1. Make students learn the calculation method of circular area and the related calculation method of circular and rectangular mixed graphics.

2. Learn to use the existing knowledge and mathematical thinking methods to derive the formula for calculating the area of a circular ring, including the application of circles and squares.

3. Cultivate students' abilities of observation, analysis, reasoning and generalization, and develop students' spatial concepts.

Emphasis and difficulty in teaching

The teaching emphasis of 1

Can use circle and other related knowledge to solve practical problems.

2 Teaching difficulties

Mixed use of circle and other graphic calculation formulas.

teaching tool

PPT card

teaching process

1 Review and consolidate previous knowledge and introduce new lessons.

2 New knowledge exploration

2. 1 ring zone

First, the introduction of the problem

Do students know what CDs can be used for? Who can describe the appearance of a CD?

Answer (abbreviated).

Today we will do some math problems related to CD.

Second, the ring zone solution

Example 2. The silver part of the CD is a ring with an inner radius of 50px and an outer radius of 150px. What is the area of this ring?

Steps:

Teacher: What do you need to find the area of a circle first?

Health: area of inner ring and outer ring

Teacher: Students can do it themselves and communicate solutions in groups.

Teacher: Give the calculation process and results:

Third, the application of knowledge

Do the second question:

The diameter of the circular island is 50m, with a circular flower bed with a diameter of 10m in the middle and lawns in other places. What is the area of the lawn?

Teacher: This is a typical round area application problem. It is very simple to get the radius from the diameter and substitute it into the formula of ring area.

2.2 Round and Square

First, the introduction of the problem

Teacher: The students know the gardens in Suzhou. Have you ever observed the windows of garden buildings? It has many beautiful designs and many common graphics, such as pentagon, hexagon, octagon and so on. Among them, the inside of the outer circle or the outside of the inner circle is a very common design.

Teacher: Not only in landscape architecture, but also in architecture and other designs in China? In the outer circle? And then what? Outer ring and inner ring? For example, the Fiona Fang Tower in Shenyang, the trademark of Shenyang and so on. Let's get to know this figure consisting of a circle and a square.

Second, knowledge points

Example 3: The radius of two circles in the figure is1m. Can you find the area between a square and a circle?

Steps:

Teacher: What does this topic tell us?

Health: the radius of the left circle = half the side length of a square =1m; The area of the right circle = half of the diagonal of the square =1m.

Teacher: What are the requirements?

Health: the area of a square is greater than that of a circle, and the area of a circle is greater than that of a square.

Teacher: What should I do?

Inductive summary

If the radii of two circles are both R, what is the result?

When r= 1, it is completely consistent with the previous results.

Fourth, knowledge application.

On page 70, do:

The picture below shows the bronze mirror inside the outer ring of China in the Tang Dynasty. The diameter of the bronze mirror is 600px. What is the area between the outer circle and the inner side?

Teacher: Students, please use what we have just learned to solve this problem.

Solution: The radius of bronze mirror is 300px.

5.3 Classroom exercises

If you have enough time, practice 5/6/7 exercises in class.

(Students can be invited to write the problem-solving process on the blackboard.)

6 abstract

1. What did we learn today?

Today, under the premise of knowing the area formulas of circles and squares, we explored the sum of circles and squares. Inside the outer circle, outside the outer circle, inside the circle? The method of calculating the graphic area. This is not to ask students to remember these derived formulas, but to hope that students can understand the derivation method and use what they have learned to solve similar problems in the future.

2. In our daily life, we often need to find the area of a circle. For example, yurts are round, because the living area can be used to the maximum extent, and the cross section of plant roots is round, because it can absorb water to the maximum extent. We can also give some other examples, such as why do plates and wheels have to be round? Everyone needs to think more!

7 blackboard writing

Example 2 Solution Steps

The area of circle teaching plan (2) teaching objectives

(1) Knowledge and skill goal: Students should know the characteristics of groups and graphs in combination with specific situations, master the method of calculating the area of combined graphs, and accurately master and calculate the area of simple combined graphs.

(2) Process and Method Objective: To cultivate students' awareness of independent thinking and cooperative inquiry through independent cooperation.

(3) Emotional attitude and values goal: In the process of solving practical problems, students will further experience the connection between graphics and life, feel the learning value of plane graphics, and improve their self-confidence in learning mathematics well.

Emphasis and difficulty in teaching

Teaching emphasis: understanding of combined graphics and area calculation.

Teaching difficulty: combined graphic analysis.

teaching tool

Multimedia courseware, various basic graphic pieces of paper.

teaching process

First, create situations and introduce dialogues.

Students, we often see it in ancient buildings in China? Inside and outside, outside, inside? Now, please enjoy some pictures. The teacher asked: Are these pictures nice? (Health: Beauty)

Teacher: What plane graphics are included in the design of these pictures? (health: round, square, rectangle, etc. )

Teacher: The combination of these different geometric figures can form exquisite patterns and give us beautiful enjoyment, which shows that our mathematics is closely related to real life. Today, we will learn the area of a circular composite figure. (Writing on the blackboard) 2. Ask questions and explore independently

1. The teacher drew two pictures of Example 3 and showed the self-study skills. Show self-study skills:

(1) What's the difference between the above two pictures?

(2) What is the relationship between the diagonal of the square in the picture on the right and the diameter of the circle?

(3) The radii of the two circles in the above picture are both R. Can you find the area of half between the square and the circle?

2. Please read pages P69-70 carefully with questions, and think independently about the questions in the self-study tips. If you have difficulties, you can discuss them in groups. (Self-study time: 4 minutes) Third, teacher-student interaction, cooperative inquiry 1. Report exchange, teacher-student interaction

Students report problems (1): These two pictures are both composed of circles and squares. The left picture shows the inside of the outer circle, and the right picture shows the inside of the outer circle.

Question (2): The diagonal of the square on the right is equal to the diameter of the circle. Student Report Question (3): The area of the shadow on the left = the area of the square-the area of the circle is: S positive =2? 2=4(m2) S circle =3. 14? 12 = 3.14 (m2) 4-3.14 = 0.86 (m2) Left: the area of the circle minus the area of the square.

( 1/2 ? 2? 1)? 2=2(m2 ) 3. 14？ 12=3. 14 (square meter) 3.14-2 =1.14 (square meter)

Teacher: The students did a good job! But I have another question. If the radii of two circles are both R, what is the result? The student representative replied:

Left; (2r2)-3. 14r2 =0.86r2

Right: 3. 14r2-( 1/2? 2r？ r)？ 2= 1. 14r2 When r= 1m, it is completely consistent with the previous results.

A: The area between the square and the circle in the left picture is 0.86m, and the area between the circle and the square in the right picture is1.14 m. ..

Fourth, summarize and guide, and generate knowledge. What did you gain from this class?

The way of moral education for students by teachers: In our future life, we must be flexible, flexible, generous and harmonious in external and internal justice. Five, scientific training, improve the ability of 1, show the textbook P70 to do 2, complete the textbook P72, Question 9, clean up the homework in class.

Seven. Task p73 number 10, 1 1.

Summary after class

What did you learn from this course?

homework

1. Show the textbook P70 and do it.

2. Complete the ninth question in the textbook P72.

Write on the blackboard.

An area containing a combined graph of circles.

Left: s is positive =2? 2=4(m2) Right: (1/2? 2? 1)? 2=2 (square meter)

S cycle =3. 14? 12 = 3. 14(m2)3. 14？ 12=3. 14 (m2)

4-3. 14=0.86 m2 3.14-2 =1.14 m2