Draft course on the meaning and nature of fractions

As a conscientious people's teacher, it is essential to write a good speech. Do you know about this? The following is a sample essay of the lecture on "The Meaning and Nature of Fractions" that I collected for you, for reference only. Let's have a look.

Lecture Notes on the Meaning and Nature of Fractions 1 I. Textbooks

1, teaching content:

Nine-year compulsory education primary school mathematics textbook Book 10 Unit 4 Lesson 1.

2. Teaching objectives:

(1) Let students understand the unit "1" in the experience activities such as speaking, drawing, writing, folding and drawing, feel and understand the meaning of the score, and cultivate students' practical operation ability and abstract generalization ability.

(2) Cultivate students' ability to collect and process information, as well as the ability of independent inquiry and cooperative learning in practice.

(3) Cultivate students' interest in learning by creating cooperative and active learning situations, and infiltrate the idea that mathematics comes from real life.

3. Teaching emphasis: Establish the concept of unit "1" and understand the meaning of score.

4. Teaching difficulty: Understanding the concept of "1".

Second, talk about teaching methods.

Students know things from easy to difficult, and step by step from shallow to deep. Although students have a preliminary understanding of the score in their previous study, they must follow their cognitive rules in order to understand the concept of unit "1" and further clarify the meaning of the score. Therefore, this course adheres to the principle of taking students as the main body and teachers as the leading factor. Teaching methods such as inspiration, induction and inquiry are adopted, interspersed with self-study and practice. Through hands-on operation and intuitive demonstration, let students fully perceive, and then through comparison and induction, break through the difficulty that a whole composed of many objects can also be regarded as the unit "1", step by step, and understand the meaning of scores on this basis, so as to cultivate students' various abilities.

Third, the guidance of speaking and learning methods.

Students' learning process is always inseparable from the method of starting school. In the teaching of this course, the guidance of learning method runs through the whole teaching process.

1. Teach students how to explore knowledge. The teacher provided the students with some hands-on materials, including 8 pieces of chess, 2 pieces of candy, 10 beans, a picture of a panda, etc. And ask students to use these learning tools to divide them into points in the form of group cooperation, draw a picture and fold it to represent 65,438+0/2. Then observe and compare their similarities and differences, and realize that the unit "1" can be not only an object, a unit of measurement, but also a whole composed of many objects. Reach the sublimation of perceptual knowledge and rational knowledge.

2. Guide students to master the method of summarizing the essence of things while acquiring knowledge. After hands-on operation and comparison, the students come to the conclusion that the unit "1" can also be a whole composed of many objects. Ask the students to operate it twice, and realize that the score is different because of the number of copies of the score. On this basis, further clarify the meaning of the score and summarize it: divide the unit "1" into several shares on average to represent such a number or share, which is called a score.

Fourth, talk about teaching procedures.

(A) display information to understand the generation of scores

Introduce naturally through conversation and ask students to tell you what they know through investigation. Let students feel satisfied, interested in learning scores, and feel the necessity of generating scores.

(2) Awakening the known and exploring the unknown

1, through reviewing the old knowledge, prepare for learning new knowledge, stimulate students' learning motivation and arouse their learning enthusiasm.

2. Understand the meaning of the unit "1" for the first time.

(1) Teacher's suggestion: 1/2 Besides dividing an apple into two parts, what else can 1 mean? In order to facilitate students to study problems, the teacher provided some hands-on materials (8 Weiqi pieces, 1 meter long rope, a round piece of paper, a picture of a panda, etc.). ) For students, divide them into a point, draw a picture, fold it in the form of group cooperation, and try to express 1/2 with these learning tools.

(2) collective communication, * * * enjoy the results. Each group sent representatives to show their operation methods and achievements in front of the physical projector.

(3) Key and difficult problems Teachers use multimedia technology to make breakthroughs.

For example, after the students used 8 pieces and 6 pandas to represent the score of 1/2, the teacher showed the courseware, and through intuitive demonstration, let the students know that the unit "1" can be a circle, a unit of measurement, or a whole composed of many objects.

(4) Guided induction, by comparing similarities and differences, let students discover, learn, explore, understand and talk about the unit "1" in combination with reality, and experience the unit "1" in life.

3. Operate it again to understand the meaning of the score.

(1) Do it again and let the students express different scores with learning tools. In the operation, let students realize that the same learning tool expresses different scores, so that the scores are different with different copywriting, so as to prepare for summing up the significance of the scores. At the same time, in the process of operation, cultivate students' innovative thinking.

(2) Guide students to try to sum up the meaning of scores.

(3) Read page 86 of the textbook, what is a score, and teach yourself the meaning of each part of the score.

(4) Take "5/73/8" as an example to consolidate the meaning of fractions and denominators.

Feedback exercise

In this link, the teacher adjusts the teaching in time according to the feedback information from the students, so that the students can effectively master the knowledge and achieve the purpose of training and improvement. In order to combine teaching students in accordance with their aptitude and make every student successful, I designed the following exercises:

1, which indicates the colored parts in the figure below with scores.

2. Use the following scores to represent the colored parts in the picture, right? Why?

The above two questions are basic exercises, the purpose of which is to highlight the key and difficult points of this lesson and deepen the understanding of the meaning of fractions.

3. The game "Grab the Red Flag".

The men's and women's teams sent representatives to the front to win the red flag, but they had to listen to the teacher's instructions. If they get the right red flag, they will be transferred to the next team. If they get the wrong chance, the teacher will be the starter and the other students will be the referees. Female students' representatives go to the front and get all 2/ 1 1, male students get the rest 1/9, female students get the rest 1/4, male students get the rest 2/3, female students get the rest 1/2, and the rest one is distributed to the whole class.

The design of this question deepens students' understanding of the meaning of fractions, improves their interest in learning, conforms to the psychological characteristics of primary school students, trains students' thinking and cultivates their extensiveness and flexibility.

(4) The whole class summarizes and reveals the topic.

"In this class, we learned the meaning of music together, got a better understanding of music, and had a lot of knowledge about music! Students continue to learn and explore after class! " The teacher extended the students' interest in learning to the next class.

Lecture Notes on the Meaning and Nature of Fractions II. I. Textbooks

The significance of the score is the content of the first lesson in Unit 4 of the fifth grade experimental textbook of compulsory education curriculum standard published by People's Education Press. Before this, students already know that an object, a figure and an average are divided into several parts, and such one or several parts can be expressed by fractions; The key point of this lesson is to make students understand that not only an object and a figure can be represented by natural number 1, but also many objects can be represented by natural number 1, which is usually called the unit "1". Then, we can sum up the meaning of the score, understand the unit of the score, learn the four operations of the score and apply the knowledge of the score, so as to further explore the basic properties of the score.

Second, talk about teaching objectives

According to the analysis of the content of the textbook, taking into account the existing cognitive level and life experience of fifth-grade students, combined with the characteristics of mathematics and the requirements of mathematics curriculum standards, I have formulated the following teaching objectives:

Knowledge and skills: establish the concept of unit "1", understand the meaning of score and know the unit of score.

Process and method: Through active study and exploration, we can understand and form the concept of score, and cultivate students' innovative spirit and practical ability in hands-on practice.

Emotion, attitude and values: through cooperation and communication among students, students can develop good study habits, such as listening and asking questions.

According to the mathematics curriculum standards and teaching materials, combined with the students' foundation, I established the teaching emphasis and difficulty of this class.

Teaching emphasis: mastering the meaning of scores.

Teaching difficulties: the understanding of the unit "1" and the significance of the score.

Three. Oral English teaching methods and learning methods

Students know things from easy to difficult, and step by step from shallow to deep. Although students have a preliminary understanding of the score in the previous study, in order for students to understand the meaning of the unit "1" and further clarify the meaning of the score, they must follow the students' cognitive rules. Therefore, in this class, I use the teaching method of independent inquiry and cooperative communication to review the old knowledge first.

In collective communication, the meaning of unit "1" is abstracted and the meaning of score is summarized, so as to know the unit of score and create a relaxed learning environment for students to learn mathematics actively, independently and confidently. In classroom teaching, give students enough time and space to explore independently, cooperate and communicate, draw a picture, write, choose and draw a picture, summarize the meaning of music score abstractly, and stimulate students' enthusiasm for learning. Guide students to learn to analyze, summarize, generalize, migrate and abstract, and grasp the essence of concepts.

Fourth, the teaching process

In order to complete the teaching objectives of this class, I strive to build a harmonious classroom in my own teaching process, mainly through the following aspects to organize teaching.

The first link, scenario introduction, understanding the unit "1" and understanding the meaning of the score.

In teaching, the concepts of "average score" and "score" were introduced from the beginning with stories, and it was put forward that "there are many such scores in life, and there are also such examples in books. Then let the students teach themselves textbooks to explain the generation of scores.

Next, let the students use learning tools to recall and review the existing knowledge in the actual operation of folding and drawing music scores, and let each student create a music score in various ways. Let the students show their achievements on stage, which embodies "doing mathematics". Process. At the same time, students can constantly enrich their intuitive feelings about scores in the process of listening to each other and complementing each other.

Then the teacher asked the students, what exactly is a score? Students learn textbooks by themselves again, make full use of textbooks, cultivate students' self-study ability, give students the initiative to learn, and then communicate in groups to find out what they understand and what they don't understand, so that students can realize the meaning construction of knowledge in the process of self-study, discussion and communication, embody the activity of "doing mathematics" again, reflect students' subjective status, and let each student participate in the whole process of learning as much as possible. Only when teachers guide students to grasp the key content, first have a complete concept of "the meaning of fractions", then study some doubts and difficulties, and gradually establish a complete and clear concept, can students' exploration spirit and orderly thinking ability be cultivated.

The second link is to understand the unit of the score and deepen the meaning of the score.

This link is to let students feel the characteristics of the score unit, first summarize and then learn the textbook by themselves, so as to master the score unit.

The third link: life application, consolidating the significance of the score.

Exercises are designed from easy to difficult, from shallow to deep, which not only consolidates new knowledge, but also develops thinking, reflecting hierarchy, pertinence and effectiveness. For example, in the practice of reaching the standard, we should pay attention to the gradient of the practice, cultivate students' divergent thinking, deepen the understanding of the unit: 1 through this exercise, and then internalize the meaning of the score, so as to prepare for later learning to solve practical problems with the knowledge of the score, such as "selecting the score to color" in the link of "expanding and extending". My intention is to let students choose. Let students from different situations show it.

In the whole process, students have a comprehensive understanding of the meaning of the unit "1" in the process of hands-on operation, brain thinking and reasoning. These open exercises designed in this lesson can expand students' active learning space, show students at different levels the opportunity of success and joy, thus enhancing students' self-confidence and receiving good teaching results.

The fourth link is the practice of reverse thinking.

The same student can express different scores. Guess what unit "1" is, so that students can understand it further in comparison and understand the meaning of scores naturally.

The fifth link: class summary.

Learning mathematics is essentially "doing mathematics". Teachers provide students with rich learning materials, so that students can "grade" in different forms and methods, and naturally let students experience and feel the process of grading. The exploration of the meaning of fractions is entirely obtained through students' own practice, cooperation and thinking. The color of students' "learning hegemony" is vividly reflected. Let students fully communicate, abstract, summarize, guide and summarize in time, and at the same time let students fully display themselves, and teachers properly reflect their role as instructors in the teaching process. Teacher-student interaction enables students to deeply understand and master the meaning of abstract fractions. It embodies the modern thought of "learning mathematics in activities".

Lecture notes on "the meaning and nature of fractions" 3 i. Teaching materials

Teaching content:

On the basis of students' preliminary understanding of fractions and their knowledge of divisor and multiple, greatest common divisor and minimum common multiple, the significance and nature of fractions are taught. About the meaning of fractions, in the fourth grade, students have been taught on the basis of intuitive and preliminary understanding of fractions with the help of operations. It is necessary to make students rise from sensibility to rational understanding through teaching. Understanding the unit "1" and the unit of the score according to the meaning of the score is the beginning of students' systematic study of the score, the focus of this unit, and the important basis for solving four arithmetic and application problems of the score.

Second, the teaching objectives:

1, understand the generation and meaning of the score.

2. Understand the meaning of the unit "1", know the decimal unit, and explain how many decimal units there are in a fraction.

3. In the process of understanding the meaning of fractions, mathematical thinking methods such as comparison and combination of numbers and shapes are infiltrated to cultivate students' abstract generalization ability.

Teaching emphasis: Understand the meaning of fractions.

Teaching difficulties: Understand the meaning of unit "1" and know decimal units.

Third, talk about learning:

Before learning this part of the content, students have a preliminary understanding of the scores in Grade Three, know the names of the scores, read and write simple scores, compare the scores with numerator 1 and the scores with the same denominator, and learn the simple addition and subtraction of the scores with the same denominator. This lesson consists of two parts: the generation of scores and the significance of scores. Scores are produced by human beings to meet objective and practical needs. The meaning of fraction has expanded from regarding an object as the unit "1" to regarding some objects as the unit "1".

Fourth, talk about the teaching process

(1) Review the introduction.

Show a circle evenly divided into four parts, one of which is colored. Let's use a number to represent the colored part, lead out 1/4, recall what 1/4 means, and reveal the topic: the meaning of score.

(2) Explore the meaning of the score.

1, hands-on operation

Two people at the same table cooperate:

(1) Choose a material from the envelope and express 1/4 by dividing and drawing.

(2) How do two people at the same table talk about 1/4?

(Material: 1 square paper, 1 rope, 4 pictures of apples and 8 pictures of pandas)

2. Feedback and communication. Tell me how you express 1/4.

(Important: whether it is paper, rope (one object), 4 apples and 8 pandas (some objects), divide them into 4 parts on average each time. )

3. Summarize and understand the unit "1"

Teacher: What's the difference in the process of expressing 1/4 just now? What is the difference? Like a piece of paper and a rope, we call it an object, while four apples and eight pandas, we call it some objects. Whether an object or some objects can be regarded as a whole. The whole (blackboard writing) can be represented by natural number 1, but it is different from ordinary 1. We usually call it the unit "1". (blackboard writing)

Teacher: What else can be considered as a whole/unit "1"?

Default: a class, a flock of sheep and a pile of apples. ...

4. Study 1/4 and 3/4 again.

The exposed part is a whole 1/4. Can you tell me what it is as a whole?

Default value: the cell "1" is 12 cubes. Because the exposed three cubes are integral 1/4, it means that there are still three such cubes, so we put three more cubes, three for each.

Teacher: What is the unit "1" here?

Default: 12 small cube is regarded as the unit "1".

Teacher: Good! Which score should be used to represent the covered part? Why?

Default: 3/4, because the unit "1" is divided into 4 parts and 3 parts.

(3) Know the fractional unit.

Make your own P46.

Teacher: What is the unit "1" here?

Default: treat a bunch of sugar as the unit "1".

Teacher: In this way, the unit "1" can be divided into 2, 3, 4, 6, etc., indicating one of the numbers. We call it a fractional unit.

Please tell me about the decimal units of these fractions. How many such decimal units are there?

Students report separately.

(4) practice consolidation.

1, can you just write a score and tell me what this score means?

What is its decimal unit? How many such decimal units are there?

2. Question 6 on page 48 of the textbook.

3. What is the score unit of the sixth question on page 48 of the textbook? How many such decimal units are there?

(5) Understand the generation of scores.

Teacher: Today we learned the meaning of fractions. Do you know how scores are generated? Come and listen to the introduction of the elf! ..... It seems that scores are generated when we measure and divide things in our lives, or when we can't get integer results in our calculations, and they come from the objective needs of life or mathematics. It is precisely because of these needs that we will know more other figures in the future.

(6) Expand reserves.

If this means 2/5, what unit is "1"?