The lecture of "Divide Bread" is 1.
"Divide bread" is the content of the second lesson of Unit 3 in the first volume of fifth grade mathematics in Beijing Normal University. This is a lesson after score recognition. In the third grade, students have a preliminary understanding of fractions, know the names of various parts, can read and write simple fractions, learn the meaning of fractions in the previous paragraph, and become familiar with the knowledge of units "1" and fractional units, which lays the foundation for learning this lesson. But they are all learned from the perspective of the relationship between the part and the whole. Cognitive scores are all true points. In addition, the concept of this lesson is abstract. What do you mean by false scores? How to understand when the unit "1" is not enough? Students' abstract logical thinking needs the support of intuitive thinking and image thinking to a great extent. So in this class, I will use the area model to explain first, and use the line model to consolidate and re-understand. The meaning of teaching scores properly permeates the number axis. Although the number axis is difficult for primary school students, the use of the number axis can make students better understand and distinguish the characteristics of true scores and false scores.
First of all, tell the knowledge and skills of teaching objectives:
Through the generation process of true points and false points, we can distinguish true points from false points by understanding their meanings and mastering their characteristics.
Process and method: Through the process of exploration, students' abilities of observation, analysis, comparison, abstraction and generalization are cultivated in hands-on operation, independent exploration and exchange and cooperation, and the idea of combining numbers with shapes is infiltrated.
Emotional attitude and values: in the process of studying problems, further cultivate students' sense of numbers and improve students' interest in learning and willingness to explore.
Second, preach the law.
This lesson starts with the specific situation, understands the meaning of the score with the help of the area model, and then preliminarily establishes the representation of the false score with the help of the number line model (number axis). Finally, in the process of classification, through overall observation, a true and false scoring model is constructed. Make the new concept deepen accurately in the existing concept and produce new understanding. Through students' independent exploration, independent thinking, cooperative communication and abstract generalization, students can develop in different degrees in discussion and communication, improve their thinking level and abstract generalization ability, and finally clarify the connotation of true and false points. Infiltrate the idea of combining numbers with shapes and the idea of classification. In the process of studying problems, improve students' interest in learning and willingness to explore, further cultivate students' sense of numbers, and lay the foundation for learning with fractions.
Third, talk about the teaching process
1, directly show the topic-"Divide cakes" The first activity: three cakes of the same size are distributed to four people on average. How to divide it? How many cakes will everyone get? (Examination questions: two questions) Method 1: One point, one point. Students do activities to explain the process and answers of cake sharing, 3 sections. (Slow) Method 2: Divide them together. Let the students begin to understand the quarter of 3. (slower)
2. Show the second activity of this class: 9 cakes of the same size are distributed to 4 people on average. How many cakes are distributed to each person? Method 1: Segmentation one by one (demonstrating the segmentation process with multimedia) Method 2: Stacking segmentation.
3. Insert the classification of interpretation points-divided into true points and false points. True fraction: numerator is less than denominator, and fractional value is less than.
1。 False fraction: numerator is greater than or equal to denominator, and fractional value is greater than or equal to 1.
2. In fact, there is a quick and simple method. Who knows? Cut in method three. Pay attention to timely explanation here:
1. Focus on inserting and explaining the name and composition of the score (let students add up the score with integer and true score according to the schematic diagram);
2. According to the result of dividing the cake just now, are these two scores the same? Same. The connection between band score and false score 3. (False scores can be converted into band scores or integers).
4. Classroom exercises (Challenge 1, 2 and 3)
5. What did you learn today? Talk about harvest. Summarize this lesson.
Lecture Notes on "Divide Bread" 2 I. Talking about Teaching Materials
1, teaching material analysis
Divide the cake is the content of page 37 ~ 38 in the ninth volume of mathematics, the standard experimental textbook of nine-year compulsory education. It is based on the students' initial understanding of scores, the understanding of true scores and false scores in the arrangement of teaching materials, the experience of the production process and practical significance of true scores and false scores in the activity of dividing cakes, and the descriptive definition of their concepts, and then let students talk about the characteristics of true scores and false scores. For concept textbooks with scores, the introduction method is used to treat true scores and false scores respectively, which helps students understand the relationship between false scores and scores and avoid illusions.
2. Analysis of learning situation
The fifth-grade students who grow up under the new curriculum are good at independent thinking, willing to cooperate and communicate, extremely active in class, strong in language expression, very willing to express their independent opinions, and have a good ability to learn mathematics in a flexible and open classroom. For students, although the true score has been initially known, it is still difficult to establish the production process and practical significance of true score and false score. In the activity of dividing cakes, students abstract specific scores to their generation and significance, and improve their ability to solve problems from the content itself and the methods of studying problems.
3, teaching material processing
In order to reflect the process goal of mathematics course, and according to the students' existing knowledge level, I have established the teaching goal, emphasis and difficulty of this class.
Knowledge goal: to understand the meaning of true score, false score and scored score through the process of making false score and scored score, combined with specific conditions.
Ability goal: be able to read and write match-fixing and scoring correctly, and understand the relationship between match-fixing and scoring.
Emotional goal: to explore ways to solve problems and experience the close relationship between mathematics and daily life.
Teaching emphasis: experience the generation process of false score and scored score according to the specific situation, and understand the meaning and relationship of true score, false score and scored score.
Teaching difficulties: hands-on operation to understand the method of dividing cakes and observe the characteristics of scores.
Second, oral teaching methods
It is pointed out in the standard that effective mathematics activities can't just rely on imitation and memory, and hands-on operation, independent exploration and cooperative communication are important ways to learn mathematics. This class adopts situational teaching method and guided inquiry method to organize students to carry out colorful mathematics activities.
Third, theoretical study.
Mathematics learning activities are full of exploratory and challenging activities such as observation, operation, reasoning, comparison, communication, experiment and simulation. This lesson encourages students to explore and cooperate independently many times in practice, and organizes students to observe, analyze and discuss carefully. In the process of solving practical problems in life, the task of inquiry is completed through hands-on practice and cooperative combing.
Fourth, talk about teaching procedures.
This lesson attempts to start from students' reality and interest, combine with specific situations, and experience the process of producing true, false and divided cognition in various activities, so as to understand the significance of true, false and divided cognition. Cultivate students' ability to learn mathematics through operation, observation and summary; The whole class revolves around several teaching links, such as exciting situations, exploring new knowledge by operation, consolidating application, reviewing and summarizing, etc.
(A) the story import
The teacher tells the story of Journey to the West in combination with the situational picture of the textbook, thus asking the question: How to divide three cakes of the same size among four people equally? How many cakes does everyone get? Then the teacher opened the topic and introduced the new lesson.
The design intention of this link is to make full use of the situation map of the textbook and arouse students' interest; Let students help Tang Priest and his disciples solve the problem of sharing cakes and stimulate students' thirst for knowledge; Lay the foundation for the later teaching.
(2) Operational exploration
Organize activities (1)
1. First, let the students take out three circular pieces of paper of the same size and mark three cakes respectively to help Bajie score one point. Before grading, the teacher emphasized the activity requirements:
(1) grouping,
(2) Let's talk about the method in the group.
(3) Choose one of the methods to get one point.
2. Report the results (students demonstrate, do and speak on stage)
The design intention of this link is to let students think, talk, cut, divide, perceive and experience mathematics in the activity, to reflect the autonomy and subjectivity of learning, to demonstrate in different ways, to understand the generation process of scores, and to achieve the role of migration for the next activity.
Organizing activities (2)
1, the teacher went on to tell the story and introduced the second question: nine cakes of the same size, distributed equally to four teachers and apprentices. How to divide it? How many cakes did everyone get?
2, the group points, and then reported to the exchange.
The design intention of this link is to let students understand the process of false points and belt points in the activity of dividing cakes.
3. Use fractions to teach writing and reading.
Teacher's summary: We just got two cards and the card of 1/4 by division. How to express it in fractions? (Writing and reading methods of teachers' teaching achievements)
Then the teacher asked the students to observe and communicate. Is 2 equal to 9/4? Telling students to bring scores is actually another form of false scores.
4. Reveal the meaning and characteristics of true score, false score and band score.
First, the teacher shows some scores for students to observe carefully. What are their characteristics? Communicate your findings with your classmates.
Then the students report the exchange, and the teacher reports the concepts of true score, false score and belt score on the blackboard.
Then the teacher asked: What is the relationship between the scores of these three groups and 1 cake? Students answer the teacher's blackboard and get the following results: true score is less than 1, false score is greater than or equal to 1, and band score is greater than 1.
The design intention of this link is to use the transfer of knowledge to let students speak freely and further consolidate and extend their knowledge. Using scores combined with situations to guide students to observe, discover and understand the characteristics of true scores and false scores.
(3) Integration of applications
1, exercise (the first question on page 38 of the textbook. )
2. Math clinic (Now we are doctors together, seeing a doctor for the topic. )
3. Write true and false scores with 7 as the denominator. (The second question on page 38 of the textbook)
4. Write scores as required.
5. Fill in (the third question on page 38)
This link is designed to enable students to enhance their understanding and deepening of knowledge and experience the connection between knowledge and life through practice.
(4) Review and summary
Let the students talk about the gains of this class.
This link is for students to organize, internalize, reflect and consolidate this knowledge.
Prediction of teaching effect of verbs (abbreviation of verb)
This lesson, from the introduction of stories, can narrow the distance between teachers and students, activate students' interest in learning, activate the classroom atmosphere and build a harmonious relationship between teachers and students. Qi Xin, a teacher and student, worked together to help Tang Priest and his disciples solve difficult problems. The story runs through the whole class, making students feel like they are in the journey to the West. In the process of dividing the cake, students are guided to cooperate in groups, so that students can think, speak, cut and divide, feel and experience mathematics in the activity, which embodies the autonomy and subjectivity of learning, and allows students to find ways to divide the cake in a specific situation, one by one, overlap, demonstrate in different ways, understand the generation process of scores, and realize the role of migration for the next activity. According to the specific situation, guide students to observe, discover and explore the characteristics of scores, so that students can learn knowledge and methods in activities.
Lecture Notes of "Divide Bread" 3 I. Talking about Teaching Materials
1, oral teaching content
Today, I'm teaching "Divide Bread" in Unit 3, Section 2, Volume 1, Grade 5, a primary school mathematics textbook published by Beijing Normal University. The third-grade students have learned the fraction whose numerator is smaller than the denominator, but they don't know it is called the true fraction. On the basis of further understanding of scores, the textbook also arranges the understanding of true scores and false scores, and realizes the production process and practical significance of true scores and false scores in the activity of "dividing cakes". In order to draw out and help students understand the true points, false points and belt points, the textbook has created a situational activity of "dividing cakes", which is taught at two levels.
2. Tell my thoughts and thoughts:
The first activity is that the problem of "three cakes for four" is abstract, so students should be organized to carry out activities to explore and understand. Mathematics curriculum standard clearly puts forward that "mathematics is a practical subject", so in teaching, I organize students to cut, spell and draw pictures, and then communicate with each other, so as to acquire knowledge and cultivate their abilities in practice. In order to help students better understand the concept and characteristics of "true points and false points", I deliberately changed the order. After learning each one, I introduced the concept and characteristics of "true score and false score". This arrangement is to prevent students from juxtaposing true scores and false scores as a class, because the teaching staff specially pointed out that "having scores" is only a special manifestation of false scores to prevent students from being confused. Homework after class consists of three questions. After research, I found that the first and third questions mainly introduced the relationship between false scores and false scores, which laid the foundation for the integration of false scores and false scores in the next new lesson. So I arranged it as an introduction to the next class, thus supplementing the new consolidation homework.
3, the student analysis said:
Some students may be familiar with false marks and band marks, but few students really understand their meaning. Then one of the key points of this lesson is to make students understand its meaning. Feel the relationship between false points and scored points. Can read and write fake scores, have scores.
Second, talk about teaching objectives
1, combined with the specific situation, let students experience the process of producing false scores and having scores, and understand the meanings of "true scores", "false scores" and "having scores". Can correctly read and write false scores and band scores, understand the relationship between false scores and band scores, and understand the relationship between band scores and integers.
2. In the process of exploration, I can think methodically, convincingly explain the rationality of the conclusion, explore ways to solve problems, and try to find other ways.
3. Being able to actively participate in the math activities organized by teachers, and experiencing math is closely related to daily life. Teaching emphases and difficulties
Teaching emphasis: let students understand the meanings of "true points", "false points" and "points" in the situation of sharing cakes.
Difficulties in teaching: use fake scores and band scores to represent the same thing, and feel the relationship between fake scores and band scores.
training/teaching aid
Computer courseware, some round paper, scissors.
Three. Oral English teaching methods and learning methods
The new curriculum standard points out that teachers are organizers, guides and collaborators of learning. According to this idea, I followed the principle of stimulating (stimulating students' interest)-guiding (guiding students to think)-exploring (encouraging students to explore independently)-allowing students to solve problems independently. In teaching, I carefully design questions to induce students to think and operate. Encourage students to communicate and let them use their knowledge to solve problems.
As the main body, students' participation in the learning process is an important factor to determine the teaching effect. Therefore, the choice of learning methods reflects. Use the thinking of problem-based learning-hands-on learning-cooperative learning-cooperative learning, and cooperation after learning.
In order to show that students are the main body of learning activities, I have designed the following teaching process based on students' learning:
Fourth, talk about the teaching process
(A) the introduction of stories, create a situation, arouse suspicion. (4 minutes)
1, I fully attracted the students' attention through the situation diagram, stimulated their interest in learning, and put forward the question of how to distribute three cakes to four people, which aroused their thinking. 2. uncover the topic: divide the cake.
(Design Intention: At the beginning of the class, students can create a story situation by watching the familiar cartoons of Four Saints of the Tang Dynasty, which can not only attract students' desire to explore knowledge, but also stimulate students' interest in learning, so that students can explore and think with questions. )
Can you estimate that everyone can get a complete cake?
(2) Hands-on operation to explore new knowledge: (16 minutes)
Activity operation 1, 4 cakes are distributed to 3 people on average. (8 minutes)
Design intention: The process of cooperation and communication between students and groups can cultivate students to feel various ways of thinking from practice. Let every student experience the process of exploring knowledge.
2. Main points and results of each group report.
3. Courseware shows students' pictures in two ways:
Design intention: let students move, think and speak, feel mathematics in the whole activity, reflect the autonomy of learning, let students demonstrate different methods, and cultivate students' emotion and ability to speak boldly.
4. Summarize the concept of truth.
(3) Enlighten and guide doubts (5 minutes)
1. Understand concepts and distinguish features.
What do you know about grades through the study just now? Fractions with numerator less than denominator are called true fractions, which are less than1; Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions, which are greater than1; Fractions consisting of integers and true fractions are called banded fractions, which are greater than 1.
(4) Practical application. (13 minutes)
1. Tell me which scores are true and which are false. What is the score?
2. True or false
① The true score is less than 1 ()
② All error scores are greater than 1 ()
③ The numerator of the false fraction is greater than the denominator. () (5) Fill in the blanks: Let students know the characteristics of true marks and false marks.
(6) Use false scores and band scores to represent the shaded parts in the following figure. Deepen the understanding of the relationship between false score and band score. (7) Expanding the problem. Compare the size of the score. Strengthen students' comprehensive knowledge application ability.
Design intention: This session aims to practice from easy to difficult, so that students at different levels can get exercise and every student can get the happiness of learning success. Let the students know the characteristics of true marks and false marks through practice. This kind of exercise not only pays attention to the foundation, but also jumps the classroom atmosphere and mobilizes the enthusiasm of social answers.
(8) Summarize knowledge and evaluate yourself. (2 minutes)
What did you learn in this lesson? Let the students sum up and consolidate what they have learned. Teachers can help students solve their questions, which will deepen their impression of knowledge.
(9) Blackboard design
Divide the cake (true and false)
Fractions with numerator less than denominator are called true fractions. True score < 1, if the numerator is greater than the denominator or the numerator and denominator are equal, it is called false score, and the false score is ≥ 1, such as
Fractions composed of integers and true fractions are called banded fractions, and banded fractions are > 1.
Design intention: The blackboard writing design should be concise, intuitive, vivid and focused, highlighting the places where students are prone to problems, attracting students' attention and deepening their impression of knowledge. )
That's the end of my lecture, thank you!
Reflections on the teaching of "dividing bread" in the first volume of fifth grade mathematics in Beijing Normal University.
In this lesson, I combine situational activities and teaching materials to create "dividing cakes" and start teaching at two levels. Let students understand the meaning of "true score", "false score" and "scored" through two activities. On this basis, students are required to read and write this score correctly and understand the relationship between false score and the same score.
In this lesson, I first introduce the story of Pig and Bajie sharing cakes, and ask questions, so that students can participate in the whole learning process together with the questions. In the whole teaching process, I let students solve problems through hands-on practice and group discussion. In the two practical activities, students can actively participate and the classroom atmosphere is relatively strong. In the group report stage, everyone spoke actively. Reflecting on this lesson, the group activities are carried out smoothly. Thanks to the structured preview before class, the usual training and the arrangement of this class, children have the courage to express their views, show their creativity and personality, and group activities move forward in disorder, which is the biggest progress compared with previous open classes. However, due to the long reporting and communication time, the practice time was diluted, which made the arranged training questions unfinished. In the future, we should think more about the time schedule and use the limited classroom time on the cutting edge. Throughout this class, I first play short stories with multimedia courseware, ask questions and arouse students' interest. Then through the form of group discussion and communication, * * * can solve problems together, which fully embodies the main role of students and cultivates their hands-on operation ability, observation ability and mathematical language expression ability. In concept teaching, I let students explore knowledge independently and cultivate their ability of analysis, comparison and generalization. Make abstract and boring mathematical concepts intuitive and easy to understand. Exercise design strives to have a gradient so that students at different levels can get the joy of success.
Lecture Notes of "Divide Bread" 4 I. Talking about Teaching Materials
"Divide the cake" is the content on pages 37-38 of the ninth book of the standard experimental textbook for nine-year compulsory education. It is based on students' initial understanding of scores, the understanding of true scores and false scores in the arrangement of teaching materials, the production process and practical significance of true scores and false scores in the activity of "dividing cakes", and the descriptive definition of their concepts, and then let students talk about the characteristics of true scores and false scores. For concept textbooks with scores, the introduction method is used to treat true scores and false scores respectively, which helps students understand the relationship between false scores and scores and avoid illusions. For students, although the true score has been initially known, it is still difficult to establish the production process and practical significance of true score and false score. In the activity of dividing cakes, students abstract specific scores to their generation and significance, and improve their ability to solve problems from the content itself and the methods of studying problems.
Based on the above understanding, I established the teaching purpose of this class:
1, combined with the specific situation, experienced the generation process of false score and band score, and understood the meanings of "true score", "false score" and "band score".
2. Be able to read and write fake scores and scored correctly, and understand the relationship between fake scores and scored.
3. Seek solutions to problems and experience the close relationship between mathematics and daily life. Teaching emphasis: experience the generation process of false score and scored score according to the specific situation, and understand the meaning and relationship of "true score", "false score" and "scored score".
Teaching difficulties: hands-on operation to understand the method of dividing cakes and observe the characteristics of scores.
Second, talk about teaching methods and learning methods.
1, the generation process of the score and the understanding of the actual meaning should reflect the thinking process from intuition to abstraction. This lesson adopts the form of group cooperative learning, which fully allows students to combine the methods of observation, discovery and comparison, reflecting the teacher's leading role and the students' dominant position in the learning process.
2. Students explore independently in a harmonious learning atmosphere, learn to observe, discover, compare and classify through hands-on operation, brain thinking and language expression, and learn knowledge and ability better.
Third, talk about the teaching process
This lesson tries to understand the meaning of "true score, false score and scored" by experiencing the process of producing true score, false score and scored cognition in various activities based on students' actual interests and combining with specific situations. Cultivate students' ability to learn mathematics through operation, observation and summary; Throughout the class, Mr. Lin can start teaching around several teaching links, such as arousing interest in situations, introducing dialogues, exploring new knowledge by operation, reviewing and summarizing, and practical application. The specific analysis is as follows:
(A), pay attention to the cultivation of students' interest in learning.
Interest is the best teacher for students. Only when students are interested in mathematics can they enjoy learning, be eager to learn and learn. For example, before class, the teacher plays a cartoon of Journey to the West, so that students can sing the theme song together, which relieves students' nervous mentality and creates a harmonious learning atmosphere. By helping Tang priest and his disciples solve the problem of sharing cakes, and paying attention to the successful experience in teaching, students are often encouraged and encouraged, such as "good, great, very good, thank you", so that students can experience the success of learning mathematics and stimulate their interest in learning and curiosity.
(2) Implementing "taking students as the main body and teachers as the leading factor" to provide students with creative space. The relationship between "guidance" and "learning" is particularly important in classroom teaching. The ultimate goal of teachers' guidance is students' learning. Here, teachers create a dialogue stage for students through cooperative learning and self-presentation, so that students can share their experiences. The new curriculum advocates the spirit that "the classroom should give students space for choice and freedom". At the same time, the teacher is guiding students to question and ask questions, so that students have enough time to think, thus giving students the initiative to learn; So students can ask questions like what is the score of 4/4 in class. It provides good learning resources for the classroom, and teachers can also capture information in time. This kind of teaching enriches students' creative space and cultivates students' creative spirit and ability.
(3), operation perception, the establishment of the concept.
Understanding in operation and learning in operation are the important teaching concepts of the new curriculum. In teaching, teachers pay attention to students' operations, establish representations and understand meanings and concepts. In this class, the teacher can let the students know the score by hand, and each operation has certain significance. operate
First, let the students divide the cake of 1 among four people equally. How much does everyone get? Make students consolidate the average score and perception score. Operation 2: Divide 3 cakes among 4 people equally. What is everyone's share? In the operation, the perception points are different, but the results of the same number of copies are the same, that is, three 1/4 and three 1/4 are all 3/4. With the transfer of knowledge, students distribute 9 cakes to 4 people on average, and each person can get 9/4 and 2 1/4 points. After students have a comprehensive understanding of these scores, they can produce true scores, false scores and band scores through observation, comparison and induction. And understand its meaning. This kind of teaching cultivates students' cognitive mathematical laws and generalization ability.
Four, close contact with real life, cultivate students' ability to apply mathematics.
From the practice of design, on the one hand, consolidate and summarize the key knowledge of this lesson. On the other hand, let students solve the problem of sharing bread and apples, and improve students' application of mathematical knowledge to solve problems in life. Mathematics originates from life and returns to life; Let students experience that mathematics is everywhere in life.
Five, say blackboard writing.
In order to highlight the key points of this lesson and help students master the knowledge points, the descriptive definitions in the book are designed to be easy to understand and easy for students to remember on the blackboard.