Teaching material analysis, the second lesson of sixth grade mathematics interest in Beijing Normal University.

The magical Mobius belt is a good theme to stimulate students' interest in learning and broaden their horizons in mathematics. It is operable, interesting and challenging for students, so the textbook arranges this content as "fun in mathematics" in order to let students feel the infinite charm of mathematics through mathematical activities, expand their mathematical horizons and further stimulate their curiosity and interest in learning mathematics. Of course, for primary school students, it is mainly through mathematical activities that students can understand and appreciate its characteristics and infinite charm of mathematics, and it is not necessary to master the knowledge of bilateral surfaces and unilateral surfaces.

Analysis of learning situation

Mobius belt belongs to "topology", so it is not easy for teachers to organize teaching. Mobius belt is a good theme to broaden students' horizons, which can make students feel the fun of learning mathematics and then stimulate students' interest in learning mathematics. Grade six students have certain spatial thinking ability and hands-on operation ability. In the teaching process, students should be guided to observe carefully and discover the mystery of Mobius belt independently.

Teaching objectives

1. Let students know "Mobius belt" and learn to make rectangular paper into Mobius belt.

2. Guide students to discover and verify the characteristics of Mobius belt through thinking and operation, and cultivate students' spirit of bold speculation and exploration.

3. Feel the infinite charm of mathematics in the magical change of "Mobius Belt", expand the vision of mathematics, further stimulate students' interest in learning mathematics, and cultivate students' good mathematical feelings.

Emphasis and difficulty in teaching

Key points: let students know Mobius belt and learn to make rectangular paper into Mobius belt.

Difficulties: guide students to discover and verify the characteristics of Mobius belt through thinking and operation, and cultivate students' spirit of bold speculation and exploration.

Preparation before class

Courseware, scissors, double-sided tape, rectangular paper.

teaching process

Item 1: "Three Ones" Habit Formation Course

Moderator: The "Three Ones" habit formation course begins now!

Moderator: the first item: recite what you said, and accumulate over time.

Slogan: knowledge points, hidden in the brain, articulate, bright voice, I will be the king of memory.

Content: lateral area of cylinder = perimeter of bottom × surface area of high cylinder = bottom area× 2+volume of lateral area cylinder = bottom area× volume of high cone = bottom area× height × (preset evaluation: everyone speaks clearly and has a bright voice, which is a veritable king of memory).

Moderator: the second item: practice and practice again, and draw inferences from others.

Slogan: Practice, strive for the first place, calculate carefully, use your head, and I will be an expert in calculation.

Content: Oral calculation exercise (the host arranged to open the train to answer) 3.14× 4 = 210× 3 = 2.5× 4 =1.25×1000 = 3.14× 3.

(preset evaluation: the calculation speed is fast, a. the correct rate is high, and b. it is completely correct. Everyone deserves to be a small expert in calculation. )

Moderator: Item 3: Talk about it and be willing to share it.

Slogan: Speak clearly, express clearly, speak accurately and think clearly. As a mathematical genius, I can do it.

Moderator: XXX students will share it.

Content: Share a "three-leaf kink" model in the lobby of China Science and Technology Museum.

I am xxx, and I will share a magical model with you today. This is the iconic object of Beijing China Science and Technology Museum-"trefoil knot". Its magic lies in that the flashing lights can wander around the model and rotate a wonderful curve. After reading the introduction, we know that this model has an overall width of10m, a height of12m and a bandwidth of1.65m, which evolved from the Mobius belt. I was both surprised and puzzled by its magic. What exactly is Mobius belt? Why is this "three-leaf kink" so magical? Today, I want to ask my classmates to help me explore.

(Default host evaluation: A. Wow, what a wonderful speech! Let's applaud him! B: It's beautiful (handsome) that you try hard actively! )

Moderator: The "Three Ones" habit formation course is over, please wait for the teacher to participate in the second item: the teaching process.

Design 1: Positioning and Guidance

This is really a magical model! I must go to Beijing and visit the China Science and Technology Museum when I have the chance.

Today, we will help xxx explore what the Mobius belt is. Let's walk into today's math class "Magic Mobius Belt"

Second, autonomous learning and inquiry activities

One: do and understand the Mobius belt.

1. Each student takes out a rectangular piece of paper. First, please look at what's on the desk. These are the learning tools that we need to explore in this course. Please pick up a rectangular piece of paper first. Look, this is an ordinary note, but it is also a magical note. How many sides does it have first? How many noodles? (Four sides, two sides)

2. Who can make it have only two sides and two faces? (Students try to do it) Good, yes, think boldly and try boldly! Students can connect its two ends. Teacher: Are there two sides and two faces?

2. Can students connect its two ends? Students try to make it with a piece of paper. Please show it on the stage. )

Tell me how you docked. In this way, the note becomes a circle. This is how students learn. Feel it. How many faces does it have now?

Teacher: Is it amazing? (Health: Not magical) Yes, nothing magical. Magic is in the back. I have a way to turn it into only one side and one face. (pause, look at the students around you. ) try again. It seems a little difficult, but it's good. I'm trying. Did you succeed? Do you want to see me change? Look carefully. Like this, it has only one side and one face. Try to do it. Talk to the teacher: first make an ordinary paper ring, then turn one end over 180 degrees, and then stick it.

(Intention: From "How many sides does this note have" to "Who can turn this note into two sides and two sides", and then to "How to turn it into one side? The problems are getting deeper and deeper, and each one is more difficult, which further stimulates students' interest in learning mathematics. Interesting questions can encourage students to think and explore. In the process of exploration, the questions get deeper and deeper, which improves students' thinking ability. )

Teacher: As I said just now, there is only one side and one face. what do you think? Why the edge? Have you tried? Who are the classmates?

It looks like two sides, but in fact the two sides have been connected.

Teacher: The second question, is it the face? Let's do it together. Let's test it. Let's draw a line in the middle of the note from this side with a pen. What did you find?

Health: I have painted my face. It is really a face. Teacher: Is it fun? Lift the paper tape that has just been made. Does anyone know the name of this strange circle? Do you know that?/You know what? Yes, this circle is called Mobius belt.

(Blackboard: Mobius Belt) Teacher: 1858 German mathematician Mobius accidentally discovered such a magical paper circle, with only one side and one face. So it was named Mobius circle or Mobius belt after him. What else do you want to study after seeing this Mobius belt? what do you think?

The default student answers:

1. Why can this note become a circle with only one side? I admire you very much. Sometimes we should ask why. )

2. How to find its area and perimeter? Great, everyone asked so many good questions, and every question came to my mind. Let's take a look first. It turns out that this note has four sides and two sides. Why has it become one-sided?

Let's take another piece of paper and look at this Mobius belt. While doing it, think about why it has become a face, an edge. Students do the operation again, and then talk to their classmates. When you know how to do it and then ask why, you will understand it more deeply.

(Intention: From notes to ordinary paper circles to Mobius tape, students have experienced a process of knowledge formation from familiar to unfamiliar, from ordinary to magical. This process is fresh and interesting for students, guiding them to uncover the mystery of Mobius belt step by step. )

Third, discuss and dispel doubts.

Is this note magic? Mobius belt is more magical! Below we will use the method of "cutting" to study. Inquiry 1: Cut along the half line Teacher: (showing ordinary paper rings) What if I cut along the middle of the paper tape?

Health: It will become two paper circles of the same size. Teacher: Really? Please watch carefully how the teacher cuts it. (Teacher demonstrates) It really is.

Teacher: (showing a Mobius belt) Didn't you just draw a line in the middle of this Mobius belt? If we cut this paper circle along this line? What will happen? (Students guess)

Teacher: I want to know what it is like. What should I do?

Health: Cut it yourself. Teacher: Yes, practice makes true knowledge! Student reporter: After I cut it, it's not two circles as my classmates said just now, but together.

Teacher: Is it a circle or two circles?

Health: One lap. Teacher: We all think that cutting from the middle should be two circles, and the result is a circle. This is the magic of Mobius.

(showing the cut paper ring) Is this still one-sided? Now check it, draw a picture with a brush and tell me what you find.

Health: After painting, only one face was painted, and one face was not painted. Teacher: So did Mobius take it?

Health: No (blackboard writing: bold guess, careful verification) Come, read this sentence together! Teacher: Now draw another line in the middle. If you cut along this line again, think about it. What will happen? Health 1: It's still a circle.

Health 2: I think it's two laps.

Teacher: Let's do it (students do it, teachers do it) and report the results. Student: There are two groups of circles. Wow, you didn't expect to come again. Isn't it amazing?

Question2: Cut along the third line.

Teacher: shall we continue to feel the magic of this paper circle? Please take out the paper with bisector drawn, paint the middle part with your favorite color, and paint both sides to make Mobius tape.

Teacher: OK, what do you think now?

Health: Can you cut this Mobius belt along the line? Teacher: Yes, if we cut this Mobius belt along the bisector, how many times do we need to cut it? Health: twice.

Teacher: What will it look like after cutting it?

Health 1: Maybe three traps are together.

Health 2: It will become a big circle. Teacher: I really admire your imagination. What will happen next? Let's get started! Roll call answer (cut once, two traps together) summary: a big trap and a small circle. Teacher: Is this big circle and small circle the Mobimos belt? (Health: No) Please use the method just now to prove it.

Teacher: Which part of the original rectangular note is a small circle? Student report (by letting students cut along the half-third line, students can experience a process from guessing to verifying, which not only satisfies students' curiosity, but also permeates students with mathematical ideas such as guessing, verifying and exploring, guides children to find the Mobius belt in life and use it creatively, so that they can realize that mathematics comes from life and returns to life. (4) application division in life: a seemingly simple small paper circle is so magical (blackboard title: magic)

Mobius belt is not only fun, but also applied to all aspects of life. Let's follow Mobius into life and enjoy pictures (courseware) (1) roller coaster (2) Mobius ladder (3) recyclable sign (4) factory conveyor belt (5)20 19 Special Olympics logo "eyes".

Verb (abbreviation of verb) feedback and summary

Teacher: This class is coming to an end. What did you gain from today's class?

Finally, the teacher made a gift for everyone with Mobius tape-two closely connected hearts, one for you and one for me. I hope that students will observe carefully, make bold guesses, verify carefully and explore more mathematical mysteries!

Teaching reflection

Mobius took this activity class, which is very novel for the teacher. I've never been in contact with them before, and I'm even stranger to students. I have never seen it before. Many teachers skip it or let students watch it by themselves. There is no introduction about this content in the reference book, and there is no ready-made reference material. Only the use of Mobius tape is briefly introduced on the Internet, and there are few videos of this lesson. But I think this is an opportunity to exercise and challenge myself. I discussed, discussed, practiced and designed four activities with other teachers. First, make the Mobius belt, then cut it along the line 1/2, then cut it along the line 1/2 of the new circle, and finally cut it along the line 1/3. My original intention of designing this activity class is to broaden students' horizons, broaden their knowledge and let them feel the infinite charm of mathematics. I decided to use the idea of "doing mathematics by hands, doing middle school mathematics" to design, so that students can discuss in operation, analyze in discussion and verify in analysis. From the perspective of the whole class, the teaching objectives have been well completed, and students have deeply felt the infinite charm of Mobius belt in the process of "hands-on", which has aroused strong curiosity and creative desire. When I began to explore the wonderful characteristics of Mobius belt, I insisted that students think, guess and think after cutting: Why? In this way, students should not only do it themselves, but also use their brains to think, so as to cultivate their own spatial imagination, the consciousness of "boldly guessing and carefully verifying" and the habit of being diligent in reflection. In the general classroom, students' hands-on operations are mostly done according to the teacher's instructions. Students are operators, not explorers. I let go at the right time, giving students enough time and space to create independently. Students use their brains to guess, verify and experience happily, which effectively stimulates students' creative enthusiasm and discovery desire. There are also many problems in this class, and students are found to be too rigid and weak in practical ability. The whole class lacks time control, and the time allocation of each link is not reasonable enough. After the students cut along the line 1/2, they should cut it again, but they didn't do it because of time. Moreover, when students have objections, they have not verified them. In the future, we need to continue to work hard to polish a better classroom.