for calculating the value of the algebraic sum of two numbers).

We write down the topic of the lesson: “RULE FOR CALCULATING THE VALUE OF THE ALGEBRAIC SUMM OF TWO NUMBERS.”

6.Learning new material.

The motto of our work will be the words “There's no shame in not knowing something

but it’s a shame not to want to learn” (Socrates)

How do you understand the meaning of this motto?

We need to learn how to add numbers without the help of a coordinate line.

A) When one of the terms is “0”, then everything is very simple:

0 + a = a, 0 + (-a) = -a, for any value of a.

B) There are only 2 cases left to consider:

1) both terms are positive or both negative;

2) the terms have different signs.

Let's repeat these rules once again (working with the textbook p. 58)

TASK (group)

Divide into two groups, each group needs to come up with 1 example of 2 rules and ask the other group to solve it.

Group 1 when both terms are negative and have different signs

Group 2 when both terms are positive and have different signs.

7. Physical education minute

Get ready to warm up!

Spin left and right

Count the turns

One-two-three, don't lag behind(Rotate your body to the right and left.)

We begin to squat -

One two three four five.

The one who does exercises

Maybe we should do a squat dance.(Squats.)

Now let's raise our hands

And let's drop them with a jerk.

It's like we're jumping off a cliff

Summer sunny day.(Children raise their straight arms above their heads, then with a sharp movement lower them and take them back, then with a sharp movement up again, etc.)

And now walking in place,

Left-right, stand one-two.(Walk in place.)

We'll sit at our desks together

Let's get down to business again.(Children sit at their desks.)

8. Consolidation of new material

Using the rule, we find the meanings of the expressions:

Task No. 1

• (+16) + (+4) =
• (+16) + (-4) =
• (+8) + (+2) =
• (-7) + (-12) =
• (-16)+ (+4) =
• (-16) + (-4) =
• (-8) + (-2) =
• (-8) + (+2) =
• (+8) + (-2) =
• (+7) + (+12) =
• (+7) + (-12) =

Students say the rule in each example:

• (+16) + (+4). Both terms have the same sign - “+”, which means the sum has the same sign “+”, then we add the modules 16 + 4 = 20, as a result we get +20;
• (+16) +(-4) The terms have different signs, and the term with a larger module has a “+” sign, therefore the sum has a “+” sign, then we subtract the smaller one from the larger module (or find the difference in modules) 16 – 4 = 12, we get +12, etc.

Task No. 2.

Calculate: (next to the answer we put the corresponding letter)

6 -3 = -9 R 2- 8 = -6 B -1.5 - 1.5 = -3 M

2 + 11=13 X -3 + 6= 3 Y 4.5- 6.5 = -2 A

5- 7.5 = -12.5 G -7.2+ 10 = 2.8 P 7 – 12 = - 5 T

What word did you get?And what does Brahmagupta have to do with it?

BRAHMAGUPTA - an Indian mathematician who lived in the 9th century, used negative numbers. He represented positive numbers as “properties”, negative numbers as “debts”. The rules for adding positive and negative numbers are expressed as follows:

• “The sum of two properties is property” “+” + “+” = “+”
• “The sum of two debts is a debt” “ - ” + “ - ” = “ - ”

Now try, using signs and symbols, to depict the rule for adding an algebraic sum with different signs. What sign does it have in this case and why?

“+” + “-” = “+” if ¦ + ¦ > ¦ - ¦

“+” + “-” = “ - ”, if ¦ - ¦

Task No. 3

Now let’s return to our example, which caused you difficulty, and let’s solve it:

357+(-3299)=? (-2942)

To add two numbers with different signs, you need to:

Put the sign of the term with a large module,(-)

Subtract the smaller one from the larger module 3299-357=2942

ANSWER: -2942

9. Solving problems on the topic of the lesson

Textbook page 59

In writing:

No. 262(a,b) What are these numbers called?

A) 5.3 + (- 5.3) = 0 c) 3.2 + (-3.2) = 0

Output: a + (- a) = 0

Task (We work in pairs).

One tenant has 2 debts: 300 rubles for electricity and 250 for gas. What is the amount of his debt?

The second tenant also has 2 debts: 200 rubles for the telephone and 350 for the Internet. What is the amount of his debt? Compare the debt of the first and second tenant?

1)(-300) + (-250) = - 550(r) debt of the first

2)(-200) + (-350) = - 550 (r) debt of the second.

550 = -550

Using this problem as an example, is it necessary to be able to find the valuealgebraic sum of two numbers?

10.Independent work (test in pairs)

Students do independent work on the assignment on cards. Works are checked against a standard (by your desk neighbor). Errors are analyzed and corrected.

1 option

16-18; -9+24; -9-24; -16-18; -47+52; -47-52; 3-13; 5-87.

No. 2. Calculate:

a) -34-72+34-18;

b) 96-45-26+15.

Option 2

No. 1. Write expressions whose values ​​are positive in the right column, and expressions whose values ​​are negative in the left column

15-24; -8+32; -6-27; -15-24; -39+81; -39-81; 9-19; 6-27.

No. 2. Calculate:

a) -72-65+72-14;

b) 86-38-52+44.

11. Homework.

$8, rule No. 258 (3,4 table), 264 (c, d)

Come up with 5 examples for the algebraic sum of 2 numbers.

12. Reflection.

Schoolchildren are offered a small questionnaire, the content of which can be changed and supplemented depending on which elements of the lesson are paid special attention to. You can ask students to justify their answer.

1. During the lesson I worked (actively / passively)

2. I am (satisfied/dissatisfied with my work in class)

3. The lesson seemed (short / long, interesting / uninteresting) to me

4. During the lesson I (not tired / tired)

5. My mood (became better / became worse)

6. I found the lesson material (clear / not clear, interesting / boring, useful / useless)

7. My homework seems (easy / difficult) to me.

13. Lesson summary. Grading.

Today in class we formulated a rule for calculating the algebraic sum of two numbers and applied it to solve examples. While completing the tasks, we repeated the concept of opposite numbers. You have demonstrated the ability to think independently, draw conclusions, and correctly formulate solutions to examples. Today you receive the following grades for the lesson:………………Thanks for the lesson!

The bell rings, class is over

And I wish everyone, friends,

Let your knowledge be strong,

After all, you can’t do without mathematics!