The teaching design article 1 teaching goal of the second volume of the sixth grade "Magnification and Reduction of Graphics";

1, combined with specific situations, so that students can understand the significance of graphic enlargement and reduction in independent exploration and cooperative communication.

2. Simple graphics can be enlarged or reduced by grid paper in a certain proportion.

3. Make students experience the similarity of graphics in observation, thinking, comparison, verification and communication, and further develop the concept of space.

Teaching emphasis: understand the enlargement and reduction of graphics, and be able to enlarge or reduce a simple graphic according to the specified proportion by using grid paper.

Teaching difficulties: let students feel the enlargement and reduction of graphics in activities such as observation, comparison, thinking and communication. Understand the similarity of graphics and further develop the concept of space.

Prepare learning tools: ruler, square paper

teaching process

First, situational import

1, show me a rectangular diagram (smaller one)

Q: Can the students in the back see it clearly?

The teacher enlarged it.

Show me three enlarged photos. Compared with the original, which one do you think is not deformed?

Figure 1: Enlarge the length and keep the width unchanged.

Figure 2: Stretch the width and keep the length unchanged.

Figure 3: Enlarge the original image to a certain scale.

After students' observation, it is concluded that Figure 3 has not changed.

Teacher: Figure 1 and Figure 2 intuitively show that the shape has changed, while Figure 3 intuitively shows that the shape of the original figure has not changed. Is it true?/You don't say. Let's verify it together.

Second, the operation verification

1, and explore the changing law of graphic amplification.

(1) Show the original drawing and Figure 3.

Teacher: These two pictures are original and enlarged. Please observe them carefully.

Thinking: What is the relationship between the length of the enlarged picture and the length of the original picture? How wide is it?

After students think independently, communicate in groups.

Summarize the exchange:

① The enlarged length is twice as long and the width is twice as wide as the original.

② The ratio of the enlarged length to the original length is 2: 1, and the ratio of the width to the original width is 2: 1.

Teacher: What do you find by observing these two sentences?

2: 1 indicates the ratio of two quantities (students can also point up and point out the corresponding edge).

Teacher's guidance summary: the ratio of the enlarged figure to the corresponding edge of the original figure is 2; 1

Teacher: When the ratio of the enlarged rectangle to the corresponding side of the original rectangle is 2: 1, we say that the rectangle is enlarged according to the ratio of 2: 1. This is the new content we are going to learn in this class: the enlargement of graphics. Writing on the blackboard (enlargement of graphics)

Teacher: What should I do if I want to enlarge this rectangle by 3: 1?

2. Try to operate and deepen your understanding.

(1) Want to try to enlarge a graphic yourself?

Example 2 (Drawing a Rectangular Enlarged Diagram at the Ratio of 3: 1)

Students draw a picture in the textbook, tell how to draw it, check it collectively, and the teacher demonstrates it.

(2) Just now, we studied the characteristics of graphic magnification. Who can talk about what problems should be paid attention to when looking at graphic enlargement?

After the students checked, the teacher said: It seems that your verification is correct.

3. The significance of simplification of analog graphics

Teacher: When the number is enlarged, it will be reduced. (blackboard writing)

Teacher: If the original rectangle is reduced by the ratio of 1:2, what will happen to the reduced rectangle?

After group communication, call the roll and pay attention to the integrity of language expression.

Teacher: 1:2 stands for the ratio of which two quantities?

Teacher: Draw a rectangle with the original picture of Example 2 on page 39 of the textbook reduced 1:2.

Name the students and say, is this how you draw them? The team corrected it.

Teacher: Just now, we enlarged and reduced a rectangle according to a certain proportion. What's the difference between these two ratios?

Teacher: Look carefully at the length and width of each rectangle on the screen. What did you find?

After thinking independently, discuss in groups. (The teacher visits, prompting that the shape remains unchanged)

Communicate with the class, summarize and write on the blackboard: the figure is enlarged or reduced, the size changes, and the shape remains the same.

Third, consolidate and deepen.

1, Teacher: Through the study just now, I believe the students have a deep understanding of the enlargement and reduction of graphics. If you were given a triangle, would you enlarge it as required?

Take out your textbook, turn to page 39 and have a try (draw a triangle with a magnification of 2: 1).

Name the students and say how they draw.

Teacher: Is the hypotenuse twice as big as before? How to prove it? (measurement, comparison)

Teacher: Through the practice just now, it is explained again that the figure is enlarged or reduced according to a certain proportion, and each corresponding edge is enlarged or reduced according to the same proportion, and the shape remains unchanged.

2. Students practice independently and review collectively.

Fourth, the class summarizes.

In this lesson, we learned the enlargement and reduction of graphics. What have you gained and experienced?

Five, the classroom test

1. Fill in the picture.

1. In the figure, the length of the long right angle side of the No.2 triangle is () times that of the No.2 triangle, and the length of the short right angle side of the No.2 triangle is () times that of the No.2 triangle.

2. The triangle ② in the figure is obtained by enlarging the triangle ① according to the proportion of (). ① Triangle is obtained by shrinking ② triangle according to the proportion of ().

Second, draw a rectangle in the box below according to the ratio of 1:2.

Third, the workbook has 26 pages, 1, 2, 3 questions.

Sixth, expand and extend.

The enlargement and reduction of graphics are widely used in our daily life. Think about it, where is this knowledge used in our lives?

Seven. homework

The second volume of the sixth grade, "Magnification and Reduction of Graphics", the second part of the teaching design, teaching material analysis

The enlargement and reduction of graphics are selected from the second volume of the eighth grade of Mathematics (Beijing Normal University Edition), a standard experimental textbook for compulsory education. This chapter is based on students' existing life experience, preliminary mathematics activity experience and related geometric content. Starting with similar polygons, through enlarging and reducing a figure, similar figures and their simple features are introduced, and skillfully combined with the learned figures, coordinates, simple drawing and other contents, so that students can further understand the application value and rich connotation of similar figures and similar figures, consciously cultivate students' positive emotions and attitudes, and promote students' observation, operation and simple drawing.

Teaching focus

By making similar graphics, you can enlarge or reduce the graphics.

Teaching difficulties

Drawing method of similar graphics.

Student analysis

Students in the eighth grade age group are active in thinking, eager for knowledge, strong in self-awareness, and full of curiosity about observation, conjecture and exploratory questions. Therefore, students should set interesting and challenging contents in the selection and presentation of teaching materials and the arrangement of learning activities, so that students can feel that mathematics comes from life and returns to real life, which will inevitably produce strong learning interest and enthusiasm for exploration.

design concept

Establish a teacher-student relationship of equality, cooperation and mutual respect, and create a learning atmosphere of teacher-student interaction and mutual learning. Pay attention to students' learning process and individual differences, so that different people can play different roles in mathematics learning, and use "Z+Z intelligent education platform" to make courseware and operation exercises to help students understand and learn mathematics. Through observation, analysis, hands-on, brainstorming and other activities, let students learn while doing, so as to achieve "I want to learn".

Teaching objectives

1. Knowledge and skills: Understand potential graphics and related concepts, and be able to enlarge or reduce a graphic by making potential graphics.

2. Process and method: Students experience the method of enlarging or reducing graphics, and develop the sense of mathematical application in the process of learning and application.

3. Emotional attitude and values: cultivate students' good hands-on habits, explore mathematical knowledge with positive and enterprising ideas, and realize the practical application value and cultural value of these knowledge.

teaching resource

1, using "Z+Z intelligent education platform" to make courseware to assist teaching;

2. Several kinds of cardboard drawing boards with similar graphics;

3. Two sets of triangular plates and several magnetic buckles.

teaching process

First, the creation of situational operation profile

1. Show courseware: Two sets of pictures, one is the magnificent picture of the Great Wall in Wan Li, and the other is the mark of shenzhou spaceship's successful first flight, demonstrating the scaling process of the two sets of pictures.

Review the related concepts and properties of similar polygons, pave the way for introducing new courses, and at the same time infiltrate patriotic education to stimulate students' interest in learning and patriotic enthusiasm.

2. Operation experiment: instruct the whole class to operate and conduct experiments. Each student takes out two pieces of paper with similar graphics, puts them in any position, connects the corresponding points, and observes whether the connecting lines of the corresponding points pass through a point. At the same time, please ask three students to choose different types of similar graphics (triangle, quadrilateral, pentagon) to demonstrate for the class's reference and guess.

3. Show a group of enlarged photos of China famous star Yao Ming's dunk posture, highlighting that the straight lines where the corresponding points are located all pass through the same point, and compare them with the students' experiments to lead to the topic.

Writing on the blackboard: 4. 9 graphic enlargement and reduction

Second, the practical perception of independent activities

1, building new knowledge: similarity graph and its related concepts

If two graphs are not only similar graphs, but also the straight lines of each group of corresponding points pass through the same point, then such two graphs are called potential graphs, and this point is called potential center. The similarity ratio at this time is also called the potential ratio.

2. Let the students operate further and feel the connection and difference between similar graphics and similar graphics. Through observation, thinking, communication and discussion, the following conclusions are drawn:

Similar figure is a special kind of similar figure, and similar figures do not necessarily constitute a similar relationship.

(Guide students to use their hands and brains, observe and think, and realize the' generation and change' of knowledge)

3. Identify it:

See figure 4-28 (1), (2) and (3) of the textbook P 136 to identify similar figures and similar centers.

(Strengthen students' understanding of alignment graphics from both positive and negative aspects)

Step 4 practice:

Example 1 The following statement is true ()

Answer: If two figures are similar, they must be congruent;

B. If two pictures are similar, they are not necessarily similar;

C. If two graphs are similar, they must be similar;

D. If two graphs are similar, they must be similar.

Example 2 The following two polygons in each group of graphs are similar to graphs, and those are ().

Example 3 The following quadrilateral ABCD and quadrilateral EFGD are similar figures, and their similarity center is ().

Answer. EB point. Point f, point c, point GD and point d

Example 4 Given AE∶ED=3∶2 in the above figure, the potential similarity ratio of quadrilateral ABCD to quadrilateral EFGD is ().

A.3: 2b.2: 3c.5: 2d.5: 3.

Develop students' thinking ability and help them master new knowledge.

Third, cooperation and exploration have been significantly strengthened.

1, a quantity:

Measure the ratio of the distance between any pair of corresponding points and the potential center in the textbook P 136 (1)(3). After speculation and discussion, we can get the attributes of potential graphics:

The ratio of the distance between any pair of corresponding points on the potential diagram to the potential center is equal to the potential ratio.

Courseware made by "Z+Z Intelligent Education Platform" is used to demonstrate and help students understand the essence of potential graphics.

2. think about it:

What methods have you learned to enlarge graphics in this chapter?

(Let students think and communicate, deepen their understanding of the knowledge before and after, and realize the internal relationship between knowledge) Student summary: Cartesian coordinate system enlarged graphic method; Enlarged graphic method of rubber band. All belong to the practice similar to graphics.

(Use the mathematical software "Z+Z" to demonstrate how to use the rubber band method to enlarge the graph, which is dynamic, intuitive and clear, and further verify that it belongs to similar graphs)

3, do:

According to the following methods, the three sides of △ABC can be reduced to half:

As shown in the figure, take any point O to connect AO, BO and co, and take the three sides of point D, E and f △DEF as half of the three sides corresponding to △ABC.

(1) Draw a triangle at will and try it yourself with the above method;

(2) If points D, E and F are taken on rays A0, B0 and c0 respectively,

Let DO = 2OA, EO = 2OB and FO=2OC, then what will happen?

(Let students take the initiative to participate in and explore cooperatively, and arouse students' learning enthusiasm)

Fourth, consolidate the practice summary.

1, try it:

Known pentagonal ABCDE, make pentagonal A'B'C'D'E, so that the ratio of corresponding line segments of new pentagonal A'B'C'D'E and original pentagonal ABCDE is 1: 2.

Students use "Z+Z" mathematical software to draw on the spot, which can demonstrate:

(1) The pentagon is on the same side as the center;

(2) Pentagon is located on both sides of the center;

(3) The center of the position is inside the Pentagon;

(4) The center of the position is located on one side like a pentagon;

5] The center of the position is on a vertex of the Pentagon;

(Let students draw with "Z+Z" mathematical software, which is not only fast and accurate, but also can drag the potential center at will to construct potential pentagons in different positions and forms. New form, many changes and good classroom effect. Feel the charm of exploring the mystery of mathematics with "Z+Z intelligent education platform")

2. Class summary:

(1) Talk about your gains and feelings in this class.

Cultivate students' ability of analysis, induction, generalization and language expression)

(2) Summary: The concept, nature and application of similarity graph.

Give full play to students' main role and exercise their ability of induction, arrangement and expression.

3. Practical application: the application of similar graphics in home decoration design.

Reflect the new curriculum idea that mathematics comes from life and serves life, and cultivate students' innovative spirit.