Work program of the circle “Preparation for the Unified State Examination in Mathematics” for 9th grade

Work program of the circle “Preparation for the Unified State Examination in Mathematics” for 9th grade

MBOU Lyceum of Architecture and Design No. 3 of Penza

Working program of additional educational classes in mathematics for children 14-15 years old

"Preparation for the OGE in mathematics."

teacher: Sudakova O.A.

Penza

2017-18 school year G.

Explanatory note

A written exam in mathematics for a basic school course is mandatory for 9th grade graduates. Club program “Mathematics. Workshop on preparation for the OGE" contributes to better mastery of the mathematics course and successful completion of the OGE.

The content of the circle program is determined based on:

1. Federal component of the state standard of basic general education in mathematics (Order of the Ministry of Education of Russia dated March 5, 2004 No. 1089.

“On approval of the federal component of state educational standards of primary, general, basic general and secondary (complete) general education”).

1. Provisions of the Federal State Educational Standard

basic general education (Order of the Ministry of Education and Science of Russia dated December 17, 2010

No. 1897 “On approval of the federal state educational standard of basic general education”).

The following components can be distinguished in the readiness of students to pass the exam in the form of the OGE:

- information readiness (awareness about the rules of conduct during the exam, awareness about the rules for filling out forms, etc.);

-subject or content readiness (readiness in a specific subject, ability to solve test tasks);

-psychological readiness (state of readiness - “mood”, internal disposition towards a certain behavior, focus on expedient actions, updating and adapting the individual’s capabilities for successful actions in an exam situation). The material included in the program involves repetition and deepening of the following sections of algebra and geometry.

The program of this circle has a number of features:

_ integration of different topics;

_ practical significance for students;

• the use of theoretical material in electronic form, which corresponds to the codifier of the content elements of the OGE test materials, which allows you to independently study the materials in case of missing classes - the use of test materials and assignments compiled on the basis of the test materials of the OGE in mathematics 2020. and allowing for monitoring and self-monitoring of knowledge in all blocks of OGE content.
• differentiated approach to graduates in preparation for the OGE.

The course is focused on developing basic mathematical competence and helps create positive learning motivation. In my work I apply the following principles of preparation for the OGE.

The first principle is training. During consultations, students are offered practice tests, by completing which children can assess their level of preparedness for exams.

The second principle is individual. During consultations, the student can not only complete the test, but also get answers to questions that caused difficulty.

The third principle is temporary. All practice tests should be carried out with a time limit so that students can control themselves - in how much time and how many tasks they manage to solve.

The fourth principle is controlling. This is necessary because the test, by its intended purpose, puts everyone on an equal footing and involves objective control of the results.

Following these principles, I develop in students the skills of self-education, critical thinking, independent work, self-organization and self-control.

Goals and objectives of the program

Classes are aimed at systematizing knowledge. Forms of organization of the educational process are aimed at deepening the individualization of the learning process. The main result is the successful completion of the exam tasks. The practical use of classes is the opportunity to successfully pass an algebra exam, as well as objectively assess the level of your knowledge.

The study of a multi-level program is aimed at achieving the following goals:

• formation of ideas about the ideas and methods of mathematics; about mathematics as a universal language of science, a means of modeling phenomena and processes;
• mastery of oral and written mathematical language, mathematical knowledge and skills necessary for studying school natural science disciplines, for continuing education and mastering the chosen specialty at the modern level;
• development of logical thinking, algorithmic culture, spatial imagination, development of mathematical thinking and intuition, creative abilities at the level necessary for continuing education and for independent activity in the field of mathematics and its applications in future professional activities;
• education of personal culture through mathematics: acquaintance with the history of the development of mathematics, the evolution of mathematical ideas, understanding the significance of mathematics for social progress.

In this program, the content of education is developed in the following directions:

• systematization of information about numbers; formation of ideas about the expansion of numerical sets from natural to real numbers; improvement of computing technology;

• development and improvement of the technique of algebraic transformations, solving equations, inequalities, systems;

• systematization and expansion of information about functions, improvement of graphic skills;

• development of ideas about probabilistic and statistical patterns in the surrounding world;

• improving mathematical development to a level that allows you to freely apply the learned facts and methods when solving problems from various sections of the course, as well as use them in non-standard situations;

• developing the ability to build and explore the simplest mathematical models when solving applied problems, problems from related disciplines, deepening knowledge about the peculiarities of applying mathematical methods to the study of processes and phenomena in nature and society.

Goals :

1. Generalization, deepening and systematization of knowledge on solving OGE options.

2. Show the need to prepare for successfully passing the OGE in accordance with the requirements of new educational standards.

3. Acquiring practical skills when solving OGE tasks..

4. Development of students’ logical thinking, cognitive interests, intellectual and creative abilities in the process of working with various sources of information, skills in performing standard tasks used in the testing and measuring materials of the OGE;

5. Fostering a work culture when working with digital educational resources.

Course Objectives

1. Equip students with a knowledge system for solving OGE options.

2. To develop skills and abilities in solving various problems of varying complexity.

3. Contribute to the formation of cognitive interest in mathematics and the development of students’ creative abilities.

4. Increase the level of mathematical preparation of students.

5. Prepare students to successfully pass the OGE.

Place of the subject in the federal basic curriculum

Club program “Mathematics. Workshop on preparation for the OGE "for students of the 9th grade of basic education is designed for 36 hours (1 hour per week during the school year) in accordance with the curriculum of MBOU LAD No. 3 for the 2017-18 school year. year.

Basic teaching aids:

• electronic teaching aids;
• theoretical materials in electronic and printed format;
• videos, tables, diagrams, mathematical models in electronic format;
• various options for testing and measuring materials for the OGE in mathematics.

Pedagogical technologies:

developmental education, ICT.

General characteristics of the course

The examination paper contains three modules: “Algebra”, “Geometry”, “Real Mathematics”.

The modules “Algebra” and “Geometry” include two parts corresponding to testing at the basic and advanced levels, the module “Real Mathematics” includes one part corresponding to testing at the basic level.

Parts 2 of the modules “Algebra” and “Geometry” are aimed at testing mastery of the material at an advanced level.

The Algebra module contains 11 tasks: part 1-8 tasks, part 3 tasks.

The "Geometry" module contains 8 tasks: in part 1-5 tasks, in part - 3 tasks.

The Real Mathematics module contains 7 tasks.

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

Program content

Topic 1 . Introducing the codifier and the demo version of the math option.

Topic 2 . Algebraic expressions and their transformations (4 hours)

Properties of degrees with natural and integer exponents. Properties of the arithmetic square root. Standard type of number. Abbreviated multiplication formulas. Methods of factorization. Expressing a variable from a formula. Finding the values ​​of a variable.

Topic 3 . Equations and inequalities and their systems. (4 hours)

Methods for solving various equations (linear, quadratic and reducible to them, fractional-rational and equations of higher degrees). Various methods for solving systems of equations (graphical, substitution method, addition method). Application of special techniques when solving systems of equations. Methods for solving various inequalities (numerical, linear, quadratic). Interval method. The scope of the expression. Systems of inequalities.

Topic 4 . Number sequences. (4 hours)

Definition of arithmetic and geometric progressions. Formula for the nth term. Characteristic property. Sum of the first n terms. Combined tasks.

Topic 5 . Functions and graphs (4 hours)

Functions, their properties and graphs (linear, inversely proportional, quadratic, etc.) “Reading” the properties of a function from its graph. Analysis of graphs describing the relationship between quantities. Establishing a correspondence between the graph of a function and its analytical task.

Topic 6 . Coordinates on a straight line and plane. (2 hours)

Establishing a correspondence between the graph of a function and its analytical task. Equations of lines, parabolas, hyperbolas. Geometric meaning of coefficients for straight line and parabola equations.

Topic 7 . Geometry (6 hours)

Calculation of lengths. Calculation of angles. Selecting the correct statements. Calculation of areas of plane figures. Trigonometry. Solving applied geometry problems.

Topic 8 . Statistics and probability theory . (2 hours )

Topic 9. Solving word problems. (6 hours)

Problems involving percentages. Tasks for “movement”, “con”, “work”. Practical tasks.

Topic 10.

Diagnostic work based on materials from the OGE in mathematics grade 9 (2 hours)

Thematic planning

"Mathematics. Workshop on solving problems for preparing the OGE.”, 9th grade.

Forms of control:

Current control of the level of mastery of the material is carried out based on the results of students completing independent, training and diagnostic work. There are both qualitative and quantitative assessments of activities. A qualitative assessment is based on an analysis of the level of motivation of students, their social behavior, independence in organizing educational work, as well as an assessment of the level of adaptation to the proposed life situation (passing an algebra exam in the form of an OGE). Quantitative assessment is intended to provide students with objective information about their mastery of educational material and is carried out using a five-point system.

Requirements for the level of training of graduates

Part 1

Bibliography:

1. OGE: 3000 problems with answers in mathematics. All tasks of part 1/

I.V. Yashchenko, L.O. Roslova and others; edited by A.L. Semenova, I.V. Yashchenko-M., Publishing house “Exam”, publishing house MCNMO, 2014

2. Semenov A.V. State final certification of 9th grade graduates in a new form. Mathematics 2014. Textbook./A.V. Semenov, A.S. Trepalin, I.V. Yashchenko, P.I. Zakharov; edited by I.V. Yashchenko; Moscow Center for Continuing Mathematical Education._M.: Intellect_Center, 2014.

3. Mathematics. Basic level of GIA_2014. Manual for “dummies”. Module 1: Algebra / Edited by F.F. Lysenko. - Rostov-on-Don: Legion, 2014

4. Mathematics. Basic level of GIA_2014. A manual for “dummies”. Module 2: Geometry / Edited by F.F. Lysenko. - Rostov-on-Don: Legion, 2014

5. Mathematics. Basic level of GIA_2014. Manual for “dummies”. Module 3: Real mathematics / Edited by F.F. Lysenko. - Rostov-on-Don: Legion, 2014

List of electronic resources:

http :// www . prosv . ru

— website of the publishing house “Prosveshchenie” (section “Mathematics”)

http :/ www . drofa . ru
—
website of the publishing house Drofa (section “Mathematics”)

http :// www . center . fio . ru / som
-
methodological recommendations for a subject teacher (all school subjects are presented). Materials for independent development of profile tests and activation of the learning process in high school.

http :// www . edu . ru
-
Central educational portal, contains regulatory documents of the Ministry, standards, information about conducting experiments, information support server for the Unified State Exam.

http :// www . internet - school . ru
-
website of the Internet school of the publishing house Prosveshcheniye. The curriculum is developed on the basis of the federal basic curriculum for general education institutions of the Russian Federation and represents the field of knowledge “Mathematics”. The site presents Internet lessons on algebra and the beginnings of analysis and geometry, including preparation for passing the OGE.

http :// www . legion _ ru

– website of the publishing house “Legion”

http :// www . intellectcentre . ru

– website of the Intellect-Center publishing house, where you can find educational and training materials, demo versions, a bank of training tasks with answers, methodological recommendations and sample solutions

http :// www . fipi . ru

— information support portal for monitoring the quality of education, here you can find the Federal Test Bank

https://www.mathgia.ru/ _ _

— open bank of tasks in mathematics

9

Extracurricular activity program “Real Mathematics” in mathematics in 9th grade

Methods and forms of training

To work with students, the following forms of work are used: lectures, practical work, testing, presentations: “defending a solution”, “deriving formulas”, “proving theorems”.

The tasks are aimed at testing such qualities of graduates’ mathematical preparation as:

confident command of formal operational algebraic apparatus;

the ability to solve a planimetric problem using various theoretical knowledge of a geometry course;

the ability to solve a complex problem that includes knowledge from different topics of the course;

the ability to write down a solution mathematically and clearly, while providing the necessary explanations and justifications;

mastery of a wide range of techniques and methods of reasoning.

Planned results of mastering the course

Personal

the ability to emotionally perceive mathematical objects, reasoning, problem solving, and problems under consideration;

the ability to construct speech structures (oral and written) using studied terminology and symbolism, to understand the meaning of the task. Translate from natural language to mathematical language and vice versa.

Metasubject

the ability to plan one’s activities when solving educational mathematical problems, to see different strategies for solving problems, and to consciously choose a solution method;

ability to work with educational mathematical text (find answers to questions posed, highlight semantic fragments);

the ability to conduct simple evidentiary reasoning, based on studied definitions, properties, signs; recognize true and false statements; illustrate the studied concepts and facts with examples; refute false statements using counterexamples;

the ability to act in accordance with the proposed algorithm, to create simple algorithms for calculations and constructions;

application of self-control techniques when solving educational problems;

the ability to see a mathematical problem in simple practical situations.

Subject

mastery of the basic conceptual apparatus for the main sections of content;

mastery of calculation skills with natural numbers, ordinary and decimal fractions, positive and negative numbers;

the ability to solve word problems in an arithmetic way, using various strategies and methods of reasoning;

assimilation at a visual level of knowledge about the properties of plane and spatial figures; acquiring the skills to depict them; the ability to use geometric language to describe objects in the surrounding world;

gaining experience in measuring the lengths of segments, angles, calculating areas and volumes; understanding the idea of ​​​​measuring the lengths of areas, volumes;

acquaintance with the ideas of equality of figures, symmetry; the ability to recognize and depict equal and symmetrical figures;

ability to carry out simple practical calculations (including calculations with percentages, performing the necessary measurements, using estimates and estimates);

using letters to write general statements, formulas, expressions, equations; the ability to operate with the concept of “literal expression”, to carry out elementary activities related to the concept of “equation”;

performing standard procedures on the coordinate plane;

understanding and using information presented in the form of tables, bar charts and pie charts;

ability to solve simple combinatorial problems by searching through possible options.

12. Computational skills: the ability to apply computational skills in solving practical problems, household, culinary and other calculations.

13. geometric skills: the ability to calculate area, perimeter when solving practical problems on drawing up estimates for the renovation of premises, tasks related to design.

14. analyze and comprehend the text of the problem; simulate the condition using diagrams, drawings; build a logical chain of reasoning; critically evaluate the answer received;

15. solve problems from real practice, using a calculator if necessary;

16. extract the necessary information from the text, exercise self-control;

17 extract information from tables and diagrams, perform calculations using tabular data;

18. collect information in simple cases, present information in the form of tables and diagrams, including using computer programs;

19. build speech structures;

20. depict geometric figures using tools and by hand, on checkered paper, calculate the areas of figures, be able to perform calculations for repairing an apartment, room, plot of land, etc.;

21. perform calculations with real data;

22. conduct random experiments, including using computer modeling, and interpret their results.

Program content

Introduction (2 hours)

Numbers and calculations (2 hours)

Numbers: natural, rational, irrational. Correspondences between numbers and coordinates on a coordinate ray. Comparison of numbers. Standard notation of numbers. Comparison of square roots and rational numbers. The concept of percentage. Word problems on percentages, fractions, ratios, proportionality. Rounding numbers.

Algebraic expressions (2 hours)

Expressions, identities. Expression definition area. Drawing up letter expressions based on tasks or drawings. Monomials. Polynomials. Actions with monomials and polynomials. Abbreviated multiplication formulas. Factoring polynomials. Reducing algebraic fractions. Convert numeric expressions containing square roots. Degrees with an integer exponent and their properties. Root of the nth degree, degree with a rational exponent and their properties.

Equations, systems of equations. Inequalities, systems of inequalities (6 hours)

Equations with one variable. Quadratic equations. Incomplete quadratic equation. Vieta's theorem on the roots of an equation. Study of quadratic equations. Fractional rational equations. Equations with two variables. Systems of equations. Methods for solving systems of equations: substitutions, addition method, graphical method. Problems solved using equations or systems of equations. Inequalities with one variable. Systems of inequalities. Set of solutions to quadratic inequality. Methods for solving inequalities and systems of inequalities: interval method, graphical method.

Functions and graphs (5 hours)

The concept of function. Function and argument. The scope of the function.

Function range. Function graph. Function zeros. Function,

increasing on the segment. A function that decreases on an interval. Linear

function and its properties. Graph of a linear function. Slope factor

functions. Inversely proportional function and its properties. Quadratic

function and its properties. Graph of a quadratic function. Power function. Even, odd function. Properties of even and odd power functions.

Graphs of power functions. Maximum and minimum value. Reading graphs of functions. Features of the location of graphs of some functions in the coordinate plane depending on the values ​​of the parameters included in the formulas. Dependence between quantities.

Word problems (2 hours)

Problems on percentages, problems on movement, problems on calculating the amount of work, problems on the percentage content of substances in alloys, mixtures and solutions, methods for solving them.

Triangles (4 hours)

Height, median, midline of the triangle. Isosceles and

equilateral triangles. Signs of equality and similarity

triangles. Solving triangles. Sum of angles of a triangle.

Properties of right triangles. Pythagorean theorem. Theorem

sines and cosines. Triangle inequality. Area of ​​a triangle.

Polygons (2 hours)

Types of polygons. Parallelogram, its properties and features.

Area of ​​a parallelogram. Rhombus, rectangle, square. Trapezoid.

Midline of trapezoid. Area of ​​a trapezoid. Regular polygons.

Circumference (4h)

Tangent to a circle and its properties. Central and inscribed angles.

A circle circumscribed around a triangle. Circle inscribed in

triangle. Properties of circumscribed and inscribed quadrilaterals. Circumference. Area of ​​a circle.

Progressions: arithmetic and geometric (3 hours)

Number sequences. Arithmetic progression Difference

arithmetic progression. Formula for the nth term of arithmetic

progression. Formula for the sum of n terms of an arithmetic progression.

Geometric progression. Denominator of a geometric progression.

Formula for the nth term of a geometric progression. Formula for the sum of n terms

geometric progression. Sum of an infinite geometric progression.

Solving training options and tasks from an open bank

tasks GIA-9 (2 hours)

Calendar and thematic planning