Elective course in geometry - course 51,136 rubles. from SkySmart, training 64 lessons, Date: December 3, 2023.
Miscellaneous / / December 06, 2023
How are geometry classes conducted?
1. Let's remember the last lesson
- We repeat the theorems that we have already studied in the geometry course
2. Let's sort out the homework
- The student talks about how he coped with independent work
3. Let's dive into a new topic
- The teacher explains the material with examples
4. Honing our skills
- Solving advanced tasks and building figures
5. Discussing the last lesson
- We find out whether the goal has been achieved and plan homework
Progress and results from the first lessons
We will select non-standard tasks
We will help you maintain interest in geometry when the regular education program is no longer adequate.
Let's conduct lessons without boring lectures
We will supplement the lessons on the course with topics that are interesting to teenagers and real-life problems.
We will help you develop your potential
Let's show what doors open to a student with strong abilities in geometry.
19
coursesBachelor and Master of Moscow State Pedagogical University, Master of MIREA. Teaching experience - 10 years
My favorite book is Harry Potter, and I am Professor McGonagall in it. I’ll teach you how to bottle actions with numbers, how to cook a problem using a formula, and even how to seal the root of an equation. But as long as you ask questions and do your homework!
19
coursesShe has been teaching mathematics for 2 years. Was a volunteer teacher in a charity project
I always try to find a common language with students and gain their trust, I am in touch 24/7. In my free time I study English and German, I like to read, mainly English classics
1. 7th grade
- Straight line and segment. Beam and angle.
- Comparison of segments and angles. Measuring segments. Measuring angles.
- Adjacent and vertical angles.
- Perpendicular lines.
- The first sign of equality of triangles.
- Medians, bisectors and altitudes of triangles.
- Properties of an isosceles triangle.
- The second sign of equality of triangles.
- The third sign of equality of triangles.
- Circle.
- Signs of parallel lines. Practical ways to construct parallel lines.
- Axiom of parallel lines. Properties of parallel lines.
- Sum of angles of a triangle.
- Relationships between sides and angles of a triangle.
- Triangle inequality.
- Sum of angles of a triangle. Relationship between angles and sides.
- Right triangles and some of their properties.
- Signs of equality of right triangles.
- Distance from a point to a line. Distance between parallel lines.
- Constructing a triangle using three elements.
2. 8th grade
In online classes with a tutor for an elective course in geometry, the student will learn new figures, concepts and properties in order to practice solving complex problems and constructions.
- Polygons.
- Parallelogram. Signs of a parallelogram.
- Trapezoid.
- Thales's theorem.
- Rectangle. Rhombus. Square.
- Axial and central symmetries.
- Area of a polygon.
- Area of a rectangle.
- Area of a parallelogram.
- Area of a triangle.
- Area of a trapezoid.
- Pythagorean theorem. The theorem converse to the Pythagorean theorem.
- Definition of similar triangles. Ratio of areas of similar triangles.
- The first sign of similarity of triangles.
- The second and third signs of similarity of triangles.
- The middle line of the triangle. Property of medians of a triangle.
- Proportional segments.
- Proportional segments in a right triangle.
- Measurement work on the ground.
- Sine cosine and tangent of an acute angle of a right triangle.
- Sine cosine and tangent values for angles of 30°, 45° and 60°.
- Application of similarity theory to problem solving. Relationships between sides and angles of a right triangle.
- The relative position of a straight line and a circle.
- Tangent to a circle.
- Inscribed angle theorem.
- Theorem on segments of intersecting chords.
- Property of the bisector of an angle. Perpendicular bisector.
- Theorem on the point of intersection of the altitudes of a triangle.
- Inscribed circle. Property of a circumscribed quadrilateral.
- Circumscribed circle. Property of an inscribed quadrilateral.
3. 9th grade
In individual lessons with a teacher of an elective course in geometry, the student will be able to expand the amount of knowledge that the school has given him. He will study familiar topics in more depth and practice his skills on more complex tasks.
- Vector concept. Delaying a vector from a given point.
- Sum and subtraction of vectors.
- Multiplying a vector by a number.
- Midline of trapezoid.
- Decomposition of a vector into two non-collinear vectors.
- Vector coordinates.
- The simplest problems in coordinates.
- Equation of a circle. Equation of a straight line.
- Coordinate method. Preparation for solving problems.
- Sine, cosine and tangent of an angle.
- Theorem on the area of a triangle. Theorems of sines and cosines.
- Relationships between sides and angles of a triangle.
- Dot product of vectors. Dot product in coordinates.
- Regular polygon.
- A circle circumscribed about a regular polygon and inscribed in a regular polygon. Formulas.
- Circumference. Area of a circle and a circular sector.
- The concept of movement. Properties of movements.
- Parallel transfer. Turn.
- Prism. Pyramid.
- Volume and surface area of a polyhedron.
- Cylinder and cone. Sphere and ball.
4. Grade 10
The elective course will give the student the opportunity to look at familiar geometry topics from a different angle. In lessons with a teacher, he will analyze more complex materials and learn to solve problems that are inaccessible to other students of his age.
- Introduction to stereometry. Construction of drawings.
- Axioms of stereometry.
- Parallel lines.
- Parallelism of a line and a plane.
- Crossing straight lines.
- Angle between straight lines.
- Tetrahedron. Parallelepiped.
- Parallel planes and their properties.
- Problems on constructing sections.
- Perpendicular lines. Parallel lines perpendicular to planes.
- A sign of perpendicularity of a line and a plane.
- Theorem on a line perpendicular to a plane.
- Distance from a point to a plane.
- Theorem of three perpendiculars.
- The angle between a straight line and a plane.
- Dihedral angle.
- A sign of perpendicularity of two planes.
- Rectangular parallelepiped.
- The concept of a polyhedron. Prism.
- Pyramid. Correct pyramid.
- Truncated pyramid.
- Regular polyhedra.
- Symmetry.
- Euler's theorem.
- Introduction of Cartesian coordinates in space.
- Distance between points.
- Coordinates of the midpoint of the segment.
- Transformation of symmetry in space. Symmetry in nature and in practice.
- Movement in space.
- Parallel transport in space.
- Similarity of spatial figures.
- The angle between intersecting lines.
- The angle between a straight line and a plane.
- Angle between planes.
- The area of the orthogonal projection of a polygon.
- Vectors in space.
- Actions on vectors in space.
- Decomposition of a vector into three non-coplanar vectors.
- Equation of a plane.
- Repetition. Axioms of stereometry and their consequences.
- Repetition. Parallelism of straight lines and planes.
- Repetition. Perpendicularity of lines and planes.
- Repetition. Polyhedra.
- Repetition. Areas of the lateral surfaces of a pyramid and a prism.
5. Grade 11
The elective course program in geometry will cover topics from grades 10 and 11 and will help students test their knowledge. The classes will include advanced assignments in the subject, as well as trial versions of the Unified State Examination.
- Triangles.
- Cosine theorem.
- Theorem of sines.
- Heights of a triangle.
- Bisectors of a triangle.
- Medians of a triangle.
- Area of a triangle.
- Parallelogram. Preparation for solving problems.
- Rectangle, rhombus, square.
- Trapezoid.
- Midline of trapezoid.
- Inscribed and circumscribed angles in a circle.
- Chords and tangents.
- Triangle and inscribed circle.
- Triangle and circumcircle.
- Circle and quadrilateral.
- Circle systems.
- Stereometry. Prisms.
- Stereometry. Pyramids.
- Stereometry. Bodies of rotation.
- Stereometry. Polyhedra.
- Stereometry. Sections.
- Stereometry. Coordinate method. Introduction.
- Stereometry. Coordinate method. Angle between straight lines.
- Stereometry. Coordinate method. Angle between planes.
- Stereometry. Coordinate method. The angle between a straight line and a plane.
- Stereometry. Coordinate method. Distance from a point to a plane.
- Stereometry. Coordinate method. The distance between intersecting lines.
- Stereometry. Volume method.
- Construction of sections.
- The angle between a straight line and a plane.
- Angle between planes.
- Angle between straight lines.
- The distance from a point to a line and to a plane.
- Cross-sectional area.
- The distance between intersecting lines.
- Figures of rotation.