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Slides captions:

Mathematics - 6 Teacher: Bayyr-ool R.B.

In the previous lessons, we got acquainted with new numbers. What are these numbers called? What sign is used to represent negative numbers. What are the names of the numbers lying to the right of the reference point on the coordinate line? What are numbers that differ only in sign called? What is the sum of opposite numbers? A number indicating the position of a point on a line. Natural numbers, their opposite numbers and zero - ... numbers. Of the two negative numbers, the one whose modulus is ... is greater. Crossword

Lesson topic: Addition of negative numbers Natural numbers were created by the Lord God, and all the rest are the work of human hands. Leopold Kronecker

The purpose of the lesson: To work out the rule for adding negative numbers; Get acquainted with the historical facts related to the topic of our lesson; Develop self-esteem skills.

Lesson plan: Blitz - survey (crossword puzzle) Oral work. Individual work. Fixing the material. "Magic Square". History reference. Fizkultminutka. Mathematical dictation. Summary of the lesson.

Decipher the name of the mathematician who first introduced the coordinate line. To do this, enter the letters corresponding to the given coordinates. T E U R O K D A M (4) - ? (- four) - ? (2) -? (5) - ? (- one) - ? (- 6) - ? d e k a r t

Fill in the table a b │ a │ │ b │ -1 -3 -2 -4 -6 -1 -5 -5 -9 0 -4 1 3 4 4 2 -6 6 -7 6 1 7 -10 5 5 10 -9 0 9 9 a+b │ a │ + │ b │

To add negative numbers, you need to: Add the modules of these numbers Put a minus sign in front of the sum - a + (-b) = - (│-a │ + │-b │) The rule for adding negative numbers

Orally. Find the correct answer: -9 + (-3) = 12 6 -6 -12

Orally. Find the correct answer: -17.3 + (-7)= 10.3 -10.3 24.3 -24.3 -16.6

Orally. Find the correct answer: -8.4 + (-0.4) = 8.8 -4.4 8 -8.8 -8

Orally. Find the correct answer: -2 + (-8.2) = -6.2 6.2 10.2 -10.2 -8.4

Orally. Find the correct answer: -4.8 +(-4.8) = -1 0 9.6 -9.6 -8.16

Orally. Find the correct answer: -4.8 + 4.8 = 9.6 -9.6 8.16 0 -8.16

Find the sum of negative numbers

25 -86 -35 -98 -83 -35 -99 -55 -57 -91 -35 B R A X M A G U P T A

Indian mathematician and astronomer, the first to formulate rules for dealing with negative numbers. He made these rules in _______ year. Brahmagupta -

124 -89 0 -77 -338 -303 -214 -219 -135 -100 -11 -88 -237 -202 -113 -190 - 628 Magic Square

9.5 -42.07 -3.5 -31.6 -26.2 -83 -35 - 42.07 J N V I D M A N

Czech mathematician. Introduced the signs "+" and "-" to indicate positive and negative numbers. His book "Quick and beautiful counting" was published in ________ year. Jan Widman -

Find the module of the root of the equation: x - (-888) \u003d - 601; x \u003d - 601 + (-888); x \u003d - 1489. │ - 1489 │ \u003d 1489

1 - 18 5 - 8 2 - 9 6 No 3 0 7 Yes 4 - 14 8 Yes Math dictation

“Property and property is property” “The sum of two debts is debt” “The sum of debt and zero is debt” “The sum of property and zero is property” “The sum of two zeros is _____” From Brahmagupta’s book:

Uncertainty + - joy + - satisfaction 0 - indifference Lesson summary

Thank you for the lesson

On the topic: methodological developments, presentations and notes

Test "Addition of negative numbers", item 32

Test work, grade 6, p. 32, TMC N.Ya. Vilenkin. Test performed in Excel program- 2003, with macros....

A generalization lesson on the topic "Addition of negative numbers and numbers with different signs" was developed in the form of a didactic game ...

A lesson in learning new material. Content basis training session: 1) reference knowledge: the concept of a coordinate line, the concept of negative and positive numbers, the concept of the modulus of a number; 2) support...

Addition of negative numbers and numbers with different signs

Lesson objectives: 1. Educational: develop the skills of adding negative numbers and numbers with different signs.2. Educational: educate attention; ability to work in pairs.3. Developing: to develop lo...

The topic of the lesson "Addition of negative numbers" is, in fact, a logical continuation of the previous one - "Addition of numbers using a coordinate line." Therefore, in order to most effectively and quickly state the titled topic of the lesson and proceed to the development of the knowledge and skills acquired by students, we suggest using this educational presentation “Addition of negative numbers”.

slides 1-2 (Presentation topic "Addition of negative numbers", example 1)

In order to make it easier for students to move on to the very rule of adding negative numbers, it is proposed to first perform the addition operation on the coordinate line. For this, a task is considered in which the air temperature is measured: at the first measurement, it was -6 degrees, and then decreased by 3 degrees (that is, by -3). By performing a certain algorithm of actions with a coordinate line, students get an answer of -9. Further, the attention of schoolchildren is drawn to the fact that the number 9 is, in fact, the sum of the modules of the numbers -3 and -6.

Thus, students come to the rule of adding two negative numbers - add the models of these numbers and put a minus sign in front of the result. In order to maximize the focus on the proposed rule, it is presented in text form on a separate slide as a list of necessary actions. In order to show how the rule “works” in practice, examples are offered for solution. Not least, in these tasks, not just negative integers are considered, but decimal fractions, as well as mixed numbers.

slides 3-4 (rule of addition of negative numbers, questions)

The presentation for the lesson "Addition of negative numbers" contains a sufficient number of examples that fully reveal the rule for adding negative numbers. The explanation takes place in an accessible and understandable form, using the necessary drawings, as well as animation effects. The presentation of the educational material is logical and consistent. The slides are easy to read, and the font and picture sizes allow them to be seen clearly from all seats in the class.

This development contains questions on the material covered, which allows students to once again repeat the main points of the studied topic, and the teacher, if necessary, pay attention to where students experience difficulty in answering.

Usage educational presentation"Addition of negative numbers" will increase the efficiency of presenting new material in the corresponding lesson. In addition, the simple and understandable structure of the presentation allows not only teachers to work with it, but also parents at home - if the child missed this topic or he had some difficulties. This will allow the child to methodically correctly explain this material using the necessary examples and definitions.

MBOU "School No. 71", Ryazan

Larina L.A.

So let's start the lesson We wish you all success Think, think, don't yawn, Quickly count everything in your mind

Finish sentences:

• To the right of the origin are _________________
• To the left of the reference point are __________________
• Numbers that differ in sign are called ________________
• The distance from the point to the origin is called _________

positive numbers

negative numbers

opposite

module

the number itself

• The modulus of a positive number is _______________
• The modulus of a negative number is __________________________
• Zero modulus is _______
• An increase in any value can be expressed _____________________

opposite number

zero

positive number

• A decrease in any value can be expressed ___________________
• To the number a add a number in , this means _________________________
• If to a add a positive number a ___________
• If to a add a negative number a ___________
• Sum of opposite numbers ___________

negative number

a change to in units

- increase

- decrease

zero

No. 2. Mark the correct inequalities with a “+” sign

No. 3. Perform addition using the coordinate line:

B.1 B.2

a) -5 | -2.5 |;

b) 6 3; e) 4.8 -8.4;

AT 3 G)-(-5) 7 Z)-(+9) |-8|

1,5+3,5= -2,5+(-2)=

- 5

- a

- 5 b

- 85 x

Mark with a "+" the correct inequalities

IN 1

a) -5

b) |-6| |-3|;

in) 0 -1;

IN 2

G) | -2,6| | -2,5 |;

e) 4,8 -8,4;

AT 3

AND) -(-5) 7 H) -(+9) AND) |6| |-8|

-1 + (-3) = - 4

- 4 + 5 = 1

-5 + 7 = 2

3 + (-6) = - 3

-1,5+3,5=2 -2,5+(-2)=-4,5

Perform addition using the coordinate line:

BUT

AT

1)

-5 -4 -3 -2 -1 0 1 2 3 4 5 X

-5 + 7 = …

D

FROM

-5 -4 -3 -2 -1 0 1 2 3 4 5 X

2)

3 + (-6) = …

F

E

-5 -4 -3 -2 -1 0 1 2 3 4 5 X

3)

-1 + (-3) = …

Fill in the table with a coordinate line

│ a │

│ b │

│ a │+│ b │

a + b

Check myself :

│ a │

│ b │

│ a │+│ b │

a + b

Lesson topic:

"Addition negative numbers"

The goals of our educational activities:

• know the rule of adding negative numbers;

• learn how to add negative numbers according to the rule;

Check myself :

│ a │

│ b │

│ a │+│ b │

a + b

Addition rules negative numbers

To add two negative numbers:

1) fold their modules;

2) put a "-" sign in front of the received number.

(-10) + (-95)

Solution:

(-10) + (-95)= - (10+95)= -105.

page 177, No. 1045 (a, e, i)

To add two negative numbers, you need:

1) fold their modules;

2) put a minus sign in front of the resulting number.

So how do you add two negative numbers?

Solve examples

3) -0,5+ (-1,25)

If you solve everything correctly, you will get the name of an Indian mathematician of the 7th century

Example number

Resp. letter

It is interesting.

Brahmagupta is an Indian mathematician who lived in the 7th century.

He was one of the first to use positive and negative numbers. Positive numbers he called "property", negative "debts". He stated the rule for adding two negative numbers as follows: the sum of two debts is a debt.

Homework:

P. 32, learn the rule,

orally answer the questions on p. 176, No. 1056,1057

Continue:

I found out)…

I have learned (learned)...

I understand)…

slide 1

Development of a mathematics lesson in the 6th grade on the topic "Addition of positive and negative numbers"

slide 2

Starostenko Alla Nikolaevna, teacher of mathematics Subject: mathematics, lesson-game, consolidation of the studied material Topic: “Addition of positive and negative numbers

slide 3

The objectives of the lesson: the repetition of previously acquired knowledge on the topic "Positive and negative numbers." Tasks: to train the ability to denote rational numbers by points of the coordinate line and find the coordinate of a point from its image on the coordinate line; education of attention, memory training, development of resourcefulness and ingenuity; development of mathematical thinking, the ability to find errors.

slide 4

Today we will make a wonderful journey on a mathematical ship through the amazing and fabulous planet of rational numbers, where we will visit corners of knowledge familiar to you. The journey begins.

slide 5

Island of Correct Answers. Oral work with the class.
term term
-25 -44
-17 -65
-32 -33
-45 -45
-54 -56
-47 -11
-34 -72
-14 -200
-105 -79
term term
43 -54
88 -32
-122 42
-65 37
-45 78
309 -12
69 -39
-34 -25
-89 98
-64
-82
-65
-90
-110
-58
sum
-105
-214
-184
sum
30
-11
56
-80
-28
33
297
-59
9

slide 6

Questions from the owner of Robinson Island
Numbers with the "-" sign are called ... The positive direction on the coordinate line indicates ... The number showing the position of the point on the coordinate line is called ... points. Numbers with a "+" sign are called ... The distance from zero to a given point is called ... numbers. Natural numbers, their opposites and zero are ... numbers. Neither a positive nor a negative number is a number ... Rules for adding negative numbers. Rules for adding numbers with different signs.

Slide 7

Fight with pirates in the ocean of positive and negative numbers
0
1
(1)
(4)
(-1)
(-4)
(0)

Slide 8

The fight goes on
0
-0,4

Slide 9

Fizminutka by the sea
The seagulls are circling over the waves Let's fly after them together. Splashes of foam, the sound of the surf, And above the sea we are with you (Children wave their arms like wings) We are now sailing on the sea And frolicking in the open. Have more fun and catch up with dolphins. (children make swimming movements) Look: seagulls importantly Walk along the sea beach. (Walking in place) Children sit on the sand, We continue our lesson. (Children sit at their desks

Slide 10

Urgently calculate the coordinates of the pirate ship. (Independent work)
Option 1. C - 55. Perform the addition: Option 3. C - 55. Perform the addition:
Option 2. C - 55. Perform the addition: Option 4. C - 55. Perform the addition:

slide 11

Guys, I propose to take the helm of the ship and continue the journey! Find the sum of the number in the frame and the number in the column.

slide 13

What was the name of the mathematician who discovered these negative numbers?
-36+36
42+(-45)
55+(-55)
0,2+(-1,52)
66+(-12)+(-66)
-20+(-6)+(-3)
-3,3+9,6
-3,2+(-42)
-100+(-34,5)
-45+2,22
B
R
a
m
a
G
at
P
t
a

Slide 14

The squirrel travels along the coordinate line, on which the points A (- 2), B (5), C (3), D (- 7) are marked. Which of his routes is the shortest? The squirrel travels along the coordinate line, on which the points A (- 2), B (5), C (3), D (- 7) are marked. Which of his routes is the shortest? The squirrel travels along the coordinate line, on which the points A (- 2), B (5), C (3), D (- 7) are marked. Which of his routes is the shortest? The squirrel travels along the coordinate line, on which the points A (- 2), B (5), C (3), D (- 7) are marked. Which of his routes is the shortest?
a) ABCD b) ACBD; c) ADCB; d) ADBC.
2. How many integers are located on the coordinate line between the numbers - 7 and 8? 2. How many integers are located on the coordinate line between the numbers - 7 and 8? 2. How many integers are located on the coordinate line between the numbers - 7 and 8? 2. How many integers are located on the coordinate line between the numbers - 7 and 8?
a) 13; b) 14; c) 15; d) another answer.
3. Take action. . 3. Take action. . 3. Take action. . 3. Take action. .
a) 1.87; b) - 1.87; c) 17.47; d) another answer.
4. Arrange the numbers a = - 6.7; b=0.25; c = – 12 in ascending order of their modulus. 4. Arrange the numbers a = - 6.7; b=0.25; c = – 12 in ascending order of their modulus. 4. Arrange the numbers a = - 6.7; b=0.25; c = – 12 in ascending order of their modulus. 4. Arrange the numbers a = - 6.7; b=0.25; c = – 12 in ascending order of their modulus.
a) a, b, c; b) b, a, c; c) a, c, b; d) another answer.

Addition of negative numbers.

Targets and goals:

educational: Help students to deduce the rule for adding negative numbers.

Educational: to cultivate interest in mathematics, applying interesting tasks, using various forms of work.

Developing: develop the ability of students to work both individually (independently) and collectively; develop the ability to assess your strengths using tasks of different levels of complexity.

Lesson type: Explanation of new material.

During the classes:

1 . Organizing time.

Let's start the lesson. Today we will talk about love - about which numbers on the coordinate line love each other.

At the beginning of the lesson, we will review the studied material, check homework, we will write a mathematical dictation, then we will solve one problem and formulate the topic of the lesson, as well as a rule on this topic, at the end of the lesson we will work in pairs on cards and consider interesting tasks. For this lesson, each of you will receive an assessment and I am sure that all of them will be positive.

2. Revision of the material covered and checking homework.

Homework solution on the board. Students are encouraged to self-assess their own work and give themselves grades for homework.

And now we will repeat the studied material on this topic (slide 3-10).

What is the modulus of a number?

(Answer: the module of the number a is the distance (in unit segments) from the origin to the point a.)

What is the modulus of the number... |5|, |-9| and |0|

(Answer: 5; 9; 0)

Compare numbers...

Compare the numbers (which is greater). -3 and 1; -8 and 0; -2 and -12

If you compare a positive and a negative number, then it is always more ... what?

(Answer: positive).

If you compare a negative number and zero, then there is always more ... what?

(Answer: zero).

If you compare two negative numbers, is more then...?

(Answer: whose modulus is less or which is closer to zero on the coordinate plane).

3. "Mathematical Dictation"(slide 11-12). Task: perform addition using a coordinate line. Students change notebooks and give each other grades.

4 . A student of your class will tell us about historical information today.

History of negative numbers

The history of the emergence of negative numbers is very old and long. Since negative numbers are something ephemeral, not real, people did not recognize their existence for a long time.

It all started in China, around the 2nd century BC. Perhaps they were known in China earlier, but the first mention dates back to that time. They began to use negative numbers and considered them "debts", while the positive ones were called "property". The record that exists now did not exist then, and negative numbers were written in black, and positive ones in red.

The first mention of negative numbers we find in the book "Mathematics in Nine Chapters" by the Chinese scientist Zhang Can.

Next, in V-VI centuries negative numbers have become widely used in China and India. True, in China they were still treated with caution, they tried to minimize their use, and in India, on the contrary, they were used very widely. There, calculations were made with them and negative numbers did not seem to be something incomprehensible.

Indian scientists Brahmagupta Bhaskara (VII-VIII centuries) are known, who in their teachings left detailed explanations for working with negative numbers.

And in antiquity, for example, in Babylon and in Ancient Egypt, negative numbers were not used at all. And if the calculation resulted in a negative number, it was considered that there was no solution.

So in Europe, negative numbers were not recognized for a very long time. They were considered "imaginary" and "absurd". No action was taken with them, but simply discarded if the answer was negative. It was believed that if any number is subtracted from 0, then the answer will be 0, since nothing can be less than zero - emptiness.

For the first time in Europe, Leonardo of Pisa (Fibonacci) turned his attention to negative numbers. And he described them in his work "The Book of Abacus" in 1202.

Later, in 1544, Mikhail Stiefel in his book "Complete Arithmetic" first introduced the concept of negative numbers and described in detail the actions with them. "Zero is between absurd and true numbers."

And in the 17th century, the mathematician Rene Descartes suggested putting negative numbers on the digital axis to the left of zero.

From that time on, negative numbers began to be widely used and recognized, although for a long time many scientists denied them.

In 1831, Gauss called negative numbers absolutely equivalent with positive ones. And the fact that not all actions can be performed with them was not considered something terrible, with fractions, for example, not all actions can be done either.

And in the 19th century, Wilman Hamilton and Hermann Grassmann created a complete theory of negative numbers. Since that time, negative numbers have gained their rights and now no one doubts their reality.

5. Explanation of new material.

As you know, negative numbers first appeared in China in the 2nd century BC. And negative numbers were interpreted as debt, and positive numbers as property.

Let's analyze the problem: (slide 15-16)

Ancient China. A poor farmer borrows 3 sacks of rice from his rich neighbor for spring planting. However, the summer was bad, dry, and the poor peasant did not collect anything from his field in the fall. And winter is ahead, and the poor man had to go to his neighbor again. The rich neighbor did not refuse and loaned another 7 sacks of rice, but on the condition that the entire debt be repaid with a 10% surcharge. How many sacks of rice must a poor peasant give away?

Brief recording of the task on the screen.

Next on the board: 3 sacks of rice are borrowed, so three will be what number ... (positive or negative)? Similarly, 7 will also be a negative number. We need to find the sum of these negative numbers: -3 + (-7) = ? 10, do you think 10 will be positive or negative? (negative -10).

And so, the peasant owes 10 bags of rice, but the condition is to return the entire debt with a 10% surcharge. We need to find 10% of the number...? (10) How can we quickly find 10% of 10. (divide by 10 and answer 1)

So in total

10 + (-1) = ? … -11.

So, we calculated the debt of the poor peasant, it amounted to 11 bags of rice.

And now formulate the topic of today's lesson:

"Addition of negative numbers".

And now, guys, let's take a close look at this example and try to formulate a rule for adding negative numbers. (Slide 14)

To add two negative numbers, you need to: add their modules and put a minus sign "-" in front of the resulting number.

A short written work to consolidate the studied material, examples on the screen:

(slides -19-23)

20 + (-15) = -35

1,5 + (-4,5) = -6

12 + (-13) + (-14) = -39

6. Physical education. (slide -24)

7. Work in pairs on cards. (slide -25-26).

Work on cards of different difficulty levels (three levels of difficulty, 6 options each, three tasks per option.) Now we will work on cards. Per the right decision examples in the card you will receive points, the more points you score, the higher your score will be. Now, guys, I will talk about the rules for working with cards, each card has three examples for adding negative numbers, the cards are multi-colored (green, yellow and red) and vary in complexity.

With one star - the easiest, but for the correct solution of each example you will get 1 point.

With two stars - the level of difficulty is medium and for the correct solution of each example you will receive 2 points.

With three stars - the most difficult, but for the correct solution of each example you will get 3 points.

The complexity of the card is up to you. 5 minutes are allocated for work, and if you manage to make one card, you can take another one, any of your choice and thus dial large quantity points. When completing tasks, be sure to write down the option number and task numbers in your notebook.

Now we will check the correctness of the solutions and calculate the points scored. You can see the answers and scores on the TV screen. If the example is solved correctly, then put next to it the number of points indicated in brackets.

Students sitting at the same desk exchange notebooks and, according to the answers displayed on the screen, check the correctness of the examples, and then count the number of points scored. Then they give the notebooks to the owners.

8. Fixing the material

1) "Let's play bride" (slide - 27). Numbers are given: -1;-2; -3; -four; -5; -6; -7; -eight; -9; -ten. Using each number once, make three correct equalities.

2) "Fill in the gaps" (slide -30) -14 + ... = -37

3,8 +…= -4,08

51,22 + …= -60,1

9 . Homework. (Slide-21)

On the screen: differentiated homework.

Write down your homework, one assignment common to all p.178 ex.1056. Two additional tasks for assessment in the journal, for the fourth task No. -1058, and for the five task No. -1057 and No. -1060. Submit your notebooks for review.

10. Reflection.

If you liked the lesson, show me the appropriate emoticon.

And I would like to end the lesson with a quote from our great Russian scientist Mikhail Lomonosov: “Mathematics is only worth teaching because it puts the mind in order”. Learn math and then you will never have problems with the rest of the subjects.