The teaching plan of circle area 1 teaching objectives:
1. Make students experience mathematical activities such as operation, observation, verification, discussion and induction, explore and master the formula of circle area, correctly calculate the area of circle, and apply the formula to solve related simple practical problems.
2. Make students further understand the value of reduction method, cultivate the ability to solve new problems by using what they have learned, and develop the spatial concept and preliminary reasoning ability.
Understand that mathematics comes from the actual needs of life, feel the connection between mathematics and life, and further cultivate curiosity and interest in mathematics.
Teaching focus:
Exploring and mastering the formula of circle area can correctly calculate the area of circle.
Teaching difficulties:
Understand the derivation process of the area formula of a circle.
Teaching preparation:
Derivation diagram of area formula of circle.
First, review old knowledge and introduce new knowledge.
1. Teacher: In the fourth grade, we learned how to calculate the area of rectangle and square. Who can tell us the calculation method of their area?
The students answered, and the teacher affirmed.
2. Question: How to calculate the circumference of a circle? Given the circumference of a circle, how to calculate its diameter or radius?
3. Introduction: We have learned the calculation method of the circumference, diameter and radius of a circle. Today, in this lesson, we will learn how to calculate the area of a circle.
(blackboard writing: the area of a circle)
The design intention is to promote students to understand the perimeter and the known perimeter to find the diameter or radius, to arouse students' experience in finding the area of rectangle and square, and to prepare for the new lesson.
Second, cooperate and exchange, and explore new knowledge.
1. Teaching examples 7.
(l) Preliminary guess: What might the area of a circle be related to? Tell me the basis of your guess.
(2) What is the relationship between the area of a circle and its radius or diameter? We can do an experiment.
(3) Give the first picture of Example 7. Thinking: What is the relationship between the side length of a square and the radius of a circle? What is the relationship between the area of the square and the radius of the circle in the picture?
(4) Students fill in the blanks independently.
(5) Guess: How many times is the area of a circle about that of a square?
After the students return, it is clear that the area of a circle is less than 4 times that of a square, or it may be more than 3 times.
(6) Give the last two pictures of Example 7, and use the same method to calculate and fill in the form.
Area of a square
radius of a circle
Area of a circle
The area of a circle is several times that of a square.
(accurate to the tenth place)
2. Communication and induction: What do you find by observing the above table?
Through communication, clear
The area of the circle teaching plan 2 The area of the circle in the first lesson
First, the teaching objectives
1. Knowledge and skills
Understand the concept of circle area, understand and master the calculation formula of circle area, correctly calculate the area of circle, and answer relevant practical questions.
2. Process and method
Guide students to use existing knowledge, experience the process of deducing the formula of circular area through activities such as guessing, calculating, verifying and inducing, cultivate students' abilities of observation, calculation, analysis and generalization, develop the concept of space, and infiltrate mathematical thinking methods such as transformation and limit.
3. Emotional attitudes and values
By exploring the process of circular area transformation independently, we can cultivate students' spirit of bold innovation, courage to try and overcome difficulties, and let students experience the fun of success.
Second, the focus of teaching
Calculate the area of the circle correctly.
Third, teaching difficulties
Derivation of the formula of circular area.
Fourth, prepare teaching tools.
Courseware and learning tools.
Teaching process of verbs (abbreviation of verb)
(A) situational import
1. Narrator: As the saying goes, "Food is the most important thing for the people". The dining table is indispensable for every family. Well, Xiaoming bought a new round dining table. In order to play a protective role, his mother assigned him a task, which is to match a glass desktop with the same size as the desktop. This stumped Xiao Ming. How big should this glass desktop be? Students, what knowledge do we need to help Xiaoming solve his problems?
Today, in this class, we will learn how to find the area of a circle. (Blackboard Title: Area of Circle)
2. What do you want to know after seeing today's topic?
3. What is the area of the circle? Where is it? Feel it.
Students touch the circular paper in their hands and point out the area of the circle with their hands.
Transition: How to Find the Area of a Circle? Here, we might as well recall the derivation process of other graphic regions first.
(2) Review old knowledge
1. Do you still remember the graph for finding area that we learned?
(student: rectangle, square, parallelogram, triangle, trapezoid)
2. Looking back, how did we derive the calculation formula of parallelogram area? (Courseware demonstration)
3. Q: What about other graphics? (Students briefly describe the derivation process in other fields)
Conclusion: In this way, when we encounter new problems, we can often solve them with the help of existing knowledge.
Learn a new course
1. Please guess, how should the area formula of a circle be derived?
(Student: Convert it into a known graph for derivation)
2. How to transform? Do something. Can I divide it into several parts at will?
(Health: Divide the circle into several parts evenly along its diameter)
Let's make a practical arrangement and see if our idea can be realized. See Activity Requirements:
(1) Take the group as the unit, and put the picture first.
(2) According to the relationship between the bottom and height of the mosaic and the circle, the area formula of the circle is deduced.
(3) Record the problems in time for discussion.
(Students put them together and stick them on white paper)
4. Did you encounter any problems?
The edge is not straight, but curved.
Who can help him solve this problem?
(Students talk about their own ideas)
6. Yes, the edge is not straight. what can I do? For example, we put together a rectangle. When we divide the circle into four parts, the figure we put together is like this. Divide the circle into eight equally, and the figure is like this'; Divide the circle into 16, and the mosaic is like this; Divide the circle into 32 parts; The mosaic is like this. (Courseware demonstration)
A circular picture 27 may be used.
Students, please compare these pictures spelled on the big screen. Do you have any ideas?
(Students talk about their own ideas)
8. It seems that the more copies of a circle are equally divided, the closer the curve is to the line segment, and the closer the spelled figure is to the figure we have learned. When it is divided into countless parts, the curve becomes a straight line. Has this problem been solved? Let's continue the group cooperation and deduce the calculation formula of the circle area.
(Students talk about their own ideas)
9. Report different derivation methods:
Convert to rectangle:
Area of rectangle = area of a× b circle = = a×b r 2
=π r × r
=π r 2
Convert to parallelogram:
Area of parallelogram = a× h
Area of circle = c× r 2
=π r × r
=π r 2
Convert to triangle:
Area of triangle = 1× a× h 2
Area of circle = 1C× 4R24
c× r 2 =
=π r 2
Trapezoid: Trapezoid area = 1× (A+B )× H 2.
15c3cá(+)×2r 2 16 16
1c××2r 22
C× r 2 circular area = = =
=π r 2
10. What are the similarities between these deduction processes?
(Student: They are all derived by converting the circle into a known figure)
1 1. Summary: It can be seen that we can use all the small sectors to derive the formula for calculating the circular area, or we can use one small sector to derive it, and of course we can also use some small sectors to derive it.
Now that our formula for calculating the circular area has been derived, can Xiao Ming's problem be solved for me? What conditions do you need to know to solve its problems? (Diameter, radius or circumference of a circle)
(4) Consolidate exercises
1. Find the area of the circle (unit: cm)
R=3 Answer: s=28.26 (square centimeter)
D=20 Answer: s=3 14 (square centimeter)
C= 125.6 answer: s= 1256 (square centimeter)
Xiao Ming measured that the diameter of the desktop was 2m. Can you calculate the area of the glass desktop?
Answer: 3. 14×22 = 12.56 (square meters)
judge
(1) A circle with a diameter of 2cm and an area of12.56cm2.. ()
(2) The perimeters of two circles are equal, and the areas must be equal. ()
(3) The larger the radius of a circle, the larger the area it occupies. ()
(4) The radius of the circle is enlarged by 3 times, and its area is enlarged by 6 times. ()
4. Listen to the story and solve the problem:
Master Bayi bought a flock of sheep.
Master Bayi said, "Two generations of love, hurry up and throw the newly bought sheep back into the pen."
Afandi said, "Sir, this rectangular sheepfold is too small!" " "
Master Bayi: "What, it's too small? Don't drive all the sheep in, hum, don't get paid! Otherwise, you will spend your own money to buy some materials and make the sheepfold bigger. "
Afandi thought, "What shall we do? How to make the sheepfold bigger without spending money on other materials? "
Students who are equally smart, can you think of a way to help two generations? And please explain your reasons.
(5) Summary
What did you learn from this class today?
The area of the second kind of circle
First, the teaching objectives
1. Knowledge and skills
Mastering the calculation method of ring area can flexibly solve simple practical problems related to life.
2. Process and method
In the process of drawing and cutting rings, feel the characteristics and formation process of rings, and then explore the calculation method of ring area. Cultivate students' ability to observe, operate, compare, analyze and summarize.
3. Emotional attitudes and values
Further experience the connection between graphics and life, feel the learning value of plane graphics, and improve the interest in learning mathematics.
Second, the focus of teaching
Characteristics of circular ring, derivation and application of circular ring area formula.
Third, teaching difficulties
Flexible use of ring area calculation method to solve related simple practical problems.
Fourth, prepare teaching tools.
Courseware and learning tools.
Teaching process of verbs (abbreviation of verb)
(A review of learning methods, paving the way for memories.
What learning methods do we use when we derive the formula for calculating the area of a circle?
Student: Turn a circle into a learned plane figure and derive new knowledge from old knowledge. )
This is what we often say, when we encounter something we can't do, we will think about it and turn new knowledge into old knowledge to solve it. Blackboard: No.
think it over
New and old
In this class, we will continue to study new problems in this way.
(B) the creation of practical application of the problem situation
1. Students, do you like watching cartoons? Today, the teacher brought some CDs. Look, what is this?
(1) Animation CD (2) Song CD
(3) CD with blank cover
Do you want to know the contents of this CD? Let's take a look.
Enjoy photos of students' campus activities.
These photos have witnessed our classmates' happy campus life in the past six years, which is very precious. Do you want to keep it? The teacher is going to carve these photos into CDs and give them to you as graduation gifts when you graduate, okay?
Now the cover of this CD is still empty. Do you want to design a memorable cover for it yourself? To design, let's first understand which part of the cover can be designed.
4. Touch the prepared CD in the group, and then ask the students to put out their fingers.
Circular animation 14 can be used in the teacher's courseware demonstration (abstract line graphics and colored graphics from physical objects).
5. What are the characteristics of this picture?
Health: It consists of two circles with the same center. (Courseware clicks out of the center of the circle)
6. Teacher's Note: The part sandwiched between these two concentric circles is called a circle.
Write on the blackboard: circle
We call the outer circle the outer circle and the inner circle the inner circle. The distance between two circles is called the ring width.
The area of the circle teaching plan 3 teaching objectives:
1. Through the operation, students are guided to deduce the calculation formula of circular area, and some simple practical problems can be solved by using the formula.
2. Stimulate students' interest in participating in the whole classroom teaching activities, cultivate students' ability of analysis, observation and generalization, and develop students' concept of space.
3. Mathematical thought and limit thought of infiltration transformation.
Teaching focus:
Calculate the area of the circle correctly.
Teaching difficulties:
Derivation of the formula of circular area.
Teaching aid preparation:
Two sets of multimedia courseware, CD.
One. Import scene
1, teacher: (showing pictures) The grass is full of grass. A sheep was tied to a post in the grass. Can it eat all the grass? What range of grass can it eat at most? Please draw a schematic diagram of the range of sheep's activities. Two students are drawing on the blackboard. One draws the perimeter and the other draws the area. ) (animation demonstration)
Teacher: Does the size of this range refer to the circumference or area of a circle? Why? Who drew it right? (The area of the circle).
(blackboard writing: the area of a circle)
2. Teacher: What is the area of a circle? Speak first, then read, students read, (teacher demonstrates with courseware)
Teacher: What did you think of after seeing this topic? What problems should be solved in this course?
Student: In this class, we will learn how to find the area of a circle.
Student: Student: The area formula of the circle.
Teacher: After knowing the formula of circular area, what other problems did you think of?
Student: What is the area formula of a circle derived from?
Teacher: Yes! These students just think what the teacher thinks. We must solve two problems in this course.
By creating scenes, students' interest in learning is stimulated and good learning motivation is formed. Clear learning objectives through students' questions. )
Second, hands-on operation, exploring new knowledge.
1. Guess (each item is presented by the courseware)
Teacher: Let's use a simple method to guess the formula of circular area. Divide a circle into four equal parts and draw a square with the radius as the side length. The area of this square can be represented by r2. You can draw the same four squares on this circle, and their areas can be represented by 4 r2. Have you observed that the area of this circle is not equal to 4 r2?
Health: No. ..
Teacher: Why?
Health: Because, this circle area should be added with four small pieces outside, which is 4 r2.
Teacher: The area of this circle is less than 4 r2. Let's draw the biggest square in the circle. How can we find out the area of this square?
Health: This square consists of four triangles with the same size, each triangle has an area of 1/2r2, with a total area of 2r2.
Teacher: Whose area is bigger than a circle and a square?
Health: The area of a circle is large.
It can be observed that the area of a circle ranges from 2R2 to 4R2.
Here, let students know that they should be good at observation and dare to guess when solving problems. Infiltrate infinite and other mathematical ideas,)
2. Recall old knowledge,
Teacher: Can a circle be measured directly in area units? Why?
Health: Because a circle is surrounded by curves, it is difficult to measure it directly in area units.
Teacher: What should we do? (The classroom was silent)
Teacher: Please look at the screen. (The teacher plays the courseware) Note while watching: We have learned the solution of parallelogram, triangle and trapezoid area before. So how do we deal with it? (Show and discuss the transformation diagram of several figures with the projector)
Teacher: What does the derivation method of these figure area formulas inspire us to study the area of a circle?
Health: We can find the area of a circle by graphic transformation. (Turn the unknown into the known)
Teacher: This method is very good. So what figure do you turn the circle into?
[Comment: Inspire students to solve problems with transformed mathematical ideas. This design not only reviews the old knowledge, but also paves the way for students' new knowledge, which can promote students to make full use of the transfer law to connect the old and new knowledge and form a new knowledge structure. ]
do it yourself
(1) Teacher: Please cut it out and spell it to see what figures you can spell. (Students do it by hand. )
Teacher: Who can tell us what figure you put this circle together? (Student: Spelled. Please put your assembled graphics on the physical projection for everyone to see. A student uses 8 equal discs to form an approximate parallelogram, and one does not need 16 equal discs to form an approximate rectangle).
(2) Teacher:: Please look at the big screen. 16 or 8 equal rectangles, who is closer?
Health: 16 will be closer to a rectangle. The more copies, the finer each. )
Teacher: Yes. In other words, the number of copies is unlimited. You can close your eyes and think. The more copies are divided, the closer the long side is to a straight line and the closer the figure is to a rectangle. Courseware demonstration
(3) What is the connection between rectangle and circle? Can you deduce the formula for calculating the area of a circle from the formula for calculating the area of a rectangle? Discuss in groups. The teacher asked the students to observe the figures they spelled on the desk, discuss and write out the derivation step by step. )
Students report the results of the discussion. The answering teacher continued to demonstrate the courseware.
Answer: Yes, because the area of the rectangle is equal to the area of the circle, the length of the rectangle is equivalent to half the circumference of the circle, and the width is equivalent to the radius.
Because the area of a rectangle = length and width
So the area of the circle = half the circumference radius.
S=r
S=r2
Teacher: With the formula S = R2, how is the area of a circle derived?
(4) Teacher: Is this area formula correct? We can verify it by other charts. Some students turn a circle into a triangle. Let's use a triangle to verify it. Can the formula for calculating the area of a circle be derived from the formula for calculating triangles? (Courseware demonstration)
Answer: The base of a triangle is equivalent to the circumference of a circle, and the height is equivalent to four times the radius of a circle.
Because the area of triangle = base height 2
So the area of the circle = 4 times the perimeter radius.
S=4r2
S=r2
Teacher: We also derived the formula of circle area S = R2 by triangle. Students, do you have any other graphics to verify?
(5) Health: We transform the circle into a trapezoid to verify it. (Courseware demonstration)
Health: The sum of the upper bottom and the lower bottom of the trapezoid is equivalent to half of the circumference, and the height is equivalent to twice the radius.
Because the area of the trapezoid = (upper bottom+lower bottom) is 2.
So the area of a circle = half the circumference and twice the radius.
S=2r2
Trapezoidal area when S = S = R2.
3. Summary: What figure did you just transform the circle into, and derived the formula for calculating the area of the circle respectively? (S=r2)
We derive the same formula from the spliced approximate parallelogram, rectangle, triangle and trapezoid: S circle =r2.
Alas! What is the area of the circle we just guessed? You guys are amazing! Very close to r2!
What are the necessary conditions for the area of a circle?
[Comment: It breaks the framework of teachers demonstrating teaching AIDS to students in the past, but requires each student to operate by hand and infiltrate mathematical ideas such as transformation and infinity, so that students can deduce the formula of circular area from their own attempts. ]
Consolidation after class
1. Now can you find out how much grass this lamb can eat at most? Why? Please make it a condition.
From the beginning, I learned to calculate the practice area. )
2. Find the area of the circle according to the following conditions.
R =5 decimeters d =3 meters
How do students calculate the cross-sectional area of trees? Do they have to cut them down? (Students discuss and answer the questions after measuring the circumference. The circumference of the tree is 18.84 square meters. What is the cross-sectional area of the tree?
(Use what you have learned to solve problems in life and cultivate students' application ability)
Teacher: What did you learn in this class? What did you get?
The students spoke enthusiastically, and finally the teacher summed up and answered two questions raised at the beginning of the class. )
[Comment: Although the class summary time is short, it can make students understand the steps of sublimation and make the whole class structure clear. The biggest feature of this course is that it can fully mobilize students' initiative and enthusiasm. Students can learn vividly and fully develop their thinking. ]
The area of circle teaching plan 4 teaching content
Mathematics, compulsory education curriculum standard experimental textbook, the first volume of grade six, 69 ~ 7 1 case, 1 case, 2 cases.
Teaching objectives
1. Through observation, operation, analysis and discussion, students derive the formula of circle area.
2. Simple area can be calculated by formula.
3. Infiltrate and transform ideas, get a preliminary understanding of extreme ideas, and cultivate students' observation ability and hands-on operation ability.
Prepare teaching and learning tools
1.CAI courseware;
2. Divide the circle into 8 equal parts, 16 equal parts and 32 equal parts;
3. Some scissors.
teaching process
First, try to transform and deduce the formula.
1. Determine the strategy of "transformation".
Teacher: Students, think about it. When we can't calculate the area of parallelogram, what method is used to derive the calculation formula of parallelogram area?
Default value:
Guide the students to make it clear that we use the "cut-and-complement method" to transform the parallelogram into a rectangle, and deduce the calculation formula of the parallelogram area.
Teacher: Students, think again. How do we deduce the calculation formula of triangle area?
Teacher: Yes, we "transform" parallelogram and triangle into other figures and derive their area calculation formulas.
2. Try to "transform".
Teacher: So, how can we transform the circle into other figures we have learned? (blackboard title: the area of a circle)
Please look at the screen (demonstrate with courseware), and the teacher will give you a hint first.