Work program of the mathematics course for 8th grade students “Mathematics. Intelligence. Creation"

Work program for an elective course in mathematics for grades 8-9

Explanatory note

The work program of the elective course in mathematics for grades 8-9 is compiled on the basis of the requirements of the Federal State Educational Standard of Basic General Education, an approximate program of basic general education in mathematics.

The course is focused on textbooks for students in grades 8 and 9 of general education institutions, edited by a team of authors: A.G. Merzlyak, V.B. Polonsky, M.S. Yakir.

General characteristics of the training course

This course systematizes the content of the academic subjects Algebra and Geometry and serves as a preparatory basis for students in grades 8 and 9 in preparation for the state final certification.

A characteristic feature of this elective subject is the systematization and generalization of students’ knowledge, consolidation and development of skills on main topics.

The course involves theoretical and practical classes. Particular attention will be paid to the study of assessment criteria and the formulation of solutions and answers in each problem.

The study of mathematics in basic school is aimed at achieving the following goals:

1) in the direction of personal development

• development of logical and critical thinking, speech culture, ability for mental experimentation;
• developing in students intellectual honesty and objectivity, the ability to overcome thought stereotypes arising from everyday experience;
• nurturing personality qualities that ensure social mobility and the ability to make independent decisions;
• formation of the qualities of thinking necessary for adaptation in the modern information society;
• developing interest in mathematical creativity and mathematical abilities;

2) in the meta-subject direction

• formation of ideas about mathematics as part of universal human culture, about the importance of mathematics in the development of civilization and modern society;
• development of ideas about mathematics as a form of description and method of understanding reality, creating conditions for acquiring initial experience in mathematical modeling;
• the formation of general methods of intellectual activity, characteristic of mathematics and which are the basis of cognitive culture, significant for various spheres of human activity;

3) in the subject area

• mastering mathematical knowledge and skills necessary for continuing education in high school or other educational institutions, studying related disciplines, and applying them in everyday life;
• creating the foundation for mathematical development, the formation of thinking mechanisms characteristic of mathematical activity.

Additionally, the work program identifies the following goals: the formation of basic mathematical training in all students, which forms the functional basis of basic general education.

Achieving the above goals involves solving the following tasks :

• systematize the knowledge and skills necessary for application in practical activities, as well as for continuing education, tested during the OGE;
• to develop stable skills in solving basic-level problems, to ensure targeted preparation of students for final tests;
• improve the ability to complete tasks on a given topic, develop computational skills;
• carry out systematic correctional work with students with a low level of ability to master educational material;
• consider the main types of problems included in the second part of the OGE KIMs for students who want to prepare more thoroughly and have enough knowledge to master more difficult material in algebra and geometry.

In mathematics classes, students learn to think clearly and clearly express thoughts, work using various algorithms, use mathematical language to write arguments concisely and concisely, creative thinking, and the ability to apply theoretical knowledge in mathematics in various life situations.

Personal, meta-subject and subject results

of personal, meta-subject and subject learning outcomes in students that meet the requirements of the Federal State Educational Standard for Basic General Education.

Personal results:

1. nurturing Russian civic identity: patriotism, respect for the Fatherland, awareness of the contribution of domestic scientists to the development of world science;
2. responsible attitude to learning, students’ readiness and ability for self-development and self-education based on motivation for learning and knowledge;
3. conscious choice and construction of a further individual educational trajectory based on orientation in the world of professions and professional preferences, taking into account sustainable cognitive interests, as well as on the basis of the formation of a respectful attitude towards work, development of experience of participation in socially significant work;
4. the ability to control the process and result of educational and mathematical activities;
5. critical thinking, initiative, resourcefulness, activity in solving mathematical problems.

Meta-subject results:

1. the ability to independently determine the goals of one’s learning, set and formulate new goals for oneself in one’s studies, develop the motives and interests of one’s cognitive activity;
2. the ability to correlate one’s actions with the planned results, monitor one’s activities in the process of achieving results, determine methods of action within the framework of the proposed conditions and requirements, and adjust one’s actions in accordance with the changing situation;
3. the ability to define concepts, create generalizations, establish analogies, classify, independently select grounds and criteria for classification;
4. the ability to establish cause-and-effect relationships, build logical reasoning, inference (inductive, deductive and by analogy) and draw conclusions;
5. initial ideas about the ideas and methods of mathematics as a universal language of science and technology, a means of modeling phenomena and processes;
6. the ability to see a mathematical problem in the context of a problem situation in other disciplines, in the surrounding life;
7. the ability to understand and use mathematical visual aids (graphs, tables, diagrams, etc.) for illustration, interpretation, argumentation;
8. the ability to put forward hypotheses when solving a problem and understand the need to test them;
9. understanding the essence of algorithmic instructions and the ability to act in accordance with the proposed algorithm.

Subject results:

1. awareness of the importance of mathematics in human everyday life;
2. an idea of ​​mathematical science as a sphere of mathematical activity, of the stages of its development, of its significance for the development of civilization;
3. development of skills to work with educational mathematical text (analyze, extract the necessary information), accurately and competently express one’s thoughts using mathematical terminology and symbols, carry out classifications and logical justifications;
4. mastery of the basic conceptual apparatus for the main sections of content;
5. systematic knowledge about functions and their properties;
6. practically significant mathematical skills and abilities, their application to solving mathematical and non-mathematical problems, implying the ability to:

• perform calculations with real numbers;
• solve equations, inequalities, systems of equations and inequalities;
• solve word problems in an arithmetic way, by composing and solving equations, systems of equations and inequalities;
• carry out practical calculations: calculations with percentages;
• perform identical transformations of rational expressions;
• explore functions and build their graphs;
• read and use information presented in the form of a table, chart (column or pie);
• solve geometric problems.

Value guidelines for the content of the academic subject

One of the main goals of studying mathematics is the development of thinking, especially the formation of abstract thinking. In the process of studying the course, logical and algorithmic thinking is formed, as well as such qualities of thinking as strength and flexibility, constructiveness and criticality. For adaptation in the modern information society, an important factor is the formation of a mathematical style of thinking, including induction and deduction, generalization and specification, analysis and synthesis, classification and systematization, abstraction and analogy.

Teaching mathematics gives schoolchildren the opportunity to learn how to plan their activities, evaluate them critically, make independent decisions, and defend their views and beliefs. In the process of studying the course, schoolchildren learn to express their thoughts clearly and comprehensively, acquire the skills of clear and competent execution of mathematical notes, while the use of mathematical language allows students to develop competent oral and written speech.

Planned learning outcomes

Numbers and calculations. Algebraic expressions

The student will learn:

• perform identical transformations of expressions using a wide range of methods and techniques;

The student will have the opportunity to:

• perform multi-step transformations of rational expressions using a wide range of methods and techniques.

Equations and inequalities

The student will learn:

• solve basic types of rational equations and inequalities, systems of two equations with two variables;
• apply graphical representations to study equations and inequalities, study and solve systems of equations with two variables.

The student will have the opportunity to:

• master special techniques for solving equations and inequalities and their systems;
• apply graphical representations to study equations and inequalities and their systems containing letter coefficients.

Functions. Coordinates on a straight line and plane

The student will learn:

• build graphs of elementary functions, explore the properties of numerical functions based on studying the behavior of their graphs.

The student will have the opportunity to:

• use functional representations and properties of functions to solve mathematical problems.

Geometry

The student will learn:

• solve problems related to finding geometric quantities.

The student will have the opportunity to:

• master methods for solving calculation problems.

Probability theory

The student will learn:

• solve combinatorial problems to find the number of objects or combinations.

The student will have the opportunity to:

• learn some special techniques for solving combinatorial problems.

Number sequences

The student will learn:

• apply formulas related to arithmetic and geometric progressions.

The student will have the opportunity to:

• understand arithmetic and geometric progressions as functions of a natural argument; connect arithmetic progression with linear growth, geometric progression with exponential growth.

Place of the subject in the curriculum

The curriculum of the MBOU "Pokanaevskaya Secondary School" allocates 0.5 hours per week to study the elective course in grades 8 and 9, for a total of 17 hours per year, according to 34 working weeks. This program is intended for the general education classroom. The duration of the program is two academic years.

Forms of organization of the educational process

• individual;
• group;
• individual-group;
• frontal.

Forms of control and evaluation

• thematic (OGE training test);
• final (OGE training test).

Program content

8th grade

9th grade

Educational and methodological

material and technical support of the educational process:

Educational and methodological kit

1. Algebra: 7th grade: textbook for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, M. S. Yakir. – M.: Ventana-Graf, 2020.
2. Algebra: 7th grade: didactic materials: a manual for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, E. M. Rabinovich, M. S. Yakir. – M.: Ventana-Graf, 2018
3. Algebra: 8th grade: textbook for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, M. S. Yakir. – M.: Ventana-Graf, 2020.
4. Algebra: 8th grade: didactic materials: a manual for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, E. M. Rabinovich, M. S. Yakir. – M.: Ventana-Graf, 2015.
5. Algebra: 9th grade: textbook for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, M. S. Yakir. – M.: Ventana-Graf, 2020.
6. Algebra: 9th grade: didactic materials: a manual for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, E. M. Rabinovich, M. S. Yakir. – M.: Ventana-Graf, 2018.
7. Geometry: 7th grade: textbook for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, M. S. Yakir. - M.: Ventana-Graf. 2018
8. Geometry: 7th grade: didactic materials: a manual for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, E. M. Rabinovich, M. S. Yakir. - M.: Ventana-Graf. 2017
9. Geometry: 8th grade: textbook for students of general education institutions / A. G. Merzlyak, V. B. Polonsky, M. S. Yakir. - M.: Ventana-Graf. 2018
10. Geometry: 8th grade: didactic materials: a manual for students of general education organizations / A. G. Merzlyak, V. B. Polonsky, E. M. Rabinovich, M. S. Yakir. - M.: Ventana-Graf. 2017.
11. Geometry: 9th grade: textbook for students of general education organizations / A. G. Merzlyak, V. B. Polonsky, M. S. Yakir. - M.: Ventana-Graf. 2020.
12. Geometry: 9th grade: didactic materials: a manual for students of general education organizations / A. G. Merzlyak, V. B. Polonsky, E. M. Rabinovich, M. S. Yakir. - M.: Ventana-Graf. 2018.

Printed manuals

1. Mathematics worksheets;
2. Portraits of outstanding figures in the field of mathematics.

Information media

1. Materials posted on the sites: https://www.mathgia.ru, www.fipi.ru; www.ege.edu.ru; www.alleхlarin.ru; https://sdamgia.ru/

Technical means

1. Computer;
2. Multimedia projector;
3. Screen (on a tripod or mounted);
4. Interactive board.

Educational-practical and educational-laboratory equipment

1. Magnetic board with a coordinate grid;
2. Sets “Parts of a whole on a circle”, “Simple fractions”;
3. Sets of geometric solids;
4. Set of drawing tools: ruler, protractor, square (30°, 60°), square (45°, 45°), compass.

Calendar and thematic planning for the work program. 8th grade

Calendar and thematic planning for the work program. 9th grade

1

Work program for an elective course in mathematics, grade 8, elective course in mathematics (grade 8)

2019-2020 academic year

Elective course program “Real problems in mathematics”

1. Explanatory note

1. Regulatory and legal basis of the work program.

The elective course program in mathematics is compiled in accordance with the following documents:

1. Order of the Ministry of Education and Science of the Russian Federation dated May 17, 2012 No. 413 “On approval and implementation of the federal state educational standard of secondary general education” (as amended on December 29, 2014 No. 1645 “On amendments to the order of the Ministry of Education and Science of the Russian Federation”) Federation dated May 17, 2012 No. 413 “On approval of the federal state educational standard of secondary (complete) general education”, dated December 31, 2020 No. 1578 “On amendments to the federal state educational standard of secondary general education, approved by order of the Ministry of Education and Science of the Russian Federation” Federation dated May 17, 2012 No. 413”, dated June 29, 2020 No. 613 “On amendments to the federal state educational standard of secondary general education, approved by order of the Ministry of Education and Science of the Russian Federation dated May 17, 2012 No. 413”).
2. Order of the Ministry of Education and Science of Russia dated August 23, 2020 No. 816 “On approval of the Procedure for the use of e-learning and distance learning technologies by organizations engaged in educational activities in the implementation of educational programs.”
3. Order of the Ministry of Education of the Russian Federation dated December 28, 2020 No. 345 “On the federal list of textbooks recommended for use in the implementation of educational programs of primary general, basic general, and secondary general education that have state accreditation” (as amended on May 8, 2020 No. 233).
4. Resolution of the Chief State Sanitary Doctor of Russia dated December 29, 2010 No. 189, 2.4.2.2821-10 “On approval of SanPiN 2.4.2.2821-10 “Sanitary and epidemiological requirements for the conditions and organization of training in educational institutions.”
5. The main educational program of secondary general education of MBOU Secondary School No. 1 with in-depth study of individual subjects (Order No. 326 dated August 31, 2018).
6. Programs. Algebra grades 7-8 Federal State Educational Standards/aut.-comp. I.I. Zubareva, A.G. Mordkovich. – M. Mnemosyne, 2014 – 64 p.

The program proposes the author's approach to structuring educational material, determining the sequence of its study, ways to form a system of knowledge, skills and methods of activity, development, education and socialization of students. The program is a key component of the educational and methodological package in mathematics for primary schools (authors A.G. Mordkovich; Mnemosyne publishing house, L. S. Atanasyan; Prosveshcheniye publishing house).

1. General characteristics of the elective course.

The program of the elective course “Real Problems of Mathematics” is focused on acquiring certain experience in solving problems of various types, allowing the student to receive additional preparation for passing the exam in mathematics for a course of secondary general education. The peculiarity of the adopted approach of the elective course “Real Problems of Mathematics” is that small fragments are offered for mathematics classes, designed for 2-3 lessons, relating to various sections of school mathematics.

Each lesson, as well as all of them as a whole, is aimed at developing students’ interest in the subject, introducing them to new ideas and methods of solution, and expanding their understanding of the basic material studied.

This course offers students an introduction to mathematics as a general cultural value, developing their understanding that mathematics is a tool for understanding the world around them and themselves.

If experiment occupies a very important place in the study of natural science subjects, and it is in the process of experiment and discussion of its organization and results that the student’s interests in a given subject are formed and developed, then in mathematics the equivalent of experiment is problem solving. Actually, the entire mathematics course can be built and, as a rule, is built on solving problems of varying degrees of importance and difficulty.

1. Course learning objectives.

Prepare students to take the mathematics exam in the form of the OGE in accordance with the requirements of the Federal State Educational Standard; Providing individual and systematic assistance to tenth-graders when repeating a mathematics course and preparing for exams. Generalization and systematization, expansion and deepening of knowledge on course topics; acquiring practical skills to complete tasks; increasing the level of mathematical training of schoolchildren.

1. General characteristics of the program.

The elective course is aimed at preparing students to pass the exam in mathematics in the form of the OGE. The main feature of this course is the practice of tasks in all sections of the basic school mathematics course: arithmetic, algebra, statistics and probability theory, geometry.

The elective course “Real Problems of Mathematics” is designed for 35 hours to work with 8th grade students. The course provides for a re-examination of theoretical material in mathematics, therefore it is of great general educational importance, promotes the development of logical thinking, outlines and uses a number of interdisciplinary connections and is aimed primarily at eliminating “gaps” in the basic component of mathematics, systematizing knowledge in the main sections of the school curriculum.

1. Information about changes made to the sample program or original program and their rationale.

Distribution of hours during the academic year by quarters

To implement the elective course, the educational and methodological complex (hereinafter referred to as the EMC) of the line of textbooks for grades 7-9 by A.G. is used. Mordkovich and a team of authors, Atanasyan, which are included in the federal list of textbooks recommended (approved) for use in the educational process in educational institutions that implement educational programs of general education and have state accreditation and provide training in mathematics, in accordance with the Federal State Educational Standard.

1. Information on the number of teaching hours for which the work program is designed (in accordance with the curriculum, annual calendar educational schedule), including the number of hours for laboratory, practical and control lessons, lessons for repetition and generalization of the studied material, as well as hours allocated for excursions, projects, research, etc.

Educational and thematic plan

1. Information about the teaching technologies used, lesson forms, etc.

An important role in the educational process is played by forms of organization of training or types of training, which are sustainable ways of organizing the pedagogical process. The educational process of the elective course provides for the following methods and forms of work:

• presentation of new material by the teacher in the form of a lecture;
• differentiated approach to practical classes: assignments of varying difficulty levels are selected for all course topics;
• independent work with educational literature;
• individual consultations.

.

To develop students' interest in the subject being studied and, as a result, improve the quality of knowledge, modern innovative technologies are used, such as:

• Technology of level differentiation of training
• Problem-based developmental learning technology
• Health-saving technologies
• Collaboration technologies
• Gaming technologies

1.4.4 Types and forms of intermediate and final control

No less important are the forms of control of knowledge, abilities, skills (current control, diagnostic, milestone, final). The forms of such control are also different. This can include tests, independent homework, defense of essays and projects, transfer exams, individual interviews, diagnostic work, as well as a comprehensive interview and defense of the topic. To consolidate the fundamentals of the theoretical base, it is advisable to conduct test lessons, mathematical tests, dictations, and quick surveys.

Assessment and control of students’ mastery of the elective course “Real Problems of Mathematics”:

Methods for determining performance: completing test tasks of varying difficulty levels.

Forms for summing up the implementation of the course program: tracking results on the final test at the end of the academic year.

1. Planned results of studying an academic subject or course.

Students will understand

• the essence of the concept of algorithm; examples of algorithms;
• how mathematical formulas, equations and inequalities are used; examples of their application to solve mathematical and practical problems;
• how mathematically defined functions can describe real dependencies; give examples of such a description;
• how the needs of practice led mathematical science to the need to expand the concept of number;
• the importance of mathematics as a science;
• the importance of mathematics in everyday life, as well as as an applied tool in future professional activities

will learn

• solve tasks similar to those of the state final certification (basic part)

will gain experience:

• working in a group, both in class and outside,
• working with information, including information received via the Internet

Methodological recommendations for program implementation.

The main didactic tool for the proposed course are the texts of the types of problems under consideration, which can be selected from a variety of collections, various versions of the OGE, or compiled by the teacher himself.

The course is provided with handouts prepared on the basis of the reference list attached below.

For more effective work of students, it is advisable to use posters with supporting notes or media resources as didactic tools.

1. Requirements for the level of training of graduates.

As a result of studying an elective course in mathematics, a student

will be able to understand:

• the importance of mathematical science for solving problems arising in theory and practice; the breadth and limitations of the application of mathematical methods to the analysis and study of processes and phenomena in nature and society;
• the importance of practice and issues arising in mathematics itself for the formation and development of mathematical science; the history of the development of the concept of number, the creation of mathematical analysis, the emergence and development of geometry;
• the essence of the concept of mathematical proof; examples of evidence;
• the essence of the concept of algorithm; examples of algorithms;
• how mathematical formulas, equations and inequalities are used; examples of their application to solve mathematical and practical problems;
• how mathematically defined functions can describe real dependencies; give examples of such a description;
• compose letter expressions and formulas according to the conditions of the tasks; carry out numerical substitutions in expressions and formulas and perform corresponding calculations, substitute one expression into another; express one variable from formulas in terms of the others;
• solve word problems using the algebraic method, interpret the result obtained, select solutions based on the formulation of the problem;
• find the values ​​of a function given by a formula, table, or graph using its argument; find the value of the argument by the value of the function specified by the graph or table;
• determine the properties of a function from its graph; apply graphical representations when solving equations, systems, inequalities;
• describe the properties of the studied functions, build their graphs
• the universal nature of the laws of logic of mathematical reasoning, their applicability in various areas of human activity;
• the probabilistic nature of various processes and patterns of the surrounding world;
• use acquired knowledge and skills in practical activities and everyday life

1. Contents of the elective course

Sections of the program are built on a modular principle, that is, they are logically complete and relatively independent sections, which allows students to analyze their knowledge on each topic and study material that is not included in the compulsory curriculum.

1. The section “Analysis of charts, tables, graphs” includes working on tasks where data is presented in tabular form, in the form of tables with standards, as well as various types of charts. Students gain the skills to analyze information presented on graphs, determine the amplitude values ​​of quantities, and the difference between these values.

2. The section “The simplest word problems” develops the skill of solving problems on proportions, percentages, finding a quantity by its part, and others.

3. The section “Statistics, probabilities” includes working out problems on classical probabilities, theorems about probabilistic events, as well as statistics.

4. The section “Text problems of increased complexity” includes tasks on movement on water, alloys, mixtures, teamwork, tasks on movement in a straight line.

5. The section “Calculations using formulas” allows you to practice the skill of finding the meaning of expressions presented in the form of various formulas.

6. The “Geometric Problems” section allows you to develop the skill of applying theoretical knowledge in practice.

Calendar - thematic planning

Training and metodology complex.

1.. V.I. Zhokhov et al. DM in algebra for grade 8; B.G. Ziv et al. DM in algebra for 8th grade;

2.. Ershova A.P., Goloborodko V.V., Ershova A.S. Independent and test work in algebra and geometry for grade 8;

3.. Yu.N. Makarychev et al. DM in algebra for 8th grade.

4. Website sdamgia.rf-GIA 2020 – mathematics. Dmitry Gushchin's training system.

CORRECTION SHEET

Work program of the elective course “Practicum in Mathematics”, grade 8

Elective course program in mathematics

"Mathematics Workshop"

for 8th grade

Explanatory note

The program of this elective course is focused on the consideration of individual questions of mathematics, which are included in the content of the state final certification in mathematics for the basic school course. The course complements and develops the school mathematics course, and also provides information support for further education in high school and is focused on meeting the educational needs of schoolchildren, their analytical and synthetic abilities. The main idea of ​​this elective course is to expand and deepen students’ knowledge in certain areas of mathematics, to ensure students’ strong and conscious mastery of the system of mathematical knowledge and skills, including those necessary for passing the final exam. In the process of mastering the content of this course, students acquire new knowledge, enrich their life experience, get the opportunity to practically apply their intellectual and organizational abilities, develop their communication abilities, and master general educational skills. Mastering the subject content of the course and the process of studying it itself become the means that ensure the transition from student learning to their self-education. Studying the course involves ensuring positive motivation for students to repeat previously studied material, highlighting key course questions intended for repetition, using diagrams, models, reference notes, reference books, computer tests (including interactive ones), and independently compiling (modeling) tests. The methodological basis of the proposed course is an activity-based approach to teaching mathematics. This approach involves teaching not only ready-made knowledge, but also activities to acquire this knowledge, methods of reasoning, and evidence. In this regard, in the process of studying the course, students are offered tasks that stimulate their independent discovery of mathematical facts, new, previously unknown techniques and ways of solving problems. The developmental and educational potential of the elective course is fully consistent with the basic ideas contained in the second generation federal educational standards.

Purpose of the course

: assisting students in choosing a further profile of study in high school: creating conditions for self-realization of students in the process of educational activities, development of students’ mathematical and intellectual abilities, generalized mental skills.

Tasks _

:

1. Expansion and deepening of the school mathematics course.

2. Updating, systematizing and generalizing students’ knowledge in mathematics.

3. Formation in students of an understanding of the role of mathematical knowledge as a tool that allows them to choose the best course of action from many possible ones.

4. Developing students' interest in learning mathematics.

5. Expanding the scientific horizons of students.

6. Teaching students how to solve educational and life problems, how to analyze information received in different forms.

7. Orientation of students to professions significantly related to mathematics.

The organization of classes in an elective course should differ significantly from a classroom course: the student must be given sufficient time to think, and any attempts at independent reasoning, putting forward hypotheses, and ways to solve problems should be welcomed.

The course includes the possibility of differentiated learning. The following types of activities are used in the classroom: discussion, testing, designing tests, assignments, research activities, working with text, debates, review lectures, mini-lectures, seminars and workshops on problem solving, consultations are provided. It is essential to organize work on teaching how to fill out final certification forms, which will certainly help relieve students’ psychological stress before the exam procedure.

In this regard, the main priorities

methods of studying the elective course:

• learning through experience and collaboration;
• interactivity (work in small groups, role-playing games, trainings, outside classes - project method);
• personal-activity and subject-subjective approach (more attention to the student’s personality rather than the teacher’s goals, their equal interaction).

Forms and methods of control

: testing, self-testing, mutual testing of students with each other, interview, written and oral tests, written tests, observation.

The number of tasks in tests for each topic is not the same; they are complex in nature, and most of them are designed to reveal the level of knowledge and skills of the test taker.

Methodological recommendations for program implementation

. The main didactic tool for the proposed course are the texts of the types of problems under consideration, which can be selected from a variety of collections, various options, an open bank of GIA tasks, or compiled by the teacher. For more effective work of students, it is advisable to use media resources as didactic tools, organize independent work of students using distance educational technologies, including carrying out consultation procedures through a forum, chat, and e-mail.

You have 34 hours to study the course. The course consists of 4 sections: “Numbers and Calculations”, “Expressions and Transformations”, “Equations and Inequalities”, “Functions”. To study the topics “Equations and Inequalities”, “Functions”, 7 and 4 hours are allocated, respectively, due to the fact that they are studied in most detail in the 9th grade.

Course content

Numbers and calculations (11h)

Rational numbers. Standard type of number. Interest. Operations with rational numbers. Comparison of rational numbers. Finding the percentage of a number. Finding a number from a given percentage. Finding the percentage relationship between two numbers. The absolute value of a number. Degree with a natural indicator. Square root. Properties of degree. Properties of square root.

Expressions and transformations (11h)

Literal expressions. The scope of the literal expression. Factoring a polynomial. Addition, subtraction and multiplication of polynomials. Abbreviated multiplication formulas. Algebraic fraction. Reducing fractions. Operations with algebraic fractions. Converting rational expressions. Properties of square roots and their application in transformations.

Equations and inequalities (7 hours)

Solution of the equation. Solution of inequality. Linear equation. Linear inequality. Quadratic equation. Quadratic inequality. Parameter. Equations with parameters.

Functions (4 hours)

Linear function and its properties. Quadratic function and its properties.

Final work (1 hour)

Requirements for the level of student preparation

As a result of studying mathematics in basic school, a student

will learn:

• the essence of the concept of mathematical proof; give examples of evidence;

• the essence of the concept of an algorithm; give examples of algorithms;

• how mathematical formulas, equations and inequalities are used; examples of their application to solve mathematical and practical problems;

• how mathematically defined functions can describe real dependencies; give examples of such a description;

‘ In addition to the knowledge specified in this section, the training level requirements also include the knowledge necessary to apply the skills listed below.

• how the needs of practice led mathematical science to the need to expand the concept of number;

• probabilistic nature of many patterns of the surrounding world; examples of statistical patterns and conclusions;

• the meaning of idealization, which allows solving problems of reality using mathematical methods, examples of errors that arise during idealization.

Arithmetic

The student will learn:

• perform oral arithmetic operations: addition and subtraction of two-digit numbers and decimal fractions with two signs, multiplication of single-digit numbers, arithmetic operations with ordinary fractions with a single-digit denominator and numerator;

• move from one form of writing numbers to another, represent a decimal fraction in the form of an ordinary fraction and, in the simplest cases, an ordinary fraction in the form of a decimal, percentages - in the form of a fraction and fractions - in the form of percentages; write large and small numbers using whole powers of ten;

• perform arithmetic operations with rational numbers, compare rational and real numbers; find in simple cases the values ​​of powers with integer exponents and roots; find the meaning of numerical expressions;

• round whole numbers and decimal fractions, find approximations of numbers with deficits and excesses, evaluate numerical expressions;

• use basic units of length, mass, time, speed, area, volume; express larger units through smaller ones and vice versa;

• solve word problems, including problems related to ratios and proportionality of quantities, fractions and percentages;

use acquired knowledge and skills in practical activities and everyday life

For

• solving simple practical calculation problems, including using, if necessary, reference materials, a calculator, and a computer;

• oral estimates and evaluation of the calculation results; checking the calculation result using various techniques;

• interpretation of the results of solving problems, taking into account the limitations associated with the real properties of the processes and phenomena under consideration.

Algebra

The student will learn:

• compose letter expressions and formulas according to the conditions of the tasks; carry out numerical substitutions in expressions and formulas and perform corresponding calculations, substitute one expression into another; express one variable from formulas in terms of the others;

• perform basic operations with powers with integer exponents, with polynomials and with algebraic fractions; factor polynomials; perform identical transformations of rational expressions;

• apply the properties of arithmetic square roots to calculate values ​​and transform numerical expressions containing square roots;

• solve linear, quadratic equations and rational equations that reduce to them, systems of two linear equations and simple nonlinear systems;

• solve linear and quadratic inequalities with one variable and their systems;

• solve word problems using the algebraic method, interpret the result obtained, select solutions based on the formulation of the problem;

• depict numbers as points on a coordinate line;

• determine the coordinates of a point on the plane, construct points with given coordinates; depict the set of solutions to a linear inequality;

• recognize arithmetic and geometric progressions; solve problems using the general term formula and the sum of the first few terms;

• find the values ​​of a function given by a formula, table, or graph using its argument; find the value of the argument by the value of the function specified by the graph or table;

• determine the properties of a function from its graph; apply graphical representations when solving equations, systems, inequalities;

• describe the properties of the studied functions, build their graphs;

use acquired knowledge and skills in practical activities and everyday life

• to perform calculations using formulas, to compile formulas expressing dependencies between real quantities; to find the required formula in reference materials;

• when modeling practical situations and studying constructed models using algebra;

• to describe the relationships between physical quantities using appropriate formulas when studying simple practical situations;

• when interpreting graphs of real relationships between quantities.

• to describe real situations in the language of geometry.

Thematic planning

Work program for an elective course in mathematics

WORKING PROGRAMM

ELECTIVE COURSE IN MATHEMATICS

"Mathematical workshop"

General level

education (grade): secondary general education grade 11

Number of hours: 33

Teacher:

EXPLANATORY NOTE

The work program of the elective course “Mathematical Practicum” in grade 11 was developed in accordance with the following regulatory documents:

· Law on Education in the Russian Federation dated December 29, 2012 No. 273-FZ (as amended on May 5, 2014);

· Federal state educational standard of secondary general education (approved by order of the Ministry of Education and Science of the Russian Federation dated May 17, 2012 N 413);

· Curriculum of MBOU ______________ secondary school for the 2019-2020 academic year;

· Regulations of the MBOU________________ Secondary School on the development by a teacher of a work program for an academic subject, course, and extracurricular activities.

The program of this elective course is focused on the consideration of individual questions of mathematics, which are included in the content of the unified state exam. The course will allow schoolchildren to systematize, expand and strengthen their knowledge. Prepare for further study of topics, learn to solve a variety of problems of varying complexity, contributes to the development and consolidation of computer skills. The teaching of the course is structured as a repetition provided for by the program of basic general education. Repetition is implemented in the form of a review of theoretical questions on the topic and solving problems in the form of multiple-choice tests. Deepening is implemented on the basis of teaching methods and techniques for solving mathematical problems that require the use of logical and operational culture, developing students’ scientific, theoretical and algorithmic thinking. Particular attention is paid to tasks that require students to apply knowledge in an unfamiliar (non-standard) situation. The 11th grade basic course is designed for 4 mathematics lessons per week. This time is not quite enough to solve the student’s main task: preparing for the final certification in the form of the Unified State Exam. To successfully solve this problem, it is necessary that the student himself is aware of his choice and makes every effort to his self-education.

Course objectives:

generalization and systematization, expansion and deepening of knowledge on the topics studied; acquiring practical skills in completing tasks, increasing the mathematical preparation of schoolchildren.

Course objectives:

· equip students with a system of knowledge for solving equations;

· With

develop skills in applying this knowledge when solving a variety of problems of varying complexity;

· prepare students for final certification in the form of the Unified State Exam;

· develop independent work skills;

· develop skills in working with reference literature;

· develop skills and abilities in research activities;

· promote the development of algorithmic thinking of students;

Rating system

student achievements: administrative verification of course material is not expected. At the end of each topic, the student fills out an individual control sheet. The result of mastering the program is Internet testing using test and measurement materials of the Unified State Examination at the final lesson

Place of the course in the curriculum

The work program for the elective course in grade 11 is compiled based on the requirements of the Federal State Educational Standard.

SOO for the results of mastering the main educational program of the MBOU ________________ Secondary School, taking into account the annual calendar educational schedule of the MBOU Kryukov Secondary School for the 2020 – 2020 academic year and will be completed in 33 hours.

PLANNED RESULTS OF STUDYING THE COURSE

— mastery of mathematical knowledge and skills necessary for final certification in the form of the Unified State Exam, continuing education and mastering the chosen specialty at the modern level;

— development of logical thinking, algorithmic culture of mathematical thinking and intuition necessary for continuing education;

— developing the skills of self-education, critical thinking, self-organization and self-control, teamwork, the ability to find, formulate and solve problems.

1. Problem solving

Goals:

generalize and systematize methods for solving word problems.

Students should know:

· Algorithm for composing equations, inequalities for solving problems;

· Techniques for solving quadratic, fractional-rational equations, quadratic inequalities using the interval method, based on the sign of the leading coefficient.

Students should be able to:

· perform arithmetic operations;

· analyze real numerical data, carry out practical calculations, use assessments and estimates of practical results;

· simulate real situations in the language of algebra, create equations and inequalities according to the conditions of the problem, explore the constructed models using the apparatus of algebra;

· use acquired knowledge and skills in practical and everyday life.

2.
Conversion expressions.
Goals:

generalize and systematize methods for converting numerical expressions.

Students should know:

• methods for converting numerical expressions containing roots, powers, logarithms;
• methods for converting trigonometric and exponential expressions.

Students should be able to:

• apply methods for converting numerical expressions containing roots, powers, logarithms in practice;
• apply methods for converting trigonometric and exponential expressions in practice.

3. Function lines

Goals:

teach the skills of “reading” graphs of a function, teach methods for studying a function using its given formula.

Students should know:

• function properties,
• function research algorithm,
• geometric and physical meaning of derivative,
• functional methods for solving equations and inequalities

Students should be able to:

• find the domain of definition of a function, the set of values ​​of a function;
• explore functions for extremum, parity, periodicity;
• find the derivative of a function;
• find the largest and smallest values ​​of a function, extrema of a function;
• use a functional approach in solving non-standard equations and inequalities.

4. Equations and inequalities. Systems of equations

Goals:

generalize and systematize students’ knowledge in solving equations, systems of equations and inequalities.

Students should know:

1. basic methods for solving equations,
2. basic methods for solving inequalities,
3. methods for solving systems of equations,
4. non-standard techniques for solving equations and inequalities.

Students should be able to:

• apply methods for solving equations in practice,
• apply methods for solving systems of equations in practice,
• use the properties of monotonicity of a function when solving logarithmic and exponential inequalities.

5. Tasks with a parameter

Goals:

consider various methods for solving equations and inequalities with parameters.

Students should know:

• methods for solving equations and inequalities with parameters.

Students should be able to:

• apply methods for solving equations and inequalities with parameters.

6. Geometry

Goals:

summarize and systematize the main topics of the planimetry and stereometry course; develop skills in solving planimetric and stereometric problems.

Students should know:

• properties of geometric figures (axioms, definitions, theorems),
• formulas for calculating geometric quantities.

Students should be able to:

• apply the properties of geometric shapes to justify calculations,
• apply formulas to calculate geometric quantities,
• write down complete solutions to problems, providing references to the properties of geometric shapes used.

SUBJECT CONTENT

1.
Problem solving.
Applied problems. Text problems.

2.
Expressions and transformations
Powers and roots. Trigonometric expressions. Logarithmic and exponential expressions.

3.
Function lines
The area of ​​definition of the function. Set of function values. Even and odd functions. Periodicity of the function. Derivative function. Geometric and physical meaning of derivative. The largest and smallest value of a function. Monotonicity of a function, extrema.

4.
Equations and inequalities.
Systems of equations Trigonometric equations. Exponential equations. Logarithmic equations. Irrational equations. Combined equations. Systems of equations. Non-standard methods for solving equations (using the domains of existence of functions, using the non-negativity of functions, using the boundedness of functions, using the properties of sine and cosine, using the derivative). Logarithmic and exponential inequalities.

5.
Tasks with a parameter
Equations with parameters. Inequalities with parameters. Systems of equations with a parameter. Problems with conditions.

6.
Geometry
Solution of planimetric problems on the topics: “Triangle”, “Parallelogram. Square”, “Trapezoid”, “Circle”. Solving stereometric problems on the topics: “Pyramid”, “Prism and parallelepiped”, “Cone and cylinder”, “Combination of bodies”.

THEMATIC PLANNING

CALENDAR - THEMATIC PLANNING