First of all, teaching materials, objectives

The area of parallelogram is taught on the basis that students have mastered and can flexibly use the calculation formula of rectangular area and understand the characteristics of parallelogram. The study of this part of knowledge will lay a good foundation for students to learn the area of triangle, trapezoid and other plane graphics. It can be seen that this lesson is an important link to promote the development of students' spatial concepts and consolidate their learning of geometry knowledge. According to the requirements of the new curriculum standards and the characteristics of teaching materials, and fully considering the thinking level of fifth-grade students, I set the teaching objectives of this lesson as follows:

1. Knowledge Objective: Through students' independent exploration and hands-on practice, the calculation formula of parallelogram area is deduced, and the area of parallelogram can be calculated correctly.

2. Ability goal: Through operation, observation and comparison, let students experience the derivation process of parallelogram area formula, develop students' spatial concept and infiltrate the transformation thinking method.

3. Emotional goal: to cultivate students' ability to analyze, synthesize, abstract, summarize and solve practical problems; Let students feel the connection between mathematics and life, cultivate students' awareness of mathematics application and experience the value of mathematics.

The teaching focus of this course is to explore and deduce the calculation formula of parallelogram area and use it correctly.

Teaching difficulties: the derivation method of parallelogram area formula-transformation and equal product deformation.

Second, talk about teaching methods and learning methods.

According to the teaching content of this class, students' thinking characteristics and the new curriculum concept, students are the main body of learning, and teachers are the directors, organizers and collaborators. I intend to adopt the following teaching methods and learning methods:

1, use multimedia courseware to create life situations, stimulate students' interest in learning mathematics and motivation for positive thinking, and guide students to actively explore.

2. Hands-on practice, active exploration and cooperative communication are important ways for students to learn mathematics. From intuition to abstraction, it goes deeper and deeper, following the principle of concept teaching and the law of students' cognition. Through hands-on operation, the parallelogram is transformed into a rectangle, and the existing representation is reproduced. With the help of existing knowledge and experience, the calculation formula of parallelogram area is observed, analyzed, compared, reasoned and summarized. Students' dominant position is fully reflected in teaching, and students' enthusiasm and initiative are fully mobilized. Give students more space to carry out inquiry learning and let them think independently in specific operational activities.

3. Satisfy students' thirst for knowledge at different levels and embody the principle of teaching students in accordance with their aptitude. Through flexible and diverse exercises, we can consolidate the calculation method of parallelogram area and improve students' thinking ability.

4. Solve the problems around us in connection with the reality of life, so that students can initially feel the close connection between mathematics and life, experience the application of mathematics, and promote the development of students.

Third, talk about the teaching process

In order to better highlight the teaching concept of "independent inquiry" and achieve the teaching goal efficiently, my preset teaching procedure is divided into four parts: (I will talk about these four aspects respectively)

(A) the creation of scenarios, leading to topics

Only in this way can we jump out of the old framework of simply talking about knowledge and preaching in mathematics class and let students experience the happiness of mathematics life. At the beginning of the new class, I set questions and design practical problems in life that students' existing knowledge level can't solve according to the interesting stories of Avanti and the characteristics of students' interests. Then, encourage students to use their brains to guess and lead to the topic of this lesson: area calculation of parallelogram (blackboard writing).

(B) hands-on practice, explore new knowledge

Test the conjecture with the method of cutting and spelling.

Psychologist Piaget pointed out: "Activity is the basis of cognition, and wisdom begins with action". The process of hands-on operation is the process of students exploring and learning step by step. Only when students have strong hands-on ability can they fully perceive and establish appearances and create good conditions for analyzing and solving problems.

Because some students mentioned the method of cutting and filling to find the area when counting squares, I pushed the boat forward and let the students operate, trying to convert the parallelogram into a rectangle. Report after the operation and exchange your own verification process. When reporting, there are many ways to cut and paste. At this time, I threw a question to the students in time: "Why do you want to cut along the height?" Stimulate students to think positively. Then I guide students to observe and compare these two figures, and then discuss: compared with the original parallelogram, what has changed and what has not? What is the relationship between the length and width of the rectangle and the base and height of the original parallelogram? Through the thinking of the above questions, students have a deeper understanding of the derivation of parallelogram formula. At this time, I guide students to draw the derivation process: a parallelogram is converted into a rectangle after cutting and splicing, the length of the spliced rectangle is equivalent to the bottom of the original parallelogram, the width of the spliced rectangle is equivalent to the height of the original parallelogram, and the area of the parallelogram is equal to the area of the rectangle. Because the area of a rectangle is equal to length × width, the area of a parallelogram is equal to base ×. Then let the students at the same table communicate the whole operation process with each other, so that students can really understand the process of parallelogram changing into rectangle. In the teaching design of this link, I play the guiding role of teachers, advocate students' hands-on operation, cooperation and communication, and then build a new mathematical model in students' minds: changing graphics-establishing relationships-deriving formulas. The whole process is refined by students' continuous improvement in practice, which completely puts students on the subject of learning, completely transforms learning mathematics knowledge into mathematical activities, and cultivates students' ability of observation, analysis and generalization.

(C) hierarchical training, understanding internalization

Classroom practice is one of the main links in mathematics teaching, and it is an effective method for students to form skills and develop intelligence. New knowledge needs to be consolidated and applied in time before it can be understood and internalized. Based on the principle of "emphasizing the foundation, testing ability and expanding thinking", I designed three levels of exercises.

The first floor: basic exercises: textbook examples 1. It is helpful for students to deepen their understanding of graphics and correctly distinguish the relationship between the base and height of parallelogram.

Second floor: Comprehensive exercise: Can you know the area of this parallelogram on the court? Students are confused by different heights. Students can make it clear in the calculation that only by finding the base of parallelogram and its corresponding height can their area be accurately calculated. And according to the obtained area and another height, the bottom corresponding to this height can be found.

The third layer: expansion exercise: compare the areas of several parallelograms.

The whole exercise design covers all the knowledge points of this lesson, although the amount of questions is not large. The diversity of problem presentation methods attracts students' attention, makes them full of confidence in facing challenges, stimulates students' interest and activates their thinking. At the same time, the arrangement of exercises follows the principle of easy first and then difficult, and goes deep at different levels, which also effectively cultivates students' innovative consciousness and problem-solving ability.

(D) class summary, consolidate new knowledge

Summary: What have we learned in this lesson? What have you learned? It is helpful for students to have a systematic understanding of what they have learned in this class and fully improve their ability to summarize.

In the above teaching links, I try to embody the idea of taking teachers as the leading factor and students as the main body, and use the "transformation" thinking method and "intuitive" teaching means to change teachers' "speaking" into "guiding", students' being listened to as active exploration, so that students can actively participate in the formation of knowledge and truly become the masters of learning.

Divide a number by a decimal.

First of all, talk about textbooks.

"A number divided by a decimal" is the second content of Unit 3 in the first volume of the fifth grade of People's Education Press. Decimal division is another extension of number division after integer division and decimal division, which is divided into two situations: one number is divided by integer and the other is divided by decimal. "Divider is the division of decimals" is an important and difficult point in primary school mathematics teaching and plays a key role in calculation teaching. It is a comprehensive calculation, including the invariance of quotient, the basic properties of decimal, the method of trial quotient, the division with zero in the middle of quotient and the division with zero at the end of quotient, which lays a solid foundation for learning four decimal operations in the future. By setting the life situation, the textbook leads to questions, students have cognitive conflicts and stimulate their interest in learning. In the arrangement of teaching materials, the quotient invariance is emphasized, and the division of divisor into decimal is transformed into the division of divisor into integer, and the new knowledge is transformed into the old knowledge. The teaching focus of this lesson is to let students understand and master the arithmetic and calculation methods of dividing a number into decimals. The difficulty in teaching lies in making students understand that "the movement of the decimal point position of the dividend will change with the change of the divisor".

Second, talk about learning.

Decimal division is an important and difficult point in elementary school number and algebra. Although the fifth-grade students have formed some abstract thinking, they still focus on concrete thinking, which is difficult to learn. But they have basically mastered the operation methods of numbers, especially the division of integers, the law of division and the movement of decimal points, as well as the nature of quotient invariance. All these laid the foundation for fractional division. Moreover, in the previous class, we have learned the fractional division in which the divisor is an integer, which will be more conducive to the learning of dividing a number into decimals.

Third, talk about teaching objectives.

1. Understand and master the calculation method of dividing a number into decimals, and be able to do written calculations correctly.

2. After going through the deduction process of converting the division with decimal divisor into the division with integer divisor, I can correctly calculate a number divided by decimal vertically.

3. Cultivate students' ability of analysis, transformation and induction, and further improve students' ability of calculation and solving practical problems.

Fourth, talk about the difficulties in teaching.

It is the focus of this lesson to master the calculation rules of division with divisor as decimal and apply them to calculation. However, due to the limited analytical reasoning ability of fifth-grade students, it is difficult to understand the calculation principle of the division with decimal divisor into the division with integer divisor.

Verb (abbreviation for verb) Speaking and teaching methods

The teaching process is a process in which teachers and students participate together, which inspires students to learn independently and fully mobilizes their enthusiasm and initiative. Effectively infiltrate mathematical thinking methods and improve students' quality. According to this principle and the teaching objectives to be achieved, and to stimulate students' interest in learning, the following teaching methods will be adopted:

(1) Method for creating a scene. The story of monkeys sharing peaches not only stimulated the method of learning interest, but also laid a good foundation for new knowledge and reviewed the invariance of quotient.

(2) observation and discovery method. Students find the difference between formula and new knowledge through observation, and then work out what to learn in this lesson, that is, division with divisor as decimal.

(3) cooperative inquiry method. By setting questions, teachers guide students to cooperate in learning, gradually inspire students to use transfer and clarify the principle of transformation to solve problems. They understand the calculation principle of division with divisor as decimal as "the invariance of quotient" and "the law of decimal size change caused by decimal position movement", and then use the calculation principle of division with divisor as integer to calculate after division with divisor as decimal.

(4) Practice the consolidation method. Strive to highlight key points and break through difficulties, so that students' ability to use knowledge and solve problems can be further improved.

Six, said the learning method

This class focuses on mobilizing students to actively think and explore, and increasing the time and space for students to participate in teaching activities as much as possible. The following instructions can be given:

(1) Observation and analysis: Let students learn to observe, analyze and solve problems.

(2) Inquiry and induction: Let students explore and induce how to use the strategy of reduction to solve problems, and make it clear that the key to solving problems is to apply the division with divisor as decimal to the division with divisor as integer and the law of quotient invariance.

(3) Practice consolidation: let students know that mathematics focuses on application, so as to test the application of knowledge and find out what they have not mastered and the gaps.

Seven, talk about the teaching process.

I divide the teaching of this course into six parts.

1, (Introduction) In this class, I used monkeys to share the story of peaches, which not only stimulated my interest in learning, but also paved the way for new knowledge and reviewed the invariance of quotient.

2. (Create a situation and ask questions) I will make full use of the situation diagram provided by the textbook (making Chinese knots) to let students observe the theme diagram and ask the question "Students, what mathematical information can you get by carefully observing the diagram?" "What mathematical questions can you ask from these mathematical information?" The student asked, "How many Chinese knots can a general manager tie?" Ask the students to solve this problem. Curriculum standards point out that students should be provided with rich learning resources from their familiar life background or reality. Setting this scene closely links mathematics with life, making students feel familiar and cordial, generating enthusiasm and impulse to solve problems, and making students in a state of actively exploring knowledge.

3. (Cooperative discussion, mathematical discovery, induction) When students list the formula "7.65÷0.85", they find that this formula is new knowledge, which leads to cognitive conflicts and stimulates students' interest in learning. This is the teaching difficulty of this course. I will ask questions, guide students to turn this new knowledge into old knowledge, and let students cooperate in groups to discuss how to solve this problem. Let the group report the results of the discussion. (1) Converts a divisor into an integer by changing the unit. (2) The divisor and dividend are simultaneously amplified by 100 times according to the quotient invariance. The previous review lead-in laid the foundation for learning here, and students can easily think of this method. Therefore, on the basis of students' self-discovery, we should mainly guide students to understand why divisor and dividend should be expanded by 100 times at the same time in order to convert divisor 0.85 into an integer, and also guide students to understand why divisor and divisor should be expanded by the same multiple in order not to change the original quotient. After students understand arithmetic, I will explain the vertical writing format to students and guide them to try to complete vertical writing, so that students can not only understand the transformation process; And mastered the standard vertical writing format. Finally, let the students summarize the arithmetic and calculation methods. This design avoids indoctrination teaching. When exploring new knowledge, we should first provide students with the direction of thinking, that is, whether they can solve it with what they have learned, then provide students with sufficient thinking space, give full play to their initiative, guide students to try different mathematical activities in time through observation, comparison and contact with old knowledge, and infiltrate the mathematical thought of "conversion" into teaching, so that students can freely solve problems from different angles.

4. (Consolidation exercise) After explaining the examples, I will arrange for students to do the problems and correct them in time. In order to test the effect of students' learning, let students consolidate and strengthen arithmetic, experience the joy of success and cultivate their interest in learning mathematics.

5. (Standard assessment) consists of basic training and extended application. All students must complete the basic training part, and excellent students must complete the extended application.

Classroom evaluation

At the end of the class, I asked the students, "What have you gained from studying this course?" Students sum up and complement each other, and the teacher only gives appropriate guidance. In order to cultivate students' inductive ability and language expression ability, students are encouraged to evaluate themselves from the aspects of mathematical knowledge, mathematical methods and mathematical emotions. Then ask the students, do you have any questions? Through the students' answers, I got a comprehensive understanding of my study.

Eight, say blackboard writing design

Good blackboard writing design should be concise, neat and beautiful, highlight key points and difficulties, and strengthen students' understanding of knowledge. Therefore, the blackboard book I designed is to display the topic in the center of the blackboard. The following is the formula "7.65÷0.85", and the vertical formula for calculating this formula is below this formula.

Nine, say the gains and losses of teaching.

A good lesson does not lie in how novel and different the design is, but in stimulating students' interest in learning, cultivating students' various abilities as much as possible, and letting students master knowledge in happiness. Although the course I designed is not novel enough, through students' cooperative learning and inquiry learning, the students' ability to solve problems is improved, and the pleasure of success is experienced, which stimulates the students' interest in learning and fully embodies the new teaching concept that teachers are the dominant and students are the main body.

Through teaching, I think I have achieved the following: 1. I have achieved the teaching goal well, and students can correctly master divisor as a decimal calculation method. 2. The mathematical learning methods of transfer and analogy are realized, so that students can learn new knowledge better.

There are two aspects that are not done well: 1. Overestimating students' existing knowledge in teaching leads to lax classroom. 2. Pay attention to students' learning situation, assist students to learn according to their actual situation, and let all students learn something. 3, the time is not good enough, and I am a little nervous behind.