Teaching design of "designing awning" in the research study of mathematics in grade three.

The teaching content "project learning" is a well-designed textbook in the new textbook. Its purpose is to cultivate students' ability to comprehensively apply mathematics and other disciplines and solve practical problems in life, so that students can initially gain experience in scientific research and cultivate their sense of social responsibility. It has the characteristics of open teaching. "Design awning" is the last subject in junior high school, which aims to make students comprehensively use their knowledge (such as trigonometric function, circle, parabola and other mathematical knowledge and geographical knowledge) to solve practical problems in life and realize that mathematics is a widely related and very useful subject. Analysis of Teaching Objects Students in Grade Three have mastered the relevant knowledge needed to solve such practical problems, such as trigonometric function, circle, parabola and other mathematical knowledge and geographical knowledge, and skillfully use mathematical knowledge to solve some ready-made application problems. The disadvantage of students is that they are very blind in the process of design and investigation. Without the guidance of teachers, it will be difficult for them to "abstract the awning in their lives into geometric figures, establish mathematical models, and put forward mathematical problems in line with their existing knowledge and ability." After the first lesson of teaching strategy, I assigned the following after-school tasks: group investigation, writing investigation report, and reporting and communicating next week. In the subsequent follow-up, I found that students have put forward many ideas and questions. Some problems are beyond their knowledge and ability. During this period, I repeatedly consulted and learned about their respective designs and investigations, and studied with them how to abstract the sunshade in life into geometric figures, establish mathematical models, and put forward mathematical problems in line with their existing knowledge and ability level. A simple and fixed sunshade is extracted from the teaching content of stage class, and further research is carried out. In the hot summer of 1 class, we want to have a cool and comfortable life, keep out the sun, have bright and soft light and face the pleasant scenery outside the window ... The awning can not only shade and ventilate, but also save space and achieve elegance in the sun. Ask a question: people love the sun differently in different seasons. Please design: Requirements 1: Don't let the sun shine out of the window in summer; Requirement 2: let the winter sun shine through the window; Requirement 3: Have the best of both worlds, which can block the hot sunshine to the maximum in summer and let the warm sunshine enter the room to the maximum in winter. After-class tasks: design surveys in groups and write reports. Design, collect, sort out and sort out all kinds of shading problems. After class lasts for 2 weeks, students design by themselves according to the tasks after class, or search extensively for information, filter useful information and save it. Teachers instruct students how to abstract the awning in life into geometric figures, establish mathematical models, put forward mathematical problems in line with their existing knowledge and ability level, and strengthen the purpose of tasks. According to their own design or search data, students extract relevant mathematical problems and try to solve them. Dialogue between teachers and students: teachers' comments and students' defense. Further improve the mathematical questions raised and determine the content of the speech. Report Exchange Lesson 2 (Ⅰ) Curtain awning (Ⅱ) Folding awning (Ⅲ) Retractable awning (Ⅳ) Floor awning (Ⅴ) Rotary awning (Ⅴ) Circular awning (Ⅶ) Parabolic awning (Ⅶ) Relationship between awning style and sunlight (𔸮) Evaluation, improvement and reflection guide students to their own. The teacher will sort out the whole reporting and communication process and write teaching reflections. This topic adopts the teaching method of combining demonstration with task-driven, and teachers give priority to guidance, guiding students to learn independently. I hope that the following points can be achieved through the teaching of this topic: 1. Guide students to experience the process of "design", understand how to turn practical problems into mathematical problems, and cultivate students' ability to observe and analyze the world from a mathematical perspective. Learn to find and ask questions. 2. Guide students to use the search function of the Internet to search for needed information, enrich background information and open up their minds. Can use multimedia production software, such as geometric sketchpad and PowerPoint to report and communicate. 3. Pay attention to children with different ability levels and try to provide a suitable learning platform for each student's development. Students who can design and ask questions are excellent, and students who can solve these problems deserve our recognition. Teaching emphasis and difficulty focus: how to guide students to abstract the sunshade in their lives into geometric figures, establish mathematical models, and propose and solve mathematical problems that are consistent with students' existing ability level. Difficulties: Instruct students how to turn practical application problems into mathematical problems, cultivate students' ability to observe and analyze specific problems from a mathematical perspective, and improve students' ability to find, ask and solve problems. Teaching process "Design an awning" In the hot summer, we hope to have a cool and comfortable life, keep out the sun, have bright and soft light, face to face with the pleasant scenery outside the window ... The awning can not only shade and ventilate, but also save space and achieve elegance in the sun. (1) On-site introduction (2) People's love for the sun is different in different seasons. Please design: Requirements 1: Don't let the sun shine out of the window in summer; Requirement 2: let the winter sun shine through the window; Requirement 3: Have the best of both worlds, which can block the hot sunshine to the maximum in summer and let the warm sunshine enter the room to the maximum in winter. (III) Acceptance The following is the awning designed by Xiao Ming according to the customer's requirements. Please check it. Customer requirements: My French window is 2m high. At noon this year, the minimum angle between the sun and the ground is 30, and the maximum angle is 80. Please help me design an awning, which can not only block the hot summer sun to the maximum extent, but also let the warm winter sun shine into the room to the maximum extent. Xiao Ming's design: the awning is installed 20cm above the French window, and the protruding part is 40cm long. (4) Building a "sunshade" behind closed doors. The geographical location of Tangshan is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ How did you get these data? According to these data, the awning that meets the requirements is designed. (5) Summary: 1. How to turn practical application problems into mathematical problems? (1) The conditions for practical application problems are often not directly given, so it is necessary to recognize the objectives and analyze which quantities are known and which are unknown. (2) Discard some minor factors, grasp the main contradiction, make reasonable assumptions and simplify complex problems. 2. How to get the data needed to solve the problem? (1) field measurement (2) consulting materials (6) after-school tasks According to incomplete statistics, it is found that installing awnings on windows can save more than 60% of cooling electricity! Shading scheme is strongly recommended in the Design Standard for Building Energy Efficiency issued by the Ministry of Construction in 200 1. Question: (1) If the CD edge of the awning is required to be round, what data do you need to know before you can design it? (2) If the CD edge of the awning is required to be parabolic, what data do you need to know to design it? (3) If the CD edge of the awning is required to be retractable, how should it be designed? Investigate in groups, write investigation reports, visit some awnings on the spot, observe their shapes and their relationship with windows. If possible, make a model (physical model or plane model). Has your design been tested and realistic? If it doesn't conform to the reality, try to find out the reason, modify the original model and solve the test again to make your design as perfect as possible. Make suggestions for market research, use your mathematical knowledge to see whether the awning designed by the manufacturer conforms to the actual situation in Tangshan, and try to put forward improvement suggestions for the design of the manufacturer. The second and third class hours of "designing a parasol" are about the topic of "colorful parasols". It's been a long time since the last lecture (1) on designing a sunshade. Please review the previous contents before the exchange. As a graphic method, the "simple fixed awning" is determined. (2) The following are the contents reported by several students: (1) awning with hanging curtains (2) folding awning (3) telescopic awning (4) floor-standing awning (5) rotatable awning (6) circular awning (7) parabolic awning (7) between the style of awning and sunlight. (1) The conditions for practical application problems are often not directly given, so it is necessary to recognize the objectives and analyze which quantities are known and which are unknown. (2) Discard some minor factors, grasp the main contradiction, make reasonable assumptions and simplify complex problems. 2. How to get the data needed to solve the problem? (1) field investigation (2) consulting materials (4) homework: what questions can you ask about the design of the above students? Or do your own design and try to solve it! Describe the mathematical knowledge you used in solving the problem.