Math pigeon's nest problem teaching plan 1

I. Guiding ideology

Time is tight and tasks are heavy this semester.

Final review plan of sixth grade mathematics in primary school.

? Our guiding ideology is: relying on scientific attitudes and methods, arouse students' enthusiasm for review, highlight top students, attach importance to students with learning difficulties and improve secondary school students.

Second, the analysis of students' situation

After nearly six years of study, primary school students have contacted and accumulated a considerable amount of mathematical knowledge, formed relevant mathematical skills, and can also think and analyze relevant mathematical problems in life, and their intelligence has reached the level of all-round development. But from grade one to grade six, there is an undeniable lack of overall, comprehensive and developed understanding. Therefore, in the last period of this primary school stage, it is very necessary to organize students to comprehensively review and sort out the mathematical knowledge they have learned in primary schools. Especially for some students with learning difficulties, general review is more important.

Third, teaching materials.

The content of the general review of the textbook is not only a key point of this textbook, but also an important part of the whole primary school mathematics learning. The teaching quality of this part is related to whether the goals and tasks of primary school mathematics teaching can be successfully completed. The textbook divides the teaching content of primary school mathematics into 44 class hours for review. According to the arrangement of teaching materials, the content of 44 hours can be divided into 6 parts.

The first part focuses on reviewing the knowledge of numbers, including the meaning and nature of related knowledge points such as integers, decimals, fractions and percentages, and the divisibility of numbers.

The second part focuses on reviewing the operation of numbers, including the significance, laws, laws and properties of the four operations, solving equations of integers, decimals and fractions, and elementary arithmetic.

The third part focuses on reviewing the relevant knowledge of ratio and proportion, including the meaning, nature, ratio, simplified ratio, solution ratio, meaning and judgment of positive and negative ratio.

The fourth part focuses on reviewing the relevant knowledge of quantity and measurement. Including mass length, area, volume (volume), time and other units and their propulsion rate, conversion and summary between units.

The fifth part focuses on reviewing the relevant knowledge of geometric shapes. Including the concept, judgment, measurement and operation of lines and angles, the calculation of the characteristics, perimeter and area of plane graphics, and the calculation of the characteristics, lateral area, surface area and volume of three-dimensional graphics.

The sixth part focuses on reviewing all kinds of application problems. Including basic quantitative relations, simple application problems, general compound application problems and typical application problems of two-step and three-step calculation, equation and proportional application problems, fractional (percentage) application problems, etc.

The overall arrangement of teaching materials is rich, meticulous and systematic, trying to consolidate knowledge, master basic mathematical concepts, master basic skills and develop thinking ability through comprehensive review. At the same time, it tries to further improve students' ability to comprehensively apply mathematical knowledge and solve practical problems.

Fourth, the overall review objectives

Through general review, guide students to achieve:

1, the system firmly grasps the basic knowledge about integers, decimals, fractions (percentages), ratios and proportions, simple equations and so on. , have the ability to perform four operations on integers, decimals and fractions, and use the learned operation rules and properties to perform simple operations, so as to make the calculation method reasonable and flexible, have a certain speed and be able to solve simple equations. Develop the habit of consciously checking and checking.

2. Consolidate the appearance of the size of some units of measurement that have been obtained, firmly grasp the speed and conversion relationship of various units of measurement that have been learned, and be able to skillfully summarize and convert the names of various units.

3. Firmly grasp the characteristics of various geometric shapes such as plane graphics and three-dimensional graphics, and establish corresponding representations, so as to be able to skillfully calculate the perimeter, area (surface area) and volume (volume) of the learned assembly shapes, consolidate simple drawing and measuring skills, and solve simple graphic practical problems.

4, master the preliminary knowledge of statistics, can correctly draw (usually semi-independent) simple statistical tables and charts, can correctly understand statistical tables (charts) and solve corresponding problems according to chart information analysis, and can correctly answer the average question.

5. Firmly grasp the common quantitative relations learned and the methods of analyzing and solving application problems, correctly analyze the quantitative relations in application problems, flexibly use the learned knowledge to independently analyze and solve related application problems, solve simple practical problems in life, and improve the ability of comprehensively applying mathematical knowledge.

6, combined with the general review, guide students to develop the habit of conscious inspection, independent thinking, not afraid of difficulties.

Five, the arrangement of the general review process of primary school mathematics graduation

Because review is to re-learn what has been learned on the original basis, the original learning situation of students directly restricts the arrangement of the review process. At the same time, the review process and schedule should be determined according to the actual review object and review time of the class. Combined with the actual situation of our class, the total review period is 44 hours, and the review process and schedule are roughly as follows:

(1) Number and number operation (12 class hours)

This section focuses on a series of concepts and fractions of divisibility, the basic properties of decimals, four operations and simple operations.

1. Systematically sort out the contents of numbers, establish a concept system, and strengthen the understanding of concepts (4 class hours), including the meaning of numbers, reading and writing of numbers, rewriting of numbers, comparison of numbers, divisibility of numbers and other knowledge points.

2. Communicate the connection between the contents and promote the overall perception (2 class hours), including the comparison of the nature of fractions and decimals and the concept of divisibility.

3, a comprehensive understanding of the concept of four operations and calculation methods, improve the level of calculation (2 class hours), including the meaning and rules of four operations, elementary arithmetic.

4. Use algorithms to master simple operations and improve calculation efficiency (2 class hours), including algorithms and simple operations.

5. Carefully design exercises to improve comprehensive calculation ability (2 class hours).

(2) Basic knowledge of algebra (4 class hours)

The focus of this section should be to master simple equations and distinguish ratios and proportions.

1, form systematic knowledge and strengthen contact (1 class hour), including the knowledge points such as letters representing numbers, ratios and proportions, and positive and negative ratios.

2. Grasp problem-solving training to improve the ability of solving equations and solution ratio (2 class hours), including simple equations and solution ratio.

3. Differentiate concepts and deepen understanding (1 class hour), including proportion and proportion, positive proportion and negative proportion.

(3) Application problems (16 class hours)

In this section, we should focus on the analysis of application problems and cultivate problem-solving skills. The difficult content is fractional application problems.

1. Analysis and arrangement of simple application problems (1 class).

2. Analysis and arrangement of composite application problems (2 class hours)

3. Analysis and arrangement of solving application problems by using equations (3 class hours).

4. Analysis and arrangement of fractional application problems (5 class hours).

5. Analysis and arrangement of solving application problems with proportional knowledge (2 class hours).

6. Comprehensive training of application problems (3 class hours).

(4) Measurement of quantity (3 class hours)

This section focuses on the rewriting of nouns and numbers and practical concepts.

1, the measurement knowledge structure of finishing quantity (1 class hour), including length, area, unit of volume, weight and time unit.

2. Consolidate the unit of measurement and strengthen the actual concept (1 class hour), including the rewriting of names and figures.

3. Comprehensive training and application (1 class).

(5) Basic knowledge of geometry (6 class hours)

This section focuses on the identification of features and the application of formulas.

1, strengthen concept understanding and systematization (1 class), including the characteristics of plane graphics and three-dimensional graphics.

2. Accurately grasp the characteristics of graphics, strengthen comparative analysis, and reveal the connections and differences between knowledge (2 class hours), including the perimeter and area of plane graphics, the surface area and volume of three-dimensional graphics.

3. Strengthen the application of formulas and improve the mastery of calculation methods (2 class hours). Can realize the correct calculation of perimeter, area and volume.

4. Overall perception and practical application (1 class).

(6) Simple statistics (3 class hours)

This section focuses on the knowledge and understanding of charts according to the outline requirements, and can answer some simple questions.

1, the method of averaging (1 class hour).

2. Deepen the understanding of the characteristics and functions of statistical charts (1 class hour), including statistical tables and charts.

3. Further analyze the chart and answer questions (1 class), including drawing and answering questions according to the chart.

Math pigeon nest problem teaching plan II

Teaching objectives

1. Understand the pigeon hole principle in the process of operation, observation and comparison, and use the knowledge of pigeon hole principle to solve simple practical problems.

The key and difficult points have gone through the exploration process of archiving principles, and the problems of archiving principles have been modeled.

Student Notes (Instructor's Guidance) Content of Learning Plan

1. Knowledge review: (2 minutes)

Second, students learn by themselves: (15 minutes)

(1) self-study example 1

Put four pencils in three pencil boxes. How can I put it? There are several situations.

(1) Students think about various ways of playing.

(2) First release method: second release method:

The third release method: the fourth release method:

Teaching process:

5? 2=2 1 (at least 3 copies)

7? 2=3 1 (at least 4 copies)

9? 2=4 1 (at least 5 copies)

1, ask questions.

Anyway, there is always a pencil box with at least () in it. Why?

If only () pencils are put in each pencil box, and at most () pencils are put in one pencil box, then at least () pencils are put in the same pencil box.

(1) Tell me what you have learned.

Self-study example 2

1. Put five books in two drawers. No matter how you put it, how many books will you put in a drawer at least?

2, put a pendulum, there are several ways to put it.

It's not hard to see that there is always a drawer for at least () books.

3. Tell me about your thinking process.

If you put () books in each drawer, * * * will put () books. The remaining 1 books should be put in one of the drawers, so there will be at least 1 drawers for three books.

What if a * * * has seven books? What about nine books?

4. Can the above process be expressed by formula? What did you find?

Summary: Distribute evenly first, and then distribute the remainder to get the number of books put in at least one drawer.

Third, group cooperation and exchange (8 minutes)

Fourth, teacher evaluation dispels doubts. (10 minutes)

Verb (short for verb) Class test (5 minutes)

1. Do it.

(1) Seven pigeons fly back to five dovecotes, and at least two pigeons will fly into the same dovecote. Why?

(2) Speak your mind.

If only () pigeons fly into each pigeon house, at most () pigeons fly back, and the remaining () pigeons fly into one pigeon house or two pigeon houses respectively. So at least two pigeons flew into the same pigeon house.

Do it

Eight pigeons fly back to three dovecotes, and at least three pigeons will fly into the same dovecote. Why?

Think: Every pigeon house flies into () pigeons, and * * * flies into () pigeons. The remaining () pigeons will fly into 1 or two dovecotes, so at least () pigeons will fly into the same dovecote.

Math pigeon nest problem teaching plan 3

? course content

Textbook page 109, question 1, exercise 25, question 1, 2, 3 and 6.

? Teaching objectives

1. Review the relationship between addition, subtraction, multiplication and division.

2. Review the operation sequence of the four operations and calculate correctly.

3. Use the arithmetic and related properties of addition and multiplication to make a simple calculation.

? Important and difficult

Key points: check the relationship between addition, subtraction, multiplication and division, calculate the four operations, and use the algorithm to make simple calculations.

Difficulty: Simple calculations can be made by applying the algorithm.

? teaching process

First, scene import

Question import.

1. What is the relationship between addition and subtraction? What about the relationship between the parts of multiplication and division?

2. Do you know the sequence of the four operations? Can you calculate?

3. What operating rules do you know? Can these algorithms be used for simple calculations?

Students discuss, teachers report and teachers evaluate.

Second, explore new knowledge.

1. Review the four operations.

Show the textbook 109 page 1 topic.

(1) According to the first formula, first talk about the relationship between addition and subtraction, and then write an addition formula and a subtraction formula respectively.

(2) According to the second formula, first talk about the relationship between multiplication and division, and then write a multiplication formula and a division formula respectively.

(3) Will you list a comprehensive formula according to the 1 and the second formula? Then a comprehensive formula is listed according to the first, second and third formulas.

(4) Q: Can you sum up the order of the four operations in one sentence?

Students discuss, communicate and report in groups.

Summary: If there are no brackets, multiply first and then divide, then add and subtract. If there are brackets, count them first.

2. Review the operation method.

(1) What algorithms have we learned?

Students can discuss, report and evaluate freely.

(2) Sort out and summarize the operation rules, and express them in letters.

Addition: additive commutative law: a+b=b+a

Additive associative law: a+b+c=a+(b+c)

Multiplication: multiplication commutative law: a× b = b× a.

The law of multiplicative association: a×b×c=a×(b×c)

Multiplicative distribution law: a× (b c) = a× b a× c

(3) Think about it and tell me what algorithm is used in the following calculation. (textbook page 109, question 1 (4))

Students finish independently, communicate in groups, report and speak, and evaluate by teachers.

Third, the foundation is consolidated.

Complete Exercise 25, Question 1, 2, 3, 6.

Fourth, class summary.

Q: What have you gained from this course?

Summary: In this lesson, we reviewed the relationship between addition, subtraction, multiplication and division, and used their relationship to check the calculation. We also reviewed the operation sequence and algorithm of the four operations, consolidated and deepened this knowledge, and made a simple calculation by using the algorithm.

Five, synchronous training

At this point in teaching, please choose exercises related to the new guidance.

Math pigeon's nest problem teaching plan 4

First, teaching material analysis:

This textbook specially arranges the unit of "Mathematics Wide Angle" to infiltrate some important mathematical thinking methods into students. Compared with the previous compulsory education textbooks, this part is new. The textbook of this unit introduces the "pigeon's nest problem" to students through several intuitive examples and with the help of practical operation, so that students can "model" some simple practical problems and solve them with the "pigeon's nest problem" on the basis of understanding the mathematical method of "pigeon's nest problem".

Among mathematical problems, there is a kind of problem related to "existence". In this kind of problem, it is only necessary to determine the existence of an object (or person), and it is not necessary to indicate which object (or person) it is. This kind of problem is based on what we call the "pigeon hole principle". Pigeon hole principle was first used by German mathematician Dirichlet to solve mathematical problems in19th century, so it is also called Dirichlet principle and pigeon nest problem. The theory of "pigeon nest problem" itself is not complicated, even obvious. However, the application of "pigeon's nest problem" is ever-changing. It can solve many interesting problems and often get some surprising conclusions. Therefore, the "pigeon nest problem" has been widely used in number theory, set theory and combinatorial theory.

There are many variants of "pigeon nest principle", which is widely used in life. Students often encounter such problems in their lives. In teaching, students should be guided to judge whether a problem belongs to the category that can be solved by the "pigeon-cage principle". Whether this problem can be combined with the "pigeon cage principle" is the key to the success of this teaching. Therefore, in teaching, students should consciously understand the "generalized model" of "pigeon coop principle". The sixth grade students' understanding ability, learning ability and life experience have reached the level of mastering the contents of this chapter. Choosing familiar and easy-to-understand life examples in teaching materials and combining concrete practice with mathematical principles are helpful to improve students' logical thinking ability and ability to solve practical problems.

Second, the three-dimensional target:

1, knowledge and skills:

Guiding students to explore the "pigeon's nest principle" through observation, guessing, experiment and reasoning will be used to solve simple practical problems.

2, process and method:

(1) Experience and explore the learning process of "pigeon nest principle", and experience observation, guess, experiment and reasoning.

Activity learning method is permeated with the idea of combining numbers with shapes.

(2) Learn to cooperate with others and be able to communicate with others about the thinking process and results.

3, emotional attitudes and values:

(1) Actively participate in exploration activities, and experience mathematics activities are full of exploration and creation.

(2) Experience the close relationship between mathematics and life, and feel the role of mathematics in real life.

The fun of learning and using mathematics.

(3) Feel the charm of mathematics through the flexible application of "Pigeon Cage Principle".

(4) Understand the production process of knowledge and be educated by historical materialism.

Third, the teaching focus:

Use the "pigeon nest principle" to solve practical problems and guide the society to turn specific problems into "pigeon nest problems"

Four, teaching difficulties:

Understand the "pigeon nest principle", find out the trick to solve the "pigeon nest problem" and make repeated reasoning.

Verb (abbreviation of verb) teaching measures;

1, let students experience the process of "mathematical proof". Students can be encouraged and guided to "reason" by learning tools, physical operation or sketching. The process of understanding the "pigeon coop principle" through "reasoning" is the embryonic form of mathematical proof. This will help to improve students' logical thinking ability and prepare for studying more rigorous mathematical proof in the future.

2. Cultivate students' "model" thinking consciously. When we are faced with a specific problem, it is the key to solve the problem whether we can connect this specific problem with the pigeon coop principle, whether we can find the internal relationship between the specific situation in this problem and the generalized model of the pigeon coop principle, and what are the "things to be divided" and "pigeon coop" in this problem. In teaching, students should be guided to judge whether a problem belongs to the category that can be solved by "pigeon cage principle"; Then think about how to find the general model of "pigeon nest problem" hidden behind it. This process is a process in which students "mathematize" specific problems and find the most essential mathematical model from complex realistic materials, which is an important embodiment of students' mathematical thinking and ability.

3. We should properly grasp the teaching requirements. The "pigeon nest principle" itself may not be complicated, but it is widely used and flexible. Therefore, some difficulties are often encountered when solving practical problems with the "pigeon cage principle". For example, sometimes it is not easy to find the connection between practical problems and the "pigeon coop principle". Even if it is found, it is difficult to determine what to use as a "pigeon nest" and how many "pigeon nests" to use. Therefore, in teaching, students' "reasoning" need not be too strict, as long as they can say the general meaning in combination with specific problems, and encourage students to guess and verify with the help of intuitive methods such as physical operation.

6. Course arrangement: 3 class hours

Dove nest problem-1 class hour

The concrete application of "pigeon's nest problem"-1class hour

Practice class-1 class hour.

Math pigeon's nest problem teaching plan 5

Teaching objectives:

1. After going through the inquiry process of "pigeon nest problem" and having a preliminary understanding of "pigeon nest problem", we will use "pigeon nest problem" to solve simple practical problems.

2. Develop students' reasoning ability through operation and form abstract mathematical thinking.

Teaching focus:

Through the exploration process of "pigeon nest problem", I have a preliminary understanding of "pigeon nest problem"

Teaching difficulties:

Solve some simple practical problems with "pigeon nest problem"

Teaching aid preparation:

Each group has a corresponding number of cups, balls, playing cards and multimedia courseware.

Teaching process:

First, the game is introduced:

Teacher: Let's play a game today. This game requires the whole class to be divided into several groups. The leader of each group has three balls and two cups, and all the balls are required to be put in the cups. Students, let's see if the teacher guessed correctly.

Please ask the leaders of three groups to come on stage and guess how the other three groups put the ball. The student lecturer writes on the blackboard.

The teacher concluded: There must be at least two balls in a cup.

Students, do you want to know why the teacher knows? Writing on the blackboard: pigeon nest problem

Second, the principle of inquiry:

1, start swinging and feel the principle.

(1) Explore the situation that the number of objects is more than the number of drawers 1.

Example 1. Now, if you want to put four pencils in three pencil boxes, how many different ways will you put them? Please record while posing.

The whole class put a pendulum in groups.

Group leaders take notes while posing. The teacher writes on the blackboard, and the whole class counts and records together.

Contact the game of putting the ball into the cup and guide the students to say: No matter how you put it, there is always a cup with at least two sticks.

Teacher: At least there is always a cup.

Teacher: A, what do you mean there is always one?

Teacher: B, what does "at least" mean? "At least squo means two or more.

Teacher: Think of it this way. Seven sticks are put in six cups.

10 9 supported

What is the conclusion of putting 100 sticks in 99 cups?

Can you think of a simple way to prove this conclusion? Let's discuss it.

Students discuss.

Teacher: What did you think of? Somebody tell me.

How did you divide it just now? Why use the average score to prove this conclusion?

(said while swinging. How to express it by formula? Writing on the blackboard (4? 3= 1 1)

Students come to the conclusion that as long as the number of sticks is more than the number of cups 1, there is such a conclusion.

2. Explore the case that the quotient is not 1.

Discuss 7 books and put them in 3 drawers. Want to know the conclusion? Do you want to wear it?

Those eight books are put in three drawers.

What about the three drawers 10 book? What did you find?

I found seven? 3=2 1

8? 3=22

10? 3=3 1

Blackboard: at least number = quotient+1.

Summary: The principle we are discussing today is the famous pigeon's nest principle in mathematics.

Third, the lesson summary:

Pigeon nest = quotient remainder

At least number = quotient+1

Fourth, use today's knowledge to solve some practical problems in life.

1, do it

2. Play poker.

Five, blackboard writing: omitted