1. With the help of paper-cutting activities, we can further understand the symmetry and translation of graphics.

2. By using axisymmetric knowledge to solve simple practical problems, cultivate hands-on operation ability and problem-solving ability, and establish a preliminary concept of space.

3. Feel the application of graphics in life, the close relationship between mathematics and life, and the beauty of mathematics.

Target resolution:

This lesson is the last lesson of Unit 3, so the orientation of teaching objectives is based on students' understanding of axisymmetric graphics and translation and rotation movements. Let students use the knowledge of axisymmetric graphics to solve the problem of cutting a given pattern, and further deepen their understanding of axisymmetric graphics, translation and other knowledge, which not only improves their practical operation ability, but also cultivates their ability to solve problems by using what they have learned. At the same time, students are encouraged to think actively, develop the concept of space and feel the beauty of mathematics in the process of operation.

Teaching emphasis: using axisymmetric knowledge to solve the problem of cutting a given pattern.

Teaching difficulty: mastering problem-solving strategies.

Teaching preparation: courseware, scissors, handmade paper, etc.

Teaching process:

First, create a situation to stimulate interest

(1) Appreciate the works and review the old knowledge.

1. Courseware shows "Mathematics in Life" on page 3 1 of the textbook, so that students can appreciate the beauty of folk paper-cut works.

2. Find out the symmetrical figures in the paper-cut works and point out their symmetry axes.

(2) Initiate thinking and reveal the topic.

1. How are these exquisite works made? Do you want a haircut, too?

We should "cut in line" in this class. (blackboard writing topic)

Design intention: From appreciating China's folk paper-cut art works to looking for symmetrical figures and symmetry axes, it not only reviews old knowledge to pave the way for new knowledge, but also makes students feel the mathematical knowledge contained in paper-cut works, the close relationship between mathematics and life, and the beauty of mathematics in life, and stimulates a strong desire for exploration.

Second, practical exploration method.

(1) ask questions.

1. Example 4: Can you cut out four little people holding hands like the following?

2. Observe and think: What are the characteristics of these little people? (symmetry, translation)

3. Infiltration idea: To cut out four consecutive numbers, start with the number of 1.

(2) solve the problem.

1. Explore cut 1 villain.

(1) independent operation, cut.

(2) communicate in groups and show their works.

(3) Talk about the experience and feel it.

The winner talks about cutting method: first fold in half, then draw half of the villain, and finally cut.

2 Losers should pay attention to: draw a half villain, starting from the closed part of the paper. Why?

2. Explore cutting two little people.

(1) Teamwork and hands-on operation.

Discussion: How to fold, draw and cut?

(2) Report communication and explore the folding method.

① Default folding mode:

Method 1: Fold the paper in half twice in a row, and then draw half a villain.

Method 2: Turn the paper over, fold it three times, and then draw half a villain.

Method 3: Fold the paper inward from one end for three times in a row, and then draw half a villain.

Method 4: Fold the paper in half once and draw a complete villain.

② Optimized folding method: Different folding methods can cut out two continuous figures, but the first method is simpler.

(2) Explore the painting method and question the cutting method.

① Thinking: Why did some students cut two and a half villains?

Pay attention when painting: start painting from the closed part of the fold.

② Question: Why are the two villains cut out and separated by some students?

Attention should be paid when cutting: the arm of the scissors should extend all the way to the edge of the paper and cannot be broken.

3. Explore cutting four little people.

(1) Think independently and operate by hands.

(2) Demonstration and AC cutting

Ten percent off: three times off.

The second painting: draw half a villain from a closed place.

Three scissors: the joint cannot be cut.

(3) Summarize the law.

1. Discover the rules and experience translation.

2. Use the law to solve problems.

How many times do I have to cut eight little people? Can you cut a villain in half five times?

Design intention: Through the whole process of "asking questions, solving problems and summing up laws", students use axisymmetric knowledge to solve simple practical problems, cultivate their hands-on operation ability and problem-solving ability, and establish a preliminary concept of space in independent exploration, cooperation and exchange. At the same time, the mathematical idea of "simplifying the complex" was infiltrated, and the problem was gradually solved from "cutting 1 villain" to "cutting two villains" and then cutting four villains. Finally, by discovering and summarizing the laws and thinking deeply, we can solve the problem of "cutting eight villains" and improve students' thinking level.

Third, practical application to enhance understanding

(1) Exercise 7 on page 36 of the textbook 12.

1. Can you cut out the picture on the right?

2. Observe and think: how to fold, how to draw and how to cut?

3. Hands-on operation, reporting and communication.

4. Show the courseware and experience the rotation.

(2) Give full play to imagination and create independently.

Can you cut a new paper-cut work with the knowledge of symmetry, translation and rotation?

Design intention: let students further consolidate the method of cutting continuous symmetrical figures, communicate the relationship of symmetry, translation and rotation, feel the beauty of mathematics, cultivate students' observation, imagination and creativity, improve students' problem-solving ability and develop their initial concept of space.

Fourth, class summary, expansion and extension.

(1) What did you learn in this class? What knowledge have we learned?

(2) Go into life and appreciate the beautiful patterns designed by the transformation of graphics in life. (Courseware soundtrack display)

Design intention: review what you have learned, communicate the relationship between what you have learned in this unit, and let students enjoy the joy of learning success. At the same time, with the beautiful music coming into life, we can appreciate the beautiful patterns designed by graphic transformation, feel the close connection between mathematics and life, and appreciate the beauty of graphic transformation.