Cognitive teaching design of the reciprocal of the first volume of sixth grade mathematics

Understanding the reciprocal of the sixth grade mathematics teaching design article 1 This part is taught on the basis of learning fractional multiplication, mainly to prepare for later learning fractional division, because the calculation method of dividing a number by a fraction comes down to multiplying the reciprocal of this number.

This part arranges two examples, the significance of teaching reciprocal and the method of finding reciprocal.

1. Example 1.

Let the students know the meaning of reciprocal, arrange several groups of multiplication formulas with the product of 1, find out their * * * similarity through students' observation and discussion, and deduce the definition of reciprocal.

Teaching suggestion

(1) Let the students fully observe the discussion and find out the similarities and differences of the formulas.

(2) After giving the definition of reciprocal, discuss the characteristics of reciprocal with the definition, especially understand the meaning of "reciprocal", that is, reciprocal represents the relationship between two numbers, which are interdependent and reciprocal cannot exist alone. It can also be combined with judgment questions, such as "73 is the reciprocal", right? Deepen students' understanding.

(3) Students can say several groups of reciprocal according to their own understanding of the meaning of reciprocal to see if they really understand and master it.

2. Example 2.

Here is a method to find the reciprocal of picture teaching. The textbook first arranges the activities of finding the countdown, and initially experiences the method of finding the countdown. Then summarize the method of finding the reciprocal, which is divided into two situations. Finding the reciprocal of a fraction is the position of the numerator and denominator of the exchange fraction; To find the reciprocal of an integer is to regard the integer as a fraction with a numerator of 1, and then exchange the positions of the numerator and denominator. Finally, the problem of reciprocal of 1 and 0 is put forward, so that students can think and discuss and draw a conclusion.

Teaching suggestion

(1) exchange discussion methods by looking for reciprocal activities.

(2) Combining the data given in the textbook, discuss the inductive method. How to find its reciprocal? How to find its reciprocal?

(3) Take out the reciprocal, leaving 1 and 0. Question: Do they count down? What's the reciprocal? Organize students to discuss and give reasons. On the basis of discussion, it is concluded that the reciprocal of 1× 1= 1 is 1 according to the meaning of reciprocal; Because 0 multiplied by any number is 0, 0 has no reciprocal.

(4) Finish "doing one thing" and check the understanding of the meaning of reciprocal and the mastery of the method of finding reciprocal.

3. Explanations of some exercises in Exercise 6 and teaching suggestions.

The second question is an activity. You can communicate with each other at the same table. One person says a number, the other says its reciprocal, and then exchange words.

The third question deepens the understanding of reciprocity through the activity of judging right and wrong.

The question (1) is correct according to the meaning of the reciprocal.

In question (2), two numbers are reciprocal, not three, so it is wrong.

Question (3), 0 has no reciprocal, so it is wrong.

Question (4), not necessarily. The reciprocal of a false score greater than 1 must be less than this false score, while the reciprocal of a true score is greater than this true score.

Completion and review

Organize and review the learning content of this unit. It is divided into two parts. The first part reviews the main learning contents of this unit in the form of knowledge collation to guide the review; The second part arranges exercises.

Specific content description and teaching suggestions

recitation

Question 1, review the calculation method of fractional multiplication, and put forward three questions: fractional multiplication by integer, integer multiplication by fraction, and fractional multiplication by fraction. Students can finish it independently first, then talk about the calculation method of each problem and recall the calculation method of fractional multiplication. Find out where the mistakes are, and then complete 1, 2, 3 in Exercise 7.

Question 2: Make a simple calculation by using the law of multiplication. Let the students finish it independently first, and then talk about what algorithm to use. Then complete question 4 in exercise 7.

Question 3, solve the problem. Question (1), what is the score of a number? Let the students draw a line diagram to show the quantitative relationship, solve the problem in a row, and then talk about the idea of solving the problem. Question (2) is a slightly complicated question, that is, what is the score of a number. Students are also required to draw a line diagram to express the meaning of the question, then answer it continuously and exchange ideas of different methods. Then complete questions 5 and 6 in Exercise 7.

Question 4: Let's talk about what is reciprocal first, then find the reciprocal of each number, and talk about the method of finding it. Then complete Exercise 7, Question 7.

Understanding of the reciprocal of the first volume of sixth grade mathematics;

1. Make students 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 focus:

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.

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. Look at the top two reciprocal numbers. 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 this 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 countdown to 3.0? Why? (No product of a number multiplied by zero is 1, so 0 has no reciprocal. )

Fractions and integers (except 0) have their reciprocal. Do decimals have reciprocal numbers? Can you express your opinion?

What is the reciprocal of 0.25 0. 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?

The understanding of the reciprocal of the first volume of the sixth grade mathematics teaching design 3 teaching material analysis:

This part is based on the education of fractional multiplication, mainly to prepare for the later study of fractional division, because the calculation method of dividing a number by a fraction comes down to multiplying the reciprocal of this number. Through two examples, this part mainly teaches the meaning of reciprocal and the method of finding reciprocal.

Design concept:

This course emphasizes that starting from students' learning interest, life experience and cognitive level, through experience, practice, participation, communication and cooperation, students can learn to communicate, evaluate each other and experience the process of knowledge construction in the process of cooperative learning. When finding the reciprocal of a number, let students learn first and then teach, stimulate their enthusiasm for learning, and cultivate their ability of observation, induction, reasoning and generalization.

Teaching objectives:

Make students know the meaning of reciprocal through inquiry activities and master the method of finding reciprocal.

Ability goal:

Cultivate students' abilities of observation, induction, conjecture, reasoning and generalization.

Emotional goals:

Provide appropriate problem situations to stimulate students' interest and enthusiasm in learning. Let students experience the happiness of success in exploration and cultivate their innovative consciousness and scientific spirit.

Teaching focus:

Make students know the meaning of reciprocal through inquiry activities and master the method of finding reciprocal.

Teaching difficulties:

Make students know the meaning of reciprocal through inquiry activities and master the method of finding reciprocal.

Teaching process:

First, talk before class and break through the difficulties.

1, conversation-contains "two" and breaks through "interaction"

Teacher: The teacher also wants to be friends with the students in Class 6 (1). Would you like to be friends? That teacher is your … (friend), and you are the teacher's … (friend). You and the teacher are friends. (refers to writing on the blackboard: mutual)

Second, introduce topics and guide questions.

Teacher: Actually, we have a similar situation in math. In today's class, let's look for similar problems in mathematics. Uncover the topic-(blackboard writing: understanding of reciprocal)

Teacher: What's wrong with your mind when you see the new mathematical term "reciprocal"?

Default: What is reciprocal? How to find the reciprocal? ……

Let's discuss these problems together in this class.

Third, create an activity scene and understand the concept-"What is the reciprocal"

Teacher: We just learned fractional multiplication. The teacher wants to know how you have mastered it. Please look at the calculation.

1, understand the "what" in the classification.

①5/8×8/5②0。 25×4③3/4+ 1/4

④ 1。 6—3/5⑤ 13/7×7/ 13⑥3/2×6/5×5/9

What did you find after the calculation?

Teacher: If you please divide these six formulas into two categories, how are you going to divide them?

Student report: The product is 1. ) [If applicable: the product is 1]

Summary: Different classification criteria lead to different answers. Today, we will study this formula.

Teacher: Are there any similarities between these three formulas?

Default: the product is 1.

2. Give examples to understand "how to do it"

Teacher: Can you give another example like this?

Can you give examples different from these formulas? Can you give different formulas?

Summary: Like the examples just cited, they all have the same characteristics as * * *! (The product is 1) In mathematics, "the product is 1 and the two numbers are reciprocal". If 5/8×8/5= 1, we can say that 5/8 and 8/5 are reciprocal. What else can we say? For example, we express the relationship between friends.

The reciprocal of 5/8 is 8/5, and the reciprocal of 8/5 is 5/8.

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.

②0。 What can be said about the relationship between 25×4? Please tell your deskmate.

(Student activities)

⑤ 13/7×7/ 13

3, in-depth understanding of speculation

Teacher: Can you say that 3/4 and 1/4 are reciprocal? Why?

Teacher: Can you say that 3/2, 6/5 and 5/9 are reciprocal? Why?

Fourth, use concepts and exploration methods-"how to find the reciprocal"

Transition: Everyone understands the reciprocal very well, so I'll give you a number. Can you find its reciprocal?

(Projection, Example 2)

1, find the reciprocal of the following number.

3/5267/20/6 10/250

Students try.

Reward communication.

Teacher: Which numbers do you like to find the reciprocal of? Why?

Default value:

Health 1: I like to find the reciprocal of a fraction best, because the product of the numerator and denominator of a fraction is 1 in turn. Very simple, so I like begging.

Health 2: I like to find the reciprocal of 1 best, because the reciprocal of 1 can be written as a fraction, the numerator and denominator are reversed, and the reciprocal of 1 is 1. Very interesting, so I like to find the reciprocal of 1 Health: Do the calculations.

Teacher: Which number do you like the reciprocal least?

Default value:

1: I don't like to find the reciprocal of 0, because if you write 0 as a fraction, if you change the position of the numerator and denominator, 0 can't be used as the denominator (0 can't be divisible). There seems to be no countdown to 0.

Health 2: In addition, 0 multiplied by any number equals 0, and it is not equal to 1. 0 is definitely not the countdown.

Teacher: Then how do you find the reciprocal of 26?

How do you find the reciprocal of the decimal?

Summary: 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 number, just switch the numerator and denominator.

2. Emphasize the writing format

Teacher: Just now, the teacher saw some students write like this, is that ok? (3/5=5/3)

Summary: The two reciprocal numbers are not equal (except 1). When writing, you should write clearly who is whose reciprocal, or whose reciprocal is who, just like what the teacher wrote on the blackboard.

Let's talk about the reciprocal of each group number first, then see what you can find.

The reciprocal of (1)3/4 is () (2) The reciprocal of 9/7 is ().

The reciprocal of 2/5 is (), and the reciprocal of 10/3 is ().

The reciprocal of 4/7 is (), and the reciprocal of 6/5 is ()

(3) The reciprocal of1/3 is (). (4) The reciprocal of 3 is ().

The reciprocal of110 is (), and the reciprocal of 9 is ().

The reciprocal of113 is () and the reciprocal of 14 is ().

Ask the students to say the reciprocal of each number.

Please observe carefully and see what you can find from it. The more you find, the better.

Teacher: The groups can communicate with each other first.

Report:

Default value:

Health 1: I found from the first group that the reciprocal of the true score is false.

Health 2: I found out from the second group whether the reciprocal of the false score is true or false.

Health 3: The reciprocal of true score is less than 1, and the reciprocal of false score is greater than 1.

3. Fill in the blanks:

7×()= 15/2×()=()×0。 25=0。 17×()= 1

Understanding of the reciprocal of the first volume of sixth grade mathematics;

1, make students understand the meaning of reciprocal and master the method of finding reciprocal through inquiry activities.

2. Cultivate students' abilities of observation, induction, reasoning and generalization.

teaching process

First, create an activity scene and introduce concepts.

Give a set of formulas for example 1, and carry out group activities: calculation and search. What are the characteristics of this set of formulas?

Group report and communication. (Through calculation, it is found that the product of each formula is 1. Through observation, it is found that the positions of the numerator and denominator of the multiplied two fractions are reversed ...)

Teacher: The students found that the numerator and denominator of the two fractions in each formula were just reversed, so we called these two fractions "reciprocal".

Let the students read: "Countdown".

Indicate the meaning of reciprocal: the product is 1, and the two numbers are reciprocal.

Second, explore and discuss, in-depth understanding

Let the students talk about their understanding of reciprocal.

Q: What does "mutual cooperation" mean? (reciprocal refers to the relationship between two numbers, which are interdependent. A number cannot be called reciprocal. )

What's wrong with the following sentence? How to describe it.

Because 3/4×4/3= 1, 3/4 is the reciprocal, and 4/3 is the reciprocal.

Third, use concepts and exploration methods.

Example 2, which two numbers are reciprocal?

Report the search results and tell us how to find it.

1, see if the product of two fractions is1;

2. See if the numerator and denominator of the two fractions are reversed respectively.

Which is faster to discuss the two methods? (The second method can be observed directly. )

Summarize the method of finding the reciprocal through concrete examples.

(1) Find the reciprocal of a fraction: swap the positions of the numerator and denominator.

Example:

(2) Find the reciprocal of an integer: first treat the integer as a fraction with the denominator of 1, and then exchange the positions of the numerator and denominator.

Example:

Fourth, show special cases and understand them deeply.

Take a look, which data in Example 2 did not find the reciprocal? ( 1,0)

Question: Are 1 and 0 reciprocal? If so, how much?

Group discussion and report.

The reciprocal of 1, 1.

Because 1× 1= 1, according to "two numbers whose product is 1 are reciprocal", the reciprocal of 1 is 1.

It can also be deduced as follows:

The reciprocal of 1 is 1.

2. It is about the reciprocal of 0.

Since 0 multiplied by any number is not equal to 1, 0 has no reciprocal.

It can also be deduced as follows:

The denominator cannot be 0, so 0 has no reciprocal.

Verb (abbreviation for verb) consolidation exercise

1, finish "doing". Do it independently first, and then communicate with the class.

2. Exercise 6, question 3.

Show the problems one by one with multimedia or projection. Students judge and explain the reasons.

3. Interaction at the same table (Exercise 6, Question 2).

Abstract of intransitive verbs

What did you learn today?

What is reciprocal? How to find the reciprocal of a number?

Understanding of the reciprocal of the first volume of sixth grade mathematics;

1, through practical activities such as experience, research and analogy, guide students to understand the meaning of reciprocal, let students experience the process of asking questions, exploring questions and applying knowledge, and independently summarize the method of finding reciprocal.

2. Cultivate students' habit of cooperation and communication through cooperative activities.

3. Cultivate students' awareness of independent learning and innovation through students' independent implementation of practical programs.

Teaching focus:

Understand the meaning of reciprocal and how to find reciprocal. Understand the meaning of reciprocal and master the method of finding reciprocal.

Teaching difficulties:

Master the method of finding the reciprocal.

Teaching aid preparation:

Multimedia courseware.

Teaching process:

First, the old knowledge bedding (courseware display)

1, oral calculation:

( 1)× × 6× ×40

(2)××3××80

Today, let's study "countdown" and see what their secret is. Exhibition theme: understanding of reciprocity

Second, new funding.

1, courseware shows knowledge objectives:

(1) What is reciprocal? How to understand "reciprocity"?

(2) How to find the reciprocal of a number?

(3) Is there a reciprocal between 0 and 1? What is this?

2. The significance of teaching reciprocity.

(1) Students teach themselves, form discussion groups to conduct research, and then report to the whole class.

(2) Students report research results: the product is 1, and the two numbers are reciprocal.

(3) Prompt students to know what "interaction" means. (reciprocal refers to the relationship between two numbers, which are interdependent, and a number cannot be called reciprocal)

(3) What are the characteristics of two reciprocal numbers? (The numerator and denominator of two numbers are just reversed)

3. Teach the method of finding the reciprocal.

(1) Write reciprocal: To find the reciprocal of a fraction, just switch the numerator (the number 3 flashes to the denominator of the fraction) and denominator (the number 5 flashes to the numerator of the fraction).

(2) Write the reciprocal of 6: First, consider the integer as a fraction with the denominator of 1, and then exchange the positions of the numerator and denominator.

4, teaching special cases, in-depth understanding

(1) 1 Is there a countdown? How to understand? (Because 1× 1 = 1, according to "two numbers whose product is 1 are reciprocal", the reciprocal of 1 is 1. )

(2) Is there a countdown to 0? Why? (Because 0 multiplied by any number is not equal to 1, 0 has no reciprocal. )

5, the same table means equivalence, and the teacher patrols.

Third, in-class evaluation

1, Exercise 6, Question 2:

2. Discrimination exercise: Exercise 6, Question 3, "True or False".

3. Open training.

3/5×( )=( )×4/7=( )×5= 1/3×( )= 1

Fourth, class summary.

How much do you already know about reciprocity?

What do you associate with it?

What else do you want to know?

Design intent

The content of the penultimate comprehension lesson is relatively simple, and students can fully understand the content of this lesson through preview and self-study. According to the characteristics of this class, I let students understand the meaning of "mutual opposition" through self-study and discussion. Among them, some concepts are still key, such as "reciprocity", so I also ask questions and give directions appropriately. As for the method of finding the reciprocal, I also give students independent space to learn examples by themselves and find the reciprocal of a number according to their own understanding and text summary. However, I didn't ignore the special cases of "0" and "1", but gave full play to the guiding role of teachers to help students strengthen their understanding.

Teaching postscript

The eleventh and twelfth lessons: sorting and reviewing.