Tisch
Teaching content: the area of a circle.
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.
Analysis of learning situation:
This lesson is taught on the basis that students have mastered the meaning of area and the calculation method of the area of rectangular and square plane graphics, and can know and calculate the circumference of a circle. In teaching, we should follow students' cognitive rules, pay attention to students' thinking process of acquiring knowledge, and proceed from their life experience and existing knowledge.
Legal learning guidance:
In teaching this lesson, we should focus on guiding students to put forward the idea of combining circular tangent with learned graphics, organizing students to operate by hands, and let students actively participate in the process of knowledge formation, so as to cultivate students' innovative consciousness and practical ability and develop students' spatial concept.
Teaching aid preparation:
Multimedia courseware, CD.
Learning aid preparation:
Divide the disc into sixteen equal parts and cut it into an approximate rectangle as shown in the textbook.
Instructional design:
First, review old knowledge and introduce new lessons.
1. In front of us, we studied the circle and the circumference of the circle. If r is used to represent the radius of a circle, what is the circumference? How to express the half circumference of (2πr)? (πr)
2. Courseware: Show a round tablecloth. If you want to sew lace on the edge of this tablecloth, what is it? (The periphery of a circular tablecloth)
3. Work: Show me a round picture frame. If you want a frame with glass, what is the minimum size? What is this? (Area of a circle) Who can point out the area of this circle? Who can sum up the area of a circle? Please touch the area of the study tool circle with your hand.
Question: If the radius of the circle is 2 decimeters, can you guess how big this glass is? Students have speculated that some students may say that this round surface is smaller than the square area.
How big this round glass is, that is, the area of the round is required. In this lesson, we will learn how to calculate the area of a circle. (blackboard title: the area of a circle)
Second, hands-on operation, exploring new knowledge.
1. Recall the derivation process of parallelogram, triangle and trapezoid area calculation formulas.
(1) Before that, we learned the formulas for calculating the area of parallelogram, triangle and trapezoid. Please recall, how are the formulas for calculating the area of these figures derived? Students answer, and the teacher demonstrates with courseware. )
(2) Looking back on the derivation process of these three formulas for calculating the area of a plane figure, what did you find? It is found that these three kinds of plane figures are transformed into learned figures to derive their area calculation formulas. )
(3) Can a circle be transformed into a learned figure to derive its area calculation formula? Then students think about it, what plane figure can a circle be transformed into to calculate?
2. Derive the calculation formula of circular area.
(1) Take out the prepared school tools and tell me what shapes you put together with the circular scissors.
(2) Students discuss in groups.
What is the connection between rectangle and circle?
Students report the results of the discussion.
(3) Courseware demonstration: Look at the big screen. Divide the circle into 16 equal parts to make an approximate parallelogram, then divide it into 32 equal parts to make an approximate parallelogram, and then divide it into 64 equal parts to make an approximate rectangle. What did you find? If you divide it into several parts, each part will be thinner and the figure will be closer to a rectangle. )
(4) Can the formula for calculating the area of a circle be derived from the formula for calculating the area of a rectangle? Discuss in groups.
Show the courseware while answering the teacher.
Answer: Because the area of a rectangle is equal to the area of a circle, the length of a rectangle is equivalent to half the circumference of a circle, and the width is equivalent to the radius.
Because the area of a rectangle = length x width
So the area of the circle = half circumference × radius.
S=πr × r S=πr2 Teacher summed up the formula.
S=πr2。 Let's talk about how the area of the circle is derived among the students.
(5) Read formulas and understand memory.
(6) What do you need to know about the area of a circle? (radius)
3. Calculate by formula.
(1) Recalculate: How big was the glass just now? See who guessed closer just now. (Students calculate and report)
(2) Example 3, students try to practice and give feedback.
Question: If this question is not about the radius of a circle, but about the diameter, how to answer it? Does anyone know what the result is without calculation?
(3) Complete the 95-page 1 question.
(4) reading questions.
Third, apply new knowledge to solve problems.
1. Find the area of each circle below, except the formula. (showing CAI courseware)
2. Measure the diameter of a circular object and calculate its perimeter and area.
3. Courseware demonstration
Tie the sheep to a stake with a rope and demonstrate the scene of the sheep eating grass while walking. What is the area where sheep graze, that is, the circular area? )
Fourth, the class summarizes.
What methods did you use and what knowledge did you learn in this class?
Verb (abbreviation for verb) assigns homework.
1. Questions 3 and 4 on page 97.
2. Find the circle around you, measure the radius at the same table and calculate the area (complete the experimental report).
Measurement object, diameter (cm), radius (cm) and area (cm 2)
Blackboard design:
Area of a circle
Area of rectangle = length × width
Area of circle = half of circumference × radius
S=πr×r
S=πr2
extreme
Teaching content:
Compulsory education curriculum standard experimental textbook XI, volume P69 ~ 7 1 example 1 example 2.
Teaching objectives:
1, cognitive goal: let students understand the meaning of circular area; Master the formula of circle area, and can use the knowledge to solve simple problems in life.
2. Process and Methods Objective: To experience the derivation of the area formula of a circle, experience the experimental operation and learn the logical reasoning method.
3. Emotional goal: to guide students to further understand the mathematical thought of "transformation" and initially understand extreme thoughts; Experience the joy of discovering new knowledge, enhance students' awareness and ability of cooperation and exchange, and cultivate students' interest in learning mathematics.
Teaching focus:
Mastering the formula for calculating the area of a circle can correctly calculate the area of a circle.
Teaching difficulties:
Understand the derivation of the formula for calculating the area of a circle.
Teaching preparation:
Corresponding courseware; Demonstration teaching aid for area of circle
Teaching process:
First, situational introduction
Show me the scene? -"The Confusion of Horses"
Teacher: Students, do you know what the figure is when a horse is eating grass?
Health: It's a circle.
Teacher: So, if you want to know the size of the horse eating grass, what is the circle?
Health: the area of a circle.
Teacher: Today, let's learn the area of a circle. (blackboard title: the area of a circle)
[Design intention: Through the scene of "horse's confusion", let students discover the problems themselves, and at the same time let students realize that what they want to learn today is closely related to their lives around them, and at the same time understand the learning tasks and stimulate students' interest in learning. ]
Second, explore cooperation and deduce the formula of circular area.
1 permeates the mathematical thought and method of "transformation".
Teacher: How to calculate the area of a circle? What is the calculation formula? Do you want to know?
Let's first recall how the area of the parallelogram is derived.
Student: Cut it into two parts along the height of the parallelogram and put the two parts into a rectangle. Teacher: Oh, look, is that right? (Teacher demonstrates).
Yes, the base of the parallelogram is equal to the length of the rectangle, and the height of the parallelogram is higher than the width of the rectangle. Because the area of a rectangle is equal to the length times the width, the area of a parallelogram is equal to the bottom times the height.
Teacher: The students have mastered the original knowledge well. Just now, we cut a figure first, then spell it out and then transform it into other figures. What are the benefits of this?
Health: This will turn a problem that we don't understand into a problem that we can solve.
Teacher: Yes, it's a good way for us to learn math. Today, we use this method to convert the circle into the learned figure.
Teacher: What figure can that circle be transformed into? Do you want to know? (thinking)
2. Demonstrate to solve doubts.
Teacher: (Explain the demonstration) Divide this circle into 16 equally, cut it along the diameter, turn it into two semicircles, and make an approximate parallelogram.
Teacher: If the teacher divided the circle into 32 equally, what figure would he spell? Let's have a look (teacher's courseware demonstration).
Teacher: Imagine that if the teacher keeps dividing, the more copies are divided, the smaller each copy is, and the closer the total number is to what number. (Rectangular)
[Design Intention: Through this link, an important mathematical idea, namely, the idea of reduction, is infiltrated, and students are guided to abstract and summarize new problems, transform them into old knowledge, and use old knowledge to solve new problems. With the help of the demonstration of computer courseware, the cutting and spelling process of turning music into a straight board is vividly displayed. ]
3. Students collaborate to explore and deduce formulas.
(1) Discuss and display the prompt.
Teacher: Let's look at three questions given by the teacher. Please work in groups of four, take out the learning tools prepared before class and spell them out. Observe and discuss to complete these three questions.
(1) Their (shapes) changed during the transformation, but their (areas) remained unchanged?
② The length of the transformed rectangle is equivalent to the length (half circumference) of the circle, and the width is equivalent to the width (radius) of the circle?
③ Can you deduce the formula for calculating the area of a circle from the area of a rectangle? Try to use a relative word like "because ...".
Teacher: Do you understand the requirements? Ok, let's get started.
The students reported their grades and the teacher scribbled on the blackboard.
After observation and discussion, the students found out the formula for calculating the area of the circle, which is really remarkable.
(2) Teacher: If the radius of a circle is represented by R, how can half of the circumference be represented by letters?
(3) Reveal the letter formula.
Teacher: If S is used to represent the area of a circle, the formula for calculating the area of the circle is: S=πr2.
(4) Read the formula in chorus, emphasizing r2=r×r (representing the multiplication of two r's).
According to the formula, what conditions must be known to calculate the area of a circle? What should be calculated first in the calculation process?
Design intention: Through group discussion, students can further clarify the corresponding relationship between the spliced rectangle and the circle, which effectively breaks through the difficulty of this lesson. ]
Third, use formulas to solve problems.
1. Teaching examples 1.
Teacher: Students, from this formula, we can see that what must we know first to ask for the area of a circle? (Example 1) Given the radius of a circle, students are required to calculate the area of the circle according to the formula for calculating the area of the circle.
Premise: Teachers should strengthen inspections, give timely guidance when problems are found, and remind students whether formulas and units are used correctly.
2. If we know that the diameter of a circular flower bed is 20m, how can we find its area? Please write and calculate the area of this round flower bed!
3. Find the area of each circle below.
[Design Intention: Students have mastered the formula for calculating the area of a circle, so they can boldly try to solve it, thus promoting the combination of theory and practice and cultivating students' ability to flexibly use what they have learned to solve practical problems. ]
3. Teaching example 2.
Teacher: (Example 2) This is a CD, which consists of two circles, an inner circle and an outer circle. The silver part of the CD is a ring. Please read the questions quietly. Let's go
Teacher: How to find the area of this ring? Let's discuss it and do something!
Teacher: Have you found a solution to the problem?
Teacher: ok, just calculate the area of this ring according to the method that students come up with!
Teachers continue to strengthen the inspection of students with learning difficulties, and give guidance if there are still problems.
[Design Intention: Students have mastered the calculation formula and calculation of circular area. Teachers can guide students to analyze and understand, boldly let students try to answer, and cultivate students' ability to use what they have learned to solve practical problems. ]
Fourth, class assignments.
1, the second small question of "Do it" on page P69 of the textbook.
2. True or false
Let the students judge first and talk about the reasons for the mistakes.
Step 3 fill in the blanks
Review the relationship between radius, diameter, perimeter and area of a circle.
4. Exercise on page 70 of the textbook 16 Question 2.
5, complete the courseware exercise (know the circumference to find the area)
The teacher stressed that students should carefully examine the questions, and guide them to ask the area of a circle. They must know which condition (radius) and how to find the area of a circle by knowing its perimeter. Teachers pay attention to counseling middle and lower students.
Verb (abbreviation of verb) course summary
Teacher: Students, what have you learned from this class?
Distribution of intransitive verbs
Tisso
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 "conversion" method, cultivate their ability to solve new problems by using what they have learned, and develop their 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) Given the last two figures of Example 7, calculate and fill in the form in the same way.
The area of a square/
Radius of a circle/
Area of 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
(1) The area of a circle is more than three times the square of its radius.
(2) The area of a circle can be five times the square of the radius.
3. Teaching examples 8.
(L) Talk: Just after learning, we already know that the area of a circle is about three times the square of its radius, so how should we calculate the area of a circle?
(2) Operating experience: The teacher demonstrated that the circle was divided into 16 parts and made into an approximate parallelogram.
(3) Question: What kind of graphics does the mosaic look like? Ask: Why is it like a parallelogram?
Imagine: If you divide the circle into 32 parts and spell it in a similar way, think about it. What's the change between the mosaic and the previous one?
(4) Further imagine: If the circle is divided into 64 parts and 128 parts on average, spell it in a similar way. Close your eyes and think about it. As the number of copies increases, which graphics will get closer and closer to each other?
(5) After the communication, the teacher shows the derivation diagram. What is the connection between the rectangle and the original circle? Discuss and communicate in groups.
(6) In the collective communication, summarize with the help of charts: the area of rectangle is equal to the area of circle; The width of a rectangle is the radius of a circle; The length of a rectangle is half the circumference.
(7) Question: If the radius of a circle is R, how should the length and width of a rectangle be expressed? According to the calculation method of rectangular area, how to calculate the area of circle?
(8) According to the students' answers, the teacher writes on the blackboard.
The area of a rectangle is a length x a width.
Area of circle =
(9) Follow-up: With such a formula, we can calculate the area of a circle by knowing what conditions it has.
4. Teaching examples 9.
(1) Example 9 Question: Have you ever seen an automatic rotating device in your life?
(2) Imagine the figure of the sprinkler irrigation location after the robot rotates once, and what is the meaning of the farthest distance.
(3) Students complete the calculation independently.
(4) Collective communication.
5. Teaching examples 10.
(1) Please read the question and interpret the meaning.
(2) Find out the known conditions in the problem.
(3) Analyze the problem-solving process.
(4) Make clear the conversion relationship between the quantities.
Third, consolidate practice and deepen understanding.
1. Complete the Exercise.
(1) Students answer independently.
(2) Collective communication.
2. Complete the exercise 15, question 1.
(l) Students answer independently.
(2) Collective communication.
3. Complete question 3 of exercise 15.
(1) Students list and calculate with a calculator.
(2) Collective communication.
4. Complete question 4 of exercise 15.
(1) Students answer independently.
(2) Collective communication, pointing out that to calculate the area with the known perimeter, we must first calculate the radius according to the perimeter.
5. Homework: Exercise 15, questions 2 and 5.
Fourth, class summary.
Teacher: What did you gain from today's study?
Students speak and teachers comment.
Area of a circle
Area of rectangle = length × width
Area of circle =