Tisch
Talk before class: 1. Organize students to organize learning tools.
The teacher likes the students to look at me. It's good. Everyone is looking at me. Do you still remember me Remember me what?
How about introducing yourself? Does the name "Wuyi Primary School" have any special meaning?
The teacher has a habit of telling a short story before each class, which is called "short story, great wisdom". Before class, tell a short story. Do you know the story of an elephant barking in Cao Chong? I wanted to know the weight of the elephant, but I weighed the stone. Why? Why not just weigh the elephant? At that time, it was difficult to weigh an elephant, so Cao Chong could weigh an elephant by weighing stones with the same weight. ……
Comments: In the form of short stories, the mathematical thinking method of infiltration and transformation before class provides the thinking basis for students' later exploration. If "the area of a circle" is a bright line in the class, exploring the relevant knowledge of "the area of a circle" is a dark line throughout the class.
Teaching process:
First reveal the topic and understand the circle area.
1. Show me a round piece of paper. What is this?
Today we are going to learn the area of a circle. Write on the blackboard.
Please think about it. What is the area of a circle?
Please come on stage and point it out. It is revealed that the size of the plane occupied by a circle is the area of the circle.
Comments: Straight to the point, concise and clear.
Secondly, through the derivation of the formula for calculating the circular area.
(1) Upward
1, enlightening thinking: how to find the area of a circle, search in the brain, what new things have we studied before, and what methods have we used? Turn it into a figure that you have already learned. Students will take the example of transforming a triangle into a parallelogram.
2. Can a circle be transformed into other figures? Let's discuss it in groups and have a try.
Group cooperation (it is estimated that each group will send out a piece of lead drawing paper, several blue circular pieces of paper, a pair of scissors, a pair of double-sided tape, a ruler, etc. )
3, group representatives on stage display method:
(1) group 1: We divide the circle into four sectors on average. In this way, the area of one of the sectors is multiplied by 4, and the area of the circle can be found.
Teacher: What's the problem?
Health 1: Sector area is not counted.
Health 2: Think of it as a triangle.
Teacher: Is that all right? Why? But it's still close, right?
Comments: This method rarely appears in the previous teaching design of "circle area". After students' exploration, the formula for calculating the area of a circle can also be derived, which is simple and easy to understand. Why didn't we notice this method? According to teacher Ma's introduction after class, before designing this courseware, I did a preliminary test and found that students' minds were not blank when solving the problem of circular area. Some children naturally fold the disc in half (this is the original thinking under the influence of children's life experience), which is similar to a triangle. Therefore, Mr. Ma has some presuppositions about this method. It seems that to overcome some blind spots in our teaching design, on the one hand, we should improve our mathematics literacy, on the other hand, we should approach students and respect their original thinking.
(2) The second group: We divide the circle into four sectors on average, and then cut out a figure similar to a parallelogram.
Teacher: How about it? Why is it similar to parallelogram? It's still a little close. Oh!
Comments: I didn't notice whether the teacher guided the students to notice whether the area had changed. The premise of transformation is that the essence of the problem has not changed. If it is not mentioned, then why not point it out here.
4. Review summary:
Two methods, one is to fold into a triangle; One is the cutting and spelling method of turning graphics into parallelograms.
What do * * * have in common? (They all change the circle into other figures. )
(2) Commitment letter
1, the graphics modified by these two methods are still very valuable, although they can not be directly regarded as learned graphics at present. Let's continue to study and see.
2. The group cooperated to choose one of the above methods to continue the research.
3. The representative of the group took the stage to show the research results:
(1) Group 1: Let's continue to fold with the first method, and each copy is more like a triangle.
Teacher: Why did you fold it into 16 copies?
Group 1: The more overlapping, the more like a triangle.
Teacher: Then how can it be folded more like a triangle?
Health: Fold it down again.
Teacher: Is it easy to discount? Then the teacher will use the computer to help everyone fold.
Courseware demonstration 16 division and 32 division, constantly asking: Is division like a triangle? Can it be more like it? -Re-division
Visually, it is more like a triangle. Close your eyes and imagine the number of copies of128,256, just ... can you imagine?
The teacher repeated the demonstration process from quartile to 32.
Guided observation: the bottom of this triangle is-this arc. Height is the radius of a circle.
Will the area of this triangle be worked out? (Bottom * Height /2) So can you work out the area of this circle?
Comments: operation, demonstration, questioning, imagination, infiltration, distinct levels. But why is it more and more like a triangle? Looking at the 32-point sector, can students understand why the sector can finally be regarded as a triangle? You know, the arc radian at this time is quite obvious. I think, first of all, we should guide students to pay attention to the fact that with the increase of equal parts, the fan-shaped arc gradually becomes straight, which is called turning the curve into a straight line; Second, if the equal number goes on indefinitely, the last sector will be infinitely close to the triangle.
(2) The second group: We use the second method to divide the disc into eight parts, cut it out and put it together like a parallelogram.
The average score of the other group is 16, which is similar.
The teacher displayed the students' works together on the blackboard. Q: What should I do if I want to be closer to a parallelogram?
The teacher's courseware demonstration is 32 equal parts and made into a parallelogram. 64 volumes, 128 volumes.
The more copies are divided, the more similar the graphics are. Divide it like this and it will become a rectangle.
Comments: I don't know if I didn't pay attention in class or if Teacher Ma didn't point it out. If this is divided equally, it will eventually become a parallelogram. However, if you divide one of them into two parts and put them at both ends, the whole mosaic will become a rectangle. Secondly, why must it become a rectangle? Is parallelogram not good? The correspondence between the height and radius of a circle is not too difficult.
4. Check the summary.
(3) Combination
1, we have transformed the circle into the figure we have learned, and mathematics is not just an operation. Can you deduce the formula for calculating the area of a circle on the basis of just now?
The teacher provides the students with auxiliary paper (a circle and a transformation figure are printed on the paper), and the students try to deduce the formula.
2. Feedback:
Sheng 1: describes the process of converting a circle into a rectangle and deducing the calculation method of the circle area.
After the lecture, the teacher asked: (1) What is the relationship between length and circle? (2) What is the width? (3) How to calculate the area?
You got it? Then refer to the student, native cooperation reference screen.
Teacher: Convert a circle into a rectangle with equal areas. In this way, the area of a rectangle is obtained, and the area of a circle is also obtained.
The teacher will explain the derivation process of the circle area and the blackboard writing process, and tell the students the representation method of the area: S.
Health 2: Describe the method of folding into triangle, and put forward the formula: (C÷32×r÷2)×32.
Teacher: What do you mean by dividing by 32?
Health 2: If it is divided into 32 equal parts, then the base of the triangle is 32 times the circumference of the circle. So the perimeter is divided by 32.
Teacher: Why divide by 2?
Health 2: Find the area of a triangle.
Teacher: What about multiplying by 32?
Health 2: 32 copies of the whole circle.
After praising and encouraging, the teacher asked: The formula is a little annoying. Can it be improved?
Health 4: c = 2 ∏ r, multiply by 2 and divide by 2 to cancel.
Teacher: You also have to ∏r2. What if it's 64 equal parts? 128?
Health: It will also offset, and the result is also ∏r2.
3. It seems that no matter which method, no matter how many parts, the calculation method of the area of the circle is -∏ R2.
Third, consolidate the practice.
1, so what conditions do you need to know to find the area of a circle? Tell the students that the radius of the disk on the blackboard is 10 cm, and let the students calculate it by themselves. Feedback proofreading.
2. If we know the diameter or circumference of a circle, how can we calculate the area? The time relationship will be discussed in the next class.
Comment: Some people say that there is not enough practice in this class. But why keep practicing? Students practice thinking through this course, don't they?
Fourth, class summary.
1. What did you learn from this course?
2. Summarize the thinking method and echo the dialogue before class.
Experience:
1 As experts say, listening to Mr. Ma's class has a shocking feeling. What is shocking is that Mr. Ma's class is the ideal math class we have always wanted to pursue. This class has all the elements that a new class should have: the teacher is the organizer and the leader, not offside thinking instead of students, and the atmosphere is free and easy; Students have sufficient thinking space, independent exploration and participation, and experience the beauty of mathematics and thinking to the maximum extent. What is particularly profound is teacher Ma's teaching design, which guides students to explore step by step. It is very beneficial to cultivate students' inquiry thinking by discussing how to change-become closer-how to calculate and go through the process of putting forward ideas-try-reflect-further practice-communication and construction.
2. The scale of infiltration of mathematical thinking methods.
In the after-class interaction, Mr. Ma raised his own confusion: how to grasp the scale of infiltration of mathematical thinking methods? In fact, his class has given a good answer. The infiltration of mathematical thinking method is really meaningful. Compared with mathematical knowledge and skills, mathematical thinking method is more universal in students' future life and work. In particular, the mathematical thinking method of this course is of great practical significance, and no amount of time can be spent. But not every mathematical thinking method is suitable for primary school students' thinking level, such as extreme thinking in this class. When Mr. Ma was dealing with this class, "transformation" ran through the whole class and was repeatedly pointed out, except for not telling the students the term "transformation". "Limit" is just for students to imagine properly. Therefore, the scale of infiltration should be: according to the thinking level and characteristics of primary school students, the camera should be clear, and there should be no ambiguity and encouragement.
extreme
First, the teaching philosophy
Cuboid and cube are three-dimensional figures that students are very familiar with. In life, we often need to know their surface area, such as calculating how much material is needed to make a rectangular fish tank. Although students have learned how to calculate the surface area of a cuboid, due to the lack of practical experience in life, the calculated result does not meet the actual requirements: an additional upper area is added. A seemingly simple question, the students seem to understand: what shape is the fish tank? A cuboid? Is it the same to calculate the area of the required material as the surface area of this cuboid? There are no noodles in the fish tank, so on which surfaces is the actual total area counted? How to calculate the area of these surfaces? The surface areas of cuboids and cubes guide students to explore and discover the above problems according to their actual situation, teaching materials and educational resources, and carry out inquiry activities driven by understanding how contradictions and conflicts arise and how to solve problems, so that students can solve the problems of fish tank making to carry out teaching. In the process of exploration and discovery, students learn how to apply what they have learned to life practice and cultivate their ability to analyze, solve and express problems. At the same time, students have experienced the pleasure of exploring, finding problems and solving practical problems flexibly in their study, which fully embodies their position in the subject study in teaching.
Second, the teaching objectives:
1. Make students understand and master the calculation method of cube surface area, and calculate the surface area of cube correctly.
2. Enable students to calculate the total area of several faces in cuboids and cubes according to the actual situation, further cultivate students' exploration consciousness and spatial concept, and improve their ability to solve simple practical problems.
Third, the process of teaching activities:
First, guide students to learn the calculation method of cube surface area.
1. Memory
Last class, we learned the concept of the surface area of a cuboid and how to calculate the surface area of a cuboid. So who says what is the surface area and how to calculate the surface area of a cuboid?
2. Lenovo:
(Pick up a cube model and touch the face) Question: What are the characteristics of a cube face? What is the surface area of a cube? How to calculate the area of each face in a cube? So how do you calculate the surface area of a cube?
3. Induce and introduce new courses:
The total area of six identical square faces of a cube is the surface area of the cube. How to find the surface area of a cube? This is the main content of this lesson (blackboard writing topic)
4. Teaching Example 2
Question: What are the conditions of the topic and what do we want? What does it mean to require a cube to require at least square centimeters of cardboard? Can you calculate?
(Classroom Record: Some students suggested that the surface area of a cuboid can be calculated, because cuboids are special cubes, so they can be done. A small number of students agree with this view, but after calculation, they think that the method is too complicated and can be used simply. )
(Comment: A good beginning is half the battle. Whether a class has a good beginning is the key to a good class. According to the psychological characteristics of primary school students, at the beginning of class, I first used the models of cuboid and cube to import, let students think about how to calculate the surface area of cube, and then deduce it according to the knowledge they have learned before, thus leading to a new calculation method, so that students can enter the learning situation happily and actively, strengthen their intentional attention, stimulate their desire for knowledge and explore new knowledge. Through the introduction of teaching, it will be twice the result with half the effort to clarify the teaching objectives and research direction, and then guide students to learn. )
Teacher: Summary: All six faces of a cube are squares with equal areas, so to find its surface area, you can find the area of a face by multiplying the side length by the side length, and then multiply it by 6.
Second, the production of fish tanks.
Explanation: We have learned to calculate the surface areas of cuboids and cubes. In the actual production and living process, sometimes it is not necessary to calculate the total hungry area of six faces, but only the total hungry area of some faces. We need to think about which areas need to be summed up and how to calculate the area of each face according to the actual situation. Like 3.
1. Help students remember the shape of a fish tank (a cuboid without a top).
2. How to calculate the area of required materials? (that is, find the surface area of this cuboid, but subtract the upper area)
3. Teaching Example 3
Show me the cuboid model and treat it as a fish tank model.
(1) Which glass is missing from the fish tank? (Above)
(2) How many square decimeters of glass are needed and the sum of several surface areas? Which have the same two opposites? There is only one on which side? How to calculate the area of each surface? (5 faces, no top, left face = width * height front face = length * height bottom face = length * width)
(3) roll call for students to perform and modify collectively.
(Comments: In teaching, the familiar object "fish tank" is used to inspire students to calculate the area of materials needed to make a fish tank, that is, to calculate the sum of the areas of some faces of a cuboid. This kind of case is more common in life. Some molds are used for teaching, so that students can better connect with reality in their study. The above series of activities show a complete inquiry process, which shows that students can experience the whole inquiry process of teaching. )
(4) Change the topic requirements to make the width and height of the cuboid equal, and observe the model. What did you find? How is it easier?
Student 1: When the width and height of a cuboid are equal, its left and right sides are two identical squares.
Student 2: When the width and height of a cuboid are equal, its front, back, upper and lower surfaces are all identical rectangles.
Student 3: This cuboid has no top, so as long as you calculate the areas of five faces, its front, back and bottom are exactly the same.
Note: When the width, height and appearance are equal, the front, back and bottom of the cuboid are exactly the same (the fish tank has no top), so you only need to calculate the area of one surface multiplied by 3, and then add the areas of the left and right sides to get the area number of materials needed for the fish tank.
(Comment: Mathematics is very rigorous, and it is necessary to standardize the language of students' narration. I also pay attention to evaluation in teaching, and give appropriate encouragement and guidance in time by using language and posture to promote students' learning and development. The third student gave the perfect answer, so I praised his rigor in describing math problems and asked the whole class to learn from him in this respect. )
4. Practice
The first and second questions in Exercise 2 on page 42 of this book.
(Comment: To calculate the sum of the areas of some faces of a cuboid, the key is to know how to calculate the area of each face of a cuboid. These exercises can help students to consolidate, and by naming students to answer questions, they can know the students' mastery in time, which is conducive to the implementation of teaching in the future. )
Teaching thinking on the surface area of cuboid and cube;
First, actively participate and find problems.
In order to establish students' dominant position in teaching, we must attach importance to students' experience of student research in teaching. In the activities, on the one hand, we should consolidate our study.
Tisso
Teaching objectives:
1. Guide students to understand the meaning of multiplication through independent exploration and cooperative communication in the situation, and work out the multiplication formula of 7.
2. Guide students to memorize the multiplication formula of 7 in the activity and solve simple practical problems with the multiplication formula of 7.
3. In the process of writing and using formulas, improve students' autonomous learning ability, accumulate learning emotions and enjoy the joy of success.
Teaching emphasis: experience the process of compiling formulas, understand the method of compiling formulas, master the multiplication formula of 7 and memorize it.
Teaching difficulties: memorize the multiplication formula of 7 and apply it to solve practical problems in life.
teaching process
First, put forward the learning objectives.
1. Create a situation: show a ship made up of seven triangles.
Teacher: What did the elf bring us? What is it made of? How many triangles does it take to make such a ship? Teacher: How do you know? What does this mean? (1 7s) Teacher: How many triangles does it take to spell two boats? (14) What do you think? (7+7 = 14) Teacher: Oh, how many does 7 add up to? How many triangles does it take to spell three boats? How about four? ..... seven? Today, in this lesson, we will learn the multiplication formula of 7.
2, put forward the learning goal: students think about it, what are the problems of the multiplication formula of 7 worth learning?
Show learning objectives:
(2) Understand the meaning of multiplication and work out the multiplication formula of 7.
(3) If you remember the multiplication formula of 7, you will use the multiplication formula of 7 to solve simple practical problems.
Second, show the learning results.
1, displayed separately in the group.
Students learn independently according to the form, fill in the formula in the form completely, and fill in the multiplication formula of 7. Please try to fill in the book and discuss it in the group when you are finished. (Student activities, teacher visits)
2, the whole class performance (group)
Communicate and report. According to the students' report, the teacher wrote the formula on the blackboard.
(1) constitutes the multiplication formula of 7.
Teacher: What multiplication formulas have you compiled and what multiplication formulas do you know? You can say that if you like.
Default value:
If 1: 17 gets seven, 3×7= or 7×3= can be solved.
Born 2: 274, can solve 4×7= or 7×4=.
……
(2) Verify the multiplication formula of 7.
How to verify the sentence "5735"?
Default value:
Health 1: 5735 means that five sevens add up, and five sevens add up to 35. So 57 is 35 (blackboard 1) 7+7+7+7 = 35).
Health 2: Five-seven-thirty-five also means the addition of seven, so five-seven is thirty-five (blackboard 2) 5+5+5+5 = 35).
……
(3) Recite the multiplication formula of 7
First, discover the law and guide memory
Teacher: Students, the multiplication formula of 7 is difficult to remember, but as long as we master its characteristics and laws, we can firmly remember it. Have you found these characteristics and laws?
Default value:
Health: The factors on the left side of the multiplication sign are 1 ~ 7, and the factors on the right side of the multiplication sign are all 7, and the product is also from small to large.
Teacher: Your discovery is very important. When one factor changes and the other factor remains unchanged, the product will also change. When it gets bigger, the product will get bigger and smaller, and the product will get smaller (refers to the factor and product).
Teacher: These rules are very helpful for memorizing formulas. Have you memorized these seven sentences? Let's have a try. Do you have confidence?
(Reciting formula)
Teacher: When reciting formulas, which sentence do you find difficult to remember?
Students express their opinions and give reasons. For example, 372 1 and 7749 are easier to remember. If it is difficult to remember, you can use the previous sentence or the latter sentence to help you remember.
B, using effective memory method
Teacher: There are many ways to remember. As long as you use your head and talk more, you can recite the formula. The teacher made a request to everyone. Like it or not, every student should remember these formulas. Is it necessary to recite this formula for 7749 days?
Teacher: Did the students notice that what the teacher said just now included two multiplication formulas, remember?
Health: 372 1 and 7749.
Student: OK, now let the students remember the multiplication formula of 7 by themselves with the newly discovered law.
Let the students recite the multiplication formula of 7 collectively. Then play a password game between teachers and students.
Third, expand and extend knowledge.
(1) Computer demonstration: Please do a quick oral calculation and tell its formula.
5×7=7×3=7×4=7×6=
7×7=7×2= 1×7=4×7=
(2) Application exercises
Show an ancient poem: He's Homecoming Book: (The poem is abbreviated)
Teacher: Seven is a strange number, which was inextricably linked with seven in ancient China. Let's look at an ancient poem. What was this ancient poem written in the Tang Dynasty? How many words does it contain? Can you work it out with a formula?
Health: 28,4728
Teacher: Yes, there are seven words in each sentence. Such poems are also called seven-character poems.
(3) Show
Seven classes a day, how many classes five days a week?
Dad went to Beijing for three weeks. How many days did he go?
A person should drink 6 glasses of water every day. How much water should he drink a week?
(4) Can we use the multiplication formula of 7 to solve some problems in our life?
Summary: What have we learned today? What did you get?