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Lesson Objectives:

Educational

• introduce the concept of rotation and prove that rotation is movement;
• consider the rotation of the segment, depending on the center of rotation (the center of rotation lies outside the segment, on the segment and is one of the ends of the segment);
• to teach the construction of a segment when it is rotated by a given angle;
• check the assimilation of the material studied in previous lessons and the material covered in this lesson.

Educational

• develop the ability to analyze the task, build a logical chain when problem solving to reasonably draw conclusions;
• develop the thought process, cognitive interest, mathematical speech of students;

Educational

• educate attentiveness, observation, a positive attitude towards learning.

Lesson type: a lesson in the study of new material and intermediate control of the assimilation by students of the material covered in this lesson and previously studied material.

Organizational forms of communication: collective, individual, frontal, in pairs.

Lesson structure:

1. Motivational conversation with students followed by goal setting;
2. Checking homework;
3. Updating of basic knowledge;
4. Enrichment of knowledge;
5. Consolidation of the studied material;
6. Checking the assimilation of the studied material (testing with subsequent mutual verification);
7. Summing up the lesson (reflection);
8. Homework.

Decor: multimedia projector, screen, laptop, computer presentation, signal cards.

Motivational conversation.

Without movement, life is just a lethargic dream.
Jean Jacques Rousseau

I. Communication of the topic, goals and course of the lesson.(SLIDE 2)

Guys, you know what an important role the movement has in the life of a person, society, and science. Movement also plays an important role in mathematics: the transformation of graphs, the display of points, figures, planes - all this is movement. In the previous lessons, we have considered several types of movement. Today we will get acquainted with another type of movement: turning. Lesson topic: turn.

And our lesson is also an example of movement, only movement not from a physical point of view, but movement in mental development, learning new things and acquiring new knowledge. Throughout the lesson, you will perform various tasks, tests. Therefore, be active, move forward in your knowledge throughout the lesson and improve your results from one stage to another!

Throughout the lesson, both my speech and yours will be accompanied by a presentation that will help you check the correctness of your homework, the proposed tests and independently solved problems.

II. Checking homework.

Use SLIDES 3-5 to check solution #1165.

III. Updating of basic knowledge.

Test number 1. (SLIDES 6-13)

After completing the test, the guys exchange notebooks and perform a mutual check.

IV. Learning new material.(knowledge enrichment)

(SLIDE 14) Mark the point O (fixed point) on the plane, and set the angle a- angle of rotation. By turning the plane around the point O by an angle a is called a mapping of the plane onto itself, in which each point M is mapped to such a point M 1 that OM =OM 1 and the angle MOM 1 = a.

(SLIDE 15) In this case, the point O remains in place, i.e. is mapped to itself, and all other points are rotated around the point O in the same direction by the angle a clockwise or counterclockwise.

(SLIDE 16) Point O is called the center of rotation, a- angle of rotation. Designated R o a .

(SLIDE 17) If the rotation is clockwise, then the angle of rotation a considered negative. If the rotation is counterclockwise, then the rotation angle is positive.

Guys, let's remember the concept of movement. Do you think turning is a movement? (guesses)

Turn - is a movement, i.e. mapping the plane onto itself. Let's prove it.

(SLIDE 18 or SLIDE 19)

(The proof can be done by a strong student on SLIDE 18. In this case, you can immediately after the proof go to SLIDE 20. The proof can be done by the teacher together with the class on SLIDE 19, which shows the stages of the proof.)

V. Consolidation of the studied material.

Exercise. Construct point M 1 , which is obtained from point M by turning through an angle of 60 o . Step by step, with the help of slide 20, the construction of the point M 1 is being worked out.

What tools do we need to make a turn? (ruler, compass, protractor)

Guys, what should be noted first? (point M and center of rotation - point O)

How do we set the center of rotation? Celebrate in a certain place? (no, optional)

How are we going to rotate clockwise or counterclockwise? Why? (against, because the angle is positive)

What needs to be built to set aside an angle of 60 o ? (beam OM)

How to find the point M 1 on the second side of the corner? (using a compass, set aside the segment OM 1 \u003d OM)

Consider how the segment is rotated depending on the location of the center of rotation.

Consider the case when the center of rotation lies outside the segment. We will solve No. 1166 (a). (If the class is strong, then together with the children you can draw up a plan for solving the problem, give the task to solve No. 1166 (a) on your own. Check the solution using SLIDE 21. If the guys find it difficult to complete the task, then decide collectively, based on SLIDE 21)

Work in pairs.

Exercise. Construct a figure that will be obtained by rotating the segment AB at an angle of - 100 o around point A.

(suggestive questions)

What point is the center of rotation? What can be said about her? (this is one of the ends of the segment - point A, it will be stationary, stay in place)

How are we going to rotate clockwise or counterclockwise? (clockwise as the angle is negative)

Make a plan for solving the problem.

The task is done in pairs. Check the solution with SLIDE 22.

Individual work.

Exercise. Construct a figure into which the segment AB passes when it rotates through an angle - 100 o around the point O - the middle of the segment AB.

Make a plan for solving the problem. The task is performed independently, the solution is checked using SLIDE 23.

Today in the lesson we considered the rotation of a segment depending on the location of the center of rotation. In the next lessons, we will look at the rotations of other shapes. (show SLIDES 24-25)

VI. Checking the assimilation of the studied material.

Test number 2. (SLIDES 26-30)

Self-test.

VII. Summing up the lesson. (reflection)

Guys, let's highlight those who were the best at each stage. (summarized, graded)

Raise your hands if you liked the lesson. Note what was interesting in the lesson?

VII. Homework.

• No. 1166 (b), No. 1167 - for those who received a mark of "3".
• No. 1167 (consider three cases of the location of the center of rotation: the center is vertex A, the center is located outside the triangle, the center lies on the side AB of the triangle) - for those who received marks “4” and “5”.

Rotation (rotation) is a movement in which at least one point of the plane (space) remains motionless. In physics, rotation is often called incomplete rotation, or, conversely, rotation is considered as a particular type of rotation. The latter definition is more rigorous, since the concept of rotation covers a much broader category of motions, including one in which the trajectory of a moving body in the chosen frame of reference is an open curve.

MO M1M1M1M1

O B A B1B1 A1A1

O

Parallel transfer a special case of motion in which all points in space move in the same direction by the same distance. Otherwise, if M is the original and M" is the offset position of the point, then the vector MM" is the same for all pairs of points corresponding to each other in the given transformation. Parallel translation moves each point of a shape or space the same distance in the same direction.

The topic "Turn" belongs to a large section called "Movements". In the world around us, processes often occur that are associated with the mathematical concept of rotation. Quite often, you have to perform actions when creating some items using rotation. Therefore, the study of this topic becomes an important part of the educational process. But the study of the material should not be limited only to the fact that the theory is told to the students, and whether they understand or not, the teacher does not care. After all, each action should have its own specific result. In order for the content of the material for the geometry course to be assimilated faster and better, it is necessary to use visual teaching aids, which include presentations.

This presentation was developed by the author to facilitate the work of a teacher who constantly lacks time even without preparing a presentation. And to save this time, you can use the finished presentation. It corresponds to the theme "Turn" of the school geometry course. Therefore, it fits perfectly into educational process.

Like any lesson new topic, this presentation begins with the definition of the main concept of the lesson. In this case, the author defines the concept of rotation. He defines the rotation of a plane as a reflection of the plane on itself under some condition, which can be studied in more detail on the slide of the presentation. The author attaches a figure to the theoretical data. This figure shows how a point is rotated by a certain angle.

But geometry doesn't end with point cases. After all, science is simply overflowing with all kinds of figures. Therefore, at the request of the teacher, it is possible to add an example to the presentation when a certain figure is rotated.

Also, do not forget that turning is a movement. That is what is shown on the next slide. Moreover, this is also proved here. The author attaches a drawing to the evidence. As a result, it turns out that the plane rotates through some given angle around one specific point.

The presentation can be used to explain new material on the topic "Turn". The teacher can supplement the presentation at his discretion, if required by the educational process. This presentation is filled with the most necessary information, which is enough for an average level of knowledge, namely, for a satisfactory assessment.