1. Draw a picture using the life scenes that students are familiar with to help students find the best way to make a phone call.

2. Infiltrate the idea of combining numbers and shapes to cultivate students' consciousness of solving problems with graphics;

3. Further understand the close relationship between mathematics and life and the application of optimization thought in life.

4. Feel the importance of guessing and verifying. Experience the difference between the best in theory and the best in practice.

Teaching emphasis: Understand the various schemes called and optimize the best scheme.

Teaching difficulty: let students discover the hidden law of things through drawing.

First, introduce a conversation

1, Children's Day is coming. To celebrate our festival, the school organized a chorus of 15 people. On Sunday, Miss Li received an urgent notice from the school asking 15 members of the choir to participate in the performance. How should she inform these 15 members as soon as possible? "Students help do something!

2. Students report their ideas. (Instructed by the teacher)

3. Summarize the questions and write on the blackboard.

In order to better study today's question, let's assume that each call takes one minute and every student is at home. How many minutes do you think it will take at least? (Students are free to guess)

Second, explore new knowledge.

Let the students think about the method of notification. Here it is necessary to guide students to say two methods: average grouping and uneven grouping.

Guess: Which method is faster? For example, which is faster, dividing into three groups or dividing into five groups on average? Is it that the more groups you have, the faster you will be? How can we compare which method is the fastest?

1, each student thinks independently, list all the methods you know and compare them. Which method is the best? Think about it. Did you learn anything from the comparison just now?

2, teachers patrol, participate in the discussion, understand the situation.

3. feedback. The students told each other the best method they had found. How many methods did you compare just now? (Design intent: Let students list all the methods, then compare them and go through the process of optimization)

Scheme 1 time-consuming 15 minutes. This must be too slow. How about grouping? Ask students to talk about your plan in groups.

Scheme 2 (1): 5 groups with 3 people in each group (7 minutes).

Scheme 2 (2): 3 groups with 5 people in each group (7 minutes). How do these two schemes compare with your previous guess? Is the more components, the faster? Do you have anything to say? So when guessing, be bold, think up your answer as much as possible, and then verify it. What if the number of people in each component is different? What will happen?

Scheme 2 (3): 4 groups (4, 4, 4, 3) (6 minutes)

Scheme 2 (4): 3 groups (6, 5, 4) (6 minutes)

What's the difference between these two methods and the first two methods? Why is the time shortened? (Every team leader will not be idle) Option 2 (5): 5 groups (5, 4, 3, 2, 1) (5 minutes)

Teachers, team leaders and team members are not idle. How to design the scheme?

Option 3: Tell each other.

Discuss in groups and report the results. (Design intent: It helps to convey the second scheme. When reporting, let the students talk about which schemes they have listed and compared, and which one they think is the best. Only by letting students compare themselves can we realize the process of optimization and let students realize what optimization is all about. Ask students to compare various schemes, and students can easily find the reasons for the optimization of various schemes, from the fact that the group leader is not idle, to the fact that teachers and group leaders are not idle, and then to the fact that teachers, group leaders and team members are not idle when they are notified.

Third, find the law.

This is really a good idea. Have you found any rules in this scheme?

1. Observe the schematic diagram carefully. How many people called in the first minute? How many players and teachers have been notified after the phone call? Besides the teacher, how many students have been notified? What about the second minute? What about the third minute? What did you find? What is the rule of the number of newly notified players every 1 minute?

2. Can you find a way to introduce it to everyone?

Discovery 1: The number of newly notified players per minute is exactly the total number of all notified players and teachers, that is, the number of newly notified players in the nth minute is equal to the total number of notified players and teachers in the previous (n- 1) minutes.

Discovery 2: The total number of all players and teachers notified in the nth minute is a geometric series, and the general formula is an=2n.

Discovery 3: The total number of all players notified in the nth minute is (2n- 1).

Fourth, apply the law.

1. Since everyone has discovered this rule, how many people can be notified in five minutes? What about six or seven minutes?

Organize students to discuss in groups and then report.

The teacher should inform 50 students to come to the school to hold activities. How many minutes does it take to make a phone call?

Five, contact life, expand and extend

Someone said, "If a piece of paper is big enough to be folded in half for 25 times in a row, the height of this pile of paper will exceed the altitude of Hengshan Mountain in Nanyue." Is it true?/You don't say. Can you try to solve it with the knowledge learned in this lesson?

Think about what else in life has multiplied?

Blackboard design: making phone calls

Postscript: Remind students that there is still a problem to be solved in the concrete implementation, that is, designing the order of calls, that is, each player should know how to continue to inform other players after receiving calls. Therefore, this plan also needs to make a schematic diagram of the phone in advance, so that the teacher and each team member can clearly know in what order to inform the following team members after receiving the notice. Only by strictly following the pre-made plan can we save time.

The second part of the fifth grade mathematics "call" teaching plan 2 teaching content: People's Education Edition fifth grade, page 132- 133 "call"

Teaching objectives

Draw pictures by using the familiar life scenes of students to help them find the best way to make phone calls. Further understand the close relationship between mathematics and life and the application of optimization thought in life.

Teaching preparation

Multimedia, cards, theme maps

Teaching process:

First, ask questions.

Today, we learn to make phone calls. Can you make a phone call? Then I'll see if you want to. Miss Li has just received an urgent notice from the school that 15 members of the choir will take part in the performance. How can I inform these 15 members as soon as possible? "Students help do something!

(Teaching presupposition: At this time, students may have the following two situations:

1, notify one by one;

2, help tell) This help tell, how to tell? How many people do you want to tell? Is there no other way? (Design intent: Let students think about the method of notification first. Students should be guided to say two methods: average grouping and uneven grouping. There is a thinking span from average grouping to uneven grouping, and sometimes students dare not or will not think about it. It is necessary to cultivate students' divergent thinking in teaching, which also paves the way for the later optimization scheme. Therefore, let students know that when thinking about methods, they should boldly think about ways to solve problems from different angles, so as to choose the best method from many methods. )

Guess: Which method is faster? For example, which is faster, dividing into three groups or dividing into five groups on average? Is it that the more groups you have, the faster you will be? How can we compare which method is the fastest?

In order to better study today's question, let's assume that each call takes one minute and every student is at home. How many minutes do you think it will take at least? Students can guess freely. Design intention: Guess one is to increase interest, let students have a riddle in their hearts and improve their desire to explore. The second is to make students realize the necessity of verification. )

Second, explore and compare.

1, each student thinks independently, list all the methods you know and compare them. Which method is the best? Think about it. Did you learn anything from the comparison just now?

2, teachers patrol, participate in the discussion, understand the situation.

3. feedback. The students told each other the best method they had found. The teacher took out a magnet according to what the students said. And ask, how many methods did you compare just now? (Design intent: Let students list all the methods, then compare them and go through the process of optimization)

Scheme 1 time-consuming 15 minutes. This must be too slow. How about grouping? Ask students to talk about your plan in groups.

Scheme 2 (1): 5 groups with 3 people in each group (7 minutes).

Scheme 2 (2): 3 groups with 5 people in each group (7 minutes)

How do these two schemes compare with your previous guess? Is the more components, the faster? Do you have anything to say? So when guessing, be bold, think up your answer as much as possible, and then verify it. What if the number of people in each component is different? What will happen?

Scheme 2 (3): 4 groups (4, 4, 4, 3) (6 minutes)

Scheme 2 (4): 3 groups (6, 5, 4) (6 minutes)

What's the difference between these two methods and the first two methods? Why is the time shortened? (Every team leader will not be idle)

Scheme 2 (5): 5 groups (5, 4, 3, 2, 1) (5 minutes)

Teachers, team leaders and team members are not idle. How to design the scheme? Discuss in groups and report the results.

The number of people notified per minute is indicated by pens with different colors. And let the students explain.

(Design intent: It helps to convey the second scheme. When reporting, let the students talk about which schemes they have listed and compared, and which one they think is the best. Only by allowing students to compare themselves can they realize the process of optimization and what optimization is all about. Ask students to compare various schemes, and students can easily get the reasons for the optimization of various schemes, from the fact that the group leader is not idle, to the fact that teachers and group leaders are not idle, and then to the fact that teachers, group leaders and team members are not idle. )

Third, explore the law.

This is really a good idea. Have you found any rules in this scheme?

You did a good job. This classmate's discovery is remarkable. We might as well use the list method to see more clearly.

Show me the empty form first and fill it out while asking. )

What minutes: 1, 2, 3, 4 …

Number of people notified: 1, 2, 4, 8 …

What pattern did you find? (Default: The number of people notified in the first minute is twice that of the previous minute. )

According to this rule, how many people can be notified in the fifth minute? How many people can be notified in the sixth minute?

Notify (3) individuals within two minutes.

Notify seven people in three minutes.

Notify (15) people within 4 minutes.

What pattern did you find? (Default: number of people notified within 2 minutes =2 times 2-1; Number of people notified in 3 minutes =3 times 2-1; Number of people notified in 4 minutes = 4 2 times-1; .....) How many people will be notified in five minutes? How many people are notified in six minutes? How many minutes does it take to notify 50 people like this?

Fourth, the optimization scheme

Students use their intelligence to list so many methods, which one do you like and which one do you think is the best? How can we compare which method is the best?

Blackboard design:

make a telephone call

Scheme 1: Notify one by one

Option 2: Help me out.

(1) was divided into three groups (5, 5, 5)- 7 minutes on average.

(2) Divide into 5 groups (3, 3, 3, 3, 3)- 7 minutes on average.

(3) Divide into 4 groups (4, 4, 4, 3)-6 minutes.

(4) Divide into 3 groups (6, 5, 4)-6 minutes.

(5) Divide into 5 groups (5, 4, 3, 2, 1)-5 minutes.

Mathematics "Call" Teaching Plan III of the second volume of the fifth grade: People's Education Press, the second volume of the fifth grade, page 132- 133 "Call"

Teaching objectives:

1. Draw a picture using the life scenes that students are familiar with to help students find the best way to make a phone call.

2. Infiltrate the idea of combining numbers and shapes to cultivate students' consciousness of solving problems with graphics;

3. Further understand the close relationship between mathematics and life and the application of optimization thought in life. Teaching emphasis: Understand the various schemes called and optimize the best scheme.

Difficulties in teaching: break through the "knowledge-based", let students fully experience the process of solving problems and realize the idea of optimization.

Teaching preparation: magnetic blackboard, magnetic teaching AIDS.

Teaching process:

Teacher xx has just received an urgent notice from the school, asking members of the choir 15 to participate in the performance. How can I inform these 15 members as soon as possible? "Students help do something!

Teaching presupposition: At this time, students may say to call. )

Yes, making a phone call is a quick way, but it is also learned. So what are the math problems on the phone? In this lesson, we will learn math problems on the phone. (blackboard writing: calling)

Second, explore and compare.

1. If it takes 1 minute to inform one player and everyone is at home, how long will it take to inform all 15 players? (15 minutes)

2./kloc-how did you get 0/5 minutes? We can show it with pictures. The teacher demonstrated on the magnetic blackboard.

3. Summary: How about this method? Why slow? (It's too slow, the teacher is informing alone, and others are waiting for the notice, which is very time-consuming.) Is there a faster way? (group notification)

4. Guess, do you think it might be faster to divide into several groups? Students may say three groups, four groups, five groups, etc. ) Let's work in groups and come up with a plan that you think is faster. (The teacher visited the guide, participated in the discussion and got to know the situation. )

5. Report the results.

6. Compared with one notification, how about mass notification? Why save time? (The team leader is playing at the same time)

7. Is there an optimal scheme? Teachers, team leaders and team members are not idle. How to design the scheme? The cooperation in the group is completed, the teacher visits and guides, participates in the discussion and understands the situation. Finally, report the exchange.

Third, explore the law.

This is really a good idea. Have you found any rules in this scheme?

You did a good job. This classmate's discovery is remarkable. We might as well use the list method to see more clearly.

Show me the empty form first and fill it out while asking. )

What minutes: 1, 2, 3, 4

Number of people notified: 1, 2, 4, 8?

Total population: 2,4,8, 16?

What pattern did you find? (Default: The number of people notified in the first minute is twice that of the previous minute. )

According to this rule, how many people can be notified in the fifth minute? How many people can be notified in the sixth minute? Notify (3) individuals within two minutes.

Notify seven people in three minutes.

Notify (15) people within 4 minutes.

What pattern did you find? (Default: number of people notified within 2 minutes =2 times 2-1; Number of people notified in 3 minutes =3 times 2-1; Number of people notified in 4 minutes = 4 2 times-1; How many people will be notified in 5 minutes? How many people are notified in six minutes? How many minutes does it take to notify 50 people like this?

The fourth teaching goal of the fifth grade mathematics "calling" teaching plan;

1. Let students go through the whole process of solving problems by guiding them to seek the "most time-saving telephone" scheme.

2. By drawing and filling in the form, guide students to discover the hidden laws of things and cultivate students' ability of analysis, induction and reasoning.

3. Experience the close relationship between mathematics and life and the application of optimization thought in real life.

Teaching emphasis: explore the best time-saving scheme of "calling" through drawing.

Difficulties in teaching: discover the hidden "calling" law through charts and other means.

Teaching preparation: courseware, title cards, colored pens, round and square magnetic boards.

Teaching process:

First, create a situation

Teacher: Last Sunday, the school had some things to inform some teachers to finish at school. The headmaster asked me and Miss Liu to call seven teachers and inform them to come to school. It takes about 1 minute to inform a teacher. Teacher Liu and I quickly took out the phone and were about to inform, but Teacher Liu said, "Let's play a game! Whoever spends less time will win. " ……

Design intention: The telephone to be taught in this course belongs to the abstract "ideal mode". Therefore, the situation creation should try to avoid the interference of non-mathematical factors. It is suggested to call directly to avoid students discussing the notification methods (e-mail, SMS, broadcast); With the help of students' trust in the reliability of teachers' information transmission, students' doubts about the fidelity of information transmission can be avoided. At the same time, guide students to feel the necessity of saving time by means of competition.

Second, the exploration plan

1, sort out the information.

Teacher: What information did you learn from my introduction just now?

Each person informs seven teachers to come to school. B, inform a teacher that it takes 1 minute. The less time I have to complete the notice, the better.

Design intention: It is an essential ability for students to "simplify" the messy situation and extract information from it. On the one hand, it was trained here; On the other hand, through sorting, let students know what to do and how to do it, so as to prepare for the later exploration.

2. Preliminary perception.

One by one. Show me your plan in the form of pictures.

Teacher: Is it okay to make a phone call like this? Why?

B. discussion.

Teacher: If you want to beat Mr. Liu, the less time you have to complete the notice, the better. Students, help me. What are some good ways to save time?

Teachers should guide students to make their own words clear, or let other students understand their meaning through simple performances.

Design intention: discuss, stimulate thinking, experience time-saving methods in communication, slow down the teaching slope, and lay the foundation for the later design scheme.

2. Open investigation

Teacher: The students helped me think of so many ways so quickly. It is a happy thing for teachers to know you. Students help me design a plan and see how many minutes it takes. Okay？

Current cooperation requirements:

(1) The deskmate cooperates to design the visit plan.

(2) Record the designed scheme on the operation paper.

Teachers patrol, guide students to cooperate, listen to students explain the scheme, and find typical designs.

Design intent: Simplify the complexity, and minimize the requirements for students' cooperation (requirements are also constraints). Because of the lack of rational understanding of calling, students will have more differences of opinion when designing the plan, so they will use a small number of deskmates to cooperate.

3. Comparative analysis

Show some plans and guide students to read.

According to the forms of expression, the schemes designed by students can be divided into the following categories: first, they are expressed in pure words; The second is the combination of graphic and text records; The third kind is represented by symbols.

The teacher showed several schemes expressed in different forms found in the inspection.

Teacher: Which scheme do you like? Tell me what you think!

Guide students to think from a mathematical point of view, optimize the scheme, choose the scheme represented by symbols, and realize mathematicization.

Design intention: in the demonstration and evaluation scheme, guide students to realize that on the basis of clear expression, pursue simplicity of expression and perceive the beauty of simplicity of mathematics.

B, select a scheme for analysis and optimization to form the optimal scheme.

Teacher: Please ask the designer of this scheme to explain it. What do these symbols stand for? Can you show the plan on the blackboard with cards?

Teacher: Did you understand this classmate's plan? It takes me seven minutes to notify one by one, and his plan only takes x minutes. Why is time getting less and less?

Design Intention: How did the time become less? Students think about ways to save time in cognitive conflicts, thus finding that "playing at the same time can save time".

Teacher: Then compare this scheme with Miss Liu, OK?

Teacher: Where else can we save time? How to modify it?

Guide students to optimize and form the best scheme, and sort out the best scheme, and put the people who notify every minute together (as shown above).

Teacher: Is there any plan that takes less time?

Design intention: "Where can I save time" guides students to further optimize the scheme by combining "simultaneous typing". Sort out the best plan, put people who are notified in the same minute together, clear the field, and sort out ideas. "Is there a time-saving plan?" Guide students to reflect on the best scheme and evaluate the scheme with the standard of "not being idle"

C. reflect on "not being idle" and form a comprehensive understanding.

Teacher: Think about it. How many minutes does it take to notify eight people?

Teacher: 1 minute notified one person, two people in the second minute and four people in the third minute. To inform the eighth teacher, it is obvious that there is only one more person. Why does it take a minute?

Design intention: There are two intentions here: first, let students realize that even if it is "free" at the last minute, it is also the most time-saving scheme, and form a comprehensive understanding of the standard of "not free"; Second, the preliminary experience is that the number of people who can be notified within a period of time is an "interval number".

4. organize and summarize.

Teacher: Through the activity just now, we found that there are many different ways to make a phone call. Among these different ways, we found the most time-saving scheme. Now let's review and fill in the form.

Teacher: Does the total number of people who know this news include myself?

Teacher: What will be the total number of people who know the news in the fourth minute? Guess! Why 16 people?

Teacher: What about the fifth minute? What about the sixth minute?

Teacher: What patterns have you found? Think about how to calculate the total number of people who already know the news in the ninth minute. What about the 20 th minute? What about the nth minute?

Teacher: What do you mean by the number of people notified, not including who? How to calculate?

Teacher: What about the nth minute?

Design intention: By reviewing and guessing the process of calling according to the optimal scheme, the law of "number multiplication" is explored and summarized by incomplete induction.

Third, apply the law.

1, combined with the table, teachers and students discuss and answer the following questions together.

A, according to this calculation, how many people can be notified at most in 5 minutes?

B, at this rate, how many minutes will it take to notify 50 people?

C. In this way, the shortest time to notify 33 people is the same as the shortest time to notify how many people?

2. Teacher: I found the best scheme. Can I inform you now? Think about it, what will happen?

Design intention: The three questions are arranged in gradient, and the students' ability to use the law is gradually improved through training. The question of "What will happen" makes students feel that according to the optimal scheme, it is necessary for each participant to know the object he wants to inform and feel the necessity of "preplan".

Fourth, the class summarizes.

1. Review the optimization process and realize the optimization idea.

Teacher: Just now, the students helped the teacher design various schemes. Through thinking about the scheme, we know that we need to "play at the same time and not be idle" to achieve the goal of "saving the most time". Later, we found the best scheme by modifying the scheme. In this process, we keep asking ourselves, is there a more time-saving plan? So as to realize the optimization of the scheme. ...

2. Guide students to reflect on their own gains and experiences.

Teacher: Do you have any thoughts or feelings you want to tell us after learning this lesson?

Fifth, mathematics appreciation.

Teacher: Here, we can see that with the passage of time, the number of people calling has increased exponentially. In fact, in life, many things have multiplied in this way.

Courseware playback: Do you know: Lamian Noodles, Amoeba, origami.

Design intention: In the beautiful music playing, the multiplication phenomenon in life is introduced to enrich students' cognition, realize the expansion from in-class to out-of-class, feel the charm of mathematics, and cultivate a good impression on mathematics.