Tisch
Teaching objective: (1) Knowledge and skills: I can use the quotient invariant law to calculate division.
(2) Process and method: Let students experience the process of exploration, learn to explore new knowledge through analogy transfer, and summarize the law that dividend and divisor change at the same time and quotient remains unchanged through observation, analysis, communication and cooperation. Cultivate students' ability to observe, compare, guess, summarize, discover laws and explore new knowledge.
(3) Emotion, attitude and values: guide students to experience the process of exploration, the exploration of mathematical knowledge, the fun of discovery and the promotion of successful experience.
Teaching focus:
(1) Guide students to discover and master the rules themselves;
(2) General and simple language expression rules;
(3) Simple calculation by using the law of quotient invariance.
Teaching difficulties:
(1) Introduce the process of discovering laws;
(2) Correctly express the changing law of language.
Student situation:
There is interest, teacher. Moreover, the curriculum standard clearly points out: "Mathematics learning activities must be based on students' cognitive development level and existing knowledge and experience. "The fourth-grade pupils are curious and like to explore new knowledge. Students have mastered the situation that dividend remains unchanged, quotient changes with dividend, dividend remains unchanged, and quotient changes with dividend. With these knowledge bases and knowledge transfer, they will certainly be able to explore, discover and summarize the laws.
Teaching methods:
According to the characteristics of teaching content and students' thinking, I chose the guided discovery method, supplemented by the optimized combination of conversation method and group cooperation. Fully mobilize students' various senses to participate in learning, give full play to students' main role and teachers' guidance role, embody "students are the main part of the classroom, and teachers are the dominant part of the classroom", stimulate students' interest in learning with fascinating problem situations and vivid and interesting stories, mobilize students' enthusiasm for learning, and guide them to discover laws, analyze laws, solve practical problems and acquire knowledge, so as to achieve the purpose of training their thinking and cultivating their abilities.
Teaching process:
First, create situations and ask questions.
Introduce new lessons with vivid and interesting stories. Fourth grade students generally like to listen to stories. Introducing stories into new classes can quickly attract students' attention to the classroom.
(1) Find two classmates, one to play the Monkey King and the other to play Pig Bajie: 14 cakes are eaten in an average of 2 days; 140 share the cake equally and eat it in 20 days.
(2) The teacher asked: Can I eat more every day as the pig thinks? You will know through the study of this course.
Writing on the blackboard: the unchangeable law of quotient
Second, cooperate to explore and discover laws.
(1) Question: The big screen shows the following formula. Ask the students to calculate the quotient first, and then observe these formulas from top to bottom. Pay attention to the comparison between formulas 2, 3, 4 and 5 and 1 respectively. What did you find? 5 minutes, group discussion. After discussing the results, tell the teacher by action.
(2) Group discussion. The group members had a heated discussion, and the teacher encouraged the students to express their opinions. Students complement each other and sum up the rules in their own language.
(3) Reporting and communication. After most students in the class sat down, the teacher asked two students to tell the quotient of the above formula separately, and then asked students of different groups and levels in the class to tell the rules found by their groups respectively.
Compare several formulas together.
After comparison, students can easily find the rules. First find a group on the left of the class to express the law. They will say, "Divider times a number, divisor times a number, and the quotient remains the same." At this time, the teacher asked the teacher to comment and praise in time, saying, "Your group found the dividend and the divisor multiplied by a number, and the quotient remained unchanged. It's good to have such a big discovery. " Then find other groups to supplement, and the teacher will guide you in time. There are 2 1 discussion groups in the whole class, and the teacher finds 10 groups to continuously process and supplement them. 10 group accounts for nearly 50% of the students in the class. After the supplement of so many students and the guidance of teachers, the students finally tell the law completely: the dividend and divisor are multiplied by the same number at the same time, and the quotient remains unchanged.
(4) The teacher asked: Are there any other questions? Export condition: except 0. Why except 0? Health: Because 0 times any number gets 0. The teacher guides the students: which words do you think are the key in this law? Students will find: at the same time, the same, except 0. Why do you say "simultaneous" and "same"? It can be proved by examples that the law is obtained: the dividend and divisor are multiplied by the same number at the same time (except 0), and the quotient remains unchanged. Guide students to express this law by mathematical methods.
Teacher's blackboard writing
(5) Guide students to use the laws and processes just discovered and summarized, and then observe these formulas from bottom to top. Pay attention to compare the 2nd, 3rd, 4th, 5th order formula and 1 order formula respectively. What did you find?
With the method of summing up the law just now, I believe students will soon find out and draw a conclusion: when the dividend and divisor are divided by the same number (except 0), the quotient remains unchanged.
The teacher wrote on the blackboard below the position he had just written.
(6) Teacher's summary: This is the unchanging law of business. The class reads and recites these two rules.
(7) Students discover these two laws, and then look at the story of sharing cakes in the course of class introduction, so that students can understand that in the story just now, the Monkey King educated greedy pigs with the unchangeable business law.
Third, consolidate practice and expand application.
The design of the topic is a flexible application of the law of business invariance, which enables students to further deepen their understanding and apply what they have learned.
1. I will ask and I will answer.
(1) Divider times 2. How does the divisor change, and the quotient remains the same?
(2) divide the divisor by 10. How does the dividend change and the quotient remain the same?
2. Judge right or wrong.
(1) When the dividend and divisor are multiplied by 5, the quotient is multiplied by 25. ( )
(2) The quotient of dividing two numbers is 6. If the dividend and divisor are divided by 3 at the same time, the quotient is still 6. ( )
(3) If 14 ÷ 2 = 7, then (14×5)÷(2×3)= 7. ( )
3. From top to bottom, according to the quotient of the first line, write the quotient of the following two questions.
4. Fill in operation symbols in ○ and numbers in □.
It will be difficult for students to accept the formula 1 directly, so they use the second formula and the third formula as a transition, so that students can easily understand and know how to fill in the fourth formula.
4. Independent evaluation promotes reflection
Share the harvest of this class with you! As long as the students say what they know about this lesson.
Ability, teachers are timely praise and encouragement. Let students reflect on what they have learned, not only pay attention to the summary of learning methods and emotions, but also let students realize that mathematics comes from life and is applied to life.
Five, say the content of the exercise
Classroom assignment: textbook P95 5
Blackboard design:
Constant quotient law
extreme
Design concept:
Create situations, stimulate students' interest and inquiry interest, guide students to actively build mathematical knowledge models in the process of independent exploration, cooperation and exchange, and use the laws of construction to solve problems, and infiltrate mathematical ideas and methods in the process of construction and application.
Teaching objectives:
1, through the process of exploration, we found the law of constant quotient.
2, can use the law of quotient invariance, simple calculation of division.
3. Cultivate students' ability to observe, summarize, ask questions, analyze and solve problems.
4. Students experience success in the process of observing, comparing, guessing, summarizing, verifying and other learning activities, and cultivate students' love for mathematics.
Teaching focus:
Understand and summarize the law of constant quotient.
Teaching difficulties:
Some simple calculations will be made by using the law of quotient invariance.
Teaching AIDS:
Small blackboard, calculation card.
Teaching process:
First, create a situation to stimulate interest.
Teacher: Attention, class. Let me tell you a story. Have you seen Journey to the West? The content in it is wonderful. The teacher knows that the students like the Monkey King very much. Today, the teacher told us a story about the Monkey King sharing peaches. The Monkey King couldn't wait to go to Huaguoshan to see his children after he came back from Buddhist scriptures. It brought a gift to the children-peaches. He said to the two monkeys around him, "Give eight peaches to you two monkeys equally!" " The two monkeys shook their heads again and again: "Too few! Too little! " When the monkeys outside heard about it, several monkeys came in. The Monkey King said, "Well, how about giving 80 peaches to 20 monkeys?" The monkeys pushed their luck, scratched their scalps and asked tentatively, "Your Majesty, can you have more?" All the monkeys heard the sound of sharing peaches and ran to the Monkey King. The Monkey King patted his chest and showed generosity: "Then divide the 800 peaches equally among the 200 monkeys. Are you satisfied? " ? The little monkeys laughed, and so did the Monkey King.
[Design significance: Introduce new lessons through stories that students love, stimulate students' interest in learning, create a relaxed classroom atmosphere for students, guide students to find and ask questions in story situations, and pave the way for solving problems. ]
Second, explore the law and discover the law.
Teacher 1: Students, Little Monkey and the Monkey King all laughed. Whose smile is clever and why?
Students think and answer.
(Default) Health 1: ... the Monkey King's smile is a clever smile. The total number of peaches and monkeys has changed, but the number of peaches allocated to each monkey has not changed.
Health 2: ... the Monkey King's smile is a clever smile, because the Monkey King cheated the little monkeys, and each little monkey was still given four peaches.
Teacher: How did you (you) see it? Where did you see it?
(Default) Student: ... (Calculated)
Teacher: Can you list the formulas?
Guide students to list formulas and complete them with blackboard writing.
Blackboard18 ÷ 2 = 4280 ÷ 20 = 43800 ÷ 200 = 4
2 1. What are the formulas for these operations? What is the name of the first vertical number? What's the name of the second horn? What's the name of the third horn?
2. Teacher: Please observe this set of formulas carefully. What did you find?
[Presupposition intention: This kind of presupposition will create more space for students to play than directly guiding students to observe the reserved thinking space from top to bottom or from bottom to top. If students can't find a response in class, they will guide them step by step. 〕
Students observe and think independently.
Teacher: Did you find anything important? Can you tell me your important findings?
Group communication, teacher patrol counseling.
The whole class communicates and reports.
Health: I found that their scores were all 4, and their quotients remained unchanged.
Teacher: She found a very important mathematical phenomenon, and the quotient remains unchanged. (blackboard writing: business unchanged)
Teacher: In this class, we will learn the Law of Constant Quotient. (blackboard writing topic)
Teacher: Business is still the same. Who has changed? How did it change?
(default) Born 1: both the divisor and the divisor are multiplied by 10 (expanded by 10 times).
Teacher: This classmate said a very good sentence. Do you know what this is? What does "at the same time" mean? Can you talk about it?
Health: ...
Teacher: "At the same time" means that both the dividend and the divisor are enlarged by 10 times. (instead of an expansion, a contraction, or an expansion, a constant. )
(Default) Student 2: Comparison between Type ② and Type ① …
Teacher: He found the law well and compared it with two formulas. What a good learning method! Can you find some laws of other formulas like him?
Health: ...
Teacher: How clever the students are! They have found so many rules! Can you sum up the rules you found in one sentence?
Health: ...
Teacher: Divider and divisor are multiplied by 10, 100, 1000 at the same time, and the quotient remains unchanged. (blackboard writing)
Teacher: The students just looked down and found such an important rule. So, bottom-up, is there a rule?
Health report, the teacher writes on the blackboard.
Teacher: Divide the dividend and divisor by 10, 100, 1000 at the same time, and the quotient remains unchanged.
Teacher: Is it true that only the dividend and divisor are multiplied or divided by 10, 100, 1000, and the quotient remains unchanged? Then can you check it? Please write more division formulas with quotient of 4 to see if there is such a rule.
Write the formula and the teacher will demonstrate it.
Teacher: Please observe this set of formulas carefully. Does it conform to this law?
Health observation, report.
Teacher's guidance: It seems that the digits expanded and reduced here are not necessarily all hundred digits and all thousand digits, but also 1 times, 2 times, 3 times and 4 times, so 10 times and 100 times should be changed to "the same multiple".
The teacher rewrote it on the blackboard.
Teacher: Are all the figures here ok?
(Default) Operating Status: ..... (Except zero)
Teacher: Why should we exclude zero?
Health: Because zero is multiplied by any number to get zero, and zero can't be divided.
Teacher: What we have discovered is the important Law of Constant Quotient. Does this law apply to all departments?
Teacher: Please make a set of formulas with us to verify it.
Health verification, report by name.
The teacher concluded: It seems that this rule applies to all teachers.
[Design Intention: This link guides students to gradually build a mathematical knowledge model of the Law of Quotient Constant through three levels: students' independent exploration, group cooperation and classroom communication, so that students can experience the learning process of "discovery-exploration-construction" and cultivate students' methods of learning mathematics. ]
Third, apply the law and expand it.
Teacher: Do the students understand this rule? Grandpa Wisdom wants to test how well you master it. Is it okay?
1, please calculate.
8000÷2000=
80 ...0 ÷ 20 ...0 = added under the blackboard.
100 0 100 0
You are an advanced computer, much faster than ordinary computers. It seems that this rule is so effective that so many students can work it out.
2. P75 T 1 blackboard to small blackboard.
3. From top to bottom, first calculate the quotient of the first question in each group, and then quickly write the quotient of the next two groups.
72÷9= 36÷3= 80÷4= 720÷90= 360÷30= 800÷40= 7200÷900= 3600÷300= 8000÷400=
Judge, is the following calculation correct? Why not?
14÷2=7 15÷3=5
( 14×2)÷(2÷2)=7( ) 150÷30=5( )
( 14×5)÷(2×3)=7( ) 150÷30=50( )
(14× 0) ÷ (2× 0) = 7 ()1500 ÷ 300 = 500 () 5. Competition.
Compare and see who writes the most bisection expressions in 1 minute. After the game, let 1 tell us the secret of winning.
6. Page 6.P75, Observation and Thinking
The law of perception plays a great role (it can make calculation simple).
[Design intention: design variant exercises at different levels to break through difficulties, so that students can further understand and apply the explored laws, thus achieving flexible use of knowledge to solve problems and cultivating students' application awareness and ability. ]
Fourth, class summary, summary.
Teacher: What did you learn and find in this class? Is math interesting?
Teacher's summary: Through students' exploration, we have come to such an important "Law of Business Invariance", and it is so useful. The students are really amazing! Next class, your teacher will take you to apply it to vertical calculation, and it can also make vertical calculation simple!
Verb (short for verb) homework
List several sets of mathematical formulas and talk about the law of constant quotient.
Blackboard design:
Constant quotient law
①8÷2=4 6÷3=2
②80÷20=4 24÷ 12=2
③800÷200=4 48÷24=2
8000÷2000=4 120÷60=2
80……0÷20……0=4
100 0 100 0 The dividend and divisor are expanded or reduced by the same factor at the same time, and the quotient remains unchanged.
Tisso
Teaching content:
Beijing normal university printing plate primary school mathematics fourth grade first volume page 74 to page 75.
Teaching material analysis:
The content of this textbook is that after students have gone through three learning processes of exploration and discovery: interesting formula, multiplicative associative law and multiplicative distributive law, the theme of this textbook is "exploration and discovery". Its purpose is to let students experience, observe and compare divisor and its changes and the corresponding learning process of quotient, so as to discover the "law of quotient invariance" and feel the success and happiness of exploration and discovery. On the basis of deeply understanding the connotation of "the law of business invariance", students are guided to use knowledge to solve problems in calculation and practice.
Teaching objectives:
1. Knowledge and skills: Understand and master the invariable law of quotient, and be able to use this law for oral division; Cultivate students' ability to observe, summarize, ask questions, analyze and solve problems.
2. Process and method: Students find the law of summarization in the process of participating in learning activities such as observation, comparison, conjecture, generalization and verification.
3. Emotional attitude: Students experience success in the process of participating in learning activities such as observation, comparison, conjecture, generalization and verification, and at the same time infiltrate the initial enlightenment education of dialectical materialism.
Teaching focus:
Let students understand and summarize the invariable law of quotient.
Teaching difficulties:
Let the students use the law of constant quotient to do some simple calculations.
Teaching process:
First, create a situation to stimulate interest.
Teacher: Students, do you like listening to stories? The teacher told you a story today. Please look at the big screen. Guo Huashan has beautiful scenery and pleasant climate, and a large number of monkeys live there. One day, the Monkey King asked the little monkeys to share peaches. The Monkey King said, "Give you eight peaches and divide them equally among the two little monkeys." Hearing this, the little monkey shook his head repeatedly. "No, it's too little! Too little! " "Then I'll give you 80 peaches and give them to 20 monkeys on average." The little monkey shouted, "Little, little." "Less? Then I will give you 800 peaches, giving an average of 200 monkeys. " The little monkey pushed his luck and said tentatively, "Your Majesty, please give me more." On striking the table, the Monkey King was very generous: "Tell you what, I'll give you 8,000 peaches and give them to 2,000 little monkeys on average. Now you should be full. " The little monkey smiled, and so did the Monkey King. I think everyone laughed, too. )
Teacher: Why did the little monkey laugh and the Monkey King laughed?
Let more little monkeys eat peaches. Teacher: How kind of you! How kind! )
Health 1: Because monkeys eat more peaches.
Teacher: What do other students think?
Health 2: Because no matter how you divide it, every monkey eats the same number, which is four.
Teacher: Is that right? how do you know
Health: 8 ÷ 2 = 4 80 ÷ 20 = 4 800 ÷ 200 = 4 8000 ÷ 2000 = 4.
Teacher: Oh, I see. How clever you are! Why does every monkey get the same peach every time? We will study this problem together in this class.
Second, explore the law and summarize the essence.
(1) Observe the formula and find the law.
(1) courseware demonstration
8÷2=4
80÷20=4
800÷200=4
8000÷2000=4
(2) Observation and discussion
A, from top to bottom, what's the change of dividend and divisor? What's the change in business?
After the students observe and discuss, the representative reports the conclusion. The teacher writes on the blackboard: Dividend and divisor are multiplied by a number, and the quotient remains unchanged. )
B, from bottom to top, what happened to dividend and divisor? What's the change in business?
Students observe and think, report their conclusions, and write on the blackboard: Dividend and divisor divided by a number, the quotient remains unchanged. )
C, look at the second example, is it the same?
Can you give some examples to illustrate your findings? Write an example with the form given to you by the teacher (the teacher visits and accepts the demonstration).
bonus
divisor
Quotient e, to keep the quotient unchanged, can you multiply the dividend and divisor by 0 or divide them by 0? Why?
Students can discuss at the same table, report again, and give examples.
Teacher: Great. Can you tell us what you found in one sentence?
(Students try to sum up the law of discovery, the law of writing on the blackboard)
Divider and divisor are multiplied or divided by the same number at the same time (except zero), and the quotient remains unchanged.
(2) Teachers summarize and reveal the topic: This is the unchangeable law of business (blackboard writing topic).
Third, feedback exercises to deepen understanding.
1, fill in the number.
20÷5=4
( 20 ×6 )÷( 5 × □ )=4
( 20 ÷ □ )÷( 5 ÷5 )=4
( 20 × □ )÷( 5×8 )=4
2. Given 48 ÷ 12 = 4, judge whether the following items are correct. If it is wrong, how to correct it is right.
⑴(48×5)÷( 12×5) =4 ( )
⑵(48×3)÷( 12×4) =4 ( )
⑶(48÷6)÷( 12×6) =4 ( )
⑷(48÷4)÷( 12÷4) =4 ( )
3. Answer first.
(1) In the division formula, the dividend is divided by 5, the divisor is also divided by 5, and the quotient ().
(2) In the division formula, if the dividend is multiplied by 10, the quotient should remain unchanged and the divisor should be ().
(3) In the division formula, if the divisor is divided by 100, in order to keep the quotient unchanged, the dividend is ().
Observe and think
The following is the process of naughty calculation of "400÷25". Observe every step of the calculation carefully. What is your inspiration?
400÷25=(400×4)÷(25×4)= 1600÷ 100= 16
Please tell me the advantages of this: when you see 25, you think of 4, and change the divisor to 100. Divide by 100 is to divide the dividend by two zeros, which is convenient for simple calculation.
Can you use this method to calculate the following questions?
150÷25 800÷25
2000÷ 125 9000÷ 125
Fourth, class summary.
Who can tell your feelings or gains in this class in one sentence? (Answer after thinking for half a minute)
Verb (short for verb) task.
1, from top to bottom, first calculate the quotient of the first question in each group, and then quickly write the quotient of the next two questions.
72÷9= 36÷3= 80÷4= 720÷90= 360÷30= 800÷40= 7200÷900= 3600÷300= 8000÷400=
2. Fill in the blanks (the number is □, and the operation symbol is ○).
200÷40=5
(200×4)÷(40×□)=5 (200÷2)÷(40÷□)=5
(200×3)÷(40○□)=5 (200÷4)÷(40○□)=5
(200×□)÷(40○□)=5