Lesson on the topic: "Solving inequalities by the method of intervals."
Lesson type: Lesson of generalization and systematization of knowledge.
LESSON OBJECTIVES:
To generalize, expand the knowledge of schoolchildren on the topic under study.
To promote the development of observation, the ability to analyze. Encourage students to self-control, self-analysis of their educational activities.
To cultivate such personality traits as cognitive activity, independence.
Equipment and materials : computer, projector, screen, presentation to accompany the lesson, handout for students, evaluation sheets.
The work of students consists of stages. They record the results of their activities in the evaluation sheets, giving themselves an assessment for the work at each stage of the lesson.
STUDENT EVALUATION SHEET.
stage
Type of work
Grade
Repetition. Test.
Graphic dictation.
Practical work.
Study.
Lesson evaluation.
Lesson steps:
Repetition (test)
Graphic dictation.
Practical work.
Learning new.
Summing up the lesson (reflection, self-assessment).
During the classes
Organizing time.
The teacher tells the students the topic and purpose of the lesson.
Topic "Solving inequalities by the method of intervals". The purpose of the lesson: generalization and expansion of knowledge on this topic.
Introduces the requirements for maintaining an evaluation sheet.
Message about the topic and purpose of the lesson.(Appendix No. 1-slide 1)
The topic that we are currently studying will help you guys not only pass the exams for the basic school course, but also help you successfully pass the centralized testing and you will certainly need it to continue your education. And I have no doubt that you will want to continue it.
I wish you success in today's work and let the words of the Persian poet Rudaki be the epigraph of our lesson:(Appendix No. 1-slide 2)
« Ever since the universe has existed,
There is no such thing, who would not need knowledge,
What we do not take the language and age,
Man has always striven for knowledge.
So, guys, open notebooks, write down the date and classwork.
Today in class:(Appendix No. 1-slide 3)
Repetition (test) (KIMs were used to prepare for the final certification). - 10 min.
Graphic dictation. – 5, 7 min.
Practical work. - 15 minutes
Learning new. - 10 min.
Summing up the lesson. Reflection. - 3 min.
Repetition(reading graphs; graphical way to solve equations, systems of equations, inequalities) (Appendix №2)
Graphic dictation .( application number 1- slide4)
« V» - agree with the statement; "-" - disagree with the statement.
The interval method can only solve the inequalities II degree.
To solve inequalities by the interval method, the left side must be factored.
For solutions fractional rational inequalities by the method of intervals, it is necessary to find the ODZ.
On the number line, we mark only the zeros of the function.
The signs of the function on each interval always alternate.
Inequalities may have a solution consisting of a single number.
Solving an inequality with one variable may be the set of all numbers.
The answer must be written in the form of intervals.
The interval method allows solving other problems as well.
Key: ( application number 1- slay5) 1) - 2) V 3) V 4) - 5) - 6) V 7) V 8) - 9) V
Score "5" - 9 correct answers;
Score "4" - 7, 8 correct answers;
Grade "3" - 5, 6 correct answers;
Score "2" - less than 5 correct answers.
Practical work (with check) (Appendix No. 1-slide 6)
Option 1.
№
a) b); in)
№
Option 2.
№1. Solve the inequalities using the interval method:
a) b); in)
№2. Find the scope of the function:
Self-examination of practical work( application number 1- slides 7-9).
Evaluation of practical work ( application number 1- slide10)
Learning new.( application №1-slide11 )
We have already considered the interval method for solving quadratic inequalities. We apply the same method to solving high-degree inequalities.
f(x) > 0(<, ≤, ≥)
Required Phrase : Since the functionf(x) is continuous at every point of its domain of definition, then the method of intervals can be used to solve this inequality. The function can change its sign when passing through zero or a break point. Although it may not change. Between zeros and discontinuity points, the sign is preserved. Then why, when solving an inequality, depict the function itself?
It is enough to divide the number line into intervals by function zeros and discontinuity points and determine the sign in each of them.
Example. Let's solve the inequality
Solution:
First of all, we note that if the factorization of a polynomial includes the factor, then they say that - root of multiplicity polynomial .
This polynomial has roots: multiplicity 6; multiplicity 3; multiplicity 1; multiplicity 2; multiplicity 5.
Let's plot these roots on the number line. We mark the roots of even multiplicity with two lines, odd multiplicity - with one line.
Let us determine the sign of the polynomial on each interval, for any valueX not coinciding with the roots and taken from the given interval. We get a complete diagram of the signs of the polynomial on the entire number axis:
Now it is easy to answer the question of the problem, for what valuesX the sign of the polynomial is non-negative. We mark the areas we need in the figure, we get:
It can be seen from the figure that suchX
Solution:
Option 1: x=3; x=-2; x=7; x=10
+ - - - +
2 3 7 10
Option 2: x=9; x=2; x=-6; x=1
- + _ + +
6 1 2 9
(Two students solve inequalities on the board, the rest do the task on their own, then we check the solution obtained by the options and again draw conclusions about the sign change depending on the degree of multiplicity of the root).
Summarizing your observations, we come to important conclusions( application number 1- slide13) :
Homework.( application №1-Slide14)
Solve the inequality:
Construct a sketch of the graph of the function:
Summing up the lesson. Reflection. ( application №1-slide15)
Algebra lesson on the topic " Solving inequalities with one variable»
Lesson topic: Solution of inequalities with one variable.
Lesson Objectives: introduce the concepts of "solution of inequality", "equivalent inequalities";
to acquaint with the properties of equivalence of inequalities;
consider the solution of linear inequalities of the form ax b, ax reversing
special attention to cases where a and a = 0;
teach how to solve inequalities with one variable, based on properties
equivalence;
to form the ability to work according to the algorithm; develop logical thinking
mathematical speech, memory.
Lesson type: lesson learning new material.
Equipment: computer, projector, screen, presentation for the lesson,
signal cards.
During the classes.
1 .Organization of the lesson
● French proverb says
“Knowledge that is not replenished daily decreases daily.”
2. Monitoring the assimilation of the material covered.
● The Roman mimic poet of the era of Caesar and Augustus Publius Syrah there are wonderful
the words "Every day there is a student of yesterday."
3. Actualization of basic knowledge.
● According to N. K. Krupskaya "... Mathematics is a chain of concepts: one link will fall out - and the next will not be clear."
● Check how strong the chain of our knowledge is
● To answer tasks, use signal cards with signs and
● Knowing that a put an appropriate sign or, for the inequality to be true:
a) -5a □ - 5b; b) 5a □ 5b; c) a - 4 □ b - 4; d) b + 3 □ a +3.
Tasks on the board
● Whether it belongs to the segment [- 7; - 4] (The gap is written on the board)
number: - 10; - 6.5; - four; - 3.1?
● Specify the largest integer that belongs to the interval:
a) [-1; four]; b) (- ∞; 3); c) (2; + ∞).
● Find the mistake!
a) x ≥ 7 Answer: (- ∞; 7); b) y Answer: (- ∞; 2.5)
4. Learning new material.
(Formation of new concepts and methods of action)
slide 8.
● Chinese sage xunzi said "You can't stop learning."
● We will not stop either. And let's move on to the study of the topic "Solving inequalities with one variable."
Slides 9 - 11.
● The ancient Greeks already used the concepts of inequality. For example , Archimedes
(III century BC), while calculating the circumference, indicated the boundaries of the number 
.
A number of inequalities are given in his treatise "Beginnings" Euclid . For example, he proves that the geometric mean of two numbers is not greater than their arithmetic mean and not less than their harmonic mean.
However, the ancient scientists carried out all these arguments verbally, relying in most cases on geometric terminology. Modern signs of inequalities appeared only in the XVII-XVIII centuries. In 1631 an English mathematician Thomas Harriot introduced for the relations "greater than" and "less than" signs of inequality, which are still used today.
The symbols and ≥ were introduced in 1734 by a French mathematician Pierre Bouguer .
Tell me, what is mathematics without them?
About the secret of all inequalities, that's what my verse is about.
Inequality is such a thing - you can’t solve it without rules!
● So, in order to learn how to solve inequalities, let's first find out: what is the solution of the inequality, and what properties are used to solve it.
Slides 12 - 13.
● Consider the inequality 5x - 11 3. For some values of the variable x, it turns into a true numerical inequality, but not for others. For example, for x = 4, the correct numerical inequality is obtained 5 
4 – 11 3; 9 3, for x = 2 we get the inequality 5 2 – 11 3, -1 3 which is not correct. They say that the number 4 is a solution to the inequality 5x - 11 3. The solutions of this inequality are also the numbers 28; 100; 180 etc. Thus:
The solution of an inequality with one variable is the value of the variable that turns it into a true numerical inequality.
● Is the number 2; 0,2 solution of the inequality: a) 2x - 1 3?
● Whether only numbers 2 and 0.2 are a solution to the inequality 2x - 1
● There are a lot of numbers that are the solution to this inequality, but we must indicate all its solutions.
Solving an inequality means finding all its solutions or proving that there are none.
slide 14.
● Remember, equations that have the same roots, we called equivalent. The concept of equivalence is also introduced for inequalities.
Inequalities that have the same solutions are called equivalent. Inequalities that do not have solutions are also considered equivalent.
For example, the inequalities 2x - 6 0 and 
are equivalent, since the solutions to each of them are numbers greater than 3, i.e., x 3. The inequalities x 2 + 4 ≤ 0 and |x| + 3 8 are not equivalent, since the solution to the first inequality x ≥ 2, and the solution to the second x 4.
● There is much in common between solving an inequality and solving an equation - inequalities also need to be reduced to simpler ones using transformations. An important difference is that the set of solutions to an inequality is, as a rule, infinite. It is impossible in this case to make a complete check of the answer, as we did with the equations. Therefore, when solving an inequality, it is necessary to pass to an equivalent inequality - having exactly the same set of solutions. To do this, relying on the basic properties of inequalities, it is necessary to perform only such transformations that preserve the inequality sign and are reversible.
slide 15.
When solving inequalities, the following properties are used:If we transfer from one part of the inequality to another term with the opposite
sign, t
O, we get an equivalent inequality.
If both parts of the inequality are multiplied or divided by the same positive
number, then you get an inequality equivalent to it;
if both parts of the inequality are multiplied or divided by the same negative
number, while changing the sign of inequality to the opposite, it turns out
equivalent inequality.
slide 16.
● As the Roman fabulist of the first half of the 1st c. n. e. Phaedrus: “We learn from examples”
● We will also consider using examples of the use of equivalence properties in solving inequalities.
Slides 17 - 18 .
Example 1 Let's solve the inequality 3(2x - 1) 2(x + 2) + x + 5.
Let's open the brackets: 6x - 3 2x + 4 + x + 5.
We give similar terms: 6x - 3 3x + 9.
We group the terms with the variable on the left side, and
on the right - without a variable: 6x - 3x 9 + 3.
We give similar terms: 3x 12.
Divide both sides of the inequality by the positive number 3,
while maintaining the inequality sign: x 4.
4 x Answer: (4; + ∞)
Example 2
Let's solve the inequality 
2.
Multiply both sides of the inequality by the least common denominator 
- 
2 6
fractions included in the inequality, i.e. for a positive number 6: 2x - 3x 12.
We give similar terms: - x 12.
Divide both parts by a negative number - 1, changing the sign
inequality to the opposite: x
12 x Answer: (- ∞; -12).
slide 19.
● In each of the considered examples, we replaced the given inequality with an equivalent inequality of the form ax b or Oh where a and b - some numbers: 5x ≤ 15, 3x 12, - x 12. Inequalities of this kind are called linear inequalities with one variable.
● In the given examples, the coefficient of the variable is not equal to zero. Consider the specific examples of solving the inequalities ax b or Oh at a = 0 .
Example 1 Inequality 0 x
Example 2 Inequality 0 x
● Thus, a linear inequality of the form 0 x or 0 x b , and hence the corresponding original inequality, either has no solutions, or its solution is any number.
slide 20.
● When solving inequalities, we adhered to a certain order, which is an algorithm for solving inequalities with one variable
Algorithm for solving inequalities of the first degree with one variable.
Open brackets and add like terms.
Group terms with a variable on the left side of the inequality, and without a variable - in
right side, changing signs during transfer.
Bring like terms.
Divide both sides of the inequality by the coefficient of the variable, if it is not equal to zero.
Draw the set of solutions to the inequality on the coordinate line.
Write your answer as a number span.
Inequality is such a thing - you can’t solve it without rules
I will try to discover the secret of all inequalities.
Three main rules
Then you will find the keys to them,
Then you can solve them.
You will not think and guess
Where to transfer and what to change in it.
And you will know for sure
That the sign will change when both parts are inequalities
Divide by minus a number.
But it will still be true.
Show the solution on a straight line.
Write your answer as an interval.
● I think this poem will help you remember how to solve inequalities.
5. Consolidation of the studied material. (Formation of skills and abilities)
● According to the great German poet and thinker Goethe “It is not enough just to gain knowledge; I need to find an app for them. It is not enough just to wish; need to do".
● Let's follow these words and start learning to apply what we learned today to the exercises.
Slides 21 - 22.
oral exercises.
● You have probably already noticed that the algorithm for solving inequalities with one variable is similar to the algorithm for solving equations. The only difficulty is dividing both sides of the inequality by a negative number. The main thing here is not to forget to change the inequality sign.
● Solve the inequality:
1) - 2x 6; 3) - 2x ≤ 6;
4) – х 5) – х ≤ 0; 6) – x ≥ 4.
● Find a solution to the inequality:
4) 0 x - 5; 5) 0 x ≤ 0; 6) 0 x 0.
slide 23.
● Complete the exercises: No. 836(a, b, c); No. 840(e, f, f, h); No. 844(a, e).
6. Summing up the lesson.
slide 24.
● "It's nice that you learned something," - once said French comedian
Molière.
● What new did we learn in the lesson?
● Did the lesson help to advance in knowledge, skills in the subject?
Evaluation of the results of the lesson by the teacher: Evaluation of the work of the class (activity, adequacy of answers, the originality of the work of individual children, the level of self-organization, diligence).
7. Homework.
slide 25.
● Study item 34 (learn definitions, properties and solution algorithm).
● Execute No. 835; No. 836 (d - m); No. 841.
Lesson on the topic "Solving quadratic inequalities"
Since the universe has existed,
There is no such thing, who would not need knowledge.
Whatever language and age we take,
Man always strives for knowledge.
The purpose of the lesson:introduce students to the solution of square inequalities.
Lesson objectives:
Introduce the concept of quadratic inequality, give a definition.
To introduce an algorithm for solving inequalities based on the properties of a quadratic function.
To form the ability to solve inequalities of this type.
Develop the ability to analyze, highlight the main thing, compare, generalize.
To develop the creative and mental activity of students, their intellectual qualities: the ability to "see" the problem.
To form a graphic and functional culture of students.
Develop the ability to clearly and clearly express your thoughts.
To develop the ability to work with available information in an unusual situation.
Show the relationship of mathematics with the surrounding reality.
Develop communication skills and the ability to work in a team.
Cultivate respect for the subject.
Educational:
Educational:
Educational:
Equipment:
Media Prector
Interactive presentations for the lesson
Handout
DURING THE CLASSES
I. Organizational moment
Mathematics is an ancient, interesting and useful science. Today we will once again be convinced of this. In previous lessons, you learned that the graph of a square trinomial is a parabola; how the parabola is located depending on the leading coefficient and the number of roots of the equation a x 2 + bx + c = 0. But the parabola is found not only in mathematics lessons! We will try to learn about the use of a parabola in physics, technology, architecture, in nature, in everyday life today and in subsequent lessons.
II. Actualization. The "challenge" stage
1. Frontal survey:
What equation do you see on the slide?
What is a quadratic function?
What is the graph of a quadratic function?
What parameters determine the location of the parabola on the coordinate plane?
Let's repeat the location of the parabola depending on the leading coefficient and the number of roots of the square trinomial (orally).
Verification is carried out using slide 2 (Presentation )
To perform the next task, it is called to the computer one student. Six graphs of quadratic functions and the values of the leading coefficient ( a) and the discriminant of the square trinomial (D). You need to select a chart corresponding to the specified values, to do this, click on the rectangle with the number or on the word "no" if there are no such values. If the answer is correct, a part of the picture opens, if it is incorrect, the word “error” appears, in order to return to the tasks, you need to press the “back” control button. After the correct completion of all tasks, the picture will open completely.
The student at the computer chooses an answer by reasoning aloud. The class follows the response of a friend, agrees or expresses a different opinion, perhaps provides assistance. (slides 3-15)
2. Find the roots of a square trinomial:
I option
a) x 2 + x - 12
b) x 2 + 6x + 9.
II option
a) 2x 2 - 7x + 5;
b) 4x 2 - 4x + 1.
Students work in notebooks, then check the answers according to the solutions presented by the teacher on the presentation screen (slide 16, check - slide 17).
3. To perform test tasks to determine the graph of the quadratic function of the values of the argument for which it is 0, 0, 0 can be called 2 people, two tasks for each. (Slides 18-25)
The student looks for the correct answer, thinking out loud. If the wrong answer is chosen, then a red stick appears, which the teacher usually points out errors in notebooks, and if it is correct, then a callout with the word “true”.
So, we have repeated the necessary material. What difficulties did you encounter while completing the assignments? Some have found weaknesses in themselves, but I hope they figured out their mistakes and will not make them again. (The result of the update stage is summed up).
III. Presentation of new material. Stage of "comprehension"
- And now, following the advice of academician I.P. Pavlova: “Never take on the next one without mastering the previous one”, we, having mastered the previous well, move on to the next.
Performing the last 8 tasks, you found out on what intervals the function takes positive, non-positive values, and on what intervals it takes negative and non-negative values. What type of functions are the functions presented in tasks? Name in general terms the formula that defines these functions (y = a x2 + bx + c).
Answering questions about the intervals where the function is 0, 0,
0, you had to solve inequalities. Name the general inequality that you had to solve ( a x 2 + bx + c
a x2 + bx + c0,
a x 2 + bx + c 0, a x 2 + bx + c
0).
Think about how you would call these inequalities?
The topic of the lesson is announced with a note in the notes (slides 26-27).
oral work(slide 28)
If students believe that the inequality does not apply to the named species, then they raise their hand, otherwise they sit motionless.
Here is a new kind of inequality. What should you learn in this lesson?
Students formulate the objectives of the lesson
To solve the quadratic inequality, it is enough to look at the graph of the function y = a x 2 + bx + c. What knowledge about the quadratic function will we need to compile an algorithm for solving inequalities? (students offer different options). The teacher corrects and structures the proposed.
Then the steps of the algorithm appear on the presentation slide, at the same time an example of solving a quadratic inequality appears ( slide 29).
materialization
Students begin to solve quadratic inequalities (task on the board). One student solves the inequality at the blackboard according to the algorithm. Control is carried out using presentation slides (step by step solution) (slide 30 and computer presentation)
Solve the inequalities:
x 2 +6x-92 +6x-9≤0, x 2 +6x-90, x 2 +6x-9≥0.
The purpose of the work: to fill in the scheme for solving quadratic inequalities for a 0 depending on the sign of the discriminant of the corresponding quadratic equation ( Appendix 2 ). After doing tasks results are checked with slide 31.
IV. Application of knowledge, formation of skills and abilities
At the GIA, tasks are often offered to establish correspondence. Now we will perform such tasks orally and see how we learned the new material, if there are any mistakes and why.
oral work (slides on computers)
- And now let's solve a quadratic inequality with a parameter, such tasks are also found on the GIA in part 2. Students offer solutions, discuss and write on cards. Step-by-step verification is carried out using slides 32, 33.
Then a TEST for two options is carried out ( Annex 3 ). After completion, students exchange forms and check. Answers ( slide 34)
Motivation
– Do quadratic inequalities find application in the world around us?! Or maybe it's just a whim of mathematicians?! Probably, not! After all, any phenomenon can be described using a function, and the ability to solve inequalities allows you to answer the question, for which values of the argument this function is positive, and for which it is negative.
V. Homework(slide 35)
§ 41, No. 41.02-06 (a, d). Make a scheme for solving inequalities for a
In additional literature or with the help of Internet resources, try to find areas of application of quadratic inequalities that were not considered in the lesson.
YI. Search for the use of the parabola on the Internet.
Parable
A wise man was walking, and three people were walking towards him, who were carrying carts with stones for construction under the hot sun. The sage stopped and asked each one a question.
He asked the first one: “What, did you do all day?”
And he replied with a grin that he had been carrying cursed stones all day.
The sage asked the second: “What did you do all day?” And he replied: "But I conscientiously did my job."
And the third smiled, his face lit up with joy: “And I took part in the construction of the temple!”
Guys, let's try with you to evaluate each of our work for the lesson ..
The topic of the lesson is "Solving inequalities and their systems" (mathematics grade 9)
Lesson type: lesson of systematization and generalization of knowledge and skills
Lesson technology: critical thinking development technology, differentiated learning, ICT technologies
The purpose of the lesson: repeat and systematize knowledge about the properties of inequalities and methods for solving them, create conditions for the formation of skills to apply this knowledge in solving standard and creative problems.
Tasks.
Educational:
to promote the development of students' skills to summarize the knowledge gained, to analyze, synthesize, compare, draw the necessary conclusions
organize the activities of students to apply the acquired knowledge in practice
to promote the development of skills to apply the acquired knowledge in non-standard conditions
Developing:
continue the formation of logical thinking, attention and memory;
improve the skills of analysis, systematization, generalization;
creating conditions that ensure the formation of self-control skills in students;
promote the acquisition of the necessary skills for independent learning activities.
Educational:
to cultivate discipline and composure, responsibility, independence, a critical attitude towards oneself, attentiveness.
Planned educational outcomes.
Personal: responsible attitude to learning and communicative competence in communication and cooperation with peers in the process of educational activities.
Cognitive: the ability to define concepts, create generalizations, independently choose the grounds and criteria for classification, build logical reasoning, draw conclusions;
Regulatory: the ability to identify potential difficulties in solving educational and cognitive tasks and find means to eliminate them, to evaluate their achievements
Communicative: the ability to express judgments using mathematical terms and concepts, formulate questions and answers during the task, share knowledge between group members to make effective joint decisions.
Basic terms, concepts: linear inequality, quadratic inequality, system of inequalities.
Equipment
Projector, teacher's laptop, several netbooks for students;
Presentation;
Cards with basic knowledge and skills on the topic of the lesson (Appendix 1);
Cards with independent work (Appendix 2).
Lesson Plan
| During the classes |
|||
| Technological stages. Target. | Teacher activity | Student activities | |
| Introductory-motivational component |
|||
| 1.Organizational Purpose: psychological preparation for communication. | Hello. Good to see you all. Sit down. Check if everything is ready for the lesson. If it's all right, then look at me. | Hello. Check accessories. Getting ready for work. | Personal. Responsible attitude to teaching is formed. |
| 2.Updating knowledge (2 min) Purpose: to identify individual gaps in knowledge on the topic | The topic of our lesson is "Solving inequalities with one variable and their systems." (slide 1) Here is a list of basic knowledge and skills on the topic. Assess your knowledge and skills. Arrange the appropriate icons. (slide 2) | Assess their own knowledge and skills. (Attachment 1) | Regulatory Self-assessment of your knowledge and skills |
| 3.Motivation (2 minutes) Purpose: to provide activities to determine the objectives of the lesson . | In the work of the OGE in mathematics, several questions of both the first and second parts determine the ability to solve inequalities. What do we need to repeat in the lesson in order to successfully cope with these tasks? | Discuss, call questions for repetition. | Cognitive. Identify and formulate a cognitive goal. |
| Reflection stage (content component) |
|||
| 4.Self-assessment and choice of trajectory (1-2 min) | Depending on how you assessed your knowledge and skills on the topic, choose the form of work in the lesson. You can work with the whole class with me. You can work individually on netbooks, using my advice, or in pairs, helping each other. | Determined with an individual learning path. Swap if necessary. | Regulatory identify potential difficulties in solving educational and cognitive tasks and find means to eliminate them |
| 5-7 Work in pairs or individually (25 min) | The teacher advises students working independently. | Students who know the topic well work individually or in pairs with a presentation (slides 4-10) Perform tasks (slides 6.9). | cognitive the ability to define concepts, create generalizations, build a logical chain Regulatory the ability to determine actions in accordance with the educational and cognitive task Communicative the ability to organize educational cooperation and joint activities, work with a source of information Personal responsible attitude to learning, readiness and ability for self-development and self-education |
| 5. Solution of linear inequalities. (10 min) | What properties of inequalities do we use to solve them? Can you distinguish between linear, quadratic inequalities and their systems? (slide 5) How to solve a linear inequality? Execute the solution. (slide 6) The teacher follows the decision at the blackboard. Check if the solution is correct. | They name the properties of inequalities, after answering or in case of difficulty, the teacher opens slide 4. Name the distinguishing features of inequalities. Using the properties of inequalities. One student solves inequality No. 1 at the blackboard. The rest are in notebooks, following the decision of the respondent. Inequalities No. 2 and 3 are performed independently. Check with the prepared answer. | cognitive Communicative |
| 6. Solution of quadratic inequalities. (10 min) | How to solve inequality? What is this inequality? What methods are used to solve quadratic inequalities? Recall the parabola method (slide 7) The teacher recalls the steps for solving an inequality. The interval method is used to solve inequalities of the second and higher degrees. (slide 8) To solve quadratic inequalities, you can choose a method that is convenient for you. Solve inequalities. (slide 9). The teacher monitors the progress of the solution, recalls ways to solve incomplete quadratic equations. The teacher advises individually working students. | Answer: We solve the square inequality using the parabola method or the interval method. The students follow the decision on the presentation. At the blackboard, students take turns solving inequalities No. 1 and 2. Check with the answer. (to solve nerve-va No. 2, you need to remember the way to solve incomplete quadratic equations). Inequality No. 3 is solved independently, checked with the answer. | cognitive the ability to define concepts, create generalizations, build reasoning from general patterns to particular solutions Communicative the ability to present in oral and written form a detailed plan of one's own activities; |
| 7. Solving systems of inequalities (4-5 min) | Recall the steps involved in solving a system of inequalities. Solve the system (Slide 10) | Name the stages of the solution The student decides at the blackboard, checks with the solution on the slide. | |
| Reflective-evaluative stage |
|||
| 8. Control and verification of knowledge (10 min) Purpose: to identify the quality of assimilation of the material. | Let's test your knowledge on the topic. Solve tasks on your own. The teacher checks the result according to the prepared answers. | Perform independent work on options (Appendix 2) After completing the work, the student reports this to the teacher. The student determines his grade according to the criteria (slide 11). Upon successful completion of the work, he can proceed to an additional task (slide 11) | Cognitive. Build logical chains of reasoning. |
| 9. Reflection (2 min) Purpose: an adequate self-assessment of one's capabilities and abilities, advantages and limitations is formed | Is there an improvement in results? If you still have questions, refer to the textbook at home (p. 120) | They evaluate their own knowledge and skills on the same piece of paper (Appendix 1). Compare with self-esteem at the beginning of the lesson, draw conclusions. | Regulatory Self-assessment of your achievements |
| 10. Homework (2 min) Purpose: consolidation of the studied material. | Determine homework based on the results of independent work (slide 13) | Determine and record an individual task | Cognitive. Build logical chains of reasoning. Produce analysis and transformation of information. |
List of used literature: Algebra. Textbook for grade 9. / Yu.N.Makrychev, N.G.Mindyuk, K.I.Neshkov, S.B.Suvorova. - M.: Enlightenment, 2014
