The topic of today's lesson: Comparing integers
Let's repeat:
1) What is the opposite numbergiven:
a) 21; b) -16; c) -48; d) 81; e) 0;
2) Name the modules of these numbers:
a) 16 b) -27 c) 1 d) -5 e) 0
3) Name two opposite numbers,
having a module:
a) 17 b) 8 c) 40
Equals =
We characterize many things with numbers.things in our lives: cost, weight, height,
forecast, points in the game, etc. Therefore, it is very
It is important to learn how to compare numbers.
What comparison signs do you know?
less than sign<
More sign >
equal sign
=
Number Comparison
Basic rule: more of two integersthe one that is to the right in the series of integers
0 and 5
-2 and 0
-1 and 3
5 and -4
0<5
-2 < 0.
-1 < 3
5 > -4
Let's repeat the rules for comparing integers:
1. Any positive number greater than 0
2. Any negative number less than 0
a >0
-A< 0
3. Any positive number is greater than a negative number
a > -b
Yesterday the thermometer on the street showed -2 degrees, and today it shows 1 degree. Has the temperature risen or fallen? How
write an inequality?Has risen.
1 > -2
Let's repeat the rule for comparing a negative number with a negative
|-5|=5Compare -3 and -5
-5
-3
|-3|=3
0
Of two negative numbers, the greater is
which has a smaller modulus.
|-3| <|-5| , значит -3>-5.
What numbers can be written instead of * to get the correct inequality:
- 274 > -27*-1890 < -189*
-4*6> -416
-*38> -338
-12*7< 1287
-4*15> -4015
Replace * with a number such that the inequality is true:
3 < * < 8;0 < * < 2;
-5 < * < 0;
-3 < * < 3;
-10 < * < -7;
-100 < * < -93.
Write the numbers in ascending order
-27; -14; -38; -5; 7; 10; -1; 21;5; -3; -17; -24; -20; -41; -35;
-41; -46; -32; -18; -11; -20; 7; 9.
Independent work
1. Write down the opposite numbers: +12, 9, -162. Determine modules of numbers: +11, 0, -34
3. Simplify the notation of numbers: +(+10), +(-11), -(-12), -(+13)
4. Compare numbers:
a) +22 and 0 b) -11 and 0 c) -16 and +5
d) -18 and -17 e) +300 and +400 f) -300 and -400
5. How many integers are located between -22 and +23
1
2
3
4
5
-12,-9,16
11, 0, 34
10, -11,
12, -13
a) 22>0 b) -11<0
c) -16<+5 г) -18<-17
e) 300<400
f) -300>-400
Fill in the missing words so that you get the correct statement.
a) Of the two negative numbers, the one with __________ __________ is less and the one with ____________________ _________________ is greater.
b) Any negative number ___________________ zero.
c) Any positive number ___________________ zero.
d) Any negative number __________ any positive number.
e) On the coordinate line, a point with a larger coordinate lies _______________ points with a smaller coordinate.
Fill in the missing words so that you get the correct statement.
a) Of the two negative numbers, the one with __________ __________ is less and the one with ____________________ _________________ is greater.
b) Any negative number ___________________ zero.
c) Any positive number ___________________ zero.
d) Any negative number __________ any positive number.
e) On the coordinate line, a point with a larger coordinate lies _______________ points with a smaller coordinate.
"Lesson outline COMPARISON"
MBOU "Mozhginskaya secondary school of agricultural profile"
mathematic teacher
Sobina O.A.
Lesson summary
Goals:
introduce the rules for comparing positive and negative numbers;
learn to apply the acquired knowledge in performing various tasks.
to promote students' mastery of the main ways of mental activity (the ability to compare, analyze, draw conclusions);
to promote the development of mathematical speech of students.
to promote the formation of cognitive interest;
to promote the formation of personal qualities: kindness, mutual assistance, mercy, the ability to hear and listen, work in pairs and groups.
Educational:
Educational:
Educational:
DURING THE CLASSES
1. Organizational moment
- Good morning! Look at each other, smile, and mentally wish your friends good luck and kindness!
As the epigraph of our lesson, I took the words of Confucius - ancient thinker and Chinese philosopher
Learning without thinking is useless, but thinking without learning is dangerous.
Confucius
2. Actualization of knowledge.
Repetition of the material covered- The results are included in the list of achievements.
1) Name the coordinates of these points:
A(-3), B(-1.5), C(3), D(5.5)
2) Which of the lines in the figure are coordinate lines, and which are not?
3) Calculate: a) |- 4| ∙ |-1.5| =
b) |34| - |- 16| =
c) |23| + |- 8| =
4) Numbers are given
-4; 8; 9; -1,5; 0; -16; -14; 100; -7; 120; 14; -150; -9; -8
name:
a) natural numbers; b) whole numbers; c) negative numbers;
d) positive numbers; e) pairs of opposite numbers
The number a is greater than 2. Is a necessarily positive?
The number b is less than 3. Does the number b have to be negative?
A number with greater than -1. Is positively necessary?
The number d is less than -5. Does the number d have to be negative?
The results are included in the list of achievements.
3. Preparing to learn new material. Creation of a problem situation.
Compare numbers:
The last two lines are problematic.
Why can't we compare the last 2 pairs of numbers?
What are these numbers called?
Can we compare all numbers?
Then formulate the goals and objectives of the lesson (the teacher can write them down on the board).
Get into groups and try to answer the questions. If it will be very difficult, then you can refer to the textbook (p. 163)
4. Group work
Fill in the missing words so that you get the correct statement.
a) Of the two negative numbers, the one with ________________________ is less and the one with _____________________________________ is greater.
b) Any negative number _________________zero.
c) Any positive number ________________ zero.
d) Any negative number ______________ any positive number.
e) On the coordinate line, a point with a larger coordinate lies ____________ points with a smaller coordinate.
5. Learning new material
The conclusions of the groups on these issues are voiced. We draw a general conclusion.
more module , and more than that, which hasmodule less .
b) Any negative numberless zero.
c) Any positive numbermore zero.
d) Any negative numberless any positive number.
to the right points with smaller coordinates.
6. Physical education.
1) - I read the statement, if it is true - 3 jumps, if incorrect - 2 squats:
5 is a positive number, -(-3) is a negative number, a and –a are opposite numbers, |-25|=-25
2) if the number belongs to the interval from -3 to 5, then the hands are up, if not, then the hands are to the sides ....
Numbers: 2, -3.1; 0.5.5; 2.7….
7. Fixing.
According to the textbook No. 974 (a-e), 976 (a - e), 980 (a - e) in pairs.
No. 974 (a-e) - compare numbers using a coordinate line. What rule are you using? Explain your choice.
976 (a - e) - Which rule will you use? Explain your choice.
980 (a - e) - Peer review in pairs.
8. Computer test for the primary fixation of the material.
9. Summing up. Reflection.
Calculation of points and grading in the list of achievements.
Each student assigns a grade for the work in the lesson according to the criteria
12 - 16 points - "3"
17 - 20 points - "4"
21 - 24 points - "5"
and populate the table:
Rate yourself!
| did you understand the theory? | remember the rules: | emotional mood |
|||
| understood the rules | memorized all the rules | ||||
| understood the rules (a) not all | I didn't remember all the rules | ||||
| understood nothing) | didn't remember no one |
At the end of the lesson, the result of the work is summed up, the level of achievement of the goal:
Today in class I learned...
It was interesting to me…
It was difficult for me:
I understand …
I felt that:
Most of all I liked…
I am satisfied with my work at the lesson (not quite, not satisfied), because:
10. D / z: item 29, nos. 995, 996, 991 * - task for research work.
View document content
"list of achievements"
Criteria: 12-16 b. - "3"; 17 - 20 b. - "4", 21 - 24 b. - "5". Rate yourself!
| Achievement list_______________
Criteria: 12-16 b. - "3"; 17 - 20 b. - "4", 21 - 24 b. - "5". Rate yourself!
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Achievement list_______________
Criteria: 12-16 b. - "3"; 17 - 20 b. - "4", 21 - 24 b. - "5". Rate yourself!
| Achievement list_______________
Criteria: 12-16 b. - "3"; 17 - 20 b. - "4", 21 - 24 b. - "5". Rate yourself!
|
View presentation content
"COMPARING NUMBERS"
Learning without thinking is useless, but thinking without learning is dangerous. Confucius MBOU "Mozhginskaya secondary school agricultural profile" mathematic teacher Sobina O.A.
Calculate:
a) |- 4| ∙ |- 1,5 | =
b) | 34 | - |- 16| =
c) |23| + |- 8| =
Given numbers -4; 8; 9; -1,5; 0; -16; -14; 100; -7; 14; -150; -9; -8 name: a) natural numbers b) whole numbers c) negative numbers d) positive numbers e) pairs of opposite numbers
1) The number a is greater than 2. Is a necessarily positive? 2) Number b less than 3. Is the number required b negative? 3) A number with more than -1. Is positively necessary? 4 ) Number d less -5 . Is a number required? d negative?
Compare numbers:
15 and 28;
13.7 and 8.6;
And;
12.3 and 12.29;
-8 and 6;
-25 and -32.
Comparison
numbers
The purpose of the lesson: - get acquainted with the rules for comparing positive and negative numbers; - learn how to apply the acquired knowledge in the performance of various tasks; - develop the ability to compare, analyze.
a) Of two negative numbers, the one with __________ is less and the one with _______________ is greater.
b) Any negative number __________ zero.
c) Any positive number __________ zero.
d) Any negative number __________ any positive number.
e) On the coordinate line, a point with a larger coordinate lies ____________ points with a smaller coordinate.
Fill in the missing words so that you get the correct statement.
a) Of two negative numbers, the one with more module , and more than that, which has module less .
b) Any negative number less zero.
c) Any positive number more zero.
d) Any negative number less any positive number.
e) On the coordinate line, a point with a larger coordinate lies to the right points with smaller coordinates.
№ 974(a-e),
№ 976(a - e),
980(a - e) in pairs.
Computer test for repetition (10 min)
Criteria for evaluation:
12 - 16 points - "3"
17 - 20 points - "4"
21 - 24 points - "5"
Rate yourself!
Did you understand the theory?
understood the rules
understood the rules (a) not all
Remember the rules:
remembered (a)
all the rules
understood nothing)
Emotional mood
not all rules
remembered (a)
felt (a) free, comfortable
didn't remember
no one
felt (a) shy, uncomfortable
did not like anything, felt (a) bad
- Today in class I learned...
- It was interesting to me…
- It was difficult for me...
- I realized that...
- I felt that...
- Most of all I liked…
- I am satisfied with my work in the lesson (not quite, not satisfied), because ...
Thank you
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Slides captions:
“You are talented children! Someday you yourself will be pleasantly surprised how smart you are, how much and how well you know how, if you constantly work on yourself, set new goals and strive to achieve them. Jean Jacques Rousseau
Give examples of positive numbers. - Give examples of negative numbers. What is the difference between positive and negative numbers? What can you say about the number 0? Positive and negative numbers
Negative numbers in life Positive temperature - warm Negative temperature - cold
Mountain heights Mountain heights are measured using positive numbers. Positive and negative numbers in geography Depth of the seas The depth of water is measured using negative numbers.
Positive and negative numbers in medicine
0 1 - 1 2 3 - 2 - 3 X
Compare numbers:
Number Comparison
Any negative number is less than any positive number - Of two negative numbers, the one with the greater modulus is less and the one with the lesser modulus is greater - Any negative number is less than zero. - Any positive number greater than zero
Physical education minute
Independent work:
Independent work:
Arrange the numbers in ascending order. Then replace each number with a letter. You will have a word.
was 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". Brahmagupta
Today at the lesson I learned… I was interested… It was difficult for me: I understood… I felt that… Most of all I liked… I was interested… I am satisfied with my work at the lesson (not quite, not satisfied), because ... "Ladder of achievements"
Homework: P 2.3, rule to learn No. 240, No. 241
On the topic: methodological developments, presentations and notes
Lesson in the 6th grade "multiplication of integers"
The proposed lesson for students of the 6th grade on the topic: “Multiplication of integers” involves an independent search by students for the multiplication of negative integers and numbers with different signs. Type of lesson - level ...
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Lesson Objectives:
Educational:
- repeat positive and negative numbers;
- the image of numbers on the coordinate line;
- comparison of positive numbers;
- deriving a rule for comparing numbers using their series;
- to form the ability to compare numbers using their series, give examples;
Developing:
- develop attention, speech, memory, logical thinking, independence.
Educational:
- educate the desire to achieve the goal; self-confidence and ability to work in a team.
Know: rules for comparing two numbers using their series.
Be able to: compare numbers using their series, arguing your answer.
Lesson type: the study of new material and the lesson of primary consolidation.
Equipment: screen, multimedia, presentation, handouts
| No. p / p | Lesson stage | Time | Stage tasks |
| 1 | Organizing time. | 1 min. | Greet each other, prepare students for the lesson. |
| 2 | Knowledge update. | 7 min. | Determine the topic of the lesson, goals and stages together with the students. Repeat positive and negative numbers, depict them on a coordinate line, repeat the rule for comparing positive numbers. |
| 3 | Learning new material. | 13 min. | Derivation of rules for comparing integers using their series. |
| 4 | Consolidation of the studied material. | 10 min. | To form the ability to compare integers, give examples, argue the answer. |
| 5 | Fizkultminutka. | 1 min. | Relieve the child's fatigue, provide active recreation and increase the mental performance of students. |
| 6 | Final consolidation | 9 min | Check acquired skills and abilities |
| 7 | Lesson summary | 3 min. | Summing up. Grading. Reflection |
| 8 | Homework. | 1 min. | Homework instruction. |
During the classes
1) Organizational moment.
Good afternoon. Today is great weather. I hope you have the same mood and we will work productively. I remind you that for giving correct answers, students put themselves in the margins “+” and at the end of the lesson, for 5 “+” - a score of “5” and for 4 “+” - a score of “4”. Good luck to all.
2) Actualization of knowledge.
You were doing your home lab work at home. What did you do? - They compared the air temperature, the height of the mountains, the depth of the lakes. - Right, did everyone manage to find the data and fill in the table? - Yes. - Well done. Tell me, in mathematical language, what did you do? - Compared numbers. - Right. Today in the lesson we will continue to compare numbers. We will repeat what we know and go through new material. Tell me, which numbers we already know how to compare, and which ones we still don’t? - Positives are good, but negatives are not.- Right. So what's the topic of today's lesson? – Compare negative numbers.- Well done. Let's write in a notebook (slide 1).
What are your goals for this lesson? - Learn to compare negative numbers, repeat the rules for comparing numbers.- That's right, well done. Let's start with the first step of the lesson. What is our name? - oral work. - Yes. Young.
I oral work(slide 2).
Front poll:
- What is the name of the straight line on which a point is marked, taken as zero, a positive direction is chosen, and a unit segment is chosen?
- What numbers are called integers?
- What number is zero?
- What are the opposite numbers?
- What is the opposite of zero?
- What are the numbers to the right of zero called? And to the left of zero?
- How to compare positive integers? Give examples.
Well done. Let's move on to the next step. What do we do? - Learn new material. - Yes, well done, learn new material.
3) Learning new material.
Let's turn to your home laboratory work (slide 3).
- The height of Mount Elbrus is 5642 m, and Mount Balial is 4007 m. Which mountain is higher? - Elbrus. - How to mathematically record height data? - +5642 and +4007- That's right, but if we write it down as an inequality, what will it look like? - 5642 > 4007. - Right. Write down the inequality in your notebook.
- On January 31, 2014, the thermometer in St. Petersburg showed a maximum of 17 ° C below zero, and already on February 1, 2014. Showed only 9 ° C frost. – How to record temperature data mathematically? - -17 and -9- Has the temperature increased or decreased? – Has risen. - That's right, but if we write it down as an inequality, what will it look like? - 17 < -9. –
- In Barnaul yesterday the outdoor thermometer showed 0°C, and today it shows -5°C. Has the temperature risen or fallen? – Decreased. - That's right, but if we write it down as an inequality, what will it look like? – 0 > -5. – Right. Write down the inequality in your notebook.
- In Maykop, on February 28, the outdoor thermometer showed -2°C, and on March 01 it showed 3°C. Has the temperature risen or fallen? – Has risen. - That's right, but if we write it down as an inequality, what will it look like? – -2 < 3. – Right. Write down the inequality in your notebook.
Which of these inequalities can you absolutely say is true? - First. - Why? Let's repeat the rules for comparing natural numbers. - Of two natural numbers, the one that appears later when counting is greater and the one that appears earlier when counting is smaller.
Let's look at a series of positive numbers (slide 4): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, etc. What signs can be put between numbers? - Less - Right. Is there a largest positive integer? What about the least? - no Yes.
Now consider a series of negative numbers (slide 5): ...-6, -5, -4, -3, -2, -1, 0. What signs can be put between numbers? - Less - Right. Is there a smallest negative integer? And the greatest? - no Yes.
Now let's look at a series of integers (slide 6). What signs can be put between numbers? - Less - Right. Thus, the comparison rule for both negative and positive numbers is the same.
Let's look at the rule in the textbook and see if we made up the inequalities correctly at the beginning of the lesson (page 163 of the textbook). after reading the rules. We return to the inequalities and pronounce the rule.
We have learned new material, now let's move on to the next step of the lesson. What is it called? - Problem solving.- Yes, that's right, we will consolidate the acquired knowledge.
4) Consolidation of the studied material(slide 7).
A) Let's do the exercises from the textbook No. 725, 726 (y)
B) Work individually in notebooks, followed by mutual verification on slide 7.
Compare integers:
- -2 and -6;
- 5 and -4;
- -1 and 3;
- 0 and 5;
- -7 and -8;
- -2 and 0.
Examination:
- -2 > -6
- 5 > -4
- -1< 3
- 0 < 5
- -7 > -8
- -2 < 0
Do not forget to give yourself a “+” for those who have everything right.
C) Work in pairs. Petya Lenivtsev listened inattentively to the teacher's explanations, and therefore made several mistakes when comparing integers. Check the inequalities compiled by Petya, and if necessary, correct the errors (slide 8).
Students received handouts (Annex 1) - You mark a true or false inequality, and if it is false, write the correct one next to it.
Slide 8 check.
- Right
- Right
- False -3< 2
- False 4 > -8
- False -7 > -10
- False -12< -2
Do not forget to give yourself a “+” for those who have everything right. Well done, it's time to take a break.
5) Physical education(slide 9).
1. Close your eyes tightly for 3 seconds, and then open them for the same time. Repeat 3 times.
2. Blink rapidly for 10 seconds. Open your eyes, rest 10 seconds. Repeat 3 times.
3. Close your eyes, massage your earlobes with light circular movements of your fingers.
6) Final consolidation.
Now it's time to believe what we've learned.
Test by variants with differentiated tasks. The students were given handouts, execution on leaflets. Time 8 minutes (Appendix 2).
The work is over.
| A1 | A2 | A3 | A4 | IN 1 | AT 2 | C1 | |
| IN 1 | 2 | 3 | 2 | 3 | 2 | 1 | 4 |
| AT 2 | 4 | 2 | 3 | 3 | 2 | 1 | 2 |
7) Summing up.
Here our lesson comes to an end. What are the final stages of the lesson called? - Lesson summary and homework.- Right. Let's summarize (slide 10):
1. How are positive and negative numbers arranged in a series of integers relative to 0?
2. Is it possible to find the largest positive number? What about the biggest small negative number?
3. Formulate a rule for comparing integers.
Well done, now we will set the ratings. Please count your benefits. Grading “5” for 5 pluses, “4” for 4 pluses.
Please draw a smiley under the date of today's lesson showing your mood at the end of the lesson.
8) Homework(slide number 11).
Turn to the board and write down your homework.
1) Rules to learn
2) Optional:
a) No. 727, 728, 730
b) No. 730, 736, 737.
Please look at the numbers, do you understand all the tasks?
Thank you for the lesson. Goodbye.
