As a teacher, it is often necessary to write a lecture, which is helpful to the success of teaching and improve the quality of teaching. Let's refer to how the speech is written! The following is a sample essay of the lecture on "The Area of a Circle" that I collected for you, for reference only. Let's have a look.

Lecture Notes on the Area of a Circle 1 I. teaching material analysis

1, textbook content

The content of this section is to deduce the area of the circle from an example of puppy activity combined with students' life experience.

2. The position and function of teaching materials

Before that, students have learned the concepts and formulas about the circumference and arc length of a circle. On this basis, they can learn this lesson well, master the formula of circle area and related calculations, and lay the foundation for students to learn the area of figures related to circles in the future. Especially in the process of area deduction, students' extreme thoughts are subconsciously cultivated.

Second, the target analysis

Under the background of quality education, mathematics teaching should be based on the development of students, pay attention to the cultivation of ability and strengthen the sense of application. Therefore, the determination of teaching objectives should be based on students' learning process, while preparatory students only have a certain ability of thinking in images, but their ability of abstract thinking is not perfect. Therefore, according to the characteristics of this lesson, the following teaching objectives are determined.

1, knowledge target:

⑴ Through observation, guide students to understand the derivation process of circle area formula.

⑵ Help students master the formula of circular area and apply the formula to solve practical problems.

2, ability goal:

Make students understand the transformation process from "unknown" to "known" and gradually cultivate students' abstract thinking ability.

3, emotional goals:

Through the introduction of examples, students can experience that mathematics comes from life and serves life; Show students a lively mathematical world, stimulate students' interest in learning mathematics, and let all students actively participate in exploration and experience the fun of success in participation.

Third, analysis of key points and difficulties

Emphasis: the derivation process and application of the area formula of a circle.

Difficulties: In the process of deducing the formula of circle area, students understand the infinite average division of circle, the infinite approximation of "arc length" to "line segment", and understand that when a circle is transformed into a rectangle, the length of the rectangle is half of the circumference of the circle.

Fourth, the analysis of teaching methods

1, analysis of teaching methods:

According to the age characteristics and psychological characteristics of students who have just entered junior high school, and their current knowledge level. Use heuristic teaching methods, group cooperation and other teaching methods to let as many students actively participate in the learning process as possible. In the classroom, teachers should become students' learning partners, experience the joy of success with students and create a relaxed and efficient learning atmosphere.

2. Legal study guidance

Through the introduction of examples, guide students to pay attention to mathematics around them. Students can derive the area formula of a circle with the help of the rectangular area formula, and at the same time, they can realize mathematics learning methods such as observation, induction, association and transformation, so that every student can speak, do and think in the interaction between teachers and students. Cultivate students' initiative and enthusiasm in learning.

3. Teaching methods

In order to better show the charm of mathematics, combined with certain multimedia auxiliary means, fully mobilize students' senses, increase the sense of image and interest, and make enough time and space for students to become the masters of the classroom.

Teaching process of verbs (abbreviation of verb)

1, review (1) rectangular area formula.

(2) parallelogram area formula

The solution of parallelogram area formula is to convert it into rectangular area by truncation.

2. Create problem scenarios and introduce topics.

A puppy was tied to the grass by its owner with a rope 1 meter long. What's the range of the puppy's activities?

Question: 1. What is the maximum area that a puppy can move?

2. How to find the area of a circle?

3. Teacher-student interaction to explore new knowledge.

(1) suitcase:

The area of parallelogram can be converted into rectangular area, so can the area of circle be converted into rectangular area?

(2) Experimental operation:

The teacher distributed the circles prepared before class to each group (in groups of four). Please try to see if you can turn a circle into a rectangle.

(3) Animation display: omitted

Lecture notes on "the area of a circle" 2 I. Teaching materials

1, lecture content: The lecture content is in Unit 2, Volume 11, Mathematics for Six-year Primary Schools, West Normal University Edition; The first class.

2. Textbooks and student analysis:

This is a teaching content that combines concepts and calculations to study geometric shapes. I think this content is closely related to the content before and after the textbook. It is taught on the basis of students' learning the area calculation of plane straight line, the preliminary understanding of circle and the circumference of circle. It is an important content of geometry knowledge, paving the way for learning the knowledge of cylinders and cones and drawing statistical charts in the future.

From the perspective of students' knowledge level, from learning the knowledge of straight lines to learning the knowledge of curves, both the content itself and the method of studying problems have changed. From the perspective of space concept, it has entered a new field.

3. Teaching objectives

Following the intention of compiling teaching materials, starting from students' knowledge level and life experience, I draw up the teaching objectives of this course as follows:

(1) Knowledge and skill goal: Derive the formula for calculating the area of a circle, and use the formula to calculate the area of the circle;

(2) Process and Method Objective: To further train students to establish and apply the idea of reduction, initially penetrate the idea of limit, and cultivate students' observation ability and hands-on operation ability.

(3) Emotional attitude and values goal: Pay attention to group cooperation, cultivate students' excellent quality and collective concept of mutual assistance and cooperation.

Based on the above teaching objectives: the teaching focus is to master the calculation formula of circular area;

The teaching difficulties are the derivation of the formula for calculating the circular area and the infiltration of the limit thought;

The key to teaching is to find out the relationship between each part of mosaic figure and the original circle.

Second, talk about teaching strategies

In order to highlight key points, break through difficulties and cultivate students' spirit of inquiry and innovation, I have adopted the teaching method of "based on students' development, with activity inquiry as the main line and innovation as the main theme" in the teaching of this course. I mainly adopt the following four teaching strategies: (Please refer to the teaching process section for specific teaching strategies)

1. Knowledge shows life. The foundation of Feynman Baita Tower in Jinghong, Yunnan Province is a cylindrical stone base with a bottom circumference of 42.6 meters. How many square meters does this tower cover at least? Let the red line of life mathematics run through the class.

2. The learning process is positive. Let the students explore the formula for calculating the area of a circle in the operation activities.

3. Students learn independently. Let students explore the formula for calculating the area of a circle through hands-on operation, independent inquiry and cooperative communication.

4. Cooperative learning method. In the formula for calculating the area of a circle, the method of cooperative learning by four people is adopted.

So as to truly practice that students are the masters of mathematics learning and teachers are the organizers, guides and collaborators of mathematics learning.

Third, the teaching process

Adhering to the guiding ideology of "returning the classroom to students and making the classroom full of vitality", I plan the teaching process as four links: "creating situations, stimulating interest, guiding inquiry, building models, training in different levels, expanding thinking, summarizing the whole class and assigning homework", and strive to build an independent and innovative classroom teaching model.

(A) create a situation to stimulate interest in the introduction

Interest is an important psychological basis for students to actively acquire knowledge and form skills. In order to make students enjoy it, in the first part, I first illustrated the textbook and led to the topic: the calculation of the area of a circle.

In this session, I set up a scene to close the distance between mathematics knowledge and real life, thus stimulating students' thirst for knowledge and paving the way for the next session.

(B) to guide the inquiry and build a model

The second link is the central link of classroom teaching. In order to highlight the key points and break through the difficulties, I have arranged five steps: inspiring guesses, defining the direction-turning joy into straightness, clearing obstacles-experimental exploration, deducing formulas-showing results, experiencing success-echoing from beginning to end and consolidating new knowledge:

The first step: enlighten the guess and make a clear direction.

Encouraging students to make reasonable guesses can lead their thinking to a broader space. So, the first step: enlighten the conjecture and make clear the direction. I inspired students to guess: "Compared with two circles, whose area is larger?" What do you think the area of a circle is related to? " How to deduce the formula for calculating the area of a circle? "For the first question, students will naturally make reasonable guesses through observation and comparison. However, for the problem of how to deduce the formula for calculating the area of a circle, according to the existing knowledge, students think that the circle can be transformed into a previously learned figure, and then the area can be calculated. As for how to transform a song into a straight song, students are not sure because of the limitation of knowledge. I seized this powerful opportunity and entered the next step of teaching.

Step 2: Turn the bend into a straight road and clear the obstacles.

Step 2: Turn the song to the straight and clear the obstacles in teaching. First, with the help of multimedia courseware, the circle with equal size is cut along the radius, divided into 8 equal parts, then straightened, then straightened into 16 equal parts, finally divided into 32 equal parts, and then straightened. Through observation and comparison, students found that the more the average number of copies, the closer the off-line segment of the bottom of the approximate isosceles triangle is. The discovery of this law not only permeates the students with the idea of limit, but also

It is important to completely clear the obstacles of "transformation" for students. At this time, I let go at the right time and entered the next step of teaching.

The third step: experimental exploration and formula derivation.

The third step: experimental inquiry and formula derivation teaching. First of all, I'd like to ask an open question: Can you put the circles together to make the figure you have learned before, try to cut and spell it, think about it, and discuss the relationship between each part of the figure and the original circle? Can you deduce the formula for calculating the area of a circle? Here, I don't rigidly stipulate what graphics students spell, but let students take out circular cardboard that has been divided into 16 equal parts and cut them together to encourage students to spell out a variety of results, thus cultivating students' divergent thinking and innovative ability.

Step 4: Show the results and experience success.

After the group discussion, I will guide the students into the fourth step of teaching and create an opportunity for them to show their achievements and experience success. Ask the students to introduce to the class how they spell approximate parallelogram, rectangle, triangle and trapezoid, and how to deduce the formula for calculating the area of a circle. Then the students themselves, classmates and teachers give comments. At the same time, for the situation of spelling into an approximate rectangle, the teacher combines multimedia intuitive demonstration with blackboard writing.

First of all, let students know that half of the circumference is equal to the length of this approximate rectangle, the radius is equal to the width, and the area of the circle is equal to the area of the rectangle, which is the key to teaching. Then, on this basis, it is deduced that the area of a circle is equal to half a circumference multiplied by a radius, and then students know that half a circumference is equal to πr, so that the formula for calculating the area of a circle is obtained and expressed in letters as S=πr2.

Step 5: echo from beginning to end and consolidate new knowledge.

After the students get the formula for calculating the area of a circle, I enter the fifth step: echo from beginning to end and consolidate the teaching of new knowledge. How many square meters is this tower at least? Find its area. Thereby realizing the consolidation of new knowledge.

Fourth, train in layers and expand thinking.

In order to deepen the research results, in the third link: hierarchical training, the first layer: basic exercise, the second layer: comprehensive exercise, and the third layer: development exercise. Realize layers of depth, from shallow to deep. Gradually train the flexibility and profundity of students' thinking, so that students can deeply understand the truth that "mathematics comes from life and serves life".

(with exercise design)

The first layer: basic exercises

1. Draw a circle with a radius of 2.5cm, and then calculate the area of this circle.

The second layer: comprehensive exercises

2. Find the area of each circle below.

R = 15 cm R = 24cm cm D = decimeter.

The third layer: developmental exercises

3. A sports ground (as shown in the figure below) with a rectangle in the middle and semicircles at both ends. What is the circumference of this playground? What is the area?

"The area of the circle" lecture 3 I. teaching material analysis:

The area of the circle is the content of unit 4 in the first volume of grade six. This unit is based on students' mastery of the perimeter and area of straight lines and their preliminary understanding of circles. Starting with the understanding of the circle, the circumference and area of the circle are consistent with the learning order of the straight line figure. However, the learning circle is from learning straight line to learning curve, and both the content itself and the method of studying problems have changed. Students have a preliminary understanding of the basic methods of learning curve graphics-"turning curves into straight lines" and "turning circles into squares". At the same time, they have infiltrated the internal relationship between curve graphics and straight lines and felt the extreme ideas.

In this unit, the content of this section is arranged after "knowing the circle and the circumference of the circle", so that students can learn and study the area of the circle from their own experience of learning the circumference of the circle; It is helpful for students to understand the laws and methods of plane graphics.

Analysis of learning situation

Students have basically mastered the characteristics of a circle and the calculation of polygon area, but it is the first time for students to contact the area of a curve graph like a circle, so it is difficult to convert a circle into a straight graph.

Students are no strangers to inquiry learning, but in the process of inquiry learning, they often blindly explore. Therefore, it is also a concern in teaching to organize learning materials so that students can form reasonable guesses and conduct targeted inquiry.

Based on the above considerations, the following teaching objectives are formulated:

Teaching objectives:

Knowledge goal: to understand the meaning of circular area; Understanding and mastering the formula for calculating the area of a circle can correctly calculate the area of a circle.

Ability goal: let students experience the derivation process of the formula for calculating the circular area; Let students experience the transformation method of "turning a circle into a square" in the process of hands-on operation and exploration, and feel the limit thought initially.

Emotional goal: feel the connection between mathematics and life, and experience the fun of doing mathematics.

In the inquiry activity, it is one of the basic contents of mathematics to let students experience the process of "doing mathematics", know the figure and accumulate the experience of mathematical activities. Therefore, it is the focus of this lesson to let students experience the derivation process of the formula of circular area and understand and master the calculation formula of circular area. Because the nature of the circle is very different from the straight line graph that students have learned before, it is a challenge for students to contact the "curve graph" for the first time. Therefore, the transformation method of "turning a circle into a square" and the extreme feeling of thought are the difficulties of this lesson.

In order to achieve the above teaching objectives, I carefully designed the teaching to guide students to form a classroom:

Second, review the introduction:

1, 3.14× 43.14× 63.14× 83.14× 93.10.

3. 14×20 10× 10 20×20 30×30 40×40 50×50

3 4 5 6 7 8 9 10 1 1 12 15 16

2. Question: What is the area? Does a circle have an area?

3. Create problem scenarios and introduce topics.

Review question: Li Bin of Class 6 (3) walks around a round flower bed with a diameter of 20m. How many meters did he walk?

Teacher: How many meters did he walk? What does it actually require? Li Bin saw the green workers mowing the circular lawn, so he chatted with his uncle. An uncle asked him, "How many square meters does this circular lawn cover?" At this point, Li Bin was in trouble. Students, let's help him together, shall we? How many square meters does this circular lawn need? What does it actually require? Today, let's learn together: "How to calculate the area of a circle" (blackboard title: the area of a circle)

Stimulate students' desire to learn through the math problems around them, and have a strong interest in this course.

Third, cooperative learning, * * * and derivative.

(1) Guidance: In the past, we converted new knowledge into learned knowledge by spelling (triangles and ladders form parallelograms) and cutting (parallelograms are cut and put into rectangles) to solve problems, so can we use the spelling method in this lesson? If you can cut it, how to cut it properly?

(2) Group cooperation: Let students turn the circle on their hands into the figure we have learned by folding, cutting and spelling. Divide the circle into several parts evenly and make it into an approximate rectangle. Let the group representatives report the results, eliminate unreasonable methods by asking, and find the breakthrough to solve the problem. (Show the courseware. The area of the mosaic figure can't be found with the learned knowledge, because its edges are circular arcs. When we bisect the circle, the more copies each looks like a triangle, the closer the figure is to the rectangle, and the closer its area is to the area of this rectangle. If the circle can be divided finely enough, the figure will be a rectangle. The concept of permeability limit. In this link, teachers become students' learning partners. Under the guidance and inspiration of teachers, every student can speak, do and think, and cultivate students' initiative and enthusiasm in learning. Create a harmonious and efficient learning atmosphere.

(3) Explore the relationship between rectangle and circle. Note: Although the shape of the circle has changed during this transformation, its area has never changed, which is the key to the establishment of our formula. (courseware demonstration). As can be seen from the above figure, the radius r of the circle and the length of the rectangle = (2π r) ÷ 2 = π r; Width =r, because the area of rectangle = length × width, and the area of circle =πr×r=πr2. All students actively participate in exploration and experience the fun of success in participation.

Fourth, the goal of courseware application

Compared with primary school students, the concept of graphic area is abstract. Although we have learned and mastered some formulas for calculating the graphic area surrounded by line segments, many students still find the concept of area difficult to understand. Proper use of courseware can flexibly show the relationship between graphic area and plane.

Five, the blackboard design

Area of a circle

Review: the area of rectangle, triangle and trapezoid.

The concept of circular area: the size of the plane occupied by a circle is called the area of the circle.

Formula for calculating the area of a circle: S=πr2.

Six, homework design

1, complete the exercises specified in the textbook;

2. Find the area of circular objects in life;

(1) The problem of sheep eating grass.

(2) Irrigation problem

Mathematics problems that can't be solved at the beginning of class can be solved by autonomous learning, so that students can experience the joy of learning. Applying what you have learned is the ultimate goal of learning mathematics, and this lesson is prepared to reflect this goal, which is also a positive embodiment of learning valuable mathematics.