First, the analysis of students' knowledge

Students' knowledge and skill base: After learning the basic drawing, students understand the drawing method. Through the study in the first section of this chapter, I have mastered the concepts of line segment ratio and proportional line segment, the basic properties of proportion, the calculation of proportion and proportion, and laid a solid foundation.

The basis of students' activity experience: students' painting learning strengthens their hands-on ability; The calculation of ratio and proportion makes students feel the role of mathematics in real life and enhance their confidence in learning mathematics. Through the transformation of fish into proportional line segments, proportional property derivation and transformation, the logical reasoning ability is developed. The examples in the first section of this chapter cultivate students' ability to use flexibly.

Second, the analysis of teaching tasks

Learning "golden section" not only meets the requirements of line segment proportion, but also embodies the cultural value of mathematics, the significance of 0.6 18, and the inevitable connection between mathematics and architecture, art and other disciplines. In teaching, the golden section is introduced through the five-pointed star on the national flag, so that students can truly appreciate the cultural value. At the same time, they can appreciate examples in architecture and art, and further strengthen line segment ratio, proportional line segment, golden section and other related contents in application. To this end, the teaching objectives of this lesson are:

1, know the definition of the golden section; You will find the golden section of a line segment; Will judge whether a point is the golden section of a line segment;

2. Cultivate students' understanding and practical ability by looking for the golden section of line segments.

3. Understand the meaning of golden section, find and make golden section points and figures, so that students can understand the close relationship between teaching and human life and its role in the development of human history.

Teaching emphasis: understand the meaning of golden section and apply it.

Teaching Difficulties: Finding the Golden Section and the Golden Rectangle

Third, the analysis of teaching process

This lesson designs seven links: the first link: situation introduction; The second link: picture appreciation; The third link: operational perception; The fourth link: connecting with reality and enriching imagination; The fifth link: consolidate the exercise; The sixth link: class summary; The seventh link: assign homework.

The first step is scenario introduction.

Activity content:

Show the courseware and ask questions:

Question 1. Look for the same pattern from the national flag.

Question 1. Are the distances from measuring point C to A and B equal?

Teachers operate courseware, ask questions and communicate with students.

Answer the question 1. five-pointed star

Answer the question 1. Equality.

Show courseware and introduce new knowledge.

On line segment AB, point C divides the line segment into AC and BC. If there is, it is said that the division of line segment AB by point C is called the golden section of line segment AB, and the ratio of AC to AB is called the golden section ratio.

In ...

that is

Teachers explain, students observe, think and communicate.

Activity purpose: Use the five-pointed star to create a situation that is conducive to students' exploration and comprehensive application of line segment ratio. The concept of golden section is introduced, and the golden section rate is about 0.6 18.

Note: Students observe, think and communicate, while teachers guide and answer questions. Because students have never studied the quadratic equation of one variable and can't understand why the ratio is, let them know this fact.

The second link is picture appreciation.

Activity content:

The first picture: dancer. The ratio of their legs to their bodies is also close to 0.6 18. Any solid sample with such a proportion will feel harmonious, balanced, comfortable and have a beautiful feeling.

The second picture: Shanghai Oriental Pearl Tower, the first in Asia and the third in the world, has its upper sphere at 295 meters, which is exactly at the 5:8 position of the tower, that is, the ratio of 0.6 18, which makes the tower look very harmonious and beautiful.

The third picture: The ratio of side length to height of the pyramids in ancient Egypt is close to 0.6 18.

Purpose of the activity: Re-recognize the golden section through examples in architecture and art, understand its wide application and cultural value in real life, and enhance students' awareness of mathematics application.

Note: The teacher provides three pictures. Under the guidance of the teacher, students carefully observe, think and communicate, and find out the golden section from the pictures.

The third link is operational perception.

Activity content:

Show courseware: do it.

If the line segment AB is known, draw it as follows:

(1) Make BD⊥AB pass through point B, so that

(2) Connect AD and intercept DE=DB on DA.

(3) If AC=AE is intercepted on AB, then point C is the golden section of line segment AB.

Answer the following questions according to the picture above.

(1) If AB=2, what are BD, AD, AC and BC respectively?

(2) Is point C the golden section of line segment AB?

Teachers operate courseware, ask questions, students think independently and communicate with their peers.

Answer the question:

The purpose of the activity is to introduce the production method of the golden section to students and consolidate their understanding of the golden section.

Note: the teacher operates, the students think independently, and then communicate with their peers. Because students have limited drawing methods with rulers, they can use triangular rulers and graduated rulers as drawing tools.

The fourth link is to combine practice and enrich imagination.

Activity content:

Show courseware: think about it

Please look at the screen. The picture shows the Parthenon in ancient Greece. Draw the rectangle represented by the dotted line into the rectangular ABCD as shown in the figure, and make a square AEFD inside the rectangular ABCD. Then, we will be surprised to find that.

Please think about it: Is point E the golden section of AB?

Is the aspect ratio of rectangular ABCD the golden ratio?

Watch multimedia presentations, observe and think, communicate and discuss, and solve problems.

Problem solving: from, you can get

that is

So point E is the golden section of AB.

In other words, the aspect ratio of rectangular ABCD is the golden section ratio.

The purpose of the activity is to show the cultural value of the golden section and its role in human history, and use some skills of proportional deformation to understand the importance of the basic nature of proportion and improve the ability to solve problems.

Note: Teachers fully guide students to observe, think, communicate, discuss and solve problems.

The fifth link consolidation exercise

Activity content:

The golden section can also be obtained by the following methods.

As shown in the figure, let AB be a known line segment, make a square ABCD on AB, take the midpoint E of AD, connect EB, extend DA to F, make EF=EB, and make a square AFGH with line segment AF as the edge, and point H as the golden section point of AB.

Make any line segment and use the above method to make the golden section of this line segment. Can you tell me the truth about this practice?

Watch the content of multimedia presentation, observe and think, exchange discussions and solve problems.

Solve the problem:

Let AB=2, then in

,

H point is the golden section of AB.

The purpose of the activity is to introduce students to another method of learning the golden section and further consolidate their understanding of the golden section.

Note: Teachers guide students to practice, observe, think, communicate, discuss and solve problems.

The sixth part is the class summary

Content:

1, know what the golden section is, golden ratio, golden rectangle, wonderful 0.808+08.

2. Understand the golden section phenomenon widely existing in nature and social life.

3, can use the knowledge of golden section to solve simple calculation and drawing problems.

Activity purpose: Encourage students to combine the learning process of this class, consciously sum up and apply it to practice, gradually form a correct view of mathematics and cultivate students' aesthetic consciousness.

Note: The teacher encourages students to speak freely and tell their feelings and gains.

The seventh link homework

Exercise 4.3 1, 2

Fourth, teaching reflection.

1. Instructional design focuses on revealing the cultural value of mathematics. Learning the golden section is not only the requirement to realize the proportion of line segments, but also embodies the cultural value of mathematics, which shows that the golden section is the link between mathematics and architecture, beauty and art, and makes students realize that mathematics is not an isolated and dry mathematics, but a part of culture.

2. Experience the idea of combining numbers and shapes.

Through the understanding and mastery of the golden section, the painting method of the golden section is clarified, and the idea of combining numbers with shapes is realized.

3. In the whole teaching process, there may not be enough time for students to practice, think and communicate. Teachers should actively inspire and guide students, pay attention to helping students who have difficulties in communication and cooperation, and make learning more effective.