I. teaching material analysis
Subject: 1. Discover in life, learn in life and serve life.
2. Infiltrate EPD thought.
"Mathematics Curriculum Standard" points out that the mathematics curriculum in compulsory education stage should make students "learn mathematics that is valuable to everyone". What is mathematics that is valuable to students? In my opinion, "mathematical value" is mainly reflected in students' application of what they have learned in present and future social life.
Some contents about three-dimensional graphics in space and graphics are widely used in our lives. As a review course, in the design of teaching content, I not only attach importance to students' mastery of concepts and formulas, but also let students realize the relationship between general laws and specific problems in the process of solving problems, so as to flexibly use what they have learned to solve practical problems in the future.
(1) Find problems in life.
Mathematics comes from life. As organizers, guides and collaborators of teaching activities, we have the responsibility to introduce students into colorful real life and lead them to discover and capture mathematics.
(2) learning in life.
"Mathematics Curriculum Standard" also points out: "Students' mathematics learning content should be realistic, meaningful and challenging ..." Therefore, the discovery and application of mathematical laws cannot be simply presented, but students' multiple senses need to be mobilized to participate in mathematics activities, and experience the exploration and challenges of mathematics problems and feel the fun brought by the process of mathematical thinking in the process of activities.
(3) service life.
Mathematics originates from life, and ultimately it should serve life. If the learning and application of mathematical knowledge is divorced from the reality of life, it will lose its strong social vitality. When designing this review class, I looked for learning resources that can be developed and utilized from real life, and used matchboxes to review the relevant knowledge of solid geometry. I chose "Matchbox" as the research material because students are familiar with it, because it contains many mathematical problems, and because it can be used for environmental protection education, so I named the topic "Mathematics in Life".
In short, through the study of this class, students once again feel that there are many mathematical problems worth exploring in life. As long as we are a conscientious person, we will find that mathematics is everywhere in our lives.
2. Student analysis
Our school is located in Erligou Experimental School District, Haidian District. The teaching materials that students are exposed to are brand-new, and the educational concepts that students accept are also brand-new. With the gradual popularization of internet technology and the continuous accumulation of students' learning methods, students' learning channels are also various. Most students have flexible thinking. Under the guidance of teachers, simple mathematical problems are found and put forward from daily life, and there are different solutions to understand the same problem. Have the experience of solving problems in cooperation with peers, and can express the general process and results of solving problems, explore effective methods to solve problems, and strive to find other methods. However, due to the individual differences of students, there will be differences in the existing knowledge base and the speed of exploring new knowledge. Therefore, the arrangement of teaching content, the design of teaching process, the choice of teaching methods and the application of teaching means should all proceed from the needs of students.
In this class, I choose the matchbox as the only learning tool for the whole class, and I also have the skill to let students fully understand its structure and many wonderful math problems caused by it in just 40 minutes, thus stimulating students' interest in learning math.
As a sixth-grade graduating student, there should be no big problem in mastering geometric formulas, but how to use what you have learned to solve problems flexibly is uneven, and some students find it difficult. Therefore, teachers should consciously cultivate students' problem-solving ability, give full play to the role of top students and groups, and improve all students on the basis of original knowledge.
Three. Teaching objectives
Teaching objectives:
1. By further understanding the structure of the matchbox, we can ask some mathematical questions from a mathematical point of view and tell us what relevant mathematical knowledge to answer.
2. Cultivate students' awareness of learning and using mathematics, and the spirit of daring to explore and challenge in the process of solving mathematical problems.
3. Educate students on environmental protection through teaching, and penetrate the educational concept of the Environmental Protection Department, that is, environmental protection and sustainable development.
Teaching emphasis: calculating the actual material area of matchbox.
Teaching difficulties:
1. Calculate the actual material area of the matchbox by various methods.
2. The packing problem of matchbox.
Teaching aid preparation: courseware, matchbox.
Four. Teaching process:
(1) Introduce a dialogue. 5 points
The students all have a matchbox in their hands. Have you seen it? Today we will use it to study some math problems.
Q: From a mathematical point of view, what questions can we ask? What knowledge do we need to learn to solve these problems?
The teacher asked:
(1) Think for yourself first.
(2) Talk to the classmates in the same group in a low voice to see which group speaks best.
(3) Communication with the whole class.
Issues involved:
(1) Find the surface area of the matchbox.
Knowledge used: surface area of cuboid: s = 2 (AB+AH+BH)
(2) Find the volume of the matchbox.
Teacher: If the wall thickness is ignored, it can be regarded as solving the same problem.
Knowledge used: cuboid volume: V=abh
(3) Find the floor space.
Q: How to maximize the floor space? How to put the minimum floor space?
Teacher: The size of the floor space is related to the arrangement of matchboxes.
(4) Find the actual material area (how much paper is used).
Q: How much area do you want? (9)
Which nine? (4-sided material area of outer box+5-sided material area of inner box)
(Comment: By further understanding the structure of the matchbox, we can ask some mathematical questions from a mathematical point of view, and you can tell what relevant mathematical knowledge to answer. )
(2) Find the actual material area. 10 point
Teacher: Just now, the students raised a question of great research value and asked about the actual area of the materials.
1. Do it yourself first, at least in two ways.
(Data required for students' own measurement: a=4.5cm b=3.5cm h= 1cm)
Teacher: It's a good idea to know that it's not necessary to measure immediately.
2. Communicate in groups to see which group comes up with the most methods.
3. Communicate with the whole class.
(1) Material area of outer box plus material area of inner box.
(2) Calculate according to two surface areas, and subtract the calculated part.
(3) According to the surface area, add and subtract.
(4) Count how many big faces, how many middle faces and how many small faces there are, and finally add up their areas.
(5) Other methods.
4. The teacher summed it up.
Q: Which method do you like best?
It seems that students have their own favorite methods. You can use the method you think is the best, or you can learn from others' methods.
(Comment: Effective mathematical activities cannot rely solely on imitation and memory. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. )
(3) Matching packaging. 10 point
1. Teacher: Matches should be packed before leaving the factory. I want to pack two boxes of matches together. How to pack them? How are you going to package it? Tell me why.
2. Calculate how much wrapping paper is needed to put two boxes of matches together.
(1) Students independently calculate
(2) Report calculation method
Method 1: two surface areas minus the areas of two large surfaces.
Method 2: directly calculate the surface area of the newly assembled cuboid with the formula.
Method 3: Other methods
3. Q: Do you want to know how many boxes are packed in a matchbox factory? (General 10 box) How to save paper in packaging? You can continue your research after class.
(Comment: The arrangement of this content can examine whether students can flexibly use what they have learned to solve problems)
(4) Find the volume of the matchbox. 12 point
Q: Do you know what are the main raw materials for making matches? (wood, phosphorus)
How much wood does it take to fill this matchbox (the gap is ignored)? (Find the volume of the matchbox. )
Blackboard: 4.5× 3.5×1=15.75 (cm3)
Teacher: In our opinion, it doesn't take much wood to make a box of matches, but I think you will be surprised when you see the following data.
Computer display slides (forest background)
According to the data, ① Matches, as a popular kindling appliance, have a history of 150 years in China.
Teacher: In recent years, the quantity of matches has been greatly reduced due to the impact of steam lighters. However, at present, the production and sale of steam lighters have been banned in the international market, and the production and sale of steam lighters are also restricted in China. Therefore, matches, as common kindling appliances, still have a broad market in China.
According to investigation and statistics, the country needs 200,000 TEU matches every day, and the production of matches from wood consumes 7,200 cubic meters of high-quality wood every day.
Q: According to the calculation of 365 days a year, how much wood will be used in a year?
③7200×365=2628000 (m3)
Q: Where did the wood come from? How many big trees do you need to cut down? Let's estimate together, shall we? Here are some relevant data: Poplar is generally used as matches. This tree can be cut down after 0/5 to 20 years of survival/kloc-0, with a diameter of about 40 cm and a height of 15 to 20 meters.
Teacher: What can we regard as the available part? What is the volume of the usable part (approximate cylinder)? What knowledge should I use? (find the volume of the cylinder V=Sh)
(1) Students' trial calculation.
(2) Feedback communication.
202×3. 14× 1500 = 1884000(cm3)= 1.884(m3)
2628000 ÷1.884 ≈140 (ten thousand trees)
④ The area of a tree is about 20 square meters. How many forests will we cut down that year?
140×20=2800 (ten thousand square meters) =2800 hectares.
Teacher: For a long time to come, China still needs to promote economic development on the basis of high population pressure and relatively insufficient resources. Cutting down trees in large numbers or even wrongly is tantamount to constantly destroying the environment on which we live. Therefore, it is very important to handle the contradiction between economic development and environmental protection and maintain the sustainable development of the economy. Experts pointed out that using wheat straw and straw as raw materials to produce matches can save a lot of wood and has a broad market prospect.
(Comments: Educate students on environmental protection through teaching, and infiltrate the educational concept of the Environmental Protection Agency, that is, environmental protection and sustainable development. )
(5) class summary. 3 points
1. In a word, what is your biggest gain and experience in this class?
Teacher 2: Today we are solving math problems in life. There are still many problems in life that deserve our discussion and study. Life is a big classroom. We should be good at observing life and experiencing life from the perspective of mathematics.
(6) Blackboard design
Mathematics in life
Area: The surface area of a cuboid is S = 2 (AB+AH+BH).
Volume: the volume of a cuboid V= abh
Cylinder volume V= Sh
Verb (abbreviation of verb) teacher's reflection
When it comes to review classes, not to mention students, but even teachers scratch their heads. The old knowledge learned was moved out by the teacher, and then students were mechanically asked to remember definitions, concepts and formulas, followed by a large number of exercises. For such review, students are not interested and teachers are very tired. How can we make the review class lively and interesting? In this class, I made another bold attempt. I use matchboxes to let students ask and solve problems from the perspective of mathematics, and skillfully combine mathematics with life. Not only mastered the relevant mathematical knowledge, but also carried out some ideological education, which can be described as killing two birds with one stone. More importantly, students no longer find the review class boring, but gain new gains step by step. Matchbox used to be an indispensable thing in our life, but it has been replaced by other things in recent years, and many students lack understanding of it. The new curriculum standard points out that teachers should develop and utilize all kinds of resources consciously and purposefully according to local conditions. So I introduced it into the classroom, and everyone had one. There are many ways for students to calculate the actual material area of matchbox, which really achieves multiple solutions to one problem; When discussing the packaging of matchbox, the students have different packaging methods. Most students think that how to package the biggest vanishing surface should start from the perspective of saving paper, and some students will put forward their own packaging scheme from the aesthetic point of view, which embodies the personality characteristics of modern students. The whole class organically combines students' independent exploration and cooperative communication, including both the interaction between teachers and students and the interaction between students. The most wonderful thing is the students' final speech: "I think it's time for us to protect the environment ..."