The law of product change is the third part of Unit 3, Section 2, Volume 1, Grade 4. This unit is the last knowledge point of integer multiplication in compulsory education. It is taught on the basis that students have mastered the calculation method of multiplying three digits by two digits. This lesson mainly guides students to explore the change of one factor and product when another factor remains unchanged, and summarizes the change law of product from it. Through the exploration of this process, students can not only understand that the product of the multiplication of two numbers changes with the change of a factor, but also realize that things are closely related and cultivate the ability of migration and analogy.

The design of this example is divided into three levels:

1. research question: the textbook designs two sets of multiplication formulas which are both related and different, and guides students to independently discover the law of product change caused by factor change on the basis of observation, calculation and comparison.

2. Inductive method: guide students to widely communicate the laws they found, and try to explain the changing laws of products in concise language on the basis of group communication.

3. Verification Law: Guide students to give another example to verify the correctness of the product change law.

4. Use the law: guide students to use the law to solve practical problems.

Second, student analysis

1. Students' existing knowledge base: Students have multiplication as the premise and can calculate accurately and skillfully.

2. Students already have the experience of life and learning content: Grade four students are no strangers to area calculation, and they are well prepared for basic knowledge and skills.

There may be many situations when students learn these contents, so teachers should give students more time to think.

4. The application of group cooperative learning in the process of exploration must be based on independent thinking.

5. My thinking: Students are the main body of learning activities. In the design of this course, the basic idea of letting students actively participate in learning has been reflected from beginning to end. Let the students draw a conclusion through observation and comparative reasoning. And how new knowledge and old knowledge are transformed, and how to transform each other, which pushes students to the front desk and lets them deduce the results themselves and solve practical problems.

Three. Learning objectives:

Knowledge and skills:

1, let students explore and master the changing law of one factor being constant, another factor being multiplied by (or divided by) several, and the product being multiplied by (or divided by) several; This law can be properly applied to practical calculation and solving simple practical problems.

2. Make students experience the discovery process of product change law and get preliminary exploration and discovery.

Basic methods and experiences of mathematical laws.

3. Cultivate students' dialectical thinking of observing things from both positive and negative aspects.

Teaching objectives:

1, it is very interesting for students to experience the discovery process of the law of product change and feel the law in mathematics.

2. Try to express the changing law of products in concise language and cultivate the ability of generalization and expression.

3. Get the general methods and experience of exploring laws and develop students' reasoning ability.

4. Cultivate students' inquiry ability, cooperation and communication ability and induction and summary ability in the learning process, and initially cultivate students' rigorous academic attitude.

Emphasis and difficulty in teaching:

Master the changing law of products.

Process and method:

By participating in learning activities, we can cultivate students' ability of inquiry, cooperation and communication, and their ability of induction and summary, so that students can have the fun of success and enhance their interest in learning and self-confidence.

Emotional attitudes and values:

It is interesting for students to experience the discovery process of product change law and feel the law in teaching.

Four. Teaching process:

Teaching preparation: multimedia courseware

teaching process

First of all, introduce.

We have encountered many problems when we found laws in mathematics. We can use the discovered laws to solve problems and simplify complex problems. Today, we will explore the changing law of products together.

Second, explore new knowledge.

(A) create a situation

In response to the school's call to "save pocket money and hold hands with good friends", the students donated their pocket money to buy some books and school supplies for the children in Hope Primary School.

(2) Explain the problem

Please help us figure out how much it costs to buy two boxes of art paint at 6 yuan each. 20 boxes. What about 200 boxes?

(3) Study the problem and find the law.

1, column calculation

6 × 2= 12

6 × 20= 120

6 × 200= 1200

2, very good! Students, please observe each group of formulas carefully. Can you write two more formulas according to the characteristics of this group of formulas? Just try it. Students write independently.

(D) Self-study and explore new knowledge

1. Now, please share your formulas with each other in groups and tell me what you think.

2. (Report to the first group first) Who will introduce this set of formulas? How to write next? The students said that the first set of formulas they wrote. Did you write that? You must have found the' law' of this set of formulas by writing so correctly. Who can elaborate on the characteristics of this set of formulas we found?

Teacher's guidance: Just now, in this set of formulas, students found that one factor is constant, another factor is multiplied by 10, and the product is also multiplied by 10. If you are allowed to continue writing, can you write it again?

3. Guess, if one factor is constant and another factor is multiplied by 5, what will happen to the product?

Please write a set of such formulas to verify. The students finished writing the report.

What if you multiply it by 30? What if I multiply it by 100?

4. Can you try to sum up these laws we found in one sentence?

We recorded what we just found: (on the blackboard) If one factor remains the same, the product will be multiplied by another factor.

5. Practice with the discovered rules.

(5), continue to explore and show the problem:

(1) How much is a big bag of washing powder, one bag of 20 yuan, and four bags of * * *?

(2) How much is the bagged washing powder per bag 10 yuan, and 4 bags of * * *?

(3) How much is a small bag of washing powder, each bag of 5 yuan, and 4 bags of a * * *?

Students' oral formulation and calculation:

20 × 4=80

10 × 4=40

5 × 4=20

(Observe the second set of formulas) That's how students like thinking. You must have found the characteristics of the second set of formulas, too? Who will say something?

Students, let's look at this set of formulas again. We find that one factor is constant, another factor is divided by 2, and the product is also divided by 2. Can you boldly guess what kind of rules will be drawn here?

Blackboard: One factor is constant, another factor is divided by several, and the product is also divided by several.

According to the law we found, if one factor is constant and the other factor is divided by 5, what will happen to the product? Someone has come up with a formula to test our guess!

(6) summarize the law:

Teacher: I find that we have given many examples, and there is indeed a law that students have just talked about. Who can describe this law completely?

Talk to each other at the same table. The teacher finished writing on the blackboard according to the students' answers:

One factor is constant, another factor is multiplied (or divided), and the product is also multiplied (or divided).

Fourth, use the law to do the problem.

Chapter 2: Analysis of product change law and teaching design content;

"The law of product change" is the teaching content of Unit 4 in the first volume of Grade Four. It is necessary to review and sort out the arithmetic and algorithm of integer multiplication, make some calculations simple by using the law, summarize and sort out the quantitative relationship of multiplication operation, and fully experience the process of solving some practical problems by using the corresponding quantitative relationship. This lesson mainly guides students to explore the changes of products when one factor and another factor remain unchanged, and summarizes the laws of product changes. Through the exploration of this process, students can not only understand that the product of the multiplication of two numbers changes with the change of a factor, but also realize that things are closely related and cultivate the ability of migration and analogy.

Analysis of learning situation

1. Students' existing knowledge base: Students have multiplication as the premise and can calculate accurately and skillfully.

2. Students already have the experience of life and learning content: Grade four students are no strangers to area calculation, and they are well prepared for basic knowledge and skills.

There may be many situations when students learn these contents, so teachers should give students more time to think.

4. The application of group cooperative learning in the process of exploration must be based on independent thinking.

My thinking: students are the main body of learning activities. In the design of this course, the basic idea of letting students actively participate in learning has been reflected from beginning to end. Let the students draw a conclusion through observation and comparative reasoning. How to transform new knowledge and old knowledge into each other, but also push students to the front desk, let them deduce the results themselves and solve practical problems.

Teaching idea

The teaching focus of the course "Product Change Law" is the discovery process of product change law, trying to express the product change law in concise language and cultivate the ability of generalization and expression. And can use the law to solve practical problems.

In teaching, I designed the following three links.

1. Discovery: In teaching, I first show a set of multiplication formulas, in which one factor is unchanged and the other factor has changed, so how does the product change and does it change regularly? Let students discover the changing law of products through independent thinking, group discussion and classroom communication, and explore the methods to study the changing law of products.

2. Test: On the basis of finding the law of product change, let students think about whether other multiplication formulas have such a law. Then verify the law in another topic.

Usage: Solve simple practical problems according to the changing law of products.

Through such steps, let students feel that mathematics research should be rigorous and cultivate their rigorous attitude towards mathematics learning.

Knowledge and skills:

1, let students experience the discovery process of product change law.

Try to express the changing law of products in concise language, and cultivate students' generalization and expression ability.

3. Get the general methods and experience of exploring laws and develop students' reasoning ability.

Process and method:

By participating in learning activities, we can cultivate students' ability of inquiry, cooperation and communication, and their ability of induction and summary, so that students can have the fun of success and enhance their interest in learning and self-confidence.

Emotional attitudes and values:

It is interesting for students to experience the discovery process of product change law and feel the law in teaching.

teaching process

First, create situations and introduce new lessons.

Students, today, Miss Wang has a math class with you. Are the students happy? Let's welcome Mr. Wang with warm applause. Thank you, alas, how many times did you applaud the teacher just now? (Remember to be a conscientious person in the future), all of you stand up. Look, so many teachers come to our class today. Let's give them the warmest applause. Please sit down. How many times did you clap the teachers this time? Listen up, class. The teacher asked questions. According to this calculation, how many times did the two students clap their hands? (Who can help the teacher with the table calculation), 20 students? 200 classmates?

8×2= 16 (below)

8×20= 160 (below)

8×200= 1600 (below)

What are the formulas for these three questions? What is the number before the multiplication sign in the multiplication formula? The number after the multiplication sign is also called a factor? Is the equal sign followed by the product? Students, has the product of these three multiplication formulas changed? Guess who is involved in the product change? Yes, there is a secret law between the change of products and elements. What is this? Students want to know? So today, in this class, we are going to learn the changing law of … products (blackboard writing topic).

Second, explore the law through independent cooperation.

1, students, sit still and look at the blackboard with your eyes open. Please observe carefully with a mathematical eye.

What kind of mathematical problems will you find after three multiplication formulas?

(One factor hasn't changed, another factor is getting bigger and bigger, and so is the product. ) Teacher: What a group of observant children.

2. So how does the product get bigger as the factor gets bigger? Think independently first, and then share your thoughts in the group. In order to facilitate the study, three formulas can be marked with serial numbers. )

One factor is unchanged, and the other factor is multiplied by the product. Son, the teacher had a whim. Is this discovery a universal law? Can you make a bold guess in other multiplication formulas? Don't worry, mathematicians generally don't rush to conclusions when studying mathematical problems. We need to confirm this. How can we verify it? (for example)

3. Guide students to give examples-

Teacher: After verification, have you found this rule? This is a great discovery, so read aloud the rules we found! If one factor remains the same, the product will be multiplied by another factor. )

4. Explore the law that products shrink with the shrinkage of factors.

(1) carding method

Teacher: Students, think back. How do we sum up this rule? Health: Do the math first, carefully observe the change of factor and product, make bold guesses, give examples to verify, and finally verify. (blackboard writing: observe carefully, guess boldly, verify with examples, and sum up the rules)

Teacher: Just now, we summed up this change law of products through careful observation, bold speculation and verification with examples.

Are there any other laws about product changes? Just now, we studied from top to bottom. Please use these learning methods to observe this set of formulas from bottom to top. What will you find? Think for yourself first (about 1 minute) and then say it in the group. We'll choose a little teacher to talk to you later.

(2), application method

After students think independently, communicate in groups.

Teacher: What did you find? How did you find out? Who wants to be a little teacher and show off in front of people? (Explain before naming the board of directors)

Health: Let's look at it from the bottom up and carefully observe what changes have taken place in its factors. (Answer by name) What changes have been made to the product? We can guess that one factor is constant, another factor is divided by a few, and the product is divided by a few. We can confirm that. For example, (), you also gave an example of this in your exercise book. Teacher: I can add one thing. (for example)

Health: Who can tell me what example you gave? (Name) Do you disagree with us? So we can conclude that one factor is constant, another factor is divided by several, and the product is divided by several.

Teacher: The little teacher speaks so methodically. Let's read this rule again! (Courseware demonstration)

Students, do you have any questions you want to say or ask about the rules summarized by the teacher? Teacher: Except 0.

5, summarize the law:

Teacher: I think the students in our class are really good. We discovered two laws in such a short time. Students, mathematics pays attention to simplicity and beauty. Can we combine these two laws into one? Who is it?

Chapter three: the changing law of products;

Qingdao Edition Primary School Mathematics Grade Four Volume I Page 42 and 43 1 class

Teaching objectives:

1, it is very interesting for students to experience the discovery process of the law of product change and feel the law in mathematics.

2. Try to express the changing law of products in concise language and cultivate students' preliminary generalization and expression ability.

3. Get the general methods and experience of exploring laws and develop students' reasoning ability.

4. Cultivate students' inquiry ability, cooperation and communication ability and induction and summary ability in the learning process, and initially cultivate students' rigorous academic attitude.

Teaching emphases and difficulties:

Teaching emphasis: guide students to discover and summarize the rules themselves and then apply them. Teaching difficulty: using the changing law of product to solve problems.

Teaching preparation: courseware statistics

Teaching process:

First, create situations and ask questions.

Courseware demonstration: information window 4. Figure of cleaning the bathing beach.

Qingdao is a beautiful city. In hot summer, the beaches in Qingdao attract thousands of tourists every day. In order to let tourists play on the clean and comfortable beach, the sand screen car is busy every day.

"The sand screen car cleans 80 square meters of beach every minute." According to the information in the picture, what math questions can you ask?

Students can suggest: 5 minutes, 10 minutes, 15 minutes, 30 minutes, 60 minutes. ...

How many square meters of beach can a sand truck clean?

Your questions are all very good! I can solve many problems with a relational expression. Do you know which relational expression to use? (Student answers)

Yes, it is "working efficiency × working time = total workload" and "beach cleaning area per minute × working time of sand screen car = total workload of sand screen car". Now I ask a question, "How does the total work of the sand screen car change?" Can you help me solve it?

Second, autonomous learning and group inquiry

1. Fill in the form (one for each student)

Students complete the form independently.

2. Group activities

The students shared their findings in groups.

In group activities, teachers patrol and guide.

If the group has difficulty in observing the statistical table, the teacher instructs the students to write the calculation formula and observe it again.

80×5=400

80× 10=800

80×30=2400

80×60=4800

Iii. Report exchange and evaluation inquiry

1, class communication-the law that products expand with the expansion of factors.

Tell me how the total workload of sand screen car changes with time.

Students observe from left to right by filling in the form, or from top to bottom by listing the formulas.

Every minute, the area of clean beach remains unchanged, and the total area of clean beach is expanded to several times of the original working time.

So if you use factor, factor and product to represent these three quantities respectively, can you summarize the law you found in one sentence?

Teachers guide students to sum up the law that products expand with the expansion of factors: if one factor remains unchanged and another factor expands several times, the products will expand several times.

2. Students explore the law that products shrink with the contraction of elements.

(1), just now we observed from left to right and found that the product expands with the expansion of the factor. Look at the watch from right to left and compare it with the method of comparative study just now. If one factor remains the same, will the other factor multiply? How do the product and factor change? What did you find? ② Students think independently and then communicate at the same table.

③ Classroom communication:

(4) Summarize the law of discovery (if one factor remains unchanged, the other factor will be reduced to several times, and the product will also be reduced to several times. )

Fourth, abstract generalization, summary and promotion.

Is the law just discovered universal? Generally speaking, it is not easy to draw conclusions when studying mathematical problems. We should give more examples to see if the same situation will happen. If there is a counterexample, we can't regard this discovery as a law. This is the rigorous attitude we should have in studying mathematical problems. Let's verify the law together.

(1) Fill in the blanks with the changing rules of products (courseware demonstration)

2× 18=36 20×4=80

4× 18=( ) 10×4=( )

8× 18=( ) 5×4=( )

(2) Students illustrate the changing law of products with examples.

Tip: Each student writes two groups of formulas. One group has three formulas, one of which represents the change of product expansion with the expansion of a factor, and the other represents the change of product contraction with the contraction of a factor.

(3) Whether the examples of mutual checking at the same table and the change of AC factor and product are consistent with the law we found.

(4) the overall generalization law.

Because many multiplication formulas have such product-variation characteristics, through verification, we find that our guess is correct. What we are exploring today is the changing law of products. Who can talk about this rule?

Group communication "the changing law of products"

Mathematics pays attention to concise and rigorous language. Who can sum up the two laws found above into one in one sentence? (student exchange)

Courseware presentation: one factor remains unchanged, and the other factor expands (or shrinks) to the original multiple.

Verb (abbreviation of verb) consolidates application, expansion and improvement.

Students, today we explored and discovered the "law of product change". Now let's use the law to do a few questions, shall we?

1, basic exercise

Page 43 of the textbook 1

How to calculate the feedback and communication after students complete independently?

2, improve the practice

Question 2 on page 43 of the textbook

Students give feedback and express their thoughts after completing independently.

Can you write two more formulas according to the characteristics of this group of formulas?

3. Open practice

Question 3 on page 43 of the textbook

Solve problems in life with "product change law".