Lecture notes on the circumference 1 I. Teaching materials
1, teaching content:
Circumference is the first time to learn the circumference of curves and graphs on the basis of learning the general concept of circumference and the calculation of the circumference of rectangles and squares in the first volume of Grade Three. It is the deepening of learning "the understanding of circle" in the front, and the foreshadowing of learning "the area of circle" in the back, which lays a solid foundation for learning solid geometric figures such as cylinders and cones in the next semester, so it plays a role in connecting the past with the future.
2. Teaching objectives:
Knowledge and skills: make students know the meaning of the circumference and pi of a circle; Only by experiencing the formation process of pi and exploring the calculation formula of pi can pi be calculated correctly.
Process and method: Let students experience the process of exploring the relationship between the circumference and diameter of a circle and experience the learning mode of discovery, verification and application.
Emotional attitude and values: educate students in patriotism and dialectical materialism.
3. Emphasis and difficulty in teaching
Emphasis: the derivation and application of the circle formula.
Difficulty: understanding the meaning of pi
4. Teaching AIDS:
Teaching aids: round objects and pictures.
Learning tools: three round objects, lines, rulers, and pieces of paper with different diameters.
Second, talk about learning.
Senior students can use existing knowledge and experience to discover new knowledge through migration and exploration, and can solve practical problems with new knowledge. In the learning environment of group cooperation, they adopt the learning method of independent exploration and have high learning enthusiasm.
Students have known the circle, know that the radius and diameter of the circle determine the size of the circle, and understand the relationship between the diameter and radius in the same circle, which paves the way for students to learn the circumference of the circle.
Third, preach the law.
1, teaching method: This class adopts "four links" classroom teaching method, namely "students preview, group discussion, problem statement and teacher answering questions".
2. Oral English and learning methods: This course focuses on learning methods such as measurement, calculation, guessing, verification, discussion and self-study.
Fourth, talk about the teaching process
In order to achieve the expected teaching purpose, I made a systematic plan for the whole teaching process. Design several teaching links.
(1) Game import
Push the hoop into the classroom and introduce new lessons. Q: Have you ever played this game? Do you know the circumference of a circle? (Title on the blackboard: Circle C) Touch a circular object with your hand. Who can choose one of the circular objects or circular pictures brought by the teacher to talk about the circumference of the circle?
The teacher concluded that the length of the curve around a circle is called the circumference of the circle. (Writing on the blackboard: the meaning of the circle) Let students touch the circle first, initially feel that the circle is the length of a week, and then say it orally, which cultivates students' ability to transform their thinking process into an external language.
(2) Class preview According to the key and difficult points of this class, three preview questions are designed: What is pi? How to deduce the circumference formula of a circle? How to solve the example 1 with the formula of circle circumference? Let the students read the textbook word for word with questions and take notes, so that they can have a clear purpose in the group discussion. Let students explore, discover and solve problems independently, so that students can get certain emotional experience and enjoy the pleasure of success.
(3) Group discussion
Six students discuss the puzzles that everyone encountered in the preview for a group, and a student on duty records the problems that the group can't solve. Because six people in each group are carefully selected by teachers, it is an organic combination of excellent, medium and poor students. In this way, soldiers teach soldiers and soldiers learn soldiers, which solves some problems in the regiment. This not only gives full play to the guiding role of top students, but also actively promotes middle students, without neglecting students with learning difficulties.
(4) Problem presentation
Each group shows the unresolved questions of the group, and other groups help to answer these questions.
A set of questions is: "How to deduce the formula of perimeter?"
A set of answers: "Because the ratio of the circumference to the diameter of a circle is π and the divisor is equal to quotient multiplication and division, the circumference formula of a circle is π times the diameter, and because the diameter is twice the radius, the circumference formula of a circle can also be 2 times π times the radius" (blackboard writing: formula)
Another group replied, "Because the circumference of a circle is more than three times the diameter, that is, the diameter times pi, so the formula of pi is like this."
One group asked, "Why is pi an approximation in the case of 1 and the result is equal to sign?"
(5) Teacher's question and answer
Pi is 3, 14, which has been regarded as a general value, so the future calculation result should be equal to the sign. At the same time, remind students of some problems that students have not noticed. For example, the unit of circumference is the unit of length, and the circumference of a circle can be calculated without writing a formula ... in time.
It is difficult to explore and understand pi, so the key point of this link is to answer "what is pi?" .
Zu Chongzhi, the most outstanding contributor of pi, was introduced to the students.
(6) solving problems
1, true or false
2. Application of perimeter formula
Step 3 solve practical problems
(7) Exchange gains
What did you get from this lesson?
Five, say blackboard writing design
Concise, clear and focused.
Circular handout II I. teaching material analysis
The circumference of a circle is the second section of Unit 4 in the first volume of the sixth grade of People's Education Press, which is based on the general concept of the circumference of the first volume of the third grade and the calculation of the circumference of rectangles and squares. Through a series of operation activities, the textbook tries to make students understand the meaning of pi through observation, analysis and induction, experience the formation process of pi, and deduce the calculation method of pi, which lays the foundation for learning the knowledge of circle area, cylinder and cone. At the same time, through the study of this class, students' practical ability, unity and cooperation ability and problem-solving ability are further cultivated, and students are educated in ideology and morality.
Second, the teaching objectives
According to the analysis of the above structural characteristics and students' cognitive rules, the teaching objectives of this lesson are determined as follows:
1, knowledge goal: let students know the circumference of a circle and understand the meaning of pi in a specific situation; Only by understanding and mastering the formula for calculating the circumference can the circumference be calculated correctly.
2. Ability goal: To cultivate students' observation ability, hands-on operation ability, analysis ability, generalization ability and cooperative learning ability through the measurement of pi, the exploration of pi and the derivation of pi formula.
3. Emotional goal: to educate students on dialectical materialism by exploring pi; Combine the story of Zu Chongzhi, an ancient mathematician in China, and educate students in patriotism.
Third, teaching focuses on difficulties.
The teaching emphasis of this lesson is: to understand and master the calculation method of the circumference of a circle; Circle is a curve figure and a new plane geometry, which deepens the teaching of perimeter calculation of plane figures. In particular, the concept of pi is abstract, so I take exploring the meaning of pi and deducing the calculation formula of pi as the difficulty of this lesson.
Preach the law
Students are open and creative individuals, and they will participate in the communication between teachers and students in the classroom with their existing knowledge, experience, inspiration and interest. They will enrich the classroom with their own guesses and verifications. Let the math classroom be full of vitality. Therefore, let students experience the formation process of mathematical knowledge, experience the creativity of mathematical learning, feel the rigor of mathematics and the accuracy of conclusions, and then cultivate students' consciousness of thinking about problems with mathematical thinking methods. This is the basic quality that students must have to adapt to future life. With these understandings of the new curriculum, in the teaching of the circle, I used methods such as operation, guessing and verification, as follows:
1, using the mathematical thinking method of guessing and verifying: in teaching, I first let students guess boldly, and then guide students to find ways to verify guessing with language, so that students can feel the mathematical thinking method and feel the rigor of mathematics.
2. Hands-on operation, active interaction: Teachers let students find problems and explore independently through activities such as measurement, experiment and calculation. The specific method is: let students use learning tools to calculate and find the law, so as to deduce the calculation method of the circumference of the circle. In the process of exploration, the teacher gives guidance and acts as a guide for students' learning.
3. Observation, discussion, communication and cooperation: In teaching, teachers organize students to communicate in groups on the basis of independent thinking, and put forward communication methods and steps according to the age characteristics of students, so that students can communicate in an orderly, purposeful and orderly manner. Improve the timeliness of communication.
teaching program
The whole teaching process is divided into four links.
The first link: create the situation and establish the concept of circumference.
1. Show me a clock. What is the track of the small second hand on the clock in one minute? So how far does the top of the small second hand go in an hour? Lead the topic (circle)
2. Let the students take out the circular learning tools, have a look, touch and tell which part the circle refers to. Experience and understand the meaning of the circle by yourself. Effective touch experience and sufficient rational generalization make the construction process of the concept of circumference substantial and effective. )
The second link: hands-on practice, feeling the measurement method.
1. Question: The circumference is a curve. How to measure the circumference of a circle?
2. Guide students to operate, cooperate and communicate, and find out the method of measuring circumference.
3. Students report and demonstrate the measurement method. (rope winding method, rolling method)
4. These circles are relatively small. If there is a big circle, can you measure its circumference by winding and rolling the rope? What if I can't measure it directly?
Through deliberate reflection and free evaluation of the two measurement methods, students dialectically felt the limitations of the "winding" and "rolling" methods, which stimulated their enthusiasm for exploring the "calculation formula" and made a "psychological" foreshadowing for further study of the calculation of pi. )
The third link: put forward a reasonable guess and verify it.
1, the circumference of a square is four times the length of its side, so is the circumference of a circle also related to the line segments? (Encourage students to make bold guesses)
2. As a group, take out the circular learning tools prepared before class, measure their perimeters and diameters respectively, calculate the ratio of perimeters and diameters, and fill in the following table: (The measured values are accurate to the millimeter) Project name Perimeter Diameter 1 Circle No.2 and No.3.
3. After observation and comparison, students can find that no matter how the size of the circle changes, the ratio of the circumference to the diameter of the circle is probably more than 3 times.
4. The teacher introduced pi. Π≈3、 14
5. Students should read relevant materials of pi, and teachers should carry out patriotic education in time.
6. Can the formula for calculating the circumference be obtained by analyzing the table? Because of the previous layers of bedding, students can easily get the calculation method of the circumference of the circle: c = π DC = 2π R.
(This part of the content is mainly to let students operate independently, explore independently, and through observation, find problems, participate in cooperation and exchange, summarize and get solutions to problems, so that students can get certain emotional experience and enjoy the pleasure of success. It improves students' ability of analysis, reasoning and generalization, and develops students' concept of space. )
The fourth link: using knowledge to solve problems.
1, example 1 (design purpose: through example calculation, students can better understand the role of mathematics in life, solve real life problems and lay a good foundation for the final exercise).
Now, can you tell us the distance that the tireless little second hand traveled in an hour? What kind of data do you want to get to solve this problem (design purpose: let students find the conditions to solve the problem themselves and cultivate their independent thinking ability. This problem echoes the previous introductory question, thus solving the problem from beginning to end. )
The circumference of the circle represents draft text 3. Let's talk about textbooks first.
The circumference is selected from the third section of the first volume of the sixth grade mathematics of Beijing Normal University. The teaching of this course is based on the knowledge of the perimeter of rectangle and square, which deepens the previous knowledge of "circle" and is also the basis for learning the area of circle later. This course serves as a link between the past and the future, and is an important content in elementary geometry teaching.
According to the curriculum standards and the intention of compiling teaching materials, the teaching objectives of this section are established as follows:
1, knowledge target:
Know what a circle is; Understand the meaning of pi; Understand and master the calculation formula of circumference.
2, ability goal:
Will initially use formulas to solve some simple practical problems in life.
3, ideological goals:
Inspire students' pride as sons and daughters of China through the story of Zu Chongzhi and Pi.
Teaching focus:
Explore and discover the relationship between the circumference and diameter of a circle.
Teaching difficulties:
Use the knowledge of circle to solve some simple practical problems.
Second, talk about teaching methods and learning methods.
According to the teaching content and students' cognitive rules, I first use the method of courseware demonstration to help students understand the circle, infiltrate and transform their thoughts; Then, students are guided to know and understand pi by experiments, and the calculation formula of pi is deduced, so as to cultivate students' operational skills and improve their ability of analysis, comparison, reasoning and generalization. Finally, the method of self-study guidance is adopted to guide students to think, measure and calculate themselves, and finally find out the relationship between circumference and its diameter and radius, so as to improve students' self-study level. In teaching, we should pay attention to students' independent thinking and group communication, and use various learning forms interactively to achieve the teaching goal of developing intelligence and cultivating ability.
Teaching preparation:
1, multimedia courseware.
2. Each student prepares three disks with different sizes and integer diameters, a line and a ruler.
Third, talk about the teaching process
(A) create a situation, passionate investment
The courseware shows the story of a race between a little black donkey with two generations of affection and a little yellow donkey with a king. Guide the students to observe and think: what is it that requires the donkey to walk? Ask the students to reveal the topic: the circumference of a circle.
Using multimedia courseware to assist teaching can effectively stimulate students' interest in learning and make them have a strong desire to learn, thus forming a good learning motivation. )
(B) independent cooperation to explore new knowledge
1, teaching aid demonstration, intuitive perception, combined with cognitive understanding of the circle.
Students experiment independently, measure the circumference around the coil, and the teacher guides the operation points to cultivate students' practical ability. )
2. Complete the experiment in groups.
A. Measurement record: Students measure the circumference and diameter of a circle, and then record the data to cultivate students' practical operation ability.
B comparison: compare the data and reveal the relationship.
Students continue the experiment, work out the quotient of dividing the circumference of each circle by its diameter, and record the quotient. Through calculation, students find that the perimeters of these three circles are all more than three times their diameters and lengths. It is concluded that the circumference of other circles measured is also more than 3 times its diameter.
Cultivate students' practical ability and skills in the process of experimental operation, and improve students' ability of analysis, comparison, reasoning and generalization. )
3. Introduce pi.
(1) First, introduce a number that is more than 3 times. This is a definite number, which we call pi. Expressed by the formula: circumference/diameter = pi.
② Introduce the reading and writing methods of π.
(3) Finally, the story of Zu Chongzhi and ancient mathematician Pi is introduced in combination with the portrait, so as to inspire students' pride as sons and daughters of China. At the same time, it is pointed out that pi is an infinite decimal and its approximate value in primary schools is 3. 14.
④ Students summed up the formula for calculating the circumference:
The circumference of a circle = the diameter of a circle ×π, which is expressed by letters as c =π× d.
The courseware shows a circular runway with a diameter of 50 meters and a schematic diagram of its circumscribed square runway. Let the students observe and think about the diameter of the circle and the side length of the square, and then quickly calculate the perimeters of the two runways with formulas. Let's see if the game between the king and the two generations is fair.
4. Courseware demonstration: The radius of circular grassland is 25m, and the circumference of circular grassland is calculated. Arouse students' thinking, and get the formula of finding the perimeter by radius: c = 2π r.
The application of multimedia courseware teaching can increase the amount of classroom information, make students easily accept what they have learned, take the initiative to participate in teaching, grasp the key points and difficulties of teaching in a pleasant atmosphere and interactive discussion, and the teaching effect is very good. )
5. Practical application.
Two generations saw that his round donkey fence was a little loose, so he decided to reinforce it three times with some thick iron wire. Two generations want to ask you for help. How long does it take to calculate this fence with a radius of 4 meters?
Students quickly calculate and communicate: first find out the circumference of a circle, that is, how many iron wires a circle needs, and then multiply it by 3 to find out how many iron wires three circles need.
Taking the fence wire as an example, the practical application value of the formula for calculating the circumference is reflected. )
(3) Strengthen training and form ability.
Courseware presentation must be done, selected and expanded.
Required questions (for students with learning difficulties):
1, choose to fill in the blanks.
A, the wheel rolling a week, the wheel forward distance is ()
A, radius b, diameter c, circumference
B, the circumference of a circle is () times the diameter.
a、3. 14B、πC.3
C, the quotient of the circumference of a big circle divided by the diameter () the quotient of the circumference of a small circle divided by the diameter.
A, greater than b, less than c and equal to 2, and find the perimeter d of the following circle = 8 dm; r = 5cmd = 6mr=3dm .
Select a question (report to ordinary students):
(1) The radius of a car wheel is 0.3m How many meters does it roll 1? How many meters 1000 laps do you roll?
(2) The perimeter of the flower bed is 62.8m.. Can you find out the diameter of this round flower bed?
Extended problem (report to top students):
Cut the largest circle from a square paper with a side length of 6 cm. What is the circumference of this circle?
Courseware shows that the questions must be done, selected and expanded, with strong pertinence and good effect: the questions must be done to help students with learning difficulties digest what they have learned and make them gain something; The topic selection is conducive to the improvement of students with learning difficulties and middle school students; Expanding questions are conducive to the expansion of top students' thinking, so that every student can develop and improve. )
(4) Summarize and improve, and guide practice.
Students report the gains of this class. Guide students to review and summarize the knowledge, learning methods and emotional experiences learned in this section. )
Fourth, comments.
In this class, teachers effectively integrate mathematics teaching with multimedia courseware, which increases the amount of classroom information, and the teaching process is illustrated and vivid. In teaching, teachers play the role of organization and guidance, give targeted guidance according to the actual situation of students, and give full play to the main role of students, thus improving teaching efficiency.