Circumferential teaching plan 1 teaching objectives
1. Let students know the circumference of a circle and understand the meaning of pi.
2. By exploring the value of pi, cultivate students' scientific exploration spirit, practical exploration spirit, generalization ability and logical thinking ability.
3. By introducing the contribution of ancient mathematicians in China to the study of pi, we can enlighten students on patriotism and dialectical materialism and enhance national pride.
Teaching emphases and difficulties
The formula for calculating the circumference is derived. Understand the meaning of pi.
Teaching process design
Review preparation
Last class, we met Yuan. Now let's talk about it. How much do you know about Yuan?
Learn a new course
In this lesson, we will learn about circles. (blackboard writing: circumference)
I want to ask the students, what round objects have you brought?
Where is the circumference of the circle that two people are pointing at each other?
Who wants to come to the front and point to the circumference of the circle in the teacher's hand?
Who is different from him? Why can't you point like this?
Teacher, here is a mirror. I want to install a stainless steel frame for this mirror. How do I know how long this frame is?
Teacher, here is a cup, too. Drinking water with it can be very hot sometimes. I want to knit a cup. How can I know how big the cover should be?
Which group is willing to help solve this problem? Each group of us brought some round things. We need to measure the circumference through group cooperation and fill in the experimental report.
Please fill in the name, circumference and diameter of the object you measured in the experimental report.
Students measure the round objects in their hands in groups and fill in the experimental report. Measure as much data as possible. )
Ask the group representative to report the experimental process and results of our group.
Students have thought of so many ways, it seems that you really have a set. To sum up, the students straighten the curve by winding. (blackboard writing: winding and rolling)
(The teacher shows the circle drawn on the blackboard) Who can measure the circumference of this circle in these two ways?
It seems impossible to measure the circumference by the actual winding method. We must study a method to find the circle.
Think about it, what geometric figures have we learned before?
Who has something to do with the perimeter of a rectangle? What does it matter?
Who is the circumference of a square related to? What does it matter?
Who has something to do with the circumference? For example, isn't it? Look at the screen
Demonstrate three rolling circles by computer, and see that the bigger the circle, the longer the rolling track, and the smaller the circle, the shorter the rolling track. )
We come to the conclusion that the circumference is related to the diameter.
(blackboard writing: circumference and diameter of a circle)
This is what we all found. Scientists often find problems and study them. Do our classmates want to be scientists when they grow up? Today, we will learn from scientists to study a problem: by calculating and analyzing the data we have measured, what is the relationship between the circumference and diameter of a circle? What pattern did you find?
(Students discuss in groups. )
Through students' experimental research, we come to a conclusion that the circumference of a circle is always more than three times its diameter. (blackboard writing: more than 3 times)
Is that so? Let's verify it.
Computer demonstration: The circumference of a circle is more than three times its diameter. )
This is a fixed multiple relationship, which we call pi. (blackboard writing: pi)
Who can tell us how pi is obtained?
Let the students read this book. What does it say?
As early as 20xx years ago, China's ancient mathematical classic "Parallel Calculation of Classics in Weeks" pointed out: The circle is on Wednesday. At that time, it was a great achievement, and it was often used to estimate the circumference. Just now, the teacher used this method to estimate whether the students' calculations are accurate. Who knows who is the first person in the world to make Pi accurate to 7 decimal places? He is Zu Chongzhi, a great mathematician and astronomer in China.
(A portrait of Zu Chongzhi appears, and the soundtrack recording is played to introduce Zu Chongzhi. )
About 65,438+0,500 years ago, Zu Chongzhi, a great mathematician and astronomer in China, accurately calculated the values of pi between 3.65,438+0.465,438+0.5926 and 3.65,438+0.465,438+0.5927. He was the first person in the world to accurately calculate the value of pi to seven decimal places, 65,438 places earlier than European mathematicians. The largest crater in the world is named after Zu Chongzhi.
We should really be proud of the intelligence and wisdom of our predecessors. Later, the Swiss mathematician Euler used Greek letters to represent pi. (blackboard writing:)
Pi is an infinite cyclic decimal. When calculating, it is not convenient to use this infinite acyclic decimal to participate in the calculation, so two decimal places are generally taken. (blackboard writing: 3. 14)
Since it is a fixed value, we can find the circumference of a circle as long as we know what it is. (diameter. )
Now can we calculate the circumference of the circle on the blackboard?
I don't know what the terms are. (diameter. )
Who will measure the diameter? Use decimeters as units. (blackboard writing: decimeter)
What is the radius if the diameter is 2 decimeters?
Can you calculate the circumference of a circle according to the radius?
Now let's try to find the circumference of a circle with diameter or radius on the blackboard.
Who uses the diameter to find the circumference of a circle?
(blackboard writing: 3. 142=6.28 (decimeter))
Why is this happening?
(blackboard writing: circumference = diameter pi)
If c represents the circumference of a circle and d represents the diameter and pi, what about the letter formula?
(blackboard writing: C=d)
Who can find the circumference of a circle by radius? Why are you doing this?
If the radius is represented by the letter R, what is the letter formula?
(blackboard writing: C=2r)
(3) Integrated feedback
1. Find the perimeter of the following circle. (Unit: cm)
2. Judge whether you think the painting is right or wrong.
(1) The circumference of a circle is always twice its diameter. ( )
(2) A circle has a circumference of 6.28 cm and a radius of 2 cm. ( )
(3) Half of the circumference is equal to the circumference of half a circle. ( )
3. Choice: Give the card number of the answer you think is correct.
(1) When the wheel rolls once, the distance traveled is [] of the wheel.
① radius
② Diameter
③ Perimeter
(2) The diameter of a circular pool is 4m, and it has a circumference around the pool [].
① 25. 12m
②12.56m
③ 12.56 m2
(3) The diameter of circle A is 6 cm, and the diameter of circle B is 2 decimeters, pi []
A is round and big.
②B is round and big.
③ The size is the same.
4. Party A and Party B walk from one end to the other along the routes ① and ② respectively. Who walks the longer way?
(4) Summarize the whole class
What did you learn in this class? Guide the students to summarize what they have learned in this lesson. )
Description of classroom teaching design
This lesson leads students to explore pi and deduce the calculation formula of pi. The first step is to measure the circumference of a circle in an object. The method of measuring the circumference of a circle is the winding method. Then a circle drawn on the blackboard appeared. When students find that the circumference of this circle cannot be measured by winding or rolling, they must study a method to find the circumference of the circle. The second step is to derive the formula for calculating the circumference. First, lead the students to recall: What geometric figure perimeter calculation have we learned before? Who are the perimeters of rectangles and squares related to? Guide the students to find out who is related to the perimeter. The third step is to study the relationship between circumference and diameter, understand the significance of pi, and deduce the calculation formula of circumference. Through the exploration of pi value, we can cultivate students' scientific and realistic exploration spirit, generalization ability and logical thinking ability.
The second part of the circular teaching plan;
Use the knowledge of the perimeter and side length of the square to guide students to guess and discuss, so that students can have a clear purpose in the subsequent practical inquiry process. The race between two rabbits in the courseware is a life problem, but it is a math problem that compares the circumference of a circle with the circumference of a square. Create teaching situations, stimulate students' interest in participation, and lay the foundation for further study and exploration. The concept of perimeter is well displayed in the animation demonstration process, and the concept of square perimeter is migrated in combination with the actual operation, so that students can firmly grasp the concept of perimeter and fully reflect their dominant position in the classroom learning process.
Teaching content:
Primary school mathematics compulsory education textbook page 137~ 138 "circumference of a circle".
Teaching objectives:
1. Make students understand the meaning of pi, deduce the calculation formula of pi, and make simple calculations correctly;
2. Cultivate students' abilities of observation, comparison, analysis, synthesis and hands-on operation;
3. Educate students in patriotism by studying the historical development of pi.
Teaching focus:
The formula for calculating the circumference of a circle is derived and summarized.
Teaching difficulties:
Deeply understand the significance of pi.
Teaching preparation:
Computer courseware, round object, ruler, ribbon, measurement result record table.
Teaching process:
First, create a situation, causing speculation
(A) teachers play courseware to stimulate students' interest.
The black rabbit and the white rabbit are racing. The black rabbit runs along the square route and the white rabbit runs along the circular route. As a result, the little white rabbit won. The black rabbit was not convinced when he saw that the white rabbit had won the first prize. It says competition is unfair. Students, do you think this kind of competition is fair?
(b) Know the number of weeks of a circle.
1. Recall the circumference of the square: What is the actual running distance of the black rabbit? What is the circumference of a square?
2. Know the circumference of the circle: How far does the white rabbit run? What does circumference mean?
Teacher: The length of a curve around a circle is called the circumference of the circle. (Show the circumference of the topic circle)
3. Measure the circumference of three round pieces of paper prepared by yourself in groups and record them.
4. Feedback: How do you measure it?
Health 1: "roll"-roll a true circle around a ruler;
Student 2: "winding"-winding an object with a ribbon and opening it;
5. Summarize various measurement methods: (blackboard writing) Turn bending into straightness.
6. Create conflicts and realize the limitations of measurement.
Teacher throws the ball: Can you measure the circle with the method just now? Just now, the big white rabbit ran in a circle on the big screen. Can the circumference of this circle be measured? (health: no) it seems that the method just now has limitations. Today we are going to discuss a method that can quickly know the circumference of all circles.
(C) reasonable speculation, strengthen the main body
1. Please draw two circles of different sizes on the blackboard with a piece of string tied with chalk. Discuss in groups of four and guess what the circumference of this circle is related to.
Health: I guess the circumference of a circle is related to its diameter.
2. The teacher's courseware demonstration: the larger the diameter, the longer the circumference; The smaller the diameter, the smaller the circumference.
Please think about it. The circumference of a square is related to its side length, which is always four times the side length, so the circumference of a square = side length ×4. The circumference of a square is always four times the length of its side. Look at this picture again and guess, how many times should the circumference of a circle be the diameter?
(health 1: I guess three times. Health 2: I guess 3.5 times 3: ...)
4. Can you find a general method to find the circumference of a circle like the circumference of a square?
Second, actually do it and find the law.
(a) teamwork
1. Clear requirements: Fill in the table with the previous measurement results, calculate the result of dividing the circumference by the diameter, and fill in the table.
2. Feedback data
Health 1: Our group calculated that the circumference of a circle is about 3.4 times the diameter.
Health 2: Our group calculated that the circumference of a circle is about 3.2 times the diameter.
Health 3: Our group calculated that the circumference of a circle is about four times its diameter.
Teacher: Courseware demonstration: The circumference of a circle is always more than three times its diameter.
(2) Introduce Zu Chongzhi.
This multiple is usually called pi, which is expressed by the Greek letter π.
Writing on the blackboard: pi = circumference ÷ diameter
As early as 1500 years ago, a great mathematician in ancient China calculated this multiple accurately. He first discovered that this multiple was indeed fixed. Do you know who he is?
What is this multiple? Let's look at a message.
(Projection shows: Zu Chongzhi was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. On the basis of predecessors' achievements, Zu Chongzhi used the method of inscribed regular polygons to divide the circumference of a circle into several parts. The more copies are divided, the closer the circumference of a square is to the circumference of a circle. Finally, the pi is calculated by calculating the perimeter of the regular polygon. After hard study and repeated calculation, it is found that π is between 3. 14 15926 and 3. 14 15927, and it is accurate to the seventh place after the decimal point. It was not only the most accurate pi at that time, but also kept the world record for more than 900 years ...)
4. Understanding mistakes
After reading these materials, the students are proud of having such a great mathematician in our country, but I wonder if the students have ever wondered why our calculation results are not accurate enough.
(3) Summarize the formula for calculating the circumference.
1. If you know the diameter of a circle, can you calculate its circumference?
On the blackboard: circumference = diameter × pi
C = πd
If you know the radius of a circle, how do you calculate its circumference?
Blackboard writing: C = 2πr
3. Application
(1) Shake the ball and tell the students that the rope is 3 minutes long. Please choose a formula to calculate the circumference of a circle.
Health: I choose C = 2πr, 2×3. 14×3= 18.84 decimeter, and the circumference of this circle is 18.84 decimeter.
(2) The diameter of the excircle of the main body is 20cm. Which formula was used to calculate it?
Health: I use C = πd, 3. 14×20=62.8 cm, and the circumference of this circle is 62.8 cm.
(3) Answer the original question: Now, can you accurately judge who runs longer, the black rabbit or the white rabbit?
Third, consolidate practice and form ability.
1. Judgment
(1) The circumference of a circle is π times the diameter. ( )
(2) The great circle pi is greater than the small circle pi. ( )
(3)π=3. 14 ( )
2. For example, 1, students can do their own calculations.
3. If the black rabbit runs along the big circle and the white rabbit runs around the number 8 along two small circles, who runs the shortest distance?
Fourth, summarize in class and grasp it firmly.
What did you gain from today's study?
Fifth, extracurricular extension, expand thinking.
How do you know the diameter of the cup mouth?
Circumferential Teaching Plan 3 teaching material analysis
(It can be elaborated from the following aspects, and it is not necessary to cover everything. )
L Requirements in this section of the curriculum standard; The knowledge system of this section; The position of this section in the textbook and the logical relationship between the contents of the textbook before and after.
L The function and value of the core content of this section (why do you want to learn this section), we should not only think about the help of other contents to the study of this section, but also think about the help of the study of this section to the establishment of the discipline system and the study of other disciplines; We should also think about the help of this section of study to students' academic ability and even comprehensive quality, as well as the influence brought by the change of thinking mode.
Starting from the life situation, the textbook introduces the concept of circumference by asking students to think about how many meters a bicycle has ridden around a circular flower bed. Then let the students think about how to find the circumference of a circle and guide them to measure it in different ways. On this basis, let students find that the ratio of pi to diameter is a constant value by measuring the diameters and perimeters of several groups of circles, thus leading to the concept of pi and summarizing the formula for calculating the circumference of a circle.
The focus of this teaching is to let students understand and master the calculation method of the circumference of a circle through the process of measuring, calculating, guessing the relationship between the circumference and diameter of a circle, and verifying and guessing.
In this teaching design, the presentation form of teaching materials has changed slightly. This design introduces the teaching of this course from perimeter, which can deepen the connection and difference between the perimeter of a circle and the perimeter of other graphics. The circumference of a figure enclosed by a straight line is the sum of the lengths of several straight line segments, and the calculation method of a figure enclosed by a circular curve is to turn it into a straight line.
Analysis of learning situation
(It can be elaborated from the following aspects, but it does not need to be formatted and comprehensive. )
Teachers' subjective analysis, interviews between teachers and students, analysis and feedback of students' homework or test questions, and questionnaire survey are effective measurement methods for learner analysis.
Analysis of students' cognitive development: mainly analyze students' current cognitive basis (including knowledge basis and ability basis), and form the cognitive development line that this section should take, that is, starting from students' existing cognitive basis, through which links, the knowledge to be achieved in this section will finally be formed.
L Students' cognitive obstacles: The main obstacles for students to form knowledge in this lesson may be the lack of knowledge base, old ideas or ability methods, and the change of thinking mode.
On the basis of learning the general concept of circumference and the calculation of rectangle and square circumference in the first volume of Grade Three, I further learned the calculation of circumference.
Teaching objectives
(The determination of teaching objectives should be analyzed according to the three-dimensional objective system of the new curriculum)
1, let students know the meaning of the circumference and pi of a circle, and master the approximate value of pi. Understand and master the formula for calculating the circumference of a circle, and can apply the formula to solve simple practical problems.
2. By discussing the measurement and calculation formula of circumference, cultivate students' ability to observe, analyze, compare, synthesize, actively study and explore and solve problems.
3. Through the exploration of dialectical materialism education, combined with the story of Zu Chongzhi, an ancient mathematician in China, students are educated in patriotism.
Teaching emphases and difficulties
Teaching emphasis: correctly calculating the circumference
Difficulties in teaching: Understand the meaning of pi and deduce the calculation formula of pi.
Instruction of teaching process
Design the teaching process according to the class hours. The teaching process should be able to clearly and accurately express the teaching link and the core activities of the teaching link. Therefore, it is necessary to avoid simple links without specific content of link realization; It is also necessary to avoid detailing links. Generally speaking, it is better to control the main links of a class between 4 and 6, which is more conducive to the implementation of teaching links. )
First, create a situation to understand the perimeter.
Second, explore the method of finding the circle in groups.
Third, solve problems with knowledge.
Fourth, class summary.
Verb (abbreviation for verb) assigns homework.
Sixth, teaching reflection.
Teaching process (the expression of the teaching process does not need to be detailed enough to record all the conversations and activities of teachers and students word by word, but it is necessary to clearly reproduce the implementation process of the main links. )