Teaching plan of compulsory 4 "arbitrary angle and curvature system" in senior high school mathematics

Teaching plan of 4 "Arbitrary Angle and Curvature System" required for senior high school mathematics preparation 1

Teaching objectives

I. Knowledge and skills

(1) Understand and master the definition of arc system; (2) Understand the rationality of the definition of arc system; (3) Mastering and applying the formula of arc length and sector area expressed by arc system; (4) skillfully changing the angle system and the arc system; (5) One-to-one correspondence between the set of angles and the set of real numbers. (6) Through the study of arc system, students can understand and realize that both angle system and arc system are diagonal measurement methods, and they are dialectical and unified, not isolated and separated.

Second, the process and methods

Create a situation, introduce the arc system to measure the size of the angle, and grasp the rationality of the definition by exploring and understanding the definition of the arc system. According to the definition of arc system, arc length formula and sector area formula are derived and used, and the relationship between angle system and arc system is studied with specific examples in order to use the calculator correctly.

Third, modality and value.

Emphasis and difficulty in teaching

Key points: understand and master the definition of arc system; Proficient in the conversion between angle system and arc system; Application of arc system.

Difficulties: Understanding the definition of arc system and its application.

teaching tool

Projector, etc

teaching process

First, create situations and introduce new lessons.

Teacher: Someone asked: How far is it from Haikou to Sanya? Some people answered about 250 kilometers, while others answered about 160 miles. Which answer is correct? (called 1 mile =1.6km)

Obviously, both answers are correct, but why are there different values? That's because the measurement systems used are different, one is the kilometer system and the other is the mile system. Their length units are different, but they can be converted into: 1 mile = 1.6 km.

In angle measurement, there is a similar situation. One is an angle system that we are no longer unfamiliar with, and the other is another angle measurement system-radian system that we will learn in this lesson.

Second, explain the new lesson.

1. Angular system stipulates that a circle is divided into 360 parts, and each part is called 1 degree, so a week is equal to 360 degrees, a right angle is equal to 180 degrees, a right angle is equal to 90 degrees, and so on.

What is an arc system? What does 1 radian mean? How many radians is a week? How about half a week? How many radians is a right angle equal to? How to convert arc system and angle system? Please read the textbook and solve the above problems by yourself.

2. Definition of curvature system

The central angle of an arc with a length equal to the radius is called 1 radian angle, and it is recorded as 1 radian, 1 radian, or 1 (the unit can be omitted).

(Teachers and students * * * have the same activity) Inquiry: As shown in the figure, the center of the circle with radius coincides with the origin, the terminal edge of the angle coincides with the positive semi-axis of the shaft, intersects with the circle at the point, and the terminal edge intersects with the circle at the point. Please fill in this form.

We know that an angle can be divided into positive and negative zero degrees, and its radian number should also be divided into positive and negative zero degrees, such as-? ,-2? Wait, generally speaking, the radian number of positive angle is positive, the radian number of negative angle is negative, and the radian number of zero angle is zero. The positive or negative angle is mainly determined by the rotation direction of the angle.

After the popularization of the concept of angle, under the radian system, there is a one-to-one correspondence between the set of angles and the set of real numbers R: that is, each angle has a unique real number (that is, the radian number of the angle) corresponding to it; On the contrary, every real number has a unique angle corresponding to it.

Fourth, class summary.

Conversion between degrees and radians is also possible? Calculator? Middle School Mathematics Table; In the specific operation,? Radian? Words and unit symbols? Rad? It can be omitted, for example, 3 means 3rad sinp means the sine of prad angle, and the following concepts should be established: after the concept of angle is popularized, a one-to-one correspondence can be established between the set of angles and the set of real numbers, regardless of the angle system or the arc system.

Verb (abbreviation for verb) assignment

Homework: Exercise 1. 1 A Group Questions 7, 8 and 9.

Summary after class

homework

Homework: Exercise 1. 1 A Group Questions 7, 8 and 9.

Write on the blackboard.

Teaching preparation of teaching plan 2 of compulsory 4 "arbitrary angle and curvature system" in senior high school mathematics

Teaching objectives

1, knowledge and skills

(1) Popularize the concept of angle and introduce greater than angle and negative angle; (2) Understand and master the definitions of positive angle, negative angle and zero angle; (3) Understand the concepts of arbitrary angle and quadrant angle; (4) Mastering the representation methods of all angles (including angles) which are the same as the terminal edges of the angles; (5) Establish the viewpoint of action change and deeply understand the concept of promotion angle; (6) Reveal the knowledge background and stimulate students' interest in learning. (7) Create problem situations, stimulate students' learning attitude of analysis and exploration, and strengthen students' awareness of participation.

2. Process and method

By creating situations:? Turn around. Turn counterclockwise? The angle is greater than the angle, the angle of zero degree and the angle formed by different rotation directions. The concepts of positive angle, negative angle and zero angle are introduced. After the concept of angle is popularized, the angle is put into the plane rectangular coordinate system, and the concepts of quadrant angle and non-quadrant angle and the judgment method of quadrant angle are introduced. List several angles with the same terminal edge, draw the position of the terminal edge, find out their relationship, and explore the representation of angles with the same terminal edge; Explain examples, summarize methods and consolidate exercises.

3. Modality and value

Through the study of this section, students have a new understanding of the concept of diagonal, that is, positive angle, negative angle and zero angle. After the popularization of the concept of angle, they know the relationship between angles, understand and master the representation method of the same angle at the edge of the terminal, and learn to understand things from the perspective of motion change.

Emphasis and difficulty in teaching

Key points: understand the definitions of positive angle, negative angle and zero angle, and master the representation of the same angle at the edge of the terminal.

Difficulty: Angular representation with the same terminal edge.

teaching tool

Projector, etc.

teaching process

Create a situation

Thinking: Your watch is five minutes slow. How did you adjust? If your watch is 1.25, it is fast.

Hours, how should I calibrate? How many degrees did the minute hand turn when calibrating the time?

[Take out a clock and actually operate it] We find that in the calibration process, the minute hand needs to rotate forward or backward, sometimes less than a week, sometimes more than a week, that is to say, the angle is not limited to the middle, which is the main content we will learn in this lesson.

Explore new knowledge

1. In junior high school, we learned the concept of angle. How is it defined?

[Display Projection] An angle can be regarded as a graph formed by a ray rotating from one position to another around an endpoint on a plane. As shown in figure 1. 1- 1, a ray rotates counterclockwise around its endpoint o to form an angle a, and the ray at the beginning of rotation is called the starting edge of the angle, OB is called the end edge and the ray is the starting edge.

2. As mentioned above, the problem of calibrating clocks and terminology:? Turn around? (that is, turn for 2 weeks), turn? (that is, turn three times) and so on. Is all angles greater than and rotating in different directions. Think about it: How many more can you name in real life? Angle greater than or rotating in different directions? Examples, what do these show? How to distinguish and express these angles?

For example, when bicycle wheels and screw wrenches rotate in different directions, the angles are different, which shows the necessity of studying and popularizing the concept of angle. In order to distinguish, we stipulate that the angle formed by counterclockwise rotation is called positive angle and the angle formed by clockwise rotation is called negative angle. If a ray does not rotate, we call it a zero-degree angle.

8. Learning summary

(1) Do you know how speakers are popularized?

(2) How is the quadrant angle defined?

(3) Are you familiar with the representation with the same final angle? Drop the edge of the write terminal on the X axis and Y axis, straight.

A set of angles on a straight line.

Verb (abbreviation of verb) evaluation design

1. Homework: Exercise 1.1Group A1,2,3.

2. Give more examples of daily life? Greater than the angle and negative angle? Examples, mastering their expressions,

Further understand the characteristics of corners with the same terminal edge.

Summary after class

(1) Do you know how speakers are popularized?

(2) How is the quadrant angle defined?