Lecture Notes of "Circle" for Grade Six 1 1. teaching material analysis and Students' Analysis
1, teaching material analysis:
This is a teaching content that combines concepts and calculations to study geometric shapes. It is taught on the basis of students' previous understanding of straight lines and their preliminary understanding of circles in the last class. 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. Moreover, in the process of deducing and demonstrating the knowledge about the circle, the students' ability to actively explore, practice and solve practical problems in life is cultivated.
2. Student analysis:
Although students have the foundation to calculate the circumference of a straight line, the concept is abstract and difficult to understand when they first come into contact with curve graphics, so it will be difficult to deduce the calculation method of circumference and understand the significance of pi.
3. Teaching objectives
(1) Knowledge objective: Make students understand the meaning of pi, deduce the formula of pi, and make simple calculations correctly.
(2) Ability objectives:
① Cultivate students' abilities of observation, comparison, analysis, synthesis and hands-on operation.
(2) To understand the dialectical materialism concept that things are interrelated and developing with each other and the dialectical thinking method of seeing the essence through phenomena.
(3) Emotional goal: By introducing the great achievements of Zu Chongzhi, an ancient mathematician in China, to educate students in patriotism and inspire national pride.
4. Analysis of teaching emphases and difficulties
According to the writing intention of the textbook and students' cognitive rules, if students can understand the problem that the circumference of any circle is more than three times its diameter, then the induction of the formula for calculating pi can be easily solved. Therefore, it is important for students to understand the derivation process and practical application of the formula of pi, and it is difficult to understand the meaning of pi in teaching.
Second, the analysis of teaching methods and learning methods
Mathematics curriculum standard points out that "hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics" and "students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning". So, how to embody the learning and teaching methods advocated by the new curriculum?
My idea is:
1. Provide students with a platform for cooperative exploration. I divide the students into several study groups, each group has middle school students with different levels, and require students to be equipped with learning tools such as straightedge and rope, so that each study group can measure the circumference by rope method and rolling method, find out the multiple relationship between diameter and circumference according to the measured data, and deduce a circle circumference formula to experience the formation process of knowledge.
2. In teaching, interactive learning methods such as independent thinking, cooperative operation and group communication are used to guide students to think, explore, find and solve problems in cognitive contradictions and practical operation.
Third, the preparation of teaching AIDS and learning tools:
According to the teaching tasks and students' learning needs, I prepared a ruler, round cardboard, rope, scissors and multimedia courseware for teaching, and the students prepared a ruler, round cardboard (one for large, medium and small), rope and scissors for learning.
Fourth, the classroom structure design:
According to the content characteristics of this class and students' cognitive rules, I designed the classroom structure like this: first, let students recall what the perimeter of a square or rectangle refers to. What is the unit of measurement? Then inspire students to say the meaning of perimeter, and then organize students to understand the meaning of perimeter through three activities, understand pi and deduce the calculation formula of perimeter. Then arrange exercises to consolidate knowledge, guide students to solve practical problems, and finally evaluate and check the effect of students' learning.
My design intention is to introduce new knowledge from old knowledge, which is easy for students to accept, deepen their understanding through personal practice, and then arrange basic and practical questions to consolidate new knowledge in time, which is conducive to the formation of students' skills.
Five, the teaching process theory:
(1) Introduce stories to stimulate interest.
Design intention: In this link, I use vivid stories to attract students' attention and stimulate their interest in learning, which not only reviews old knowledge, but also naturally leads to topics.
(B) hands-on practice, explore new knowledge
1, know the circumference and summarize the method of measuring the circumference. The teacher first took out the teaching aid-circle to inspire students to observe, and then asked students to describe the meaning of circle by pointing and touching; Finally, let the students cooperate and communicate, and try to measure the circumference with learning tools. The teacher will guide and summarize the basic methods of measuring the circumference: rope measurement and rolling method.
2. Explore the relationship between the circumference and diameter of a circle.
Question 1: Is it possible to help rabbits get off the runway by tumbling? What about the rope method
Question 2: The circumference of a square is related to its side length. What does the circumference of a circle have to do with me?
Ask questions at different levels, and use learning tools (big, medium and small circles) to guide students to fill in the form on page 63 of the textbook in groups. The circumference of a circle (cm) The diameter of a circle (cm) The circumference of a circle divided by the quotient of its diameter (cm) Through careful observation, students can easily find that the circumference of a circle is related to its diameter, and the larger the diameter, the longer the circumference. Through calculation and report, it is found that "the circumference of a circle is always more than 3 times its diameter". Finally, the relationship between the circumference and diameter of a circle is demonstrated by courseware. Through data comparison, students can independently discover the multiple relationship between the circumference and diameter of a circle and be more interested in cooperative exploration.
3, self-study pi, and guide the calculation formula of pi.
While students are experiencing success, I sublimate the teaching difficulties of this course by the way, introduce pi with courseware, and draw the key and difficult points of this course in the form of a report: the concept of pi and the design intention of pi calculation formula: through hands-on practice, cooperative communication, autonomous learning and other activities, students can not only break through the difficulties, but also master learning methods, enhance national pride, feel the profoundness of Chinese culture, and implement three teaching goals.
(C) practical application, expanding innovation
According to the characteristics of this section, I designed the following three levels of exercises:
1, the first level: basic questions help rabbits calculate the circumference of a circular runway with a diameter of 100 meters.
2. Level 2: The equatorial radius of the earth is about 6,378 kilometers. How many kilometers is it to walk around the equator? (Numbers are reserved as integers)
3, the third level: the teacher wants to know the diameter of the cross section of the old locust tree in Wenfeng Middle Road. Do you have any good ideas? Design intention: help students form a complete knowledge chain, and at the same time extend classroom teaching to extracurricular activities, so that students can feel that mathematics comes from life and is applied to life.
To sum up, the teacher asked: What did you gain from today's study? Student: I know ... I learned. ...
Say blackboard writing: Design intention: My blackboard writing is concise and clear, highlighting the key and difficult points of this lesson.
Design concept: Before class, I used vivid stories throughout, which not only stimulated students' interest in learning, but also laid the foundation for exploring new knowledge. In class, I adopt various teaching methods, which reflects the diversity of learning. Guo Moruo once said: "The purpose of teaching is to train students to study, study, think, see with their own eyes and do this spirit with their own hands."
Sixth grade "Circle" lecture 2 Dear judges and teachers,
Hello everyone! I am Chang Fan from Free Road Primary School in Anyang.
I. teaching material analysis
The content of the class I'm talking about today is the circumference of a circle, the standard experimental textbook for compulsory education courses, the first volume of sixth grade mathematics, pages 62 to 64. This is a teaching content that combines concepts and calculations to study geometric figures. Through a series of operation activities, the textbook tries to make students understand the meaning of pi through observation, analysis and induction, verify 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. So as to cultivate students' ability to explore, practice and solve practical problems in life.
Second, the analysis of learning situation
Circle is a kind of curve figure and a new plane figure, which deepens the teaching of perimeter calculation of plane figure. Before teaching the course "Pi", most students have learned about Pi through various channels, but only on the surface. How to make students verify and understand the significance of pi is a difficult point.
Third, the teaching objectives
(1) Knowledge objective: Verify and understand the meaning of pi, understand and master the calculation formula for finding the circle, and calculate the circle correctly.
(2) Ability goal: To cultivate students' ability to reason, analyze, summarize and solve simple practical problems through teaching activities such as measuring, verifying and deducing the calculation formula of the circle.
(3) Emotional goal: cultivate students' good behavior habits of being brave in exploration, positive thinking, unity and cooperation, and let students experience the value of mathematics in their study. In addition, by introducing the historical materials of pi, patriotism education is carried out.
Teaching emphases and difficulties:
Key points: By measuring, calculating and verifying the relationship between circumference and diameter, students can understand and master the calculation method of circumference.
Difficulties: verify and understand the significance of pi.
Fourth, teaching preparation.
Teaching aid preparation: multimedia courseware, experimental record sheet.
Preparation of learning tools: round objects, CDs, round pieces of paper, white paper with circles drawn on it, ruler, rope and calculator.
Verb (abbreviation of verb) teaching method and learning method
This course mainly adopts trial teaching method and heuristic teaching method, which embodies the main position of students and the leading role of teachers.
In learning the law, the ancients said that "it is better to teach people to fish than to teach people to fish." In the teaching of this course, I created a free and broad space for students.
(1) Independent inquiry method, through hands-on practice, seeks the method of measuring circumference, and cultivates students' hands-on operation ability.
(2) Cooperation and communication method, through students' unity and cooperation, independent exploration, discussion and communication, can better break through the teaching difficulties and cultivate students' spirit of unity and cooperation.
Sixth, the teaching process.
I designed the following teaching process in this class:
(A) create a situation to stimulate interest.
1, story introduction, revealing the topic.
Interest is the best teacher. When I introduced the new lesson, I showed the little yellow dog and the little gray dog in a race with the courseware. The little gray dog runs along the square route and the little yellow dog runs along the circular route. The little yellow dog won. The little gray dog was very unconvinced when he saw that the little yellow dog won the first prize. It says such competition is unfair. Students, do you think this kind of competition is fair? Students can't wait to tell their findings, and then guide them to observe: what is the actual distance that the little greyhound runs in a square? How to ask? What's the distance the little yellow dog runs? What is seeking a circle? Lead out the learning content of this lesson (blackboard writing: circumference)
Design intention: By creating problem scenarios, students can not only review the meaning of the perimeter of a square, but also transfer knowledge, perceive that the length of a circle is the perimeter of a circle, and stimulate students' interest.
2. Perceive the circumference of a circle
There are coins, rings, pen containers, cans and other items on each student's desk. Find a circle, touch and point to the circumference of the circle, and say what the circumference of the circle is in your own words.
Design intention: Let the students touch the circumference with objects, and let them grasp the concept of circumference more firmly.
(2) Hands-on operation to explore new knowledge.
1, measure the circumference of a circle.
Activity 1: Measure the circumference of a circle.
I prepared a schoolbag for the students. There are disks (each group is the same) and circular pieces of paper (each group is different in size), a circular white paper (the circumference is the same), a ruler and a rope. Ask the students to find the perimeters of these three circles in groups. Here are three different circles for students to measure the circumference, so that students can find the circumference of the circle in different ways. For the circumference of a disk circle, students can use the rope winding method and the rope rolling method to find the penetration, and students can "turn the curve into a straight line"; Fold the circular piece of paper in half and measure its 1/4 (or 1/8, or116, ...) (the finer the score, the closer the result). The circumference of a circle drawn on rectangular paper is difficult to operate in practice, in order to arouse students' further thinking about whether it can be calculated.
Design intention: In the form of group study, students are allowed to explore the circle freely, with the purpose of embodying the teaching concept of allowing students to explore independently and cultivating students' sense of cooperation and ability. For these three different methods, our deeper significance lies in making students' thinking not stay at the same level and giving full play to each student's "inquiry" ability.
2. Verify and understand pi.
Activity 2: Verify and understand pi.
Through the understanding of some relevant materials and the investigation of 9 classes in grade six in our school, most students have learned about pi through various channels before teaching, and a few students have learned about the calculation formula of pi. So I asked the students directly, how are you going to calculate the circumference of this circle? What do you know about pi? Students may say, I want to multiply pi by pi to calculate the circumference of a circle. What do you know about pi? Students may say that pi is expressed by the letter π, which is between 3. 14 15926 and 3. 14 15927, and π≈3. 14. At this time, the teacher praised the students' understanding of extracurricular knowledge. Then let the students cooperate in groups, explore independently, fill in the following table and communicate with the whole class.
(1) Measure the circumference and diameter of CD and round paper and fill in the form.
measure
Circumference of object circle
Diameter of circle (cm)
(cm) circumference ÷ diameter
(Keep two decimal places)
laser record
Circular paper
(2) Report
Table 1: CD-ROM
Serial number 12345
Perimeter (cm) 383837,737,537,2
Diameter (cm)121,71212.
Circumference ÷ diameter 3,173,253.143, 133, 10.
Table 2: Circulated documents
Serial number 12345
Circumference (cm)1419,52038,5314
Diameter (cm) 4,56,261210
Circumference ÷ diameter 3, 1 13,153,333,213.438+04.
Observation table 1. What did you find? Compare table 1 with table 2. What do you find? By observing and comparing different data of the same CD, students realize that the circumference and diameter of a circle are measured in approximate values, which is the fundamental reason for the difference in quotient, that is, there are errors in measurement. With this kind of activity experience, students can think that the data of other circular objects must have errors through simple analogy. Then, let students observe the characteristics of this series of quotients, and they will find that although most quotients are different, they are very different from each other. In the process of guessing, guide students to think comprehensively and rationally: if there is no error factor, the quotient obtained by dividing the circumference of a circle by its diameter should be the same, so as to deeply understand and experience that pi is a fixed number.
Design intention: In this process, students can truly understand the error, truly feel the influence of the error on the experimental results, and skillfully use the experimental error to "turn the error into treasure", deeply understand that the fixed pi is the result of "idealization", and their thinking can be constructed and improved.
3. Introduce the research history of pi.
Courseware demonstration:
For thousands of years, countless famous mathematicians have devoted their lives to the study of pi. Do you know that?/You know what? Do you know that?/You know what? China mathematicians have made great achievements in calculating pi.
About 2000 years ago, there was a saying in China's ancient algebra book "Zhou Bi suan Jing" that the circumference of a circle is three times its diameter. About 1500 years ago, there was a great mathematician and astronomer Zu Chongzhi in China. He calculated pi between 3. 14 15926 and 3. 14 15927, becoming the first person in the world to calculate pi to seven decimal places. His great achievements are at least earlier than the calculation results of European mathematicians 1000 years. Now people can use computers to calculate hundreds of millions of decimal places.
Design intention: Through cooperative learning, independent exploration and report exchange, we can not only break through difficulties, but also master learning methods and cultivate students' interest in scientific knowledge. I am also proud of the outstanding achievements of ancient mathematicians in China, and I have educated students in patriotism.
4. Derive the formula for calculating the circumference.
Activity 3: Derive the formula for calculating the circumference.
Through the verification of pi and the results of each group, and the relationship between pi and diameter, the formula of pi is extracted and expressed in letters as C=πd (blackboard writing)
According to the relationship between diameter and radius, C=2πr (blackboard writing) is deduced.
Now can you calculate the circumference of the circle on our paper? It is known that the radius of a circle is 3 cm. Students calculate and report
Design intention: Let students learn learning methods by thinking, exploring, analyzing, discovering and summarizing laws.
5. Example of autonomous learning 1
Because the students have worked out the formula for calculating the circumference, I let them learn independently in the study of example 1.
The courseware gives an example of 1:
Children, please work out the example 1 with your friends and talk about your thinking process. Students independently solve the teacher's patrol, and then find students to play and talk about their own ideas.
[Design intent: Let students use their brains and mouths when answering questions, and cultivate students' habit and ability of autonomous learning. ]
(3) Consolidate practice and form ability.
1, I'm an expert in calculation.
d=5cm，c=？ r= 14dm，c=？ C=94、2m，r=？
Design intention: Through practice, students can further consolidate the new knowledge they have learned today.
I am a little judge.
( 1)π=3. 14。 ()
(2) The circumference of a circle is always three times the diameter. ()
(3) Pi is an infinite acyclic decimal. ()
(4) The perimeters of two circles with equal radii are also equal. ()
Design intention: this set of judgment questions further strengthens the focus and difficulty of this lesson from both positive and negative aspects.
I am a small referee.
Little yellow dog and little gray dog race, little gray dog runs along the square route, little yellow dog runs along the circular route, and little yellow dog wins. Do you think this game is fair? Why?
Design intention: solve the problems at the beginning of class and make students feel that mathematics is used to learn mathematics.
4. Mathematics in life
(1) The minute hand of the wall clock is 20 cm long. How many centimeters does the minute hand tip move after 30 minutes? In 45 minutes?
(2) Beautiful semi-circular floor mats. Its straight side is 80 cm long. What's its length in a week?
Design intention: expand basic knowledge and improve application ability, so that students have room for thinking and solve problems in life with what they have learned.
(4) Summarize the evaluation and experience success.
I summed it up in words:
1. What have you learned?
2. How did you learn it?
3. In your experience, what other practical problems are similar to the circle in your life?
Design intention: This way of talking and summarizing not only summarizes and combs the knowledge learned, but also embodies the guidance of learning methods and enhances the emotional experience.
Seven, blackboard design
perimeter of a circle
π≈3. 14 cases 1:
C=πd
C=2πr
Sixth grade "circle" handout draft III I. Teaching materials
In this lesson, students learn the general concept of circle and some basic knowledge of circle, and then further learn the calculation of the circumference of circle. Learning this lesson well not only enriches the calculation method of students' figure perimeter, but also makes theoretical preparation for the second class to calculate the diameter or radius of a circle by using the formula of circle perimeter. Pi discussed in class is also the necessary knowledge to learn the area of a circle.
For students, the formula for calculating the circumference of a circle is not as easy to get as that of a rectangle or a square. Therefore, the teaching materials pay more attention to intuition and operability. On the basis of understanding the textbook, I made some flexible adjustments, and filled the whole classroom with round smiling faces with different perimeters, both as prizes and as learning tools for students to learn the circumference.
According to the cognitive law from concrete to abstract and the psychological characteristics of students. I have set the following teaching objectives:
Second, talk about teaching objectives
1, knowledge and skills: enable students to understand the meaning of pi and circumference, master the approximate value of pi л, and master the calculation method of circumference.
2. Process and method: By exploring the relationship between the circumference and diameter of a circle, we will further establish the sense of group cooperation and guide students to communicate, learn and interact in cooperation.
3. Emotional attitude and values: Introduce the great achievements of China ancient mathematicians Liu Hui and Zu Chongzhi to students, and stimulate their national pride.
4. Evaluation goal: use evaluation to examine students' learning situation, stimulate students' learning enthusiasm, and let students learn to evaluate others, evaluate themselves and build self-confidence.
Third, talk about the importance and difficulty of teaching.
The calculation of pi, the understanding of the meaning of pi and the derivation of pi calculation formula.
Fourth, talk about teaching methods and learning methods.
The new curriculum standard points out that there is no fixed method in teaching, but it is important to have correct methods. Mathematics teaching activities must be based on students' cognitive level and existing knowledge and experience. Grade six students have a certain practical ability and calculation ability. I boldly let go and organize students to carry out inquiry learning activities by asking questions to stimulate interest, operating discovery and quoting classics. Let them learn new knowledge through independent exploration.
Effective mathematics learning activities are not simply dependent on imitation and learning, but a purposeful and active process of constructing knowledge. To this end, I attach great importance to the guidance of students' learning methods. In this class, I guide students to learn through hands-on operation, independent inquiry, cooperative communication and observation and discovery. Let the students take detours, measure, calculate, discuss, see and gain new knowledge.
V. Presentation teaching aids and learning tools
And several round smiling faces, round cardboard, ruler, soft ruler, ribbon and calculator with different perimeters are teaching AIDS and learning tools for this class.
Sixth, talk about the teaching process.
(-) Stimulate interest in objects and introduce new lessons.
I will ask: students, look, what is this?
Smiling face!
If the teacher turns it upside down, it is the plane figure we have learned, called circle!
What do you know about circles, children? Students will say some basic knowledge about circles. )
At this time, I follow the trend. In this lesson, we will learn "circumference". Words on the blackboard: the circumference of a circle
Please point out the circumference of your round cardboard. And ask the students: What is a circle? According to the students' answers, both teachers and students concluded that the length of the curve forming a circle is called the circumference of the circle. (written on the blackboard)
We know what a circle is, and what does the length of the circle have to do with it? And show it. Verify that the longer the radius of the circle, the longer the circumference of the circle. That is, the larger the diameter of the circle, the longer the circumference of the circle.
(B) hands-on, explore the proportion
1, operation stage
(1) gives the measured value of the tool. Then if the teacher gives you some tools, ribbons, rulers and soft rulers, can you use these tools to find a way to measure the circumference of the round cardboard in your hand? I give students space to explore and let them solve problems with their own wisdom.
After exploring, let the students report how to measure the circumference of a circle. Children can speak in many ways. I commented in time: Son, your method is really creative! The teacher rewarded each group with a smiling face of Zhang Yuanyuan.
(Design intent: First, encourage students to study hard and actively participate in learning activities; Second, use the round smiling face as a learning tool to find the relationship between circumference and diameter. )
And explain that all these methods just now are to convert curves into straight lines. This is a very important mathematical method called "turning a curve into a straight line". (written on the blackboard)
(2) continue to doubt. I then asked this question: If the circle is very big, how do you find the circumference? Guide students to explore the relationship between the circumference and diameter of a circle.
Let's recall that when learning the perimeter of a square, the perimeter of the square is four times the length of the side. Is there such a multiple relationship between the circumference and diameter of a circle? (blackboard writing: the circumference of a circle is several times the diameter, which can also be said to be the ratio of circumference to diameter. c/d=)
(3) Explore the proportion. Please turn the smiling face that the teacher gave you upside down and try to measure its circumference and diameter with the learning tools in the learning tool bag and calculate its ratio. And fill in the results on the record table. Before the activity, I asked the students to read the activity requirements carefully.
(Design intention: Really realize the value of group cooperation, and let every student participate, with both division of labor and cooperation. )
2. Report comparison stage: After the students fully explored, I asked the neighboring group to compare the ratio of circumference to diameter first, whether it is near or far. Because the circumference of the round smiling faces I sent to each group is different, this is to give the students a preliminary understanding. At first, the circumference and diameter of a circle were different, but the ratio of the two was more than three times.
Then let each group in the class report and observe the ratio of the circumference to the diameter of a circle, between two integers. Once again, let the students deeply realize that the circumference of the circle in the first group of the class is different and the diameter of the circle is different, but the ratio of circumference to diameter is more than three times. )
3. Extend and deepen the understanding stage
Introduce the great achievements of Liu Hui and Zu Chongzhi.
Design intention: let children further master the ratio of the circumference to the diameter of the circle and stimulate national pride. We call this ratio π, π.
Then show the pi calculated by modern computer technology, which is an infinite acyclic decimal. We use the Greek letter ∏, (supplementary blackboard writing) 3. 14 15926535 ... and derive the formula, (blackboard writing).
At this time, I emphasize that in the calculation, although pi is an infinite acyclic decimal, it is impossible for all of them to participate in the calculation, so we only take two decimal places 3. 14 to participate in the calculation. (The dot on the blackboard indicates 3. 14)
(C) practice to consolidate and deepen understanding
1, say it. What conditions do you need to know to calculate the circumference of a circle? What formulas are used respectively?
2. Judgment.
3. Do the math. (1) Give the diameter of the circle on the blackboard and calculate the circumference of the circle.
(2) The circumference of the circular flower bed.
(4) class summary, self-evaluation and mutual evaluation.
(Display evaluation form)
Design intention: This evaluation form is not only an understanding of students' learning situation, but also an evaluation of students' emotional attitude and cooperative spirit.
Seven, say blackboard writing
The blackboard writing design strives to be concise and practical, highlighting the key points.
perimeter of a circle
The length of the curve surrounding a circle is called the circumference of the circle.
Pi = c/d = 3. 14 15926 ...
Turn the curve into a straight line c=∏d, c = 2 ∏ r.