Simple arrangement and combination teaching plan

Before teaching activities, teachers often need to prepare teaching plans, which are the main basis for implementing teaching and play a vital role. Let's refer to how the lesson plan is written! The following are the simple arrangement and combination of teaching plans I collected for reference only, hoping to help you.

Simple permutation and combination teaching plan 1 background

In order to further improve classroom efficiency and enhance students' learning ability, we should gradually implement the autonomous learning teaching mode of combining mathematics class with "learning ability" to improve the overall quality of young teachers and cultivate their good teaching ability. Our second-grade math group launched a team competition in June of XX, and achieved good results. This lesson plan concentrates the efforts of teachers and the wisdom of group teachers, which can better reflect the mainstream teaching mode of the school and is an excellent case.

Analysis of teaching materials

The content of this section is a simple arrangement and combination of 1 in the first volume of the second grade of mathematics. The thinking method of permutation and combination is widely used, which is the knowledge base for students to learn probability and statistics and a good material for developing students' abstract ability and logical thinking ability. This textbook makes some explorations when infiltrating this mathematical thinking method, and presents it through the simplest examples in students' daily life.

The example 1 in the textbook represents different two-digit numbers through the different arrangement order of two cards, which belongs to arrangement knowledge, but simple arrangement and combination have already had different degrees of contact for junior two students. For example, using 1 and 2 digital cards to arrange two digits, students have mastered it in grade one. For 1, 2, 3, these three numbers are arranged into several double digits, and many students can arrange them without repetition or omission through ordinary puzzle games. In view of these actual situations, when designing this section, the teaching materials were processed according to the age characteristics of students. The whole class insists on starting from the reality and cognition of junior children, taking "feeling mathematics in life" and "experiencing mathematics in life" as teaching concepts, and combining with practical operation activities, let students learn mathematics and experience mathematics in activities.

Teaching objectives

1. Students find out the number of permutations and combinations of the simplest things through observation, experiments and other activities, and initially experience the exploration process of simple permutation and combination laws;

2. Make students learn simple methods of permutation and combination, and train their abilities of observation, analysis and reasoning;

3. Cultivate students' orderly and comprehensive thinking consciousness and form a good habit of cooperating with others through the learning form of group cooperation and inquiry.

Teaching focus

Experience the process of exploring the arrangement and combination of simple things.

Teaching difficulties

Understand the difference between arrangement and combination of simple things.

Teaching preparation

Multimedia and digital cards. New word cards about Beijing scenery.

Preview before class

Preview page 99 of the math book and think about the following questions.

1, which two digits can be put out with 1 and 2?

2. 1, 2, 3, which two digits can be released? You can start writing.

3. think about it: how to put it, what to put first, and then what to put? Is there any good way to avoid omission and repetition?

teaching process

1, cooperative inquiry arrangement

Teacher: Students, please see that this is the wide-angle paradise of mathematics. There are so many introductory games prepared for us in the wide angle of mathematics. Do you dare to have a try? (Not afraid) You are really brave good children. Let's create the first layer first.

(Show: How many different two digits can be put in the digital card 1, 2, 3? )

Teacher: First, how many different two-digit numbers can be put in the digital card 1, 2, 3?

Health report. Right? Let's verify it and listen to the requirements.

Cooperate at the same table. One person puts the digital card, and the other person records the numbers. Write it and do it right away. See which table fits well and quickly.

Practice, teacher patrol.

Give feedback and report different postures and ideas.

Disordered report → correct report → comparative method → students' speaking method → teacher's blackboard writing → naming.

Teacher: Please read the two numbers you wrote (wrong order → correct, teacher's blackboard) and compare whose is more comprehensive? (asking other answers), why is XX student not completely right and this student so accurate? Does he have any tricks? Answer the teacher's digital board demonstration and write it on the blackboard.

Teacher: Who can give this method a name?

Who else can introduce you?

In this way, because of the different positions of numbers, different two-digit numbers are combined, which is mathematically called permutation.

Teacher: Everyone spells six different two-digit numbers in various ways. It's amazing! When we arrange numbers in the future, we must follow certain rules if we want to avoid repetition and omission. Pass the customs smoothly and enter the next level

2. Perceptual combination

Teacher: Students, the second question is: If three people shake hands, every two people shake hands once, how many times will three people shake hands?

Teacher: Look, everyone, I am shaking hands with him and he is shaking hands with me. No matter how our position changes, as long as we don't let go of our hands, the two of us only shook hands once.

How many times did the three men shake hands? As a group, the group leader records the number of times, and the other three people demonstrate how many times two people shake hands, and how many times three people shake hands?

Teacher: Two people shake hands once and three people shake hands three times.

(The blackboard shows the handshake process.)

3. Comparative thinking-pursuing the essence

Teacher: Now the teacher has a question. When arranging digital cards, you can put six numbers with three numbers, but when shaking hands, three students can only shake them three times, all of which are three. Why is the result different?

Conclusion: The pendulum number is related to the order, but the handshake has nothing to do with the order.

Swing can change places, not shake hands.

Self-examination/introspection

This part embodies two characteristics.

1, presupposing effective problems is the key to mathematical thinking.

"Thinking" originates from "problem". In order for children to obtain all-round development of knowledge, methods, abilities and thinking through "problem solving", we must first have a good "problem". Because the formation of students' mathematical thinking is the process of thinking about and solving these problems. In this section, before each activity, the teacher created an interesting and practical question for the students: "How many two digits can be compiled from the three numbers 1, 2 and 3?" "Three people shake hands with each other every two people. How many times does a * * * have to shake hands?" Only in the face of such good "problems" can students consciously and wholeheartedly devote themselves to solving the problems, and can they describe and explain the conclusions through the analysis and comparison of these problems and the observation and understanding of these laws. And this process is the process that students form mathematical thinking.

2. Gradually realize the necessity of orderly thinking.

Orderly thinking has a wide range of uses in daily life, and it is more important for students to gradually realize the necessity of orderly thinking through learning. Use the three numbers 1, 2, 3 to make up a few two-digit numbers, so that students can guess the numbers naturally and actively, resulting in the problem of how to think, without repetition or omission, thus stimulating students' interest in learning. Then through students' independent thinking, "write (swing) two digits with 1, 2, 3", guide students to choose different methods to explore new knowledge according to their actual situation, respect students' personality differences, make each student develop completely freely on the original basis, and initially realize orderly writing (swing); Tell me about it. Tell me again how you wrote it. What's so good about it? Problems, such as prompting students to observe and discover, and promoting students' understanding and understanding of their hidden mathematical thoughts; Finally, through classroom communication, guide students to obtain two basic sorting methods (list method and graphic method), further experience the value of thinking in a certain order, and initially master the methods. Finally, seize the opportunity of encouraging praise in the handshake game, break through the teaching difficulties (initially understand the difference between the arrangement and combination of simple things), and let students explore their essential laws through guessing and performing, so as to experience the difference between the arrangement and combination in the activities. Here, students have experienced a series of exploration activities such as guessing, verification and reflection, and realized that thinking should be well-founded, rational and orderly, which is not only to let students learn to think in activities, but also to learn scientific inquiry methods in inquiry activities.

This section pays attention to the order of permutation and combination, but it does not explain the rationality of permutation and combination enough. There are also some classes in which dynamically generated resources are not captured and utilized in time. I think this point should be reflected and valued in future teaching.

"Simple Arrangement and Combination" Teaching Plan 2 Background

In daily life, there is a lot of knowledge that needs to be solved by permutation and combination. For example, the number of football and table tennis matches in sports, the number of passwords arranged in the password box, and the phone number will be upgraded if the phone capacity exceeds. Reasoning is often used in mathematics learning, such as the derivation of some operational laws of addition and multiplication, and the derivation of numbers divisible by 2, 5 and 3. This class has arranged lively and interesting activities for students to learn through these activities. Example 1 gives a picture of a student using a math card to put two digits. In group cooperative learning, students use two cards first, and then use three cards after operating the feeling pendulum. Then the group exchanges the experience of putting cards: how to ensure that there is no repetition or omission.

Textbook analysis

"Mathematics Wide Angle" is a newly added content in the newly compiled experimental textbook, and it is a new attempt made by the new textbook in infiltrating mathematical thinking methods into students. The thinking method of permutation and combination is not only widely used, but also the knowledge base for students to learn probability and statistics, and it is also a good material for developing students' abstract ability and logical thinking ability. This part focuses on infiltrating students with the simple mathematical thinking method of permutation and combination, and initially cultivating students' consciousness of thinking about problems in an orderly and comprehensive way.

Teaching objectives

1. Students find out the number of permutations and combinations of the simplest things through observation, experiments and other activities, and initially experience the exploration process of simple permutation and combination laws;

2. Make students learn simple methods of permutation and combination, and train their abilities of observation, analysis and reasoning;

3. Cultivate students' orderly and comprehensive thinking consciousness through the learning form of group cooperation and inquiry, and form a good habit of cooperating with others.

Teaching focus

Experience the process of exploring the arrangement and combination of simple things.

Teaching difficulties

Understand the difference between arrangement and combination of simple things.

Teaching preparation

Multimedia and digital cards.

teaching method

Observation, hands-on operation, cooperative exploration, etc.

Preview before class

Preview page 99 of the math book and think about the following questions:

1, which two digits can be put out with 1 and 2?

2. 1, 2, 3, which two digits can be released? You can start writing.

3. think about it: how to put it, what to put first, and then what to put? Is there any good way to avoid omission and repetition?

Teaching preparation

Presentation document

teaching process

……

First, introduce new lessons in the form of games.

Teacher: Students, today the teacher took us to play a wide-angle math game. Put it at the door? ,? It has a password on it. The password of this lockbox is a two-digit number consisting of the numbers 1 and 2. Do you want to go in?

Teacher: Who will tell the teacher the password and help the teacher open this password box? (Students try to say the number of parts)

Health:12,21

Teacher: Open the password box.

Teacher: I opened the password lock and entered the wide-angle paradise of mathematics. Conduct customs clearance activities one by one. The first level: 1, which two numbers can 2,3 represent? The second level: if three people meet, every two people shake hands, how many times does a * * * have to shake hands?

(Design intention: Do not stick to teaching materials, create games that students are interested in, introduce new lessons, and arouse students' enthusiasm. At the same time, it permeates the mathematical thought of simple combination and reasonable selection of methods according to the actual situation, which plays the role of killing two birds with one stone. )

Second, the comparison of game participation activities

Teacher: Now the teacher has a question. When arranging digital cards, you can put six numbers with three numbers, but when shaking hands, three students can only shake them three times, all of which are three. Why is the result different?

Conclusion: The pendulum number is related to the order, but the handshake has nothing to do with the order.

Swing can change places, not shake hands.

(Design intent: Comparing the same number, why do more than half of people shake hands? Triggering students' knowledge conflict, thus triggering thinking and stimulating students' thirst for knowledge. )

Third, expand application and deepen exploration.

1, Digital Palace

Teacher: The third level. Where are we going to play now? Let's have a look!

Choose two numbers from 0, 4 and 6 and arrange them into two digits. How many arrangements are there?

Summary: Why is it different from the results found above? Who is the problem? (0)

Why? (0 cannot be the first digit of a number)

Step 2 choose a line

Teacher: Students, Mickey Mouse showed us the wide angle of mathematics and is ready to go home. How many roads are there for him to choose from? Demo:

Question: How many ways are there to go home from Math Castle?

(1) Group discussion.

(2) Students report and teachers demonstrate.

(3) blackboard writing: A-CA-DA-EB-CB-DB-E.

(design intent: the topic is well-defined and closely related to life. Different people get different development in mathematics, and everyone learns valuable mathematics. )

Self-examination/introspection

The design of this lesson has achieved the following highlights:

1. Create game situations to stimulate students' interest in inquiry.

The whole class always uses the created game situation to attract students' active participation and stimulate their enthusiasm. I design: What is the lock password on the door? This lesson creates an interesting arrangement of numbers in the "arrangement of numbers" through games that break through obstacles, and stimulates students' desire to solve problems. Another example is to stimulate students' interest in "independent thinking and cooperative inquiry" by creating situations similar to students' real life.

2. Student-centered cooperative learning is always reflected in the classroom.

"Autonomous, inquiry and cooperative learning" is a special learning method advocated by the new curriculum reform. When designing this class, we should pay attention to the opportunity and form of cooperation, so that students can learn cooperatively. When teaching the key points, in order to let every student fully participate, I chose to let the students cooperate at the same table; When solving the difficult problems, I chose the cooperative exploration of the six-person group of students. Before students cooperate to explore, they all put forward clear questions and requirements, so that students can know what problems cooperative learning can solve. In the process of students' cooperative inquiry, try to ensure students' cooperative learning time and give appropriate guidance in the deep group. After cooperative inquiry, it can be timely and correctly evaluated, which can stimulate students' enthusiasm and initiative in learning.

3. Let students comprehend new knowledge in colorful teaching activities.

By organizing students to actively participate in a variety of teaching activities, this course fully mobilized students' feelings, coordination and cooperation, which not only made students feel new knowledge, but also experienced success and gained mathematical knowledge, which truly reflected students' dominant position in classroom teaching.

The teaching goal of "simple arrangement and combination" teaching plan 3;

1. Knowledge objective: To enable students to find out the arrangement rules of simple things through observation, operation and experiment.

2. Ability goal: to cultivate students' initial ability of observation, analysis and reasoning and their awareness of orderly and comprehensive thinking, so that students can realize the diversity of problem-solving strategies through mutual communication.

3, emotional goals:

① Make students feel the extensive application of mathematics in real life, further understand the close relationship between mathematics and daily life, try to solve problems in real life with mathematical methods, enhance the awareness of applying mathematics, and make students form a good habit of cooperating with others in mathematical activities.

(2) Let students have a successful experience of exploring laws and enhance their interest and confidence in mathematics learning.

Teaching emphasis: find out the scheme of simple arrangement and combination, and can answer the questions of simple arrangement and combination.

Teaching difficulty: simply distinguish the similarities and differences between permutation and combination.

Teaching preparation: digital cards, clothing pictures and multimedia courseware.

Teaching process:

First of all, an exciting introduction.

Teacher: Students, today the teacher will take you to an interesting place to play. Do you want to go?

Writing on the blackboard: the wide angle of mathematics

If you want to go, you must pass the teacher's exam.

Guess: My age is a two-digit number consisting of numbers 3 and 5.

Students guess and explain the reasons.

Second, inquiry learning.

How many different two digits can be put in the numbers of 1 and 3?

Courseware demonstration: guess, my home phone number is 07 13-62 147 ().

Let the students guess first.

Teacher: When did you guess that? Well, the teacher will give you more information:

The remaining two numbers are two of 1, 3 and 8.

(1) swing.

How many possibilities are there with a digital card in hand?

The teacher prepared three digital cards for the students. Please set it up manually and work together at the same table. One person sets the numbers and one person records them. The students tried to put the pendulum together and write the results of the investigation.

Teachers patrol and pay attention to students' answers: orderly (ten firsts, one firsts), disorderly, omission and repetition.

(2) Say it out

Ask several students (representatives) to report. Present on the blackboard

Teacher: Which ones are right? Which one do you like? Why?

(If the students are still confused, the teacher can guide the students to observe where 1 is and how much 1 can be put in the two digits of ten, and the teacher can also demonstrate with cards; Besides 1, what other numbers can be ten digits, and how many two digits do they have? Like this classmate, I just thought of identifying ten first. So what did this classmate decide first? Or ask, is there any other way besides identifying ten people first? )

What are the advantages of this method of determining ten digits or one digit first? (The blackboard writing is not repeated or omitted)

(3) Guess the numbers

Teacher: The scope is getting smaller and smaller. I will give you more information.

The courseware gives the information again: the sum of these two numbers is 9, and the unit is not 8.

The content of the instructional design article "Wide Angle of Mathematics-Simple Arrangement and Combination" that you are reading now is written by! This website will provide you with more excellent teaching resources! Mathematics wide-angle teaching design-simple arrangement and combination II. combine

(1) Congratulations, you guessed it, you passed the exam! Come on, shake hands with each other at the same table.

Teacher: How many times do two people at the same table shake hands with each other? Demonstration of two people shaking hands, you can say I shake hands with you, you can also say you shake hands with me, but if you count the number of handshakes, how many times?

There are also three children shaking hands here. How do they shake hands? Show: How many times should three people shake hands for every two people?

It is necessary to clarify how many times and how they shook it. How can they make it clear that they don't have a name? Do you think the method just mentioned is troublesome or not? How to express it clearly and concisely?

Yes, our mathematics has its own language, which can be expressed by symbols and figures, faster and clearer. (standard 1, 2, 3)

(2) thinking and writing.

(3) Why do you only shake hands three times when three numbers are arranged in six double digits? (Courseware demonstration)

The teacher concluded: There are many things in life that we need to think about in an orderly way, some of which are related to the order, and some have nothing to do with the order, such as matching clothes.

Third, consolidate and upgrade.

1, bring clothes

Time to go. The teacher wants to dress up beautifully. Here are two coats and two trousers. Can you help the teacher choose a suit?

How to match? How many different collocation schemes are there?

Teacher: How many different collocation methods have you proposed? what do you think?

Please show it to the students on the stage.

Teacher: Now the teacher has put forward higher requirements. If the teacher asked you to express your ideas through connections, would you?

The students are linked together in their exercise books.

Step 2 take pictures and line up

Xiaoli, Xiao Fang and Xiaomei want to stand in a row and take pictures as a souvenir. How many standing positions do they have?

Make a report on the stage. Six different methods of station measurement are summarized.

Teacher: Is there an easier way to show the posture of the three of them? Try it in your own way. (It can be words, symbols, numbers, etc. )

4. Ways

Show courseware: How many ways to go home from wide angle of mathematics?

Which way would you choose?

Students discuss and report.

5. Telephone number

Teacher: Did you have a good time in math wide angle? Remember to call the teacher if you are happy.

Courseware demonstration: teacher's mobile phone number: 18942 167 () ().

The last three numbers consist of 1, 6, 8. Guess what the teacher's mobile phone number might be?

Fourth, expand and extend.

Teacher: Today we played math wide angle. What did you get?

freedom of speech

Teacher: The teacher left a little question after class. Please tell me after the discussion.

Courseware: Can any three different numbers in 09 be arranged into six two-digit numbers?

"Simple Arrangement and Combination" Teaching Plan 4 Teaching Objectives:

1, so that students can find out the arrangement and combination rules of simple things through observation, operation and experiment.

2. Cultivate students' initial ability of observation, analysis and reasoning, and their awareness of thinking in an orderly and comprehensive way.

3. Let students feel the extensive application of mathematics in real life and try to solve problems in real life with mathematical methods. Make students form a good habit of cooperating with others in mathematics activities.

Teaching process:

First, create an enhanced environment to stimulate interest.

Teacher: Today, we are going to visit the "Mathematics Wide Angle Paradise". Do you want to go?

Second, explore the operation and learn new knowledge.

< 1 > combinatorial problem

I, take a look and say.

Teacher: Then let's choose and put on beautiful clothes at home first. (Courseware shows the theme map)

The teacher leads the thinking: With so many beautiful clothes, how can you wear one top and another bottom? (Name the students and say them)

2. Think about it and put it on the table.

(l) Lead the discussion: There are so many different ways of wearing, how can we do it without omission or repetition?

① Students discuss and communicate in groups, and teachers participate in group discussions.

② Student report

(2) Guiding operation: Students in the group cooperate with each other and stick your design on the exhibition board in an orderly way. (Requirements: Team leader takes out pictures of school uniforms and exhibition boards)

① Students operate the pendulum together, and teachers patrol to participate in group activities.

② Students show their works and introduce the collocation scheme.

③ Evaluate each other.

(3) Teachers guide observation:

How many ways are there in the first scheme (press the upper belt and lower belt)? (4 kinds)

How many penetration methods are there in the second scheme (top pressing bottom)? (4 kinds)

Teacher's summary: No matter whether the top is matched with the bottom coat or the bottom coat is matched with the top coat, as long as the matching is orderly, all methods can be found out, without repetition or omission. In the future study and life, we will encounter many such problems, and we can all solve them in an orderly way of thinking.

< 2 > arrangement problem

Teacher: it's a wide-angle paradise for mathematics, but you must find the password before entering the door. (Courseware Display Courseware Password Gate)

The password is a two-digit number consisting of 1, 2 and 3.

(1) Group discussion put out different two-digit numbers and write down the results.

(2) Students report and communicate (the teacher clicks on the courseware to display the password according to the students' answers)

(3) Mutual evaluation among students. Method 1: Take out two digital cards at a time and put out different two digits;

Method 2: fix the number on ten digits and exchange one digit to get different two digits;

Method 3: Fix the number on one digit and exchange ten digits to get different two digits.

The teacher concluded that although the three methods are different, they can all spell six different two-digit numbers correctly and orderly. Students can use their favorite methods.

Third, classroom practice to consolidate new knowledge.

1. Table tennis venue layout.

Teacher: Let's go to the activity park first. There happened to be a table tennis match here.

(l) The teacher asked: Every two athletes play a game, how many games do they have to play against each other?

(2) Students think independently.

(3) roll call student report. rule

2. Route selection. (Courseware shows the map of tourist attractions)

Teacher: Let's go to the park. You must pass the game park on the way.

(l) Teachers guide observation: How many routes are there from the activity park to the game park? Which ones? How many routes are there from the game park to the park? Which ones? (A, B, C) (Show the courseware according to the students' answers)

How many different ways are there from the activity park to the park?

(2) Students communicate in groups after independent thinking.

(3) The whole class communicates with each other.

3. Photography activities.

Teacher: We came to the park. The scenery here is really good. Let's take some photos.

Teacher's requirements: the photographer asked three students to stand in a row to take pictures, and each group designed an arrangement plan (double or three photos) according to the number of people taking pictures at a time, and the group leader made a record of the activities.

(1) Group activities, teachers participate in group activities.

(2) Each group puts forward a recording plan.

(3) Teachers and students have the same evaluation.

4. Enjoy the photos.

Teacher: While the students are taking pictures, Xiaoli's family of three are also taking pictures to see how they take pictures.

Fourth, summary.

This is the end of today's play. Will the students shake hands and say goodbye? If four students in the group shake hands every two people, how many times should a * * * shake hands?

"Simple arrangement and combination" teaching plan 5 teaching content:

Simple permutation and combination

Teaching objectives:

1. Ask the students to find out the number of arrangements or combinations of simple events through observation, guess, experiment and verification.

2. Cultivate students' awareness and habits of orderly and comprehensive thinking.

Teaching process:

1. Help students find out the number of combinations through easy-to-understand operation activities or examples. Teachers and students * * * Same as Analysis Exercise 25, Question 1. Let the students discuss in groups and fully express their opinions.

2. Use intuitive charts to help students find out the combination number of breakfast collocation in an orderly way.

3. Show Exercise 25, Question 3.

After reading the questions, discuss in groups of four how many ways to find the combination number.

4. Student report.

(1) graphic representation (two kinds). Guide students to express abstract mathematical knowledge by sketching.

(2) Other methods, such as Congcong or Mingming, can take photos with each child (step by step, with Congcong as the first step or Mingming as the first step), so as to give full play to students' creativity in teaching. It doesn't matter which method students use to find out. However, it is necessary to guide students to think about how to do it, and cultivate their awareness and ability of orderly thinking.

(3) Students can be very open when using pictures to express themselves. For example, they can use squares to represent intelligence and circles to represent clarity, and mark numbers in squares and circles respectively. In fact, this is an embodiment of developing students' ability to express specific events with mathematical symbols.

(4) If students have difficulty in using a sketch, they can also recall the examples of the first volume of Grade Two with the aid of a learning aid card or put them on the table.

The second step is "hands-on"

(1) Exercise 25, Question 7.

Ask students to write down all the information about withdrawing money through activities.

(2) Exercise 25, Question 9.

Two graphical representations are used to represent paired combinations (two relatively simple ways). In teaching, some students should also be allowed to list all the situations one by one. As long as they explore all the combinations through their own methods, they should be encouraged.

Teaching reflection: