Circular teaching plan 1 teaching objectives:
1. Through teaching, students can learn to calculate the diameter and radius of a circle according to its circumference.
2. Cultivate students' logical reasoning ability.
3. Master the methods of transformation and transformation.
Teaching emphasis: Find the diameter and radius of a circle.
Teaching difficulties: using formulas flexibly to find the diameter and radius of a circle.
Teaching process:
First, review.
1, answer orally. 458
2. Find the circumference of the following circle.
C = r 3.14223.144 = 6.28 (cm) =83. 14=25. 12 (cm).
Second, new lessons.
1, put forward research questions.
(1) Know what it means?
(2) What does each letter of the following formula mean? What do these two formulas mean?
C=r
(3) According to the above two formulas, we can know that:
Diameter = circumference π radius = circumference (π2)
2. Learn and practice the second question of fourteen questions.
(1) Xiaohong measured the circumference of a red column in an ancient building to be 3.768 meters. What is the diameter of this column? (The number shall be kept to one decimal place)
Known: c=3.77m: d=?
Solution: Let the diameter be x meters.
3.773. 143. 14x=3.77
1.2 (m) x=3.773. 14
x 1.2
(2) do it. Bend an iron bar with a length of 1.2m into a circular iron ring. What is its radius? (Figures shall be kept to two decimal places)
Known: c = 1.2m R=c(2) Find: r=?
Solution: Let the radius be x meters.
3. 142 x = 1.2 1.223. 14
6.28 x = 1.2 = 0. 19 1
X = 0.1910.19 (m)
x0. 19
Third, consolidate practice.
1. There is a big clock hanging in the lobby of the hotel. The distance traveled by the minute hand tip of this clock is 125.6 cm. How long is its minute hand?
2. Find out the circumference of the half circle below and choose the correct formula.
⑴3. 148
⑵3. 1482
⑶3. 1482+8
The minute hand of the wall clock is 20cm long. After 30 minutes, how many centimeters did the tip of this minute hand walk? In 45 minutes?
(1) I thought: a circle of the clock face is 60 minutes. You walked the whole clock face in 30 minutes, that is, you walked a whole circle. What is the circumference of the clock face? 20xx. 14= 125.6 (cm)
(2) Thinking: One circle of the clock face is 60 minutes. If you walk for 45 minutes, you walk the whole clock face, that is, a whole circle. Then: What is the circumference of the clock face? 20xx. 14= 125.6 (cm)
How many centimeters did you walk in 45 minutes? 125.6=94.2 cm
4.P66 problem 10. What is the circumference of the picture below? How to calculate it?
Fourth, homework. P65-66 Questions 3, 6, 7 and 9
Teaching commemoration:
The formula for calculating the circumference of a circle is not complicated, but how to get this formula and how to get the fixed value in the formula are all problems worthy of students' study. Therefore, in teaching, I focus on cultivating students' inquiry consciousness and ability, so that students can understand and master the calculation method of the circumference of a circle through experiments, such as measuring, calculating, guessing the relationship between the circumference and diameter of a circle, verifying and guessing. Because of my own operation, plus I introduced some relevant materials in class and told an interesting little story, the students understood the meaning of this word thoroughly and were very interested.
Circumferential teaching plan Part II Teaching objectives:
1. Experience the process of finding the diameter or radius of a circle by knowing its circumference, and realize the diversity of problem-solving strategies.
2. Students can further understand the relationship among circumference, diameter and radius, and skillfully use the circumference formula of a circle to solve some practical problems.
3. Students feel the learning value of plane graphics, and further improve their interest and confidence in learning mathematics.
Teaching focus:
Explore the circumference of a known circle and find out the diameter or radius of this circle.
Teaching difficulties:
Can skillfully use the formula of circumference to solve practical problems.
Preparation before class:
multimedia courseware
Instructional design:
I. Teaching examples 6.
(1) The courseware shows the scene of Example 6, and the whole class communicates: How to accurately measure the diameter of this flower bed without damaging the flowers and plants in the flower bed? Measure the perimeter of the flower bed first, and then calculate the diameter of the flower bed. )
⑵ The courseware shows the measurement results: the perimeter of the flower bed is 251.2m. ..
Group communication: Knowing the perimeter of this flower bed, how to calculate the diameter of this flower bed?
Talk about your ideas in the group.
(2) Show yourself how to answer.
⑶ Show and communicate with the whole class.
(1) is solved according to the formula of pi C=πd column equation.
Solution: Let this flower bed be x meters in diameter.
3. 14x=25 1.2
x=25 1.2÷3. 14
x=80
② Calculate directly by division.
25 1.2÷3. 14=80 (m)
⑷ Summary and comparison: What are the similarities and differences between the two methods? What method do you like? Why?
Summary: Both methods are based on the formula for calculating the circumference. The column equation is based on the meaning of the question, and the division calculation directly uses the relationship between the parts in the circle circumference formula.
Relationship calculation of.
2. Learn to "give it a try".
Second, consolidate and expand.
1. Practice.
Remind students that pi can be regarded as 3 when estimating, so that students can realize that 3 is a little smaller than the actual value of pi, so pi should also be estimated a little smaller.
2. Exercise 14, question 5.
3. Exercise 14, question 6
4. Exercise 14, question 7.
5. Students finish the exercise 14, question 8.
6. Exercise 14, question 9, 10.
Third, summarize and extend.
What did you gain from this class? Is there a problem?
Blackboard design:
Circumferential lesson plan 3 teaching material analysis:
This part of the content is based on students' understanding of the concept of circle and the basic characteristics of circle, guiding students to explore the relationship between the circumference and diameter of a circle through experiments in the form of group cooperation, and learning pi by themselves, so as to summarize and explore the formula for finding the circle. On the other hand, it can improve students' ability to use formulas to solve practical problems and realize the close connection between mathematics and real life.
Teaching objectives:
1. Let students experience the exploration process of pi, understand the meaning of pi, master the formula of pi, and use the formula of pi to solve some simple practical problems.
2. Cultivate students' abilities of observation, comparison, analysis, synthesis and hands-on operation, and develop students' concept of space.
3. Let students understand the meaning of pi, remember the approximate value of pi, and combine the teaching of pi to feel the mathematical culture and stimulate patriotic enthusiasm.
Teaching focus:
The formula of circumference is deduced through various mathematical activities, and the circumference can be calculated correctly.
Teaching difficulties:
Discussion on the relationship between circumference and diameter of a circle.
Teaching preparation:
Multimedia courseware, lines, rulers, circles with different diameters cut from plastic plates, experimental reports, calculators, etc.
Teaching process:
First, quasi-cognitive conflict, stimulate the desire to learn.
1. Talk: Students, I know everyone likes to watch the cartoon Pleasant Goat and Big Big Big Wolf. Today, the teacher brought them to our class. Listen: (Courseware plays the story: On a sunny day, Pleasant Goat and Big Big Wolf held a running race. Pleasant goat runs along a square route, and Big Wolf runs along a circular route. After a lap, the two returned to the starting point at the same time. At this time, they are arguing over who will travel long distances. Students, what do you think? (Students guess)
2. How can we determine which of them runs a long distance? (Student: Find the perimeter of a square and a circle first, and then compare them. )
3. Name a lifetime and talk about the calculation method of the circumference of a square: (Student: side length ×4= circumference) Today, let's study the circumference of a circle together. (revealing topic: circumference)
Second, experience the whole process of inquiry and verify the conjecture.
(1) Understand the meaning of perimeter and preliminarily perceive the relationship between perimeter and diameter.
1. Dialogue: What is a circle? (Courseware shows 3 wheels)
2. Teacher: What do the above three numbers mean? What does "inch" mean? (Students read and answer)
3. Three wheels roll once each. Guess who rolls the longest distance? What did you find out from it? (health: the length of a wheel rolling once is the circumference of the wheel; The longer the diameter, the longer the circumference, the shorter the diameter and the shorter the circumference)
Ac method for measuring circumference
1. Students take out the circles cut before class and point out their perimeters.
2. How to measure their circumference? (deskmate communication mode)
3. Name the front projection to show the method of measuring perimeter.
① Rolling method. Remember clearly: make a mark and scroll from the zero scale until the mark points here again. The length of a circle rolling is the circumference of the circle.
(2) circle method. Clear: the line is close to the circumference, the redundant part is removed and the line is straightened. The length of the straight line between these two points is the circumference of the circle.
③ Measure with a soft ruler. Clear: Measure with the side with centimeter scale on the soft ruler. Start with the zero scale, draw a circle and see which scale is aligned.
4. Summary: These methods have a common feature: (Student: Turn a curve into a straight line) This is the method of "turning a curve into a straight line" in mathematics.
5. (There are pictures of ferris wheel in the courseware) Q: Can you measure its circumference by the method just now? (Health: No, it's inconvenient) Q: What should I do? Inspire students to explore the relationship between the circumference and diameter of a circle.
(3) Know pi.
1. Talk: Next, divide the students into four groups, choose their favorite method, measure the circumference and diameter of these circles around them, and complete the table. (Students complete the form in the book in groups) (Show the form in the courseware)
2. The team leader reports the measurement results. (Students say grades, teachers improve courseware)
Let the students observe the data in the table and tell them what they have found. (Students report in groups: the circumference of a circle is always more than 3 times the diameter)
4. (Courseware demonstration) Introduce the book Weekly Parallel Computing and the significance of "Path One on Wednesday". The circumference of a circle is about three times the diameter.
5. Introduce Zu Chongzhi's contribution to the calculation of pi, so that students can imagine the process of Zu Chongzhi's exploration of pi and realize the hardships and difficulties of scientific discovery. (Courseware plays data, students learn by themselves)
6. What did the students learn from the introduction of the materials? (Students exchange learning)
7. Teacher's summary: Zu Chongzhi is the pride of our nation, precisely because he is outstanding.
Achievements: There is a crater on the moon called Mount Zu Chongzhi, and the 1888 asteroid in the universe is also named after him. I hope my classmates can study as hard as him in the future and be an extraordinary person in the future.
(4) Derive the formula
1. When students understand the relationship between the circumference and diameter of a circle, let them talk about how to calculate the circumference of a circle. (Student: circumference = pi × diameter)
2. Dialogue: If the capital letter C is used to represent the circumference of a circle, how is this formula represented by letters?
3. Talk: What other conditions can be known to find the circumference? (health: radius) why? (Health: In the same circle, the diameter of the circle is twice the radius) Then how to change this formula?
4. Read the formula together to deepen the impression.
Third, refresh the application ability and summarize and consolidate new knowledge.
1. (The courseware shows the question 1) Students answer the perimeter of two circles.
2. What are the circumference of three bicycle wheels in Example 4? (Courseware shows three wheels) Through calculation, who has the longest circumference? What does this mean? (health: the circumference of a circle is related to its diameter)
(The courseware shows a fountain) The circumference of the circular fountain is12m. What's its circumference? Students finish their exercise books independently, and the projector displays the answers. )
4. (The courseware shows the schematic diagram of the Ferris wheel) Its radius is 10 meter. If you sit on it for a week, how many meters will it turn in the air? Students finish their exercise books independently and then communicate with each other in class.
Fourth, exchange learning gains and expand after class.
1. What have you gained from learning the circle in this lesson? (Students communicate with the whole class)
2. Dialogue: Now if the teacher asks Pleasant Goat and Big Big Wolf, who walks longer? What can students do? (Students finish independently, and then the whole class communicates) Is there any other way? (Students can solve problems by calculation, or they can directly observe the contrast between two pictures. )
3. Teacher: Various methods can help us determine who walked this long distance, so when Pleasant Goat learned the result, he shouted that the race was unfair, so the old village head redesigned a new race route for them: Q: If Pleasant Goat and Big Big Big Wolf race along this route, who will walk the longer distance? Students think after class and communicate in the next class. )
Teaching reflection:
First, the two main threads of "situation" and "knowledge" blend with each other.
Combined with the teaching content of this class and the age characteristics of students, teachers grasp the two main lines of "situation" and "knowledge" in teaching situations, and strive to create a lively, harmonious and harmonious learning atmosphere for students. As we all know, "Pleasant Goat and Big Big Wolf" is an animated film deeply loved by students. Students are very interested in this and have a certain understanding. Taking this as the learning background and the starting point of the learning circle, the "situational clues" and "knowledge clues" of this lesson are organically integrated to form a complete unity, which stimulates students' interest in learning and actively participates in learning activities.
Second, hands-on operation allows students to experience the formation process of knowledge.
Hands-on operation is an important way for students to acquire knowledge. Based on students' life experience and existing knowledge background, this course provides them with rich operational materials and open operational space, so that students can experience the derivation process of the formula for calculating the circle. In this process, teachers participate in students' learning activities as organizers, guides and collaborators, so that students' operational activities are purposeful, ideological, selective and creative, and students can do, watch and create.
Thirdly, mathematics reading makes students feel a strong mathematical culture.
In the process of mathematics learning, introducing some knowledge of mathematics discovery and history can enrich students' overall understanding of mathematics development and play a certain incentive role in subsequent learning. Combined with the teaching content of this lesson, the teacher introduced the knowledge of pi to the students. The introduction here is from "One Way of Three Weeks" and "Calculation and Preparation" by Zu Chongzhi in Zhoubian Suanjing, to the application of pi in modern life and the computer calculation of pi, so that students can have a complete understanding of the history of pi, feel the wisdom of our ancestors, and appreciate the close relationship between mathematical knowledge and human life experience and actual needs.
Circumferential teaching plan 4 teaching content
Mathematics, the standard experimental textbook of compulsory education curriculum, the first volume of grade six, 62-64 pages.
Teaching objectives
1. Understand the significance of pi through group cooperation and actual measurement.
2. Grasp the calculation formula of circle circumference through comparative analysis.
3. Some simple mathematical problems can be solved by calculating the circumference.
4. Infiltrate patriotism through the calculation of pi.
Emphasis and difficulty in teaching
Key points: Derive the formula for calculating the circumference, and calculate the circumference accurately.
Difficulties: Understand the meaning of pi.
teaching process
First, the scene is introduced.
Show me a clock.
Question 1: Can you guess the trajectory of the top of the small second hand in one minute?
Students guess.
The teacher demonstrates the movement process of the small second hand and verifies whether the students' guess is correct.
Question 2: Can you know how long the tireless little second hand has been walking in an hour? How to solve this problem?
Health: first calculate how far a lap runs, and then calculate the length of 60 laps.
Teacher: Good. How can the small second hand find the circumference of this circle when it goes around? Today we will learn how to calculate the circumference of a circle. (Topic Introduction-Circumference)
(Design purpose: Introducing new lessons through objects around students can fully arouse students' learning enthusiasm and focus on the classroom. )
Second, measure your hands.
Student activities: Please take out the prepared circles, exchange circles in groups, and cooperate to complete the following table to see which group can be completed fastest. The measurement is accurate to the millimeter.
Name of the article
bellyband
diameter
65438+ circle 0
The second lap
Third circle
The fourth lap
Teachers evaluate students' group cooperation.
(Design purpose: emphasize students' team consciousness)
Teacher: Which group will report how your group measured it and show the results of the group measurement.
Students present the results of the group.
(Design purpose: to show students in other groups the achievements of this group through physical projection, so as to enhance students' self-confidence)
Third, comparative analysis.
Teacher: Look at several sets of data we have got. Did you find any patterns?
The students speak freely.
Students found: 1. The circumference of a circle is always greater than three times its diameter. 2. The ratio of circumference to diameter can be multiplied by diameter to get the circumference of a circle.
Teacher: The teacher also drew a circle. Now let's see how the teacher measures the circumference of this circle.
The courseware shows the measurement method of circumference.
(Design purpose: Through the comparative analysis of tables, the teacher's courseware shows the measurement process of the circumference of a circle, which makes students more clear about the relationship between the circumference and diameter of a circle and stimulates students' enthusiasm for understanding the specific relationship between them. )
Courseware shows that the circumference of a circle changes with the change of diameter, and the ratio of circumference to diameter is indeed a constant value.
(Design purpose: Through courseware demonstration, let students get the conclusion that the ratio of circumference to diameter of a circle is a fixed value, and the value of pi can be calculated smoothly. )
Summary 1: pi: The ratio of the circumference to the diameter of a circle is a fixed number. We call it pi, which is expressed by the letter π. Pi is an infinite cyclic decimal. Its value is: π = 3. 14 15926535 ... In practical application, its approximate value is generally π≈3. 14.
Do you know that?/You know what? Do you know that?/You know what? Our ancestors made brilliant achievements in the calculation of pi. Can you tell them to your classmates?
The students speak freely.
We have such a great ancestor, and I believe that modern China people who stand on the shoulders of great men will surely achieve more brilliant achievements.
(Design purpose: Infiltrate patriotism through students telling stories)
Summary 2: Can you get the formula for calculating the circumference by analyzing the table?
The students answered. Students can answer this question easily, because they have already prepared the first few layers and analyzed the form. )
The formula for calculating the circumference of a circle (represented by the letter c) is: C=πd or c = 2 π r.
Fourth, do it yourself.
Let's see how to apply the formula for calculating the circumference to solve the problem.
1. Calculate the circumference of a circle.
Physical projection shows students' problem-solving process
(Design purpose: Through simple graphic calculation, let students understand the application of pi calculation formula and emphasize the writing process of solving problems)
2. The radius of the circular fountain is 5m, and how many meters is its circumference?
(Design purpose: Through transformation, the problem of finding the perimeter from radius is transformed into a practical problem, so that students can realize what they have learned. )
3. The group communicated the reasons for the mistakes. This can prevent other students from making the same mistake.
(Design purpose: Through the calculation of examples, students can better understand that mathematics comes from life, can also solve real life problems, and can also lay a good foundation for the final practical problems. )
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 their own conditions to solve problems and cultivate their independent thinking ability. This problem echoes the previous introduction problem, thus solving the problem from beginning to end)
Can you tell me what you have gained in this course?
Students can sum up their gains from knowledge points, measurement methods-ability points, knowledge of mathematical history-feelings, attitudes and values.
Sixth, extracurricular cooperation:
Work in groups and use your knowledge to try to measure the distance from the school gate to the entrance of the round tower.
(Design purpose: to make students really apply what they have learned in their studies, and to cultivate students' sense of teamwork and practical ability)
Circumferential teaching plan 5 teaching content:
Teaching objectives:
1, by exploring the process of taking the quotient of the circumference and diameter of a circle as a constant value, we can understand pi. Experience the ideological transformation from music to straightness, enhance the sense of cooperation and experience the sense of accomplishment.
2. Mastering the calculation method of circumference can correctly calculate circumference, solve simple practical problems and enhance application awareness.
3. Feel the history of pi exploration, and enhance patriotism and desire to explore mathematics.
Teaching emphasis: understanding pi and calculating pi.
Difficulties in teaching: Exploring and understanding that the quotient of the circumference and diameter of a circle is a constant value.
Teaching preparation: round cardboard of different sizes, calculator, multimedia courseware, 20 cm long rope, ruler, coin, square marked with circle and diameter.
Teaching strategies: independent inquiry, discussion and exchange, and guiding practice.
Teaching procedures:
First, activate the target.
Show me the theme of the flower bed. What does the perimeter of the flower bed mean? Show me the bike. What does the circumference of the wheel mean? Show me a square with a circle and a diameter. What does the circumference of this circle mean? How many ways can you think of to measure the circumference?
Second, the activity construction
1. Measure the circumference and diameter of four circles with different sizes, and fill in the table for calculation. Exploration and discovery: the relationship between perimeter and diameter. (with the help of a calculator)
2. Introduce the origin of pi.
The quotient of the circumference of any circle and its diameter is a fixed number. We call it pi, which is expressed by the letter π. Pi = circumference ÷ diameter, that is, π = C ÷ D. Origin of π: π is the sixteenth Greek letter and the first letter of PI in Greek. Euler, a great mathematician, began to express pi in letters and papers in 1736.
Organize students to read materials and talk about feelings.
3. Deduction: c=πd or c = 2π r.
4. Calculate the perimeter of the flower bed and solve related problems.
The diameter of the round flower bed is 20 meters. What's its circumference? The diameter of a bicycle wheel is 50 cm. How many times does the wheel turn around the flower bed?
Third, explain the application
The front wheel radius of forklift is 0.4m, and the rear wheel diameter is1.6m. How many times do you turn back and forth when driving?
Fourth, feedback evaluation.
1. The radius of the circular fountain is 5 meters. How many meters should I walk around it?
15cm
A
B
2. How far did the little ant climb from point A to point B along this curve?
There is a round artificial lake in the park. Walking around the lake requires 1570 meters. There is an island in the center of the lake. How long is the bridge from the lake to the island?
Verb (abbreviation of verb) course summary
What is my biggest gain? What regrets do I have? What's my problem?
I hope that students can experience happiness, growth and success in the process of exploring the mysteries of mathematics! Goodbye, class.