Teaching objectives:
1, so that students can correctly understand the meaning of the score and the unit "1";
2. Cultivate students' observation ability;
3. Cultivate students' abstract generalization ability.
Teaching process:
First of all, introduce.
1, what is the meter scale used for? The teacher measured his height with a meter ruler. Look carefully. Can the teacher's height be expressed in whole meters?
For another example, an apple is distributed to three children on average. Can every child get the whole meter?
3. In daily life, people often can't get integer results when measuring and calculating, so it is necessary to introduce a new number-fraction.
Today, I will learn the meaning of the score on the basis of the original study score. (blackboard writing topic)
Second, hands-on perception
(1) grade 1, and the fourth grade has a preliminary understanding of the score. Can you name a few scores?
The teacher has prepared a lot of information for you. This is a cake, a rectangle and a rope. Can you select one of them to display 1/2? (Student hands-on operation)
2. Report
(1) How to score? How did you get the score of 1/2? How big is 1/2?
The teacher emphasized that one of them is 1/2 (rectangle and rope) of this cake.
(2) Continue to report
(3) Besides these three materials, can you choose another one to represent 1/2?
3. Well, some students just parted the rope. Do they have anything in common? Why is it all 1/2?
Teacher: They are divided into two parts equally. Which original thing is this?
What is the difference?
Health: Some points, some points, some points, and the average points are different.
1. The teacher has also prepared some other study materials for you. What are these? Can you give the 1/2 of four peaches?
Everyone has prepared a small cube and a marker. Please choose any of these things to represent its 1/2, and work together in the group.
2. Report
(1) Please report to Apple's team first. How did you score? How did you get the score of 1/2?
Teacher: Four apples, of course, should be regarded as a whole first. How many shares should I share equally? How many apples are there in one serving? One belongs to this apple.
(2) Report in the form of small squares.
A small cube is 1/2 of this small cube.
(3) watercolor pen
12 branch, treat it as a whole, and get 1/2, that is, divide it into components on average, and each branch is 12 branch.
(3) Summary
We can all get 1/2 through the average score just now. Why? Do they have anything in common? (revealed: average score)
Teacher: All these objects are divided into two parts equally, that's what it means, so it is represented by 1/2. What is the difference?
(4) 1. Teacher: Some people average an object, a figure, a unit of measurement, or average a whole composed of many objects and get a score of 1/2. If the teacher asked you to get 3/4 marks, would you? Please choose any object from the material, or choose a whole composed of many objects, with one point representing 3/4.
2. Report
(1) Let's ask a person to speak according to an object first. How did you get the score of 3/4?
(2) Please consider multiple objects as a whole and get 3/4.
Just now, we divided an object and a whole composed of many objects equally and got 3/4. Why are they all three quarters? What are the similarities?
(5)1(1) Just now we shared many objects equally. Can you sort these items? What are the categories?
(2) cakes, rectangles, ropes, etc. It can be expressed by the natural number "1". Just like four apples, eight cubes and a box of watercolor pens, a whole composed of many objects can also be represented by the natural number "1". Of course, double quotation marks are needed. We usually call them "65438" units. (blackboard writing
(3) The cell "1" can represent an object such as a cake, a rectangle, a rope or a whole made up of some objects.
2. Think about it according to the actual situation. Can you give some examples of the unit "1"?
(6) 1. What about the following? The teacher doesn't want you to divide it specifically. You think of a score in your mind and then determine a unit.
For example, if the teacher wants a score of 9/ 10, determine a unit of "1" and take the line segment with the length of 1 as the unit of "1". I divided it into 10 on average, that is, 9 copies, that is, 9/ 10. Tell it to your deskmate.
2. Report
Which score are you thinking about? What unit is "1"?
3. Summary
(1) Just now, we got many points by averaging an object, a unit of measurement, or a whole composed of some objects, that is, averaging the unit "1". What about the average number of shares? It can be a copy, replica, etc. Can you sum it up in one word, that is, divide the unit "1" equally?
(2) How do you know the word several copies? What do you mean, how many?
It means that such a copy is a fraction of the cell "1" and such a copy is a fraction of the cell "1".
(3) What kind of number is the score? (Talking to each other at the same table)
Teacher, talk to a classmate. How do you define this concept?
(4) Reading 8 1 page, the meaning of students' reading scores, and the teacher writing on the blackboard.
Which words do you think are more important in this article?
Three, 1, do the problem
report
2. Do some practical exercises.
There are some small pieces of paper in the envelope, red, white and red. How about the white one? Let the students operate and express correctly according to the teacher's instructions, ok?
(1) Take out six pieces of paper and ask all the papers to be red. 1/6, how to get them?
(2) Take out six pieces of paper, which should be 2/3 of all papers.
(3) Take out a piece of paper at will, as long as it represents a score of 3/5.
Is it different from them?
(4) Take out three pieces of paper, and the requirement is 1/4 of all papers.
(4) class summary
What knowledge have you learned through this lesson?
The Significance of Fractional Teaching Plan Part II Teaching Objectives
1, which enables students to skillfully aggregate the names of low-level units into the names of high-level units and correctly solve the application problem of "a fraction of a number is another number".
2. Be able to compare scores skillfully.
3. Cultivate students' ability to think and solve practical problems in an orderly way.
Teaching emphases and difficulties
Emphasis and difficulty: compare the size of scores; Solve the application problem that a fraction of one number is a fraction of another.
Prepare teaching AIDS and learning tools
teaching process
Reserve bill
First, the practice of unit conversion
1, oral answer:
1 decimeter is 1 meter ()/(); ()/() of 1 square decimeter;
1 Yes 1 hour ()/(); 1 g is 1 kg ()/ ().
what do you think? What is the naming method of low-level units?
Display: value of low-level unit = value of high-level unit (expressed by fraction).
2. Students' independent homework: 80 pages of exercises 1. (Check and correct each other at the same table after finishing)
Second, the practice of comparing scores.
1, Teacher: What kinds of situations do you usually encounter when comparing two scores? What methods are used in the comparison? Why/can you give me an example?
Please give an example to illustrate how the same denominator fraction and the same numerator fraction are compared in size, and talk about the thinking method.
2. Students' independent homework: 865438 pages of exercises 10 Question 2 +0.
Write it directly in the book, hand it over to the whole class after finishing, and check 7/1and 5/11; 7/30 and 7/24 are about comparative thinking process.
3. How to compare the three scores with the following three questions?
5/ 14, 3/ 14 and 9/14113,11/.
Induction: compare the sizes of several scores, and first compare them carefully according to the method of comparing sizes. (pay attention to carefully examine the questions, whether it is required to arrange them from big to small, and whether to use ">" or "
Think about the following questions: Xiaoming, Xiaohong and Xiaohua ran away 100 meters. Their scores were 5/ 19, 6/ 18 and 6/ 19 respectively. Who runs fastest? Who runs the slowest?
Let the students think independently first, then discuss in groups and communicate in class. Let the students talk about their ideas.
4. Students work independently.
(1) Compare the sizes of the following groups and use "
6/ 17, 1/23 and 6/ 19 12/35, 16/35 and 9/354/ 15,1.
teaching process
Reserve bill
② Page 865438 +0 Exercise 10 Question 6.
A car has traveled 445 kilometers from A to B, which is 52 kilometers away from B. ..
(1) How many points are left? (2) How many points are left in the whole journey?
Students continue to discuss solutions and come to the conclusion: what is the key to finding the score of another number from one number? How about the method?
6. Students' independent homework: Textbook 8 1 Page 4-5.
Third, the classroom.
What have you gained from the practice of this class? What do you think should be paid attention to in practice? What other issues need to be discussed?
Four. Homework "exercise book"
Students' ability to think in an orderly way is not enough, and training needs to be strengthened.
Teaching objectives of the third lesson of the meaning of fractions;
The appearance of 1 let the students know.
2. Guide the students to understand the meaning of the score and know the names of each part of the score.
Through the study of scores, students' observation ability, thinking ability and abstract generalization ability are cultivated.
Through the generation of scores, students can realize that scores are around us, and using scores can solve practical problems in life, thus improving students' interest in learning mathematics.
Teaching emphasis: understanding the meaning of fractions
Teaching difficulty: understanding of the unit "1"
Teaching AIDS: some fruit pictures, objects (4 apples), small blackboard.
Teaching process:
A revealing topic (the generation of scores)
1. Take out four apples and ask: If you divide them equally among two children, how many will each get? (2)
2. Show two apples and ask: If you give them to two children on average, how many will each person get? ( 1)
3. Show 1 apple. Q: How many apples will each child get if they are given to two children equally? (half or 1/2)
What's the 1/2 here?
In actual production and life, people often can't get integer results when measuring and calculating, and often use fractions. Scores can be seen everywhere in our lives and are inseparable from our lives. So, what exactly is a score? We will study this problem in this class. (Board issues)
Second, the new teaching curriculum
1 Significance of heuristic score
Just now, the teacher distributed 1 apple to two children equally, and each child got 1/2 apples. (blackboard writing: paste the picture of apple, divide it into two parts on average, indicating such a copy 1/2)
Now the teacher wants you to say a score casually and what it means.
Answer by roll call, and the blackboard says: 3 schools 1 /2 schools 1/32/3.
We all got a date just now. Now the teacher has a line segment here. If I divide it into five parts on average, how many parts does one part represent? What about the four of them?
Call the roll and write it on the blackboard: —————— 5 copies 1 /4 copies 1/54/5.
Summary: divide an object and a unit of measurement into two, three, five, etc., and such one or more copies can be expressed by fractions. Blackboard: How many copies, one copy or several copies?
2. Further understand the significance of the score
Show pictures of apples (4 apples), treat them as a whole, and demonstrate putting 4 apples in a bag. Question: What does this mean? (A bag of apples) is a whole. How many apples can we divide the whole apple equally? 1 Apple is a fraction of this whole? How many parts of a whole are three apples?
Considering four apples as a whole, how many can you divide equally? How many apples are there in each serving? How much is this whole?
Blackboard books: 4 volumes 1 /2 volumes 1/42/4.
2 copies 1 copy 1/2.
How many apples are two-quarters here? How many apples are 1/2?
2/4 and 1/2 represent the same number of apples. Do they have the same meaning? (different)
Summary: divide a whole into several parts on average, and such one or several parts can also be expressed by scores.
3 The significance of inductive scores
(1) unit "1"
It seems that we can not only average an object and a unit of measurement, but also average a whole composed of many objects, and such one or several copies can also be expressed by fractions. An object, a unit of measurement or a whole here can be called the unit "1" on the blackboard: the unit "1"
Who can tell me the meaning of "1"?
(2) the complete concept
What is a score? Who can express it in one sentence? Blackboard: That's called a score.
Step 3 practice
Exercise on page 76 of the textbook 13, question 3
4. Understand the meaning and writing of each part of the score.
Just now, we divided a line segment into five parts on average, where 1 is 1/5, and 4 is 4/5, so what is the score of 3? Blackboard writing: 3/5
Name each part of the score and the meaning of each name.
Blackboard writing: denominator numerator of fractional line
What to write first, then what to write, and finally what to write? Draw with one's finger
Take out your pen and write down the score. The task is eight. While the students were writing, the teacher suddenly stopped. Q: How much did you write? Can you indicate the completion of your task with scores? Ask the students to indicate the completion of the task with scores. Others guess how much they wrote.
Three consolidation exercises
1 Exercise on page 74 of the textbook
Exercise on page 76 of the textbook 13, the first question
3 peach picking game
(1) Take six peaches as a whole, please choose one.
One student picked a few peaches at random, while others said they picked a few cents.
(2) The teacher said a score and asked the students to pick it up.
Summary of four classes
1 What is the unit "1"?
What is the meaning of the score?
What are the names of the three scores?
5. Classroom assignments
Exercise on page 76-77 of the textbook 13 question 4
Teaching reflection:
This lesson is taught on the basis of students' initial understanding of scores. I teach from the students' existing knowledge, and its teaching characteristics are mainly as follows:
1, trying to make math problems come alive.
In this class, the teaching content I choose should be combined with students' real life as much as possible, such as apples, peaches and other fruits that students like to teach, so that students can experience and understand mathematics in real situations and change the traditional "learning mathematics from books" into "learning mathematics from life".
2. Let students experience the formation of knowledge.
In this class, I try my best to let students speak and understand some important and difficult points by combining various operational activities, so that students can talk more, and the teacher only plays a guiding role. For example, when the whole of several objects is regarded as the unit "1" in teaching, the teacher puts four apples that students are interested in in in a bag, and the "bag of apples" here can be regarded as "unit 1", which can make students break through this knowledge point well. The guiding operation of the image here makes the students very clear, so many examples are given at once.
3. Students have a strong sense of subjectivity. When students are asked to explore the meaning of scores, they have high learning motivation and interest, and they can actively participate in the learning process. For example, in the peach picking game, one student goes to the front to pick peaches, and other students can quickly tell which score represents according to the number of peaches picked by the previous student. There are various methods. This fully embodies the students' sense of participation and subjective spirit. For another example, when the teacher summed up the meaning of the score, he did not show the complete concepts in the book, but let the students gradually summarize, modify and improve the concepts on the basis of understanding, which also made the students really understand the meaning of the score. It also embodies students' subjective consciousness and practical ability, and also cultivates students' generalization ability.
The Significance of Fraction Lesson 4 Teaching Purpose:
1, broaden students' learning channels, and let students get a preliminary understanding of the conditions, background and development history of the score by looking up information in the library.
2. Let students understand the unit "1" in the process of playing learning tools, feel what a score is, sum up the meaning of the score, and cultivate students' practical operation and abstract generalization ability.
3. Let students learn mathematics in a relaxed and harmonious atmosphere, experience the success and fun of learning mathematics, and cultivate students' feelings for mathematics.
Teaching focus:
Teach the meaning of units and fractions.
Teaching difficulties:
Break through the whole teaching.
Teaching aids and learning tools:
Apple, decimeter, cube, stick, flag, knife, watercolor pen.
Teaching process:
First, introduce the generation of scores.
Teacher: Before class, the teacher asked everyone to go back and check the information. Who can tell us how the score is combined with your information? (Students raise their hands)
Teacher: (referring to a girl with a book in her hand) Tell me.
(The girl walks to the podium with the checked data and puts her data under the physical projection. )
The student said: I found it in China Children's Encyclopedia. Scores are derived from integrals. In primitive society, people worked collectively and distributed fruits and prey equally, and the concept of score gradually emerged. In the future, in the process of land calculation, civil engineering, water conservancy engineering, etc., when the length unit used cannot measure the line segment as much as possible, the score will be generated.
Teacher: You did a good job. From the information she checked, we can know that the score comes from the score.
Teacher: (Seeing a student raise his hand and point to one of the boys) Tell me.
Boy: (before coming to the physical projection on the platform with the information, pointing to the information book) I found it from the newly compiled mathematics dictionary for primary school students. In the long-term productive labor practice, mankind has made achievements. At first, they used specific scores, such as "half" for half and "half" for a quarter. After a long time, half and two-thirds scores appeared.
Teacher: Well, ok, please go back. Through the information he checked, can you know that the original form of music score is the same as the present form? (Students have different opinions) 1/2 means "half" and 1/4 means "half and half". Then, according to this calculation, 1/8 is (students say half and half. )
Teacher: It seems that the students understand this truth. Does anyone have any other information?
(Students raise their hands)
Teacher: (referring to a girl) OK, you come.
Girl: (holding the data and showing it in front of the physical projection) I found it in the data book, and I copied it into my notebook. Fractions have a long history in China, and the original forms of fractions are different from the present ones. Later, India appeared a score representative similar to China's. Later, the Arabs invented the fractional line, and the expression of the score became like this.
Teacher: Good. It seems that the students' information is well checked. I won't communicate one by one today. I suggest that you exchange the information you find after class. Through the materials checked by these students, we can know that the score is actually produced by the needs of people's production and life.
Second, explore the significance of scores
1, group inquiry, * * * participated.
Teacher: In the third grade, we had a preliminary understanding of the scores. Can you name a few specific scores?
(Students raise their hands)
A student: 3/4, 1/2,1/20,88/100.
Teacher: Well, that's quite a lot.
B: 1/ 10， 1/ 100， 1/50， 1/60。
Teacher: You know a lot of grades, too.
C students: 2/4, 2/8, 5/ 10, 20/ 100.
Teacher: The students already know a lot of scores. If I give you some materials, can I divide them into points and express them in fractions?
Ok, take out the materials prepared by the teacher and discuss them in groups.
Student activities, group discussion for about five minutes. Teachers patrol and participate in group activities to understand the situation. )
2. Report and exchange, and strive for innovation.
Teacher: Did everyone get the score? Which group said how you got it?
(Students raise their hands)
Teacher: (Nailing Group) Tell me about it.
(A student represents Group A and walks to the front of the physical projection with an apple. )
A: I divide this apple into two parts on average, and taking one of them is half.
(Teacher's blackboard writing: average score 1/2)
A: I divide this apple into four parts on average, and taking one of them is a quarter.
(Teacher writes on the blackboard: 1/4)
A: I divide this apple into eight parts on average, and taking one of them is one eighth.
(Teacher writes on the blackboard: 1/8)
Group a: in this way, by analogy, it can be divided into many parts and get many scores.
Teacher: OK, the teacher thinks there is a good sentence on him. Who can say it?
Health theory: and so on.
Teacher: Do you understand what analogy is and what it means?
The student said: Yes, just one by one.
Teacher: That is to say, it can be divided again. It seems that this group has figured it out. Does anyone have any other materials to show?
(Students raise their hands)
Teacher: (referring to Group B) Tell me about it.
(Student A represents Group B, holding a one-meter piece of paper to show)
Group B: Our group divided decimeter into 10, where 1 yes 10 → If you put; Divided into two parts on average, one of which is half. If it is divided into five F-flies on average, one of them is one fifth of C.
(Teacher writes on the blackboard: 1 decimeter110)
Teacher: He said a lot of marks just now. Let's divide 1 decimeter into 10 according to what this classmate said just now. Can I get other scores besides one tenth?
Life span: Divide 1 decimeter into 10, with → for one tenth, two for two tenths, and three for three tenths. If you push it down in this way, you can get a few tenths.
Teacher: that is to say, there are only a few tenths of it. Do you agree?
(Student Qi said: Agree)
Teacher: Does anyone have any other materials to show?
(Students raise their hands)
Teacher: (referring to Group C) Tell me about it.
(Two students, representing Group C, come to the front with eight squares to show them. )
Group C: We divide the eight squares into two parts equally, and take one and half.
(Teacher writes on the blackboard: 8 1/2)
Group C: Divide eight squares into four parts, one of which is a quarter, two are two quarters and three are three quarters.
(Teacher's blackboard: 1/4, 2/4, 3/4)
The teacher saw that many students below were eager to raise their hands. )
Teacher: Do you have any questions?
A girl: He is divided into four parts on average, and one part is two squares. Why did he say it was 25 cents? The boys in group C replied: Divide the eight squares into four parts, one of which is a quarter.
The girl questioned: one of them is two squares. Why 1/4? I still don't understand.
Group C boys: Because these two squares make up one.
Teacher: Are you satisfied?
Girl: Not satisfied. Teacher: Not very satisfied. Can you explain it again?
The girls in Group C enthusiastically explained that if they were to be divided into four parts, these two squares were not discussion blocks, but discussion parts. These two squares form a part, which is a quarter, so it is a quarter.
Teacher: What you said is very distinctive. It seems that this is a difficult point. The questions asked by the students just now are very valuable. If we want to get a score, we must regard eight squares as a whole. These two or four squares are only a part of the whole, and we can express them by fractions.
Teacher: Then who has any other materials to show?
(Students raise their hands)
Teacher: (referring to Group D) Tell me about it.
(Life represents a group, and go to the front with a 10 stick.)
Group D: I have a 10 stick here. I divided it into 10 on average, and this is one tenth. Then, I divided it into five pieces on average, one of which was one fifth. Divided into two parts on average, one of which is half.
(Teacher's blackboard: 10 post110, 1/5, 1/2)
Teacher: I want to ask you a question. I regard the 10 rod as a whole, which is divided into two parts on average, one part is half. How many are there in this one?
Health: It's five sticks. Teacher: Good. Please go back. You want to show it?
Health: I have six red flags here. First of all, I get a red flag on average, one sixth. Taking down two red flags is two-sixths, and so on, taking down six red flags is six-sixths.
Teacher: What does it mean to get a red flag on average?
Sheng added: I want to put it another way, that is, divide the six red flags into six parts on average, and take one side and it will be one sixth.
Teacher: What you said is really good. If we want to get a score, we must first distribute it equally.
(Teacher writes on the blackboard: 6 flags 1/6)
3, abstract generalization, building new knowledge.
Teacher: We just got a lot of points. (of a blackboard) We learned to divide an object before, (blackboard writing: an object) into a unit of measurement. (blackboard writing: measuring unit) Today we mainly studied a whole composed of multiple objects. We can usually call these units "1". (blackboard writing: unit "1")
Teacher: Besides these, can you give some examples of the unit "1"?
Health: A watermelon.
Health: A piece of cake.
Health: An apple.
Teacher: Just now, all the students lifted the same object. Can you raise something else?
Health: 10 person.
Health: 10 books.
Health: 8 pencil boxes.
Health: Five bottles of beer.
Health: 3 erasers.
Teacher: It seems that the students have understood the unit "1". Then can you combine these examples and say what is a score in your own words? Discuss in groups first.
(Group discussion for about one minute)
Teacher: Who can tell me?
A student:' Divide an object into several parts on average, and take a few parts, that is, several parts.
B: Divide an object into several parts on average, and take a few of them, which is the score.
Teacher: Just now, they were all divided into one object. Anything else?
C: Divide several identical objects into several parts, and take a few parts, which is the score.
Teacher: From what you said, the teacher knows that you have understood, so how did the mathematician sum it up? Look at the screen.
Screen display: divide the unit into several parts on average, and the number representing one or several parts is called score.
Look for students to read, and students question.
Teacher: This is the meaning of the scores we study in this class.
(blackboard title: the meaning of score)
Teacher: So, can you tell me what the score consists of through 3/ 10?
Student: Fraction line, numerator and denominator.
Teacher: What do denominator and numerator mean?
Health: The denominator is how many parts an object is divided into, and how many parts a molecule takes.
Teacher: This object is also a unit.
Third, consolidate the practice.
1. Use fractions to represent the shaded parts in the figure below.
2. Fill in the blanks;
(1) Divide a pile of apples into five parts, one for this pile of apples () and the other for this pile of apples ().
(2) Divide the students who come to class today into group () on average. One group is the class's (), and the second group is the class's ().
3, candy bar game.
Take 9 pieces of sugar from 1/3. How many pieces? Why? Then take the rest 1/3, how many pieces? Why? Take 1/4 of the remaining sugar, how many pieces?
Four. Summary (omitted)