Interactive cognitive teaching design 1 teaching objectives;
1. Understand the meaning of reciprocal and master the method of finding reciprocal.
2. Improve the ability of observation, comparison and generalization.
3. Understand the mathematical thought of "flexibility".
Teaching focus:
The meaning and solution of reciprocal.
Teaching difficulties:
Understand the meaning of "reciprocal" and make it clear that reciprocal only represents the relationship between two numbers.
Teaching preparation:
Cards (6 rules), exercise paper (Exercise 4 after class), and competition paper.
Teaching process:
First, the game competition
1. Before studying, shall we have a "design relay" competition?
Competition content: Please design a formula for multiplying two factors so that the product is 1.
Rules of the game: everyone designs one type at a time, and immediately passes it on to other members of the group after writing.
Competition time: 1 minute.
The evaluation standard of competition results: the person who writes correctly wins. (Only one copy can be calculated)
2. Organizational evaluation: physical projection, one student in each group reads the formula, and the supervision of the whole class is correct. Choose the winning team according to the number.
Second, the meaning of reciprocity
1. In just one minute, everyone has designed so many formulas. If I give you some more time, can you still write it? How much can you write?
In all these formulas, the product of two factors is 1. In this way, two numbers whose product is 1 are reciprocal. (Two numbers whose blackboard product is 1 are reciprocal to each other, emphasizing "reciprocal").
2. Understand "reciprocity".
(1) Q: What does "mutual cooperation" mean? (mutual)
Can a person talk to each other? Mutual affirmation (between two people). Therefore, the word "mutual" fully explains the relationship between the reciprocal sum (two numbers). Numbers can also be said that (a) is the reciprocal of (b) or (b) is the reciprocal of (a).
(3) Tell the reciprocal of who the students talk about with another formula. Q: Can you say who is the countdown separately?
(4) Think about it, in the concept of numbers we have learned, which numbers can't represent a number alone? (factor, multiple, prime number)
(5) Choose a formula to tell your deskmate who is the reciprocal of who.
Third, mutual writing,
1, just now, do you have any tips when designing these multiplication formulas? Write a fraction first, and then reverse the numerator and denominator of this fraction, which is another factor. )
Why should the numerator and denominator be reversed? (After inversion, the numerator and denominator can be reduced to 1)
(If there is fractional multiplication. Q: Why don't I see the numerator and denominator inverted in the formula of 0.25X4= 1? )
(0.25 means that the numerator and denominator are reversed, that is, 4), so the reciprocal of 0.25 is 4.
According to your experience, can you tell their reciprocal? (Monitor: 6)
The first one: how to standardize writing? Please try it in your notebook. Name the board of directors. The last two talk about their own ideas.
How do you think we should find the reciprocal of a number? (Transpose numerator and denominator of fraction)
4. Do you ask the reciprocal of a number? Who wants to come up and test everyone? You say a number, we say its reciprocal. The reciprocal of 1 is itself. 0 has no reciprocal. Show the card and analyze the reasons. Some students may report decimals or fractions, and discuss collectively how to find the reciprocal of decimals or fractions. )
Fourth, deepen understanding.
1, group cooperation
Please take out your exercise paper and find the reciprocal of each group of numbers below, and then see what you can find.
2, communication found that:
Teacher: What is the reciprocal of the first group? What did you find? Who wants to show it up?
(The reciprocal of 3/4 is 4/3, the reciprocal of 2/3 is 3/2, and the reciprocal of 7/8 is 8/7. This set of scores is true, and their reciprocal is false. )
Teacher: Are the reciprocal of all true scores false?
(Show the card: the reciprocal of all true scores is a false score)
Teacher: Who will talk about the second group?
(The reciprocal of 6/5 is 5/6, the reciprocal of 7/2 is 2/7, and the reciprocal of 3/8 is 8/3. This set of scores is false, and their reciprocal is true. )
Teacher: Does it mean that the reciprocal of all false scores is the true score?
(Not all the reciprocal of false scores are true scores. If the numerator and denominator of a false score are the same, its reciprocal is still a false score. )
Teacher: What you said is a false score equal to 1. And what kind of fake scores are the scores of the second group?
(All are false scores greater than 1. )
So-(card presentation: the reciprocal of a false score greater than 1 is a true score. )
Teacher: What about the third group?
The reciprocal of this set of scores is an integer. )
What are the characteristics of this group of scores? (Molecules are all 1, that is, fractional units) Their reciprocal is (integer).
(Card demonstration: the reciprocal of decimal units is an integer)
Teacher: What about the fourth group?
(This group is an integer, the reciprocal of the integer is a true fraction, and the numerator is 1. )
Teacher: Are the reciprocal of all integers fractional units?
(Display: the reciprocal of a non-zero integer is a fractional unit)
Teacher: Through our research, we found that there is such a reciprocal rule-(read together).
3. Do you know the countdown? Do you really know him? Then please tell me. (Courseware presentation)
(1) Two numbers with the number 1 are reciprocal.
(2) The reciprocal of 9 is 9/ 1.
(3) The reciprocal of 1 is1,and the reciprocal of 0 is 0.
(4) 1/6 is the reciprocal.
(5) Because x×y= 1(x≠0, y≠0), x and y are reciprocal.
(6) The reciprocal of all false scores is the true score.
In today's class, we learned ... what do you think is the most enjoyable harvest?
What else do you want to know about the countdown?
Thinking 1: What is the reciprocal of 1? How do you think we should find a reciprocal with scores?
Thinking 2: Is there a reciprocal for decimals? If so, how do you ask?
Verb (abbreviation of verb) subject integration
Finally, let's relax. Let's look at the interesting phenomenon of "equivalence" in Chinese. (Courseware presentation)
Such as Chinese characters "Wu-Yan" and "Xing-Liu"; Isn't it interesting?
Next, please enjoy the first couplet of a couplet: "Guests come from nature, and guests descend from heaven", which was written by Qianlong. In the Qing Dynasty, there was a restaurant in Beijing called "Natural Residence". Once, Ganlong went there to eat, touched by the scene and wrote a couplet with the theme of restaurant. The first couplet is this sentence: a guest is a natural residence, but actually a guest in the sky.
"Mutual Understanding" Instructional Design 2 teaching material analysis:
The content of this lesson is "Understanding Reciprocal" in Unit 3 of Book 11. It is taught on the basis of fractional multiplication and is an important concept for further study of fractional division. In the textbook, students should first observe the formula whose product is 1, and draw the meaning of reciprocal. According to the meaning of reciprocal, to find the reciprocal of a number, we should divide it by 1, but students haven't learned fractional division yet, so the textbook then uses incomplete induction to ask students to find a way to find the reciprocal of a number.
Teaching objectives:
1, so that students can understand the meaning of reciprocal, master the method of finding reciprocal, and find reciprocal correctly and skillfully.
2. Self-study and group discussion are adopted in teaching to further cultivate students' autonomous learning ability and improve students' observation, comparison, abstraction, induction and cooperative learning ability.
3. Improve students' interest in learning mathematics and cultivate students' habit of questioning.
Teaching focus:
Know the meaning of reciprocal and find the reciprocal of a number.
Teaching difficulties:
The solution of the reciprocal of 1 and 0.
Teaching aid preparation:
courseware
Teaching process:
First, import
Teacher: Before class, the teacher found that many students came to the multimedia classroom together. Like, are you two good friends? Please tell me the relationship between the two students. )
Teacher: Good friends go both ways. It can be said that "_ _ and _ _ are good friends of each other (it can also be said that _ _ is a good friend of _ _).
The teacher found a pair of deskmates and asked them to talk about their relationship. (_ _ _ and _ _ are deskmates and come to math class together)
Second, reveal the meaning of equivalence
Teacher: What are we going to learn today?
1, (Example 7 in the courseware)
Ask the students to find out that the product of two numbers is 1.
Students answer the teacher's demonstration.
2. Teacher: Do you know? A product like this is two numbers of 1, which we call reciprocal.
The teacher asked the students to refine it, and then wrote on the blackboard: the product is 1, and the two numbers are reciprocal.
3. Give an example to illustrate the relationship between two numbers. For example, the product of 3/8 and 8/3 is 1, so we say that 3/8 and 8/3 are reciprocal. (3/8 and 8/3 on the blackboard are reciprocal)
Teacher: What else can I say? Just like we just expressed the relationship between friends and deskmates.
Guide the students to say: the reciprocal of 3/8 is 8/3; The reciprocal of 8/3 is 3/8.
Teacher: Can we say that 3/8 is the reciprocal? What does "mutual benefit" mean? How to understand these two words?
Health 1: "Interaction" refers to the relationship between two numbers.
Health 2: "Interaction" shows that these two numbers are interdependent.
Teacher: The students speak very well. Reciprocal refers to the relationship between two numbers, which are interdependent, so it must be clear that one number is the reciprocal of another number, and a number cannot be said to be reciprocal in isolation.
For example, if the product of 5/4 and 4/5 is 1, we will say that the product of 7/ 10 and 1 7 is1,and we will say ...
Please give another example to tell your deskmate.
(Student activities)
5. Teacher: Just now, we realized the meaning of reciprocal, knowing that two numbers whose product is 1 are reciprocal, and reciprocal cannot exist independently, but depend on each other. According to the understanding of the meaning of reciprocal, can we find the reciprocal of 3/5 and 2/3?
Students write on the blackboard and report to the teacher. )
Third, explore the method of finding the reciprocal.
1, Teacher: Let's have a little competition. Please write more numbers whose product is 1 to see who writes more. How to divide the work in groups of four? (Let the students make suggestions) Are you ready? One minute countdown begins!
Teacher: Time is up, stop! Who wants to read what you wrote and share it with everyone?
Students read, and the teacher has the choice of writing on the blackboard. )
Teacher: It's nice to write so many numbers whose product is 1 in such a short time. Given enough time, how many such multiplication formulas can you write?
Health: Countless.
2. Teacher: Actually, I know that there must be something tricky in the course of the competition just now, which is why you wrote so fast and so much. What are the tricks? Who wants to talk? Students speak freely, but they must not be standardized. )
The teacher instructed the students to observe the reciprocal of each group. What happened to the positions of the numerator and denominator of two numbers? Standard statement.
3. Teacher: Because the numerator and denominator are reversed, the numerator and denominator can be completely simplified when multiplying, and the product is 1. So we can find the reciprocal of a number soon, right?
4. Teachers and students sum up together: that is to say, to find the reciprocal of a number, just change the position of the numerator and denominator. (blackboard writing)
5. Students independently explore the reciprocal of 5 and 1.
Students think independently first and communicate in groups.
The teacher writes on the blackboard in time according to the students' answers.
What about the reciprocal of 6 and 0?
Inspire thinking and allow discussion.
Because 0 is multiplied by any number to get 0, it is impossible to get 1.
Fourth, summary.
Teacher: We have found the reciprocal of so many numbers. Who will summarize the method of finding the reciprocal of a number?
Health 1: To find the reciprocal of a fraction, just switch the numerator and denominator.
Health 2: If you want to find the reciprocal of an integer, you can regard this integer as a fraction with a denominator of 1, and then switch the position of the denominator of the molecule.
The reciprocal of 3: 1 is 1, and 0 has no reciprocal. A method of finding the reciprocal of a number. )
Verb (abbreviation for verb) consolidation exercise
1. Complete the first question in exercise 1 1.
2. practice.
(1) Students finish in books, teachers patrol and invite students to perform on the board. Pay attention to whether the writing format of the students is correct.
(2) Find a student's writing mistakes and communicate with the student.
(3) Show students' mistakes with the booth.
Teacher: Is this ok? (7/ 12= 12/7)
Teacher: Why? To standardize writing, it is necessary to write clearly who is whose reciprocal, or whose reciprocal is who.
3. Complete question 2 of exercise 1 1.
4. Complete question 3 of exercise 1 1.
5. Complete question 4 of exercise 1 1.
Teacher: Please observe the numbers in each group carefully. What did you find?
The deskmates can talk to each other first.
There should be a report:
Health 1: I found from the first group that the reciprocal of the true score is a false score (greater than 1).
Health 2: The reciprocal of a false score greater than 1 is a true score (less than 1).
Health 3: The reciprocal of the score is an integer.
Health 4: The reciprocal of a non-zero integer is a fraction.
Verb (abbreviation of verb) class summary
What did we learn today? What did you get?
Understanding the reciprocal part, like the transitional part in the article, is a link between the preceding and the following, and it is the necessary basis for learning the next chapter of fractional division. Please practice carefully after class, master the meaning of reciprocal and the basic method of finding the reciprocal of a number, so as to prepare for the next chapter.
Understanding Reciprocal Teaching Design Part III Teaching Purpose:
1, so that students can perceive the meaning of reciprocal, master the method of finding reciprocal and learn the correct expression of reciprocal.
2. Cultivate students' observation ability, mathematical language expression ability and the ability to discover laws.
Teaching emphasis: the method of finding the reciprocal of a number.
Teaching difficulties: understand the meaning of reciprocal and master the method of finding the reciprocal of a number.
Teaching preparation: teaching CD
Pre-class research: self-study textbook P50;
(1) What is reciprocal? Which words are more important in the concept of equivalence? Tell me how you understand it.
(2) Observe the two reciprocal numbers and tell me what happened to the positions of their numerator and denominator.
(3) Does 0 have a reciprocal? Why?
Teaching process:
First, the error analysis in the homework.
Second, the reciprocal of academic performance:
1。 Example 7
Students fill in their books and check them by name.
Teacher's blackboard: ×= 1×= 1×= 1.
2. Can you imitate it and give more examples?
The students answered, and the teacher wrote on the blackboard.
3. Observe the blackboard and reveal the meaning of reciprocal: the product is 1, and the two numbers are reciprocal. (blackboard writing)
Sum is reciprocal, or reciprocal is, yes, reciprocal.
Ask the students to imitate and say the other two formulas. Who is equal to whom? Who is the reciprocal of who?
4. Can you find the reciprocal of sum respectively?
Students sit at the same table and discuss how to find a way.
5. Observe the two reciprocal numbers above. Students discuss how to find the reciprocal of scores.
Naming communication method: to find the reciprocal of a fraction, just switch its numerator and denominator.
6. Cooperative exercise: One of the two students at the same table says a score, and the other student says the reciprocal of the score, and exchange exercises.
Third, learn the reciprocal of an integer:
1, the computer shows: What is the reciprocal of 5? What about the reciprocal of 1?
Students talk to their deskmates and exchange names.
Method 1: When finding the reciprocal of 5, you can regard 5 as first, so its reciprocal is;
Method 2: Think about 5×()= 1 and get the result.
2. What is the reciprocal of1? ( 1)
Is there a reciprocal of 3 and 0? Why? (No product of a number multiplied by zero is 1, so 0 has no reciprocal. )
4。 Fractions and integers (except 0) have their reciprocal. Do decimals have reciprocal numbers? Can you express your opinion?
What is the reciprocal of 0.250. 1? How to ask?
5。 Practice the reciprocal of demonstration writing: the reciprocal of is, and cannot be written as =.
Students complete independently and check collectively.
Fourth, consolidate exercises:
1, exercise 10, question 1
After the students finish the collective revision independently, talk about the train of thought, the significance of reciprocal and the method of finding reciprocal.
2. Exercise 10, question 2
Students look for it independently first, then communicate, and pay attention to the whole sentence. Example: and 4 are reciprocal.
3. Exercise 10, question 3
Students fill in the blanks independently and then correct them collectively.
4. Exercise 10, question 4
Write the reciprocal of each set of numbers. Tell me what you found.
The 1 group is all true scores, and the reciprocal is all false scores greater than 1.
The second group has a false score greater than 1, and the reciprocal is true.
The third group is the decimal unit of the fraction, and the reciprocal is an integer.
The fourth group, all natural numbers are non-zero, and the reciprocal is a fraction.
5. Exercise 10, question 5:
Students do it independently. How to find the surface area and volume of a cube.
6. Exercise 10, question 6
After the students solve the problem independently, analyze it.
Different meanings of scores in two questions:
The first question is to calculate the multiplication relation of two quantities.
The second question is expressed in tons, and how many tons are left is calculated by subtraction.
Step 7 think about the problem
Students discuss in groups and exchange names.
According to the length of the steel pipe, there are three situations to consider:
(1) If the lengths of steel pipes are both 1 m, then two steel pipes are used as much;
(2) If the length of the steel pipe is less than 1m, the length of the first pipe is longer;
(3) If the length of the steel pipe is greater than 1m, the length for the second pipe is longer.
Verb (abbreviation of verb) course summary:
Today, we learned a new relationship between two numbers-reciprocal relationship. Who will tell us the definition of reciprocity? How to find the reciprocal of a number? What is the reciprocal of 1? Is there a countdown of 0?