Presentation on the topic of movement of figures and rotation. Rotation (rotation) is a movement in which at least one point of the plane (space) remains stationary. In physics, it is often called a turn. II. Homework check

Rotation (rotation) is a movement in which at least one point of the plane (space) remains stationary. 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 encompasses a much broader category of movements, including those in which the trajectory of a moving body in the selected frame of reference is an open curve.




MO М1М1М1М1


О В А В1В1 А1А1


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Parallel transfer is a special case of movement in which all points in space move in the same direction at 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 this transformation. Parallel translation moves every point in a shape or space the same distance in the same direction.


































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Lesson objectives:

Educational

  • introduce the concept of turning and prove that turning 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);
  • teach how to draw a line segment when you rotate it by a given angle;
  • check the assimilation of the material studied in the previous lessons and the material passed in this lesson.

Developing

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

Educational

  • foster 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 passed in this lesson and studied earlier.

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

Lesson structure:

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

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

Motivational conversation.

Without movement - life is just a lethargic sleep.
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 plays an important role in mathematics as well: transforming graphs, displaying points, shapes, planes - all this movement. In the previous lessons, we examined several types of movement. Today we will get acquainted with one more type of movement: a turn. 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 the next!

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. Homework check.

Use SLIDES 3-5 to test solution # 1165.

III. Updating basic knowledge.

Test # 1. (SLIDES 6-13)

Annex 1

After completing the test, the children exchange notebooks and carry out a mutual check.

IV. Learning new material.(enrichment of knowledge)

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

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

(SLIDE 16) Point O is called the center of rotation, a- angle of rotation. Denoted by P about a .

(SLIDE 17) If the rotation is clockwise, then the rotation angle 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 a turn is a movement? (make assumptions)

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

(SLIDE 18 or SLIDE 19)

(Proof can be done by a strong student on SLIDE 18. In this case, you can go to SLIDE 20 right after the proof. The teacher can complete the proof 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 it at an angle of 60 o. Step by step, using slide 20, the construction of point M 1 is being worked out.

What tools do we need to complete the turn? (ruler, compasses, protractor)

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

How do we set the center of rotation? Are we celebrating in a certain place? (no, arbitrary)

How do we rotate clockwise or counterclockwise? Why? (against, since the angle is positive)

What do you need to build to postpone the 60o angle? (OM beam)

How to find the point M 1 on the second side of the corner? (use a compass to postpone the segment OM 1 = 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. Let's solve No. 1166 (a). (If the class is strong, then together with the children it is possible to draw up a plan for solving the problem, give the task to solve No. 1166 (a) independently.

Work in pairs.

Exercise. Construct the shape that will turn out when the segment AB is rotated at an angle of - 100 o around point A.

(suggestive questions)

Which point is the pivot point? What can you say about her? (this is one of the ends of the segment - point A, it will be motionless, stay in place)

How do we rotate clockwise or counterclockwise? (clockwise, since the angle is negative)

Make a plan for solving the problem.

The task is performed in pairs. Check the solution using SLIDE 22.

Individual work.

Exercise... Construct the shape into which the segment AB passes when rotated by an angle of - 100 o around the point O - the midpoint of the segment AB.

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

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

Vi. Checking the assimilation of the studied material.

Test number 2. (SLIDES 26-30)

Appendix 2

Self-test.

Vii. Summing up the lesson. (reflection)

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

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

Vii. Homework.

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

The topic "Pivot" belongs to a large section called "Movements". In the world around us, processes often occur that are associated with the mathematical concept of a turn. Quite often you have to perform actions when creating some objects using a 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 students are told the theory, and whether they understood or not, the teacher does not care. After all, every action should have its own specific result. In order to assimilate the content of the material for the geometry course faster and better, it is necessary to use visual teaching aids, which include presentations.

This presentation developed by the author to facilitate the work of a teacher who, even without preparing a presentation, constantly does not have enough time. And to save this time, you can use finished presentation... It corresponds to the "Pivot" theme of the school geometry course. Therefore, it will fit perfectly into educational process.

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

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

Also, do not forget that a turn is a movement. This is what is noted on the next slide. Moreover, this is proved here. The author attaches a drawing to the proof. As a result, it turns out that the plane rotates at a certain specified angle around one specific point.

The presentation can be used to explain new material on the topic "Rotation". 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, a satisfactory grade.

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