Lecture Draft of Mixed Operation 1 I. Textbooks
The teaching content of this class is the second volume of fourth grade primary school mathematics published by Beijing Normal University. This part is taught on the basis of mastering the four decimal operations and the elementary arithmetic order of integers. The order of integer elementary arithmetic is also suitable for decimal elementary arithmetic, which also lays the foundation for further study of elementary arithmetic. The textbook creates a situation of "TV advertisement", which allows students to solve problems by using the knowledge of four decimal operations. In this process, they realize that the order of decimal mixed operation is the same as that of integer mixed operation, and some practical problems can be solved by decimal elementary arithmetic.
Second, say the goal.
1, understand that decimal mixed operation and integer mixed operation are in the same order, can calculate decimal elementary arithmetic (mainly divided into two steps, no more than three steps), and use the decimal addition, subtraction, multiplication and division operations to solve practical problems in daily life.
2. In the process of learning the elementary arithmetic order of decimals, understand the connection of mathematical knowledge.
3. Use decimal calculation to solve problems, cultivate students' application consciousness and realize the value of mathematics.
Third, oral teaching methods
In this class, I mainly adopt the teaching methods of cooperative learning, independent inquiry and discussion and discovery. Through calculation, inquiry, discussion, observation and comparison, students can explore, discover and "recreate" new knowledge freely and openly in limited time and space according to their own learning experience and their own way of thinking.
Fourth, the methods of speaking and learning
1, cooperative discussion on learning style: The new curriculum concept attaches great importance to cooperation and communication among students. In this class, when students ask questions according to the situation of "TV advertisements", it is not only conducive to learning from each other and exerting collective wisdom, but also to cultivate students' expression ability and cooperation ability.
2. Method of calculation, observation and discovery: After calculating the average number of elements per second, let students observe the comprehensive formulas of the two solutions and find that the order of decimal mixing operation and integer mixing operation is the same. In the consolidation exercise, students are also asked to calculate their own discovery methods and cultivate the spirit of independent inquiry.
Fifth, talk about the teaching process.
1, review, introduction.
At the beginning of teaching, through a simple oral calculation problem of mixed integer operation that students are prone to make mistakes, the importance of operation order is emphasized and the order of mixed integer operation is reviewed. Then, students are interested in the situation of "TV advertising", ask questions and introduce new lessons. In this way, the connection between old and new knowledge is tightly buckled, the transfer of knowledge is promoted, the students' interest in learning is stimulated, and the topic is revealed.
2. Cooperate and explore to find the law.
(1) Question: What is the average per second?
(2) Group cooperation and exploration.
(3) the whole class communication method.
(4) Summarize the discovery rules.
In teaching, students are not only required to master mathematical conclusions, but also should pay attention to students' awareness of "discovery", guide students to participate in the process of exploring the formation of knowledge, try their best to tap students' potential, and let students solve problems by themselves. This teaching process enables students to learn knowledge and discover laws in their own exploration through cooperative learning, independent calculation and observation and discovery.
3. Consolidate exercises and expand stretching.
(1) Textbook "Try it"
(2) Clever calculation 24.
In this process, through the textbook "Try it", the calculation method of elementary arithmetic is summarized: at first glance, I realize that "mathematics comes from life and is used in life" and feel the value of mathematics; At the same time, the ingenious calculation 24 once again senses the importance of the operation order in the mixed operation, thus achieving the purpose of extension.
4. Summarize the class and assign homework.
In the form of talking about the learning gains of this class, sort out the main points of learning and sort out the learning feelings; At the same time, arrange appropriate homework to achieve the purpose of applying knowledge and cultivating ability.
The elementary arithmetic of fractions and decimals, the second handout of mixed operation, is the content of the second chapter of the first semester of the sixth grade in junior high school. The content of the class I'm talking about today is the third class in this section. I will elaborate from the following seven aspects.
First, teaching material analysis:
Operation is an important part of junior high school mathematics learning, and elementary arithmetic of fractions and decimals is its basic content. The content to be learned in this lesson is to extend the operation law of integers to the operation of fractions after learning the exchange of fractions and decimals and the general order of elementary arithmetic of fractions and decimals, so that the operation of fractions becomes simpler, thus improving the accuracy of operations and laying the necessary foundation for students' future study.
Second, student analysis
For the sixth-grade students who have just entered junior high school, they are still in the transitional stage between primary school and middle school, and their cognitive and analytical abilities are still in the primary stage, but they have a strong thirst for knowledge, exploration and expression. So I designed this course to expand students' participation and exploration space appropriately.
Third, the teaching objectives
Through the process of "practice-cognition-practice-cognition", students have obtained and mastered the operation law of fractions, simplified the elementary arithmetic of fractions and decimals, and thus improved the accuracy of calculation. Cultivate students' inquiry ability, observation and analysis ability, and then understand the importance of choosing reasonable methods. At the same time, I feel the pleasure of mutual cooperation in the process of learning.
Fourthly, the importance and difficulty of teaching.
After students' active exploration and teachers' correct guidance, the difficulty of this course is to obtain and master the operation law of scores. Accurate application of appropriate algorithms to simplify calculation is the focus of this lesson.
V. Teaching methods and learning methods
Teaching methods:
The traditional teaching methods of calculation problems are mostly taught by teachers and practiced by students. Although this course has a certain amount of practice, it is often boring and difficult to attract students. In order to make the classroom interesting, vivid, efficient and thoughtful, it conforms to the characteristics of active thinking and easy mobilization of learning emotions of sixth-grade students, but the analytical ability is still relatively weak. I use the method of combining comparison and discussion, by creating problem situations, asking questions carefully, and using enlightening language in a timely and appropriate way, to improve students' learning enthusiasm and make them actively and happily participate in the whole teaching process, so as to achieve the purpose of teaching.
Studying law:
Cognitive discovery theory emphasizes that the personal experience and discovery of learning materials in a certain situation is the most valuable thing for learners, so I encourage students to observe, guess and ask questions independently in this class. Strive to promote students to change from passive state to active state and learn to learn.
Design concept:
"Mathematics teaching is the teaching of mathematics activities, and students are the masters of mathematics learning"
Sixth, the teaching process.
In order to effectively achieve the set goals, I divide the teaching process into the following five links.
Links: (1) Review and Import
Teacher: Before the new lesson, let's have a calculation contest. Two students at the same table will compare who can do it faster and more accurately.
Before class, I prepare two sets of calculation papers, and the papers at the same table are different, so that they can compete with each other, thus stimulating their enthusiasm for learning. With this question, why does he (she) do it faster than me? Go to the next link.
Links: (2) Find problems and learn new lessons.
After comparing the papers at the same table, students will have many discoveries and ideas. I asked, "What do you see from this paper and what do you think?" . On the surface, the two papers have the same points: the answers are the same, and the numbers are the same; And the difference: different bracket positions, different operation sequences. I thought that every question in Volume A could be the second step of every corresponding question in Volume B, but I didn't expect that the law of addition and combination and the law of multiplication and distribution in integer operation can also be applied to the calculation of scores. What's more, do additive commutative law, multiplicative commutative law and multiplicative associative law in integer operation also apply to fractions? Wait, I let the students speak freely. Finally, I told them that the operation law of integers is also applicable to the operation of fractions and decimals, but because of our limited knowledge now, we can't prove it, and we will solve it in the future study. If students don't find the essence of the problem through observation and questioning, then I will ask questions step by step to guide their thinking direction.
Links: (3) Try to do examples.
In this session, I designed two groups of topics. Because students are already familiar with the operation law of integers in the process of primary school study, and the operation law of fractions is actually the promotion of integers, I take the form of oral answers to the first group of examples to make students more familiar with the operation law and have a preliminary understanding of the advantages of using the operation law.
Example 1 calculation: (answer orally) and explain what method you used and why you did it.
The second set of examples is an improvement on the first set of examples. The topic is no longer simply using algorithms, but examples of various algorithms that can be used. However, because today's students generally have a bad study habit-they don't carefully examine the questions, so I ask them to observe them carefully for a period of time (half a minute) before writing.
Teacher: Let's watch it for half a minute before we do it.
Example 2 Calculation:
Because each student's observation direction is different and the angle of thinking is different, each student's method of solving problems is different. Through the communication of the whole class, let each student be more familiar with the algorithm and further realize the advantages of using the algorithm. At the same time, it is an important feature of our mathematics discipline to feel multiple solutions to a problem, and it is also an important feature different from other disciplines. At the same time, it sometimes inspires students to think from different angles.
Links: (4) Group discussion
If students can turn knowledge into skills, then our teacher's teaching can be said to be successful. Therefore, I asked the students to try to compile several fractional calculation problems that can use the algorithm in groups, and at the same time stimulate their enthusiasm for learning through competitions, which is also an affirmation of their learning achievements. For the problems in compiling questions, it can help other students solve them, increase their spirit of mutual assistance and feel the fun of cooperation.
Links: (5) Summary and promotion
Finally, the students entered a new climax with the words "I learned today …" and "My biggest gain in the learning process is …". With the help of teachers, students can sort out what they have learned, and at the same time understand that not only reasonable methods can be used in the operation process, but also reasonable and effective methods suitable for their own learning methods should be chosen in their daily study life, so that learning will become easy.
Links: (6) Homework
The homework I left for my classmates this time was calculated reasonably. These questions were written by the students themselves after group discussion in class. Students with a good foundation can ask to solve more than one problem.
Seven, some thoughts on the process of instructional design.
As usual, before starting the entrance to explore, I created a certain scene for my classmates because of their young age and limited knowledge and ability. In the past, I always asked questions and groped for directions step by step, and my classmates always walked forward step by step according to my ideas, lacking room for independent observation and analysis. This is related to our habit of designating students' activities. This time, I designed a different way to ask questions. First of all, I gave them some space to think and explore. According to the observation and thinking of different students at different levels, I guide them to find the essential problems and enter the new classroom. Fundamentally cultivate students' comprehensive ability of observation, analysis and generalization.
According to the spirit of the second curriculum reform, taking students' development as the foundation, one of the most important points is to pay attention to students' ability to actively participate in mathematics practice, so in the final practice, I adopted the form of students compiling questions and students answering questions. In the past, we always asked them questions, but today their own cooperation and exchange meetings arouse students' interest in learning. His classmates' answers and discussions made his memory more profound. At the same time, it can also expose some misunderstandings in their understanding of the algorithm, such as: Is there a commutative law in division? In the process of using the law of association, it is preceded by a negative sign. What should I do? Wait a minute.
After letting go, this class let me see the students' intelligence, expand the space of thinking, thus improving students' interest in learning, starting autonomous learning, and harvesting useful mathematical ideas and creative talents for life.
"Mixed operation" lecture 3 I. Talking about teaching materials:
1, lecture content:
People's Education Press Nine-year Compulsory Education Six-year Primary School Mathematics Book X Page 59 to 62 Examples 1 and Example 2.
2. teaching material analysis:
Because students are familiar with the operation sequence of elementary arithmetic of integers and decimals through the study of Book 9, there are some mixed operation problems of two-step calculation when teaching the addition, subtraction, multiplication and division of fractions in this book. On this basis, this section is an elementary arithmetic problem, which teaches three-step score calculation. Therefore, when we talk about the four expressions of fractions, we don't explain the operation order in detail, but directly explain that the operation order of fractional elementary arithmetic is the same as that of integer elementary arithmetic. Then combine the example 1 and example 2 to guide students to think first. In elementary arithmetic with two levels of operation. What should be considered first, and then what to consider; How to calculate in the formula with brackets, so that students can work out the results themselves.
3. Teaching emphases and difficulties:
Master the operation order of fractional elementary arithmetic, cultivate students' good calculation ability, test students' habits and improve the accuracy of calculation.
Second, the teaching objectives:
1, so that students can master the operation order of fractional elementary arithmetic and correctly calculate four mixed questions.
2. Improve students' logical reasoning ability and calculation ability.
3. Cultivate students' good computing ability and test their good study habits.
Third, teaching methods:
The new curriculum standard points out: let children learn their favorite teaching. Let children learn the teaching they need, and let students of different levels have different degrees of gains. We can no longer use a ruler to measure students' grades. It is necessary to completely change the teaching mode of "one-word-for-one" and "full-hall irrigation", introduce information technology into the classroom, and guide students to actively explore, find and solve problems. Therefore, the teaching method of "hierarchical guidance and problem solving" is only used in the whole class. At the beginning of a new class, students can directly indicate their teaching goal, that is, to know what they will learn in this class. Then tell the students that there are two groups of learning plans, and let the students choose their own learning methods according to their actual situation to complete the content of this lesson. Then do layered exercises, basic exercises, improving exercises and thinking exercises in the exercises. Promote students' knowledge internalization. Students who have learned more than enough provide some extracurricular knowledge. Let students read to expand their knowledge.
Fourth, the methods of speaking and learning:
A good way to consciously teach students to explore knowledge independently. By allowing students to try, observe, read and discuss, we can fully mobilize the participation of students' various senses and let students fully participate in the development and formation of new knowledge. Multi-sensory participation in learning activities can help students establish multi-level and multi-network connections in their brains, which is conducive to students' understanding and memory, and can also highlight students' dominant position and create an equal, democratic and harmonious teaching environment.
Lecture note 4 of mixed operation I said today, and the topic of the class is elementary arithmetic exercises 1. I mainly report to the judges from the following aspects.
I. teaching material analysis
This lesson is the teaching content of 8-9 pages in the second volume of fourth grade primary school mathematics by People's Education Press. The teaching content of this course is an exercise class that students can perform two-step operations such as addition, subtraction, multiplication and division and three-step operations such as addition, subtraction, multiplication and division on the basis of mastering four integer operations. This lesson is based on students' understanding of elementary arithmetic laws through the inquiry and self-study in the first class, but they have no certain training and proficiency. Elementary arithmetic is widely used in daily life, production and scientific research, and is the basis for further learning mathematical knowledge and scientific knowledge. So primary school students must master the most basic knowledge and skills.
Second, the determination of teaching objectives
The new curriculum standard clearly points out the teaching objectives of practical courses: what new concepts, new properties, new laws, new laws and new formulas to consolidate and deepen; How to organize, classify and compare knowledge; What measures and methods are used to organize effective exercises? What kind of comprehensive knowledge training; What basic mathematical abilities have been formed; What positive emotional experiences have you gained?
Therefore, I have formulated the following teaching objectives according to the teaching content.
1, mastering the order of elementary arithmetic and calculating correctly can solve practical problems.
2. By letting students try to calculate, they can experience the fluidity of mathematics knowledge in learning.
3. Cultivate students' serious and careful study habits, and infiltrate the dialectical materialism enlightenment thought of things interrelated in calculation.
Key points: master the operation sequence and calculate correctly.
Difficulty: Be able to calculate correctly, solve practical problems and tell the reason.
Third, teaching methods and learning methods.
Students are the main body of learning, and teachers are the organizers, guides and collaborators of learning. In classroom teaching, teachers do not simply impart knowledge, but let students learn independently under the guidance of teachers, and no one can replace students in learning. The state and degree of students' participation is an important factor to determine the teaching effect.
In this class, I use situations, life experiences and other methods to make students turn hard study into happy study. Take "multimedia courseware" as the carrier, and take observation, comparison, group discussion, application and calculation as the main line. Guide students to carry out inquiry learning activities in various ways such as "observation, comparison and summary". The purpose is to make students interested in learning and leave room for students to study and think.
Fourth, prepare before class.
Multimedia courseware and corresponding exercises.
Teaching process of verbs (abbreviation of verb)
Communication before class:
Spring has arrived, and Tomb-Sweeping Day will arrive soon. What ancient poems about Tomb-Sweeping Day can you recite? Can you quickly tell how many words there are in this poem? (Students use mixed calculation to say the number of words in ancient poetry)
(Design intention: Now we are actively discussing whether to divide the arts and sciences. I think we can also cultivate students' humanistic quality in math class. )
(A) the introduction of retrospective scenario
Tomb-Sweeping Day is coming. In this class, the teacher will take the students to visit Cangshan in our hometown. We went to 30 classmates and teachers. How much do we need if the student tickets 2 yuan and the adult tickets 5 yuan?
(Students explore, solve and tell the calculation steps)
(Design intention: Math class is abstract, sometimes even boring, especially calculation class. This link is designed to stimulate students' interest, skillfully create situations, and let students solve problems in situations, leaving students with space and time to think, so that students have more opportunities to participate, and their enthusiasm and self-confidence are greatly satisfied. )
Introduction topic: four arithmetic exercises, teacher qualification certificate recognition, primary school mathematics handout: elementary arithmetic
(B) layered practice, strengthen and improve
1, basic exercise
Now I have entered the garden, and there is an open field in front of me, but there are not enough mines here. Can students get rid of it quickly and accurately? Show a group of calculation problems with only addition and subtraction or only multiplication and division. Students' summary method after calculation: in the formula without brackets, if there is only addition, subtraction, multiplication and division, it should be calculated from left to right in turn.
Walking through this flat land, we will face steep steps. Are students confident to climb up? Show a set of mixed operation exercises of addition, subtraction, multiplication and division, which students can complete independently.
(design intent: interest is the best teacher. This issue closely follows the situation of the previous issue and presents several simple exercises so that every student can experience the joy of success. )
2. Comprehensive exercises
We are now in front of the revolutionary martyrs memorial tower. There are three stone carvings on the front, four on the left and four on the back. Do you know how many stone carvings are around the tower?
At this moment, the teacher saw an old man thinking hard about a problem. Are you willing to help him?
3, improve the practice
Students, we have reached the foot of the mountain now and are going to climb the main peak soon. Before going up the mountain, we need to buy some things and give you 20 yuan money. Faced with so many commodities, what questions can you ask?
(design intent: the new textbook incorporates calculation in solving problems, which is because solving problems requires calculation. This is the case in real life, and calculations are only needed when solving problems. Therefore, the regulation of mixed operation order should be the same. I rectify the situation diagram in this way, which is not only convenient for students to highlight the main problems to be solved, but also convenient for students to experience and understand the relationship between the comprehensive formula and the step-by-step formula in solving problems, which is helpful to realize the construction process of analyzing the operation order-using the comprehensive formula-requiring the operation order in solving problems, and to achieve the purpose of integrating calculation and application. )
(3) Perfect independent testing and evaluation.
1, independent detection
Now we are going to climb the main peak. The road is rugged. I believe the students can overcome many difficulties and reach the summit successfully. You can do it as long as you are careful. Students finish the exercises independently.
Design intention: I design exercises in this way, which not only attaches importance to the training of basic knowledge, but also integrates knowledge and interest, so that students are full of interest and actively participate. Mathematics class is full of vitality because of students' active participation. )
2. Perfect evaluation
Report your answers all your life, and check and correct your mistakes for the rest.
Design intention: I design exercises in this way, which not only attaches importance to the training of basic knowledge, but also integrates knowledge and interest, so that students are full of interest and actively participate. Mathematics class is full of vitality because of students' active participation. )
(4) Summarize the extracurricular extension.
1, summary
What did we mainly learn in this class? What is your biggest gain? What do you think of your performance? Teachers timely evaluate students' learning situation emotionally and intellectually.
2. Extracurricular development
Thinking exercises on the ninth page of the textbook.
(Design intention: Let students sum up what they have learned, realize the importance of learning methods and the continuity of mathematics content in communication and reflection, and stimulate students' desire to further explore knowledge. Ask the students to tell the students about the gains of this class and the problems existing in the group, and solve the students' problems in the form of student-student communication and teacher-student communication, which not only solves the problems, but also cultivates the students' team spirit of mutual assistance. )
"Mixed Operation" Lecture Notes 5 I. teaching material analysis
The elementary arithmetic with brackets in Unit 1, Volume 2 of Mathematics for the Fourth Grade of Primary School, published by People's Education Press, is a summary of integer elementary arithmetic according to students' understanding of mixed operation and its operation order, as well as the role of brackets.
Second, the teaching objectives
Knowledge and skills: enable students to master the order of two-level operations (including parentheses and brackets) and calculate correctly.
Process and method: Let students actively participate in teaching activities through independent inquiry and cooperative communication.
Emotional attitude and values: cultivate students' consciousness of subject, question, exploration and cooperation. Cultivate students' habit of thinking independently and considering problems from different angles.
Third, the focus and difficulty of teaching
Key point: Understand the order of the four operations with brackets.
Difficulty: Use brackets to master the order of the four operations.
Fourth, the analysis of teaching methods
Starting from students' thinking reality, stimulate their desire to explore knowledge. The closer the teaching is to students' reality, in the process of guiding students to feel arithmetic and algorithms, let them try, let them actively participate in the formation of new knowledge, and mobilize students to speak their own methods boldly in time. Adhere to the principle of facing all and taking student development as the foundation. Let every student gain something and have the opportunity to experience the joy of success.
Teaching process of verbs (abbreviation of verb)
(A) create a situation to stimulate interest in the introduction
Do you still remember the "Snow World Amusement Park"? Two days ago, we went to the skating area and skiing area, where we explored many math problems. Today, let's take a walk in the ice sculpture area and study the math problems in the ice sculpture area together, shall we? (Show the scene of the ice sculpture area)
What mathematical information do you learn from the picture? The information given here is that there are 180 tourists in the morning and 270 tourists in the afternoon, and every 30 tourists need a cleaner. According to this information, what math questions can you ask? Students can ask questions freely.
(2) independently explore and solve problems
How to solve "how many cleaners are there in the afternoon than in the morning?" What about this question? Can students express their problem-solving process through formulas? Let the students think independently and write the formula. At this time, the teacher found different solutions by patrolling and asked the students to take out the formulas on the blackboard. Then, they asked the students on the blackboard to talk about their thinking process, and asked them to explain in detail why brackets were used in 270- 180. Summary: Parentheses are used to change the order of operations.
1, example 4 96÷ 12+4×2 group discussion, operation sequence, student report operation sequence, teacher's summary, students' independent calculation.
2. Add brackets 96 \u( 12+4)×2 to the title. The teacher explained that according to the conclusion just drawn, the students in brackets should try to calculate first.
3. Introducing Parentheses 96÷( 12+4)×2 There are two parentheses in this formula. Guess what? Students express their opinions after thinking, and finally the teacher summarizes the methods.
(3) Consolidate practice and improve feedback.
1, complete the corresponding work and practice the questions in groups.
2. Analyze the wrong questions and improve the ability to solve problems.
(D) class summary, self-evaluation.