Mathematics teaching plan and reflection analysis of the fifth grade in primary school —— Ordinary version1;
This lesson closely links students' existing knowledge and experience about temperature and height, and guides students to learn to use positive and negative numbers to represent some quantities with opposite meanings. On this basis, guide students to classify, summarize and generalize, and further understand negative numbers from the rational height of numbers. Finally, the textbook provides vivid materials to guide students to apply their knowledge and understanding of negative numbers to their lives, further enriching their understanding of negative numbers and developing their sense of numbers and application ability.
Teaching objectives:
1, understand the background and significance of negative numbers in specific situations, know negative numbers, master the reading and writing of positive and negative numbers, and know the relationship between positive and negative numbers and 0. Positive numbers and negative numbers are used to describe real-life phenomena.
2. Cultivate students' thinking abilities such as observation, comparison, association, guessing and reasoning, and their learning abilities such as independent thinking and cooperative communication.
3. Let students experience the connection between mathematics and life, get positive emotional experience, and further stimulate their interest in learning mathematics.
Teaching methods:
Situation creation, observation and comparison, group cooperation, induction and generalization, etc.
Teaching process:
Let's introduce the situation first and get a preliminary understanding.
1. Understand positive and negative numbers from the representation of opposite quantities in temperature.
(1) scenario introduction.
Dialogue: Do students usually watch TV? Please look at the screen (broadcast the news broadcast title)
-88.3+ 1030 12.4
Ask questions:
①0 Why not write?
② Observe these numbers and compare them with the positive and negative numbers on the blackboard. What did you find?
Note: In order to let students have a complete understanding of the connotation and extension of negative numbers, decimals and fractions are added to the exercises. Objective To make students realize that all the numbers they have learned in the past (except 0) are positive numbers, and to communicate the internal relationship between old and new knowledge.
Third, expand practice and activate understanding.
1, guess the temperature
(1) The lowest temperature on the earth's surface is (-88.3)℃ in Antarctica.
(2) The lowest temperature on the surface of the moon is (-183)℃.
Explain: Ask the students to guess the lowest temperature on the surface of the South Pole and the Moon according to the hints (cold or hot). This arrangement gives full play to the exercise function, transforms static reading and writing into dynamic generation, develops the sense of number in the process of approaching the answer step by step, and makes a good penetration for learning the comparison of negative numbers in the future.
2. Describe the meaning of positive and negative numbers in life.
(1) Negative number in the elevator. (2) Negative numbers in the passbook.
(3) Population information
A. According to the data published by the Russian Federal Statistical Office in 20xx 10, it shows that:
The average number of people in Russia every day is about-2,000.
B, according to the latest statistics of Xinhuanet:
China has an average increase of about 40,000 people every day.
About (3): After understanding the meaning of these two numbers, ask a question. Which do you think is better, Russian or China? Carry out appropriate dialectical thinking and responsibility education.
Description: Describing the phenomena in life with mathematics is an important way to cultivate students' application consciousness. The above exercises not only enrich the understanding of negative numbers, but also develop students' mathematical thinking and vision.
Fourth, the summary reveals the topic and questions the extension.
This class is coming to an end. Let's look back and reflect. Do you think you got anything? Do you still want to talk about negative numbers?
Do you think it's weird?
Description: Successful teaching should not be the end of a problem at the end of a class, but the beginning of a new problem. On the basis of basic cognition, students are more eager for knowledge!
Fifth, the influence of mathematical culture.
Show a short film: Do you know? Introduce the source of negative numbers.
Talk about feelings and carry out ideological education appropriately.
Reflection:
Truthfulness, solidity and effectiveness are the criteria for judging a good class. Compared with difficulties, I think this course can do the following:
1, really find the right foundation.
Starting from students' familiar life situations, students' existing knowledge and experience can be quickly mobilized, which provides a necessity and demand for the understanding of negative numbers. Active learning starts here.
2. Solidly integrate teaching materials.
I didn't stick to the materials provided in the textbook and the understanding level, and tried to dig more materials with * * * background to guide observation, discussion, comparison and discovery, so that students' understanding of negative numbers formed a deeper and more comprehensive understanding beyond temperature and altitude.
3. Effectively enrich understanding.
The openness, vividness, typicality and interest of the exercise materials make students richer in knowledge, deeper in understanding and more active in participation.
Gu teacher's comments are:
Teacher Tao's case mainly embodies the following two characteristics in design and teaching:
1. Mining curriculum resources.
The teacher creatively handled the textbook, with the example 1 and example 2 as the intuitive background. After clearly guiding students to describe with mathematical methods, he put more energy into guiding students to observe and compare, guiding students to see the essence through phenomena, and guiding students to supplement and expand in time. After listing a lot of materials with * * *, the students finally found that there are many numbers with opposite meanings in life, and they can all be summarized. At this point, students' understanding of positive and negative numbers has formed a deeper and more comprehensive understanding beyond temperature and height.
2. Activate the teaching content.
The exercises arranged in the textbook are mainly to broaden students' horizons and train them to read and write negative numbers. When using exercises, teachers fully tap the teaching value of ordinary exercises and skillfully activate static texts into attractive mathematical activity resources in class. For the temperature on the surface of the Antarctic and the moon, students are required to guess the numbers according to the prompts, which integrates fun, knowledge and participation, which not only cultivates students' sense of numbers, but also makes a good infiltration for the comparison of negative numbers in the future, and achieves the perfect combination of knowledge, emotion and artistic conception.
Teaching plan and reflection of the second volume of fifth-grade primary school mathematics 2 teaching content: median and mode in the seventh unit of the second volume of fifth-grade primary school mathematics published by Beijing Normal University.
Brief analysis of teaching materials;
This lesson is based on the average mastered by students. By tapping the rich curriculum resources in life, students can learn to find the median and mode in the process of statistical activities and understand their practical significance, learn to analyze data and further cultivate their preliminary statistical ability.
Student analysis:
Students have certain statistical ability, are good at finding problems in life and are willing to solve problems in cooperative inquiry, so this lesson is mainly to guide students to acquire new knowledge in independent inquiry activities.
Teaching objectives:
1. By analyzing the data, we will find the median and the mode, which can be explained according to specific problems.
2. Cultivate students' ability to find, analyze and solve problems, and cultivate students' awareness of inquiry and cooperation in specific activities.
3. Feel the application of statistics in life, enhance statistical awareness and cultivate statistical ability.
Teaching emphasis: to find the median and the mode, and to understand its practical significance in combination with the situation.
Difficulties in teaching: We can choose appropriate statistics to represent different characteristics of data according to specific problems.
Teaching philosophy:
First of all, it creates a situation in which Xiao Ming has problems in finding a job. Through the analysis of the average, it causes students' cognitive conflicts, which leads to the necessity of finding the median. Then through the observation, analysis and comparison of the data, learn to determine the median and mode.
Through the investigation of students' weight, age and shoe size, students can go through the process of data collection, collation and analysis, deepen their understanding of the meaning of median and mode, and experience the application of statistical knowledge in life, thus further cultivating their statistical ability.
Teaching process:
First, the creation of situations, causing cognitive conflicts
1. Teacher: What do you want to be when you grow up?
Health: Military.
Teacher: What a lofty ambition! * * * Defenders of the Republic.
Student: Teacher.
Teacher: the engineer of the human soul.
Teacher: It seems that each of you has your own ideas. In order to realize the ideal, we must start from an early age and redouble our efforts! The teacher wants to ask you a question. If you just graduated from college now, what should you pay attention to when looking for a job?
Health: Pay attention to the strength of the company.
Health: Pay attention to the company's working environment.
Health: I care more about salary.
Teacher: Yes, salary is indeed a condition that people pay more attention to. Many people should consider this problem when looking for a job. A good friend of mine, Zhang Ming, encountered this problem in the process of applying for a job. Let's have a look.
2. The teacher shows the courseware and reads the recruitment notice by name.
Teacher: What information can you get from the job advertisement?
Health: I know this company wants to recruit employees.
Health: I also know that the average salary of employees in this company is 2000 yuan.
Teacher: Yes, the average salary is 2000 yuan. Xiao Ming met his requirements at first sight, so he rushed to the recruitment office. After comprehensive evaluation, the manager said to him: According to the position you are applying for, our salary is 1400 yuan. (Show the courseware. )
Teacher: If you were Xiao Ming, what would you think when you heard the news?
Student: Didn't the job advertisement say that the average salary is 2000 yuan? Why is my salary 1400 yuan?
Student: This is a deceptive company. It is obviously a basic salary of 2000 yuan. Why did you only give me these?
Teacher: Xiaoming also has these questions, and the manager naturally has his reasons. At this time, he took out the monthly salary table of the company's employees.
Teacher: Look at this set of data carefully. What can you find?
Health: Most employees earn less than 2000 yuan.
Health: I found that the boss didn't lie, because the salaries of these employees are high or low, and the average salary is really 2000 yuan.
Teacher: the boss didn't lie, but most of the employees' salaries are below 2000 yuan? So what is the problem?
Health: Because the salaries of the two managers are particularly high, the salaries of employees are lower than the average salary.
Health: Because the manager's salary is high, the average salary increases.
Teacher: The student's analysis is very reasonable. Because the average of 2000 is influenced by big data, it can no longer reasonably reflect the general salary level of employees in this company.
Second, reveal problems and explore new knowledge independently.
1. median.
Teacher: Look at this set of data again. Which data do you think best represents the overall salary level of employees? Think for yourself first, and then communicate with your deskmate or other students. (student exchange report. )
Teacher: Which data do you think is more representative of the general salary level of employees in this company?
Health: I think it is 1800 yuan, because it is close to 2000 yuan.
Health: Our group thinks it should be 1500 yuan, because it is among the nine data.
Health: I think it's 1300 yuan, because the salaries of managers and deputy managers are not included in this set of data.
Teacher: Now everyone has a different opinion. Comparing these three figures, which one do you think is more reasonable? You can discuss it again in the group and exchange your thoughts.
Health: I think it should be 1500 yuan, because it is in the middle of the payroll.
Health: We also think it's 1500 yuan, because it can better represent the general salary level of middle-level employees.
Health: We also think it is 1500 yuan, because it is neither high nor low, which can represent the general level.
Teacher: Through the first communication, everyone expressed their opinions, and further discussion and research enabled us to reach an understanding. Now everyone thinks that 1500 can best represent the general salary level of employees. Observe the position of 1500 in this set of data.
Health: median.
Teacher: (blackboard: in the middle. ) Then there are several bigger data ahead. (4) There are several smaller data behind it. (4) Among 9 data.
Teacher: Then let's see how these nine data are arranged.
Health: From small to large. (Blackboard: Size. )
Teacher: (gesturing) How about this one? (from small to large. )
Teacher: We call a number with this characteristic the median. (blackboard writing: median. )
Teacher: Can you tell me what the median is according to your own understanding?
Teacher: Your generalization ability is really strong. Through the study just now, everyone's understanding of the median is more and more comprehensive. Let's look at the big screen. Show the concept of median and read by name. )
Teacher: Which do you think is more representative of the average salary level of employees in this company, the median or the average?
Health: median.
Teacher: So, as a store manager, why do you want to recruit advertisements evenly?
Health: Because the average here is higher than the median, it can attract more people.
Teacher: It seems that this is a strategy of the merchants. When we analyze a set of data, we often pay different attention to it because of different angles, so we choose different statistics to represent different characteristics of a set of data.
Teacher: My friend Xiaoming thought it over and accepted the job. His participation changed the payroll, so what is the median of this set of data now?
Health: 1500.
Health: 1400.
Health: The median values of this set of data are 1500 and 1400, and the median should be the number between them.
Health: I think the figure between the two is their average.
Teacher: Do you agree with him? How much should it be? (Computer display solution. )
Teacher: What rules can be found by comparing the solution of the median of these two groups of data?
Health: when the number of data is odd, the median is the middle number; When the number of data is even, the median is the average of the middle two numbers.
Teacher: Students are really smart. They can not only analyze problems, but also find laws in the process of analysis. It seems that the median is only related to the location and arrangement of data.
2. mode.
Teacher: Actually, there are many applications of median in life. The teacher wants to know how much you weigh, okay?
Teacher: How did you find the teacher writing these data?
Health: It's written in descending order.
Teacher: What is the median of observing this set of data? What does this mean? How much do you weigh compared with this set of data?
Student: The median is 80, which means that the weight of this group of students is generally 80 kg.
Student: My weight is 62 Jin. Compared with this group of students, I am at the lower-middle level.
Health: I weigh 96 Jin. Compared with them, I am above average.
Teacher: Are you as heavy as these students?
Health: I weigh 80 Jin.
Health: My weight is 80 Jin, too.
Teacher: If we look at the current set of data, besides finding the median, what other characteristics do you find?
(Display data: 62768083978080. )
Health: I found that three students weigh the same, all weighing 80 Jin.
Teacher: It means that 80 appears most frequently.
(blackboard writing: it appears most frequently. )
Teacher: Numbers with this characteristic are called the majority. (blackboard writing: mode. )
Teacher: According to your understanding, what is the majority?
Health: I think the mode is the number that appears frequently in a set of data.
Teacher: (The computer shows the concept of plural and reads it by name. What is the pattern of this set of data?
Health: 80.
Teacher: It shows that among the students surveyed, the maximum weight is 80 kg. It seems that the pattern is only related to the number of times the data appears.
Teacher: Miss Wang also wants to know how old the students are this year. ( 10、 1 1、 12。 10 raise your hand. Let's see. 1 1 raise your hand. 12 age? You said there were the most teenagers in our class? ( 1 1。 ) Then 1 1 is the age of the students in our class. )
3. New lesson summary.
Teacher: Through our research, we not only have a new understanding of the average, but also know two new friends: the median and the mode. (Write it on the blackboard. According to your understanding, what are the characteristics of their three statistics?
Health: The average is related to every data.
Health: Median is the middle number in a set of data arranged in a certain order.
Health: The number that appears most frequently in a set of data is the mode.
Health: I know that when the number of a set of data is odd, the median is the middle number; When the number of data is even, the median is the average of the middle two numbers.
Teacher: Actually, statistical knowledge is widely used in our life.
Third, contact life, highlighting the practical significance
Teacher: The teacher also wants to do a small field survey. Do you all know what size shoes you wear? Now count the shoe sizes of male and female students respectively. Students are divided into two groups, male and female, and the recorder will sort it out. )
Teacher: Let's look at these two statistics. What information can you get from them?
Health: I know that most students wear size 37 shoes, and the least wear size 40 shoes.
Teacher: If you are the manager of a children's shoe store, how can the information provided by these two sets of data help you?
Health: Wear size 37 shoes, because there are many people wearing them.
Health: I want to put more size 38 shoes, because my feet will get bigger as students grow up.
Health: There are fewer shoes in sizes 34 and 40, because fewer people wear these sizes.
Teacher: Through the study of this course, students can not only analyze the data, but also make decisions based on the data. It seems that you have gained a lot.
Fourth, the class summarizes.
Teacher: Actually, math knowledge can help us solve many practical problems in life. Mathematics is indispensable in life. If you have a heart, look for it in life!
Reflection:
In the teaching of this class, the three-dimensional goals of discussion, communication and interaction between teachers and students have been well implemented, and the students' ability has been improved. In the process of solving problems, students deepen their understanding of concepts and realize that
Different characteristics of mean, median and mode and their practical significance.
Looking back on this lesson, there are mainly the following characteristics:
(1) Only when there is conflict can we explore and only when there is cognition can we construct.
Open-ended question design can arouse students' thinking, make students have conflicts in cognitive structure, and make it a good opportunity for students to reconstruct their cognition. In the process of students' active exploration, thinking and discovery, they realize the generation process and practical background of the median. In this way, students not only complete the integration and construction of new knowledge, but also give students the right to explore and discover new knowledge.
(2) Only when there is cooperation can there be communication, and only when there is supplement can there be perfection.
In this course, cooperation and communication run through the whole teaching process, whether from the derivation of concepts, the solution of problems or the formulation of decisions. Through group discussion and deskmate communication, students at all levels have different understandings of knowledge; In the process of communication, each student's thinking and wisdom are shared by the whole group, and students' understanding of concepts is more comprehensive and in-depth.
The above points are quite successful in this class, but there are still some regrets and shortcomings. For example, although modal learning is natural and easy, it is relatively simple to understand. If we can make full use of this set of data, we can guide students to find that there may be 1, 2 or no modes in a set of data, so that students will have a more comprehensive understanding of modes. Median is not widely used in students' life. How to make students feel the significance and function of median and mode in life through rich examples is worthy of our in-depth study.
In short, the whole class has gone through the process of observing and thinking, discovering through thinking, discovering and arguing, and improving through arguing. We really returned the classroom to the students, and teachers and students felt the fun of mathematics learning in the discussion and exchange.
Teaching plan and reflection 3 of the general edition of mathematics in the fifth grade of primary school: 798 1 page, volume 9, example of Jiangsu Education Edition 1, exercise, exercise 18, topic 1 and 2.
Teaching purpose:
1, let students learn data through their favorite situations, stimulate their interest in learning mathematics, and perceive the role of mathematics in life;
2. Let students feel the process of data sorting, learn to make simple bar charts and analyze bar charts through independent learning, and get simple information from them;
3. Cultivate students' habit of thinking in an orderly way and their sense of application, and experience the sense of cooperation, exploration and innovation with their peers without the teacher's explanation.
Teaching emphasis and difficulty: master the making method of bar graph and observe and analyze it.
Teaching preparation: autonomous learning platform, courseware, LCD projector, physical projector, statistical table, exercise paper.
Teaching process:
First, create scenarios to stimulate interest
Teacher: Students, what days of the year make you particularly happy?
Health:
Teacher: Birthday is an unforgettable day for every student. Who will tell the teacher which quarter your birthday is in? (Students raise their hands to speak) So many students want to tell the teacher, but the teacher can't remember. The teacher also wants to know the number of birthdays in our class every quarter. Can you help the teacher think of a way?
Teaching plan and reflection on the second volume of mathematics in the fifth grade of primary school. Ordinary version 4 1. Create situations and practice.
Conversation Introduction in Multimedia Courseware Operation
Teacher: Can you spell a rectangle with the same small square?
Teacher: If you use two squares, how many spellings are there?
Teacher: If three squares are used, how many spellings are there?
Teacher: If you use four squares, how many spellings are there?
Organize students to discuss and operate puzzles and report them.
Teacher: Yes! So there are two spellings, with four identical small squares. If you continue to use 5, 6 and 7, can you spell it? Health: (Yes)
Teacher: Let's try it! Please cooperate with each group according to the division of labor before class, and make records. (See record sheet) (attached)
The new curriculum standard points out that students' learning process must be based on existing knowledge, and the learning process is the process of thinking development. The main task of teachers is to inspire and mobilize students' thinking. On the basis of students' existing knowledge, the teaching design of this link allows students to collect data through observation, hands-on operation and heterogeneous cooperation in groups, which not only reviews and consolidates what they have learned, but also cultivates their hands-on ability and cooperation ability. )
Second, stimulate discussion and form appearances.
Team report. (Ask the representatives of each group to show the collected data before projection, and the other groups will check and evaluate each other and correct the collected data. )
Teacher: Let's observe the number of kinds of rectangles. Can you find anything good?
This question makes students find that there are some squares and some rectangles, and the product of the length and width of a rectangle is the number of small squares we use. There is only one kind of rectangle, some have two kinds, and some have three kinds. If you continue to spell, there may be four, five or even more.
Organize students to check.
Inspire students to classify according to the number of types of rectangular blocks. (group discussion)
There may be two kinds: one is that the number of types of rectangles that can be spelled is odd, and the other is that the number of types of rectangles that can be spelled is even; Divided into three categories, those who can only spell one, those who can spell two and those who can spell three; Divided into two categories, can only be spelled into one category, can be spelled into more than two categories.
After affirming the classification of students, the teacher organizes students to discuss. Which of these points is more reasonable? More convenient for us to study?
Students gain research direction through argumentation. Divided into two categories, can only be spelled into one category, can be spelled into more than two categories. In this way, at least one category can be distinguished and its characteristics can be studied.
On the basis of data collected by students, teachers guide students through their own wisdom, so that students can sort out and analyze their own labor results, discuss and demonstrate, thus discovering the laws of data, initially perceiving the characteristics of prime numbers and composite numbers, and laying a good teaching foundation for revealing the essential attributes of concepts. )
Third, explore and discover, abstract the essence
Teacher: Do you agree with him? (Agreed) OK! (The courseware shows the classification research record table) Then let's learn it again. How many small squares can only form a rectangle?
Health (Qi): 2,3,5,7, 1 1
Teacher: Why can we only spell a rectangle when the number of small squares is these numbers?
Health (1): I found that the product of length times width is the number of squares. When the number of small squares is these numbers, there is only one way to multiply the length by the width.
Health (2): I found that the length and width that can only be spelled into a rectangle is the divisor of the number of small squares.
Teacher: We call numbers with this characteristic prime numbers. Think about what a prime number is.
Health (1): I think what can only be spelled into a rectangle is called a prime number.
Health (2): I think a number is called a prime number if it only contains two divisors.
Teacher: You summed it up very well. Let's read the definition together. (Multimedia presentation concept)
Teacher: We call numbers with features like 4, 6, 8, 9, 10, 12 and 14 as composite numbers. Think about what a composite number is.
Student: If a number has other divisors besides 1 and itself, it is called a composite number.
Teacher: Think about it. What's the difference between prime numbers and composite numbers?
Health: The prime number has only two divisors 1 and itself, while the composite number has other divisors besides 1 and itself, that is, the composite number has at least three divisors.
Teacher: Let's discuss that 1 is a prime number. Or a composite number? Why?
Students discuss freely in study groups.
Students report the debate, complement each other and draw a conclusion.
Teacher: The courseware demonstration (1 is neither a prime number nor a composite number. )
In this part of teaching, the teacher discovered the essential attributes of prime numbers and composite numbers by organizing students to observe, discuss and explore, and got the concepts. At this time, the teacher did not stop asking questions, but then guided the students to compare and analyze, and found new laws: the difference between instigation and composite number and the classification of 1. This not only improves students' understanding of the concept, but also expands students' grasp of the connotation and extension of the concept, laying a good foundation for the teaching of natural number classification)
General comments:
The teaching of concepts is often boring. Generally speaking, it is either repeated language by teachers and students or a lot of practice. The teaching in this class is great, which makes me feel particularly excited. First of all, in concept teaching, the harmonious classroom atmosphere between teachers and students infected me. It changed the boring concept teaching. Let the students learn while doing, because the textbook has surpassed the textbook. Students use the information they have just learned in this book to collect and sort out knowledge to learn this lesson, so that students' interest can be mobilized at once.
Second, inquiry, cooperation, discussion and autonomous learning are the basic concepts of the new curriculum standards. How to implement this concept in concept teaching is the characteristic of this course. In teaching, teachers can understand students through their own understanding of textbooks. Carefully design questions, skillfully guide students to think, discuss and explore, and summarize and discover laws. Students discuss and explore knowledge through heterogeneous combination, promote mutual learning and improve cooperation ability, which is beneficial to students' lifelong development.
Thirdly, the concept of macro mathematics is an important concept in the new curriculum standard of primary school mathematics. This paragraph of teaching not only embodies the comprehensive characteristics of primary school mathematics knowledge, but also truly combines the cultivation of humanistic literacy such as mathematics knowledge teaching, practical ability and cooperation ability. Students' heterogeneous combination discussion, hands-on struggle, mutual consultation and individual debate all reflect teachers' advanced educational and teaching concepts.