The meaning of decimals: lecture notes 1 1. Teaching materials
1. teaching content: unit 4 "the meaning of decimals" in the second volume of the fourth grade of primary school mathematics.
The significance of decimals is a concept teaching class, based on "the preliminary understanding of fractions". Mastering the meaning of decimals is the focus of this unit's teaching, which is directly related to the nature of decimals, the mutual rewriting of singular and composite numbers and other related knowledge.
2. Teaching objectives:
(1) Knowledge goal: Understand and master the meaning of decimals, know the names of various parts of decimals, and read and write decimals correctly and skillfully.
(2) Ability goal: correctly understand the meaning of decimals. Through operation, we can understand the relationship between decimals and decimals. Cultivate students' learning quality and abstract generalization ability of careful observation and thinking, and enhance students' sense of cooperation in cooperative learning.
(3) Emotional goal: To enable students to experience the process of describing life phenomena and solving simple practical problems with decimals, to understand the close relationship between decimals and daily life, to enhance the significance of independent inquiry, cooperation and communication, and to establish confidence in learning mathematics well.
3. Emphasis and difficulty in teaching
Teaching emphasis: understanding the meaning of decimals.
Teaching difficulties: understanding the meaning of decimal and the meaning of unit "1".
Second, oral teaching methods
According to the characteristics of the teaching content of this course and the thinking characteristics of students, I chose guided development.
Optimal combination of current method and comparative migration method. Guide them to find problems, analyze problems, solve problems and acquire knowledge, so as to achieve the purpose of training thinking and cultivating ability.
Third, theoretical study.
1. Learn to feel the existence of decimals everywhere in life and the necessity of learning decimals through observation, measurement and induction.
2. Guide students to explore independently and cultivate their ability to solve new problems by using existing knowledge.
3. Cultivate students' self-study ability and good cooperative communication habits by guiding independent reading and reporting exchange activities.
Fourth, talk about teaching procedures.
(A) stimulate the introduction of interest
Show courseware and show some decimals around the familiar life scenes of primary school students, so that students can understand the wide use of decimals and the necessity of learning decimals.
(2) Explore new knowledge
1, the meaning of decimal
(1) One decimal place
In this link, the ruler with a length of 1 meter is divided into 10 parts on average, and several parts are one tenth, all of which can be written in the form of one decimal place. Let the students understand that a decimal place is actually another expression of a fraction with a denominator of ten.
(2) Two decimal places
This link continues to follow the above-mentioned guided inquiry method, so that students can understand that a few percent of the scores can be written in the form of two decimal places. In other words, a two-digit decimal number is a number representing a percentage. In addition, students are more familiar with the methods of exploring knowledge through comparative migration.
(3) Three decimal places
With the exploration of the above two links, when exploring the meaning of the three decimal places, I let the students discuss in groups and explore independently, and the meaning of the three decimal places will come naturally. In addition, I timely guide students to expand their knowledge and explore four decimal places, five decimal places and so on, so that students can understand that the number of decimal places is endless. At this point, teachers and students * * * summed up the meaning of decimal, that is, the number representing one tenth, percentage and one thousandth is called decimal.
2. The ratio between decimal counting unit and counting unit.
(1) Counting unit
By comparing several one-digit decimals on the blackboard, let the students understand that all one-digit decimals are composed of 0. 1. We call 0. 1 as the counting unit of one-digit decimals. At this time, it is easy for students to derive the counting units with two decimal places and three decimal places by means of comparative migration.
(2) Propulsion speed
By comparing the corresponding lengths of counting units of one decimal place, two decimal places and three decimal places on the blackboard, it is deduced that the forward speed between two adjacent counting units is 10.
Fourth, knowledge application.
Show courseware for students to practice in class, digest what they have learned, apply what they have learned, and eliminate blind spots and doubts in students' learning through different forms of practice.
1. Fill in the appropriate number in ().
0.6=()0.87=()=()
Step 2 fill in the blanks
The counting unit of (1)0.8 is (), with () ().
(2) The counting unit of 0.06 is (), and there is () ().
(3) The counting unit of 0.34 is (), and there is () ().
Verb (abbreviation of verb) abstract
* * * Summary of teachers and students: A few ten thousandths are one decimal place, a few percent are two decimal places and a few thousandths are three decimal places.
The units of decimals are one tenth, one hundredth and one thousandth. Write 0. 1, 0.0 1, 0.001‥ ‥ respectively.
In decimals, the series between every two adjacent counting units is 10.
Six, homework arrangement
1, record some decimals from your life and communicate with each other tomorrow.
2. Complete the classroom workbook
Blackboard design:
The meaning of decimal
Fractions with denominators of 10, 100, 1000 ... can be expressed in decimals.
Decimals are counted in tenths, hundredths and thousandths ... Write 0. 1, 0.0 1, 0.00 1 ...
The propulsion rate between every two adjacent counting units is 10.
The meaning of decimals: Lecture 2;
The new curriculum standard puts forward that we should pay attention to the whole process of students' learning and the process of students' generating new knowledge, and at the same time, we should give full play to students' subjective initiative in learning and actively participate in the process of knowledge development. Fourth-grade pupils are not completely ignorant of decimals, and they also have contact in daily life. However, because decimal is a special form of decimal fraction, it will be difficult for students to understand its meaning. In view of this phenomenon, I fully consider students' life experience and existing knowledge level, find out the intersection of life and decimal knowledge, and use the connection between decimal and fraction to inspire students to think and let them experience the whole process of knowledge formation.
Teaching objectives:
According to the structure and content analysis of this textbook, combined with the cognitive structure and psychological characteristics of fourth-grade students, I have formulated the following teaching objectives:
1, combined with the specific situation, through operations, observation, analogy and other activities, so that students have a preliminary understanding of fractions and decimals, and further understand the meaning of decimals.
2. Through the process of exploring the meaning of decimals, let students understand and master the counting unit of decimals and the progress speed between two adjacent units, and cultivate their inductive ability.
3. In the process of learning the meaning of decimals, cultivate the interest in exploring knowledge and improve the ability of independent exploration and cooperation.
Teaching emphases and difficulties:
1, understand the meaning of decimal.
2. Decimals will be used to represent the conversion results of measurement units.
3. Make full use of visual AIDS, and take the length as an example to show that decimal is actually another representation of decimal fraction.
4. On the basis of students' preliminary understanding of one-digit and two-digit decimals, the scope of understanding is further expanded to three-digit decimals, so that students can clearly understand that decimals represent fractions with denominators of 10, 100 and 1000, and understand the meaning of decimals. Understanding the counting units of decimals and the progress between units is not only the focus of this lesson, but also the difficulty of this lesson.
5. In order to clarify the important and difficult points of the textbook and enable students to achieve the teaching objectives set by this topic, I will talk about teaching methods and learning methods again.
Teaching methods:
Considering the present situation of fourth-grade students, I mainly adopt the methods of setting up situational teaching method, intuitive demonstration method, activity inquiry method and collective discussion method. Let students actively participate in teaching activities, so that they can gain knowledge and experience in the activities and have the desire to practice. Cultivate students to combine classroom teaching with their own experiences, guide students to actively discover the objective things around them, develop their thinking ability and pay attention to their psychological state. Of course, teachers themselves are also very important teaching resources. Teachers themselves should infect and motivate students through classroom teaching, arouse students' enthusiasm for participating in activities, stimulate students' desire to solve practical problems, and cultivate students' ability to integrate theory with practice, so as to achieve the best teaching effect.
Speaking and learning methods:
We often say: "Modern illiterates are not illiterate people, but people who have not mastered learning methods", so I pay special attention to the guidance of learning methods in the teaching process. Let students change from mechanical "learning to answering" to "learning" and from "learning" to "learning" and become the real masters of learning. This course mainly adopts the following methods in guiding students' learning methods and cultivating students' learning ability: thinking evaluation method, analytical induction method, independent inquiry method and summary reflection method.
Finally, I will talk about the teaching process of this course in detail.
Talking about the teaching process:
First of all, an exciting introduction.
1: Teacher: Please read the following information (courseware presented).
(1) Teacher Yu weighs 5 15kg.
(2) Naughty height145m.
(3) Xiaoxiao's math test score is 995.
Teacher: Some students laughed. Think about it. Is this writing practical?
2. Yes! These data are missing a little (the courseware points to decimal points one by one). Read these decimal points.
In daily production and life, some quantities may not always be expressed by integers, for example, the price of commodities may not always be expressed by integers, and the exact integer results are often not obtained when measuring, and they are often expressed by decimals. Today we continue to learn decimals. (blackboard title: the meaning of decimals)
In daily life, except the price of a commodity is not a whole yuan, it can be expressed in decimals. When measuring the height of a house, when it is not the whole meter, it is often expressed in decimals in meters.
(1) By observing the meter scale, it can be concluded that tenths, hundredths and thousandths can all be expressed in decimals. Let's think about it first. What are the forward speeds of meters, decimeters, centimeters and millimeters?
Blackboard: 1 m = 10 decimeter = 100 cm = 1000 mm
Observe the instrument scale. Ask questions:
① Divide 1 meter into 10 parts. How many decimetres is each part? How many meters is the score? How many meters are written as decimals? Student observation: Divide 1 meter into 10 parts, each part is 1 decimeter. How many meters is the score written as 3 minutes? How to express it in fractions and decimals? Teachers and students are equally clear: divide 1 meter into 10 parts, and one or more parts can be expressed by one decimal place.
② Divide 1m into 100 blocks on average. How much is each piece on this ruler? How much is the meter? Write it as a decimal? After observing the meter scale, the students draw the following conclusions: divide 1 meter into 100, and 1 is 1 cm. How to write 7 cm into fractions and decimals in meters? Inspire students to think: How to write 15 cm into fractions and decimals in meters?
The first person in the group writes 1. So 15cm is 0, 15m. Clearly divide 1 meter into 100 parts, and one or several parts can be expressed with two decimal places.
③ Divide 1 meter into 1000. What is the 1 part on the ruler? How to express (1 mm) one thousandth of a meter in decimals? Enlighten the students to draw the conclusion that one thousandth is written in the third place on the right of the decimal point, and how many meters are written in meters for 0.00 16 mm and 13 mm respectively? 13mm is 0.0 13m. According to the above questions, divide 1m into 1000 parts on average. How many decimal places can 1 part or several parts represent? (Three decimal places) The teacher suggested that we can continue to divide according to the previous method, and we can get four decimal places and five decimal places.
What conclusions can be drawn from the study of the first three questions? (Divide the unit 1 into 10 parts, 1 part or parts can be represented by one decimal place, 1 part or parts can be represented by two decimal places, 1 part or parts can be represented by two decimal places. ...
Practice at once.
(2) Inspire students to summarize the meaning of decimals. Inspiring questions:
(1) The above example is divided into 1 meter. ( 10, 100, 1000)
(2) What is the score of such 1 share or several shares: (a few tenths, a few percent, a few thousandths)
The teacher pointed out: Fractions like the above can also be written in the form of integers, written on the right side of integer digits, separated by dots, to represent numbers of one tenth, one hundredth and one thousandth, which are called decimals. Decimal counting units are one tenth, one hundredth and one thousandth ... written as 0. 1, 0.0 1, 0.00 1 ....
4. Strengthen the concept. Inspiring questions:
(1) How many tenths of a number expressed by several decimal places? How many points does a decimal place represent? What is the unit of counting decimal places?
(2) What is the percentage expressed in decimals? How many fractions do two decimal places represent? What is the unit of counting the two decimal places?
(3) How many decimal places are used to express a few thousandths? What fraction do three decimal places represent? What is the counting unit of three digits after the decimal point?
(4) What is the forward speed between every two adjacent units?
-The propulsion rate between two adjacent units is also 10.
Reading textbook: 5 1 page conclusion.
Feedback: Page 5 1 "Do it"
Class summary: Consolidate the exercises and complete Exercise 9 on page 55 of the textbook, 1-3.
Blackboard design:
The meaning of decimal 1 m = 10 decimeter =100cm =1000 mm.
Divide 1 meter into 10 parts, and the length of each part is 1 decimeter.
Divide 1 m into 100 blocks, each block is 1 cm long.
Divide 1m into 1000 blocks, each block is 1m long.
One decimal place indicates a few tenths, and the counting unit is 0. 1.
What percentage does two decimal places represent? The counting unit is 0.0 1.
Three decimal places represent thousands, and the counting unit is 0.00 1.
The propulsion rate between two adjacent counting units is 10.
Eight. Concluding remarks
Leaders and teachers, in this class, according to the psychological characteristics and cognitive rules of fourth-grade students, I adopt the teaching methods of intuitive teaching and activity inquiry, with teachers as the leading factor and students as the main body. Teachers' "guidance" is based on students' "learning", focusing on learning methods, allowing students to explore independently and actively participate in the whole thinking process of knowledge formation, so that students can improve themselves in a positive and pleasant classroom atmosphere. My speech is over, thank you!
Significance of decimals: Lecture Notes 3 I. Talking about Teaching Materials
1, teaching content
This lesson is 2-3 pages of the first lesson of Unit 1, Book 2, Grade 4 Mathematics, the standard experimental textbook for compulsory education (Beijing Normal University Edition).
2. teaching material analysis
The content of this lesson is divided into four parts. First, "talk about it", let students talk about decimals in life and their meanings. The second is "recognition", which mainly helps students understand the relationship between decimals through intuitive models and practical operations. The third is "filling", which helps students understand the meaning of decimals through the combination of numbers and shapes. Fourthly, a "recognition-recognition" counter is used to visually represent decimals, which helps students to understand the numerical values and sequence tables corresponding to decimal places and know that decimals and integers are usually represented by decimal counting.
3. Teaching objectives
According to the requirements of the new curriculum standards and the characteristics of teaching materials, combined with the cognitive ability of fourth-grade students, I have determined the following teaching objectives of this lesson:
Knowledge and ability goal: Combining with practical operation, students can understand the meaning of decimals, understand the relationship between decimal fractions and decimals, interact with each other and read and write decimals correctly.
Process and Methods Objective: To explore the generation and development of decimals and understand their wide application in life.
Emotion, attitude and values: in the process of inquiry and communication, cultivate students' habit of independent inquiry and cooperative communication, and improve students' interest in learning mathematics.
4. Emphasis and difficulty in teaching
According to the characteristics of this teaching content, I will focus on understanding the relationship between decimals and fractional fractions and the meaning of decimals. The difficulty lies in making students really understand the meaning of decimals.
Second, talk about learning.
The significance of decimals is concept teaching, which is to let students experience the learning process of knowing, reading and writing decimals under the background of existing experience and understand the close relationship between decimals and life.
Three. Oral English teaching methods and learning methods
1, teaching methods
According to the teaching characteristics of this class and students' thinking characteristics, I chose the optimal combination of situational teaching method, intuitive guidance and observation method, group discussion and exchange method, layered practice and trial method, and guided discovery method. Guide them to find problems, analyze problems, solve problems and acquire knowledge, so as to achieve the purpose of training thinking and cultivating ability.
Step 2 study law
Students are the main body of classroom teaching, and leaving more time and space for students is one of the important ways to mobilize and give play to students' subjective consciousness. Starting from the problem, let students actively participate in the mathematical activities of exploration and communication. In the process of exploration, teachers respect each student's personality and allow differences.
Knowledge and methods to solve problems. Through discussion, questioning, guessing and comparison, students can find that decimals are everywhere in life, so as to preliminarily understand the meaning of decimals.
Fourth, talk about the teaching process
1, the generation of teaching decimals
A. The introduction of textbook unit price in students' hands not only reviewed the relevant knowledge of "Yuan, Angle, Minute and Decimal", but also mobilized students' learning enthusiasm. Learn to be a conscientious person in life and feel that mathematics is around us.
B. summarize the generation of decimals. When we encounter problems that can't be solved by integers, we can solve them by fractions and decimals.
2. The application of decimal teaching in life.
A. where can I see decimals in daily life?
Students communicate with each other.
C. After reading the decimals listed in the textbook, the students once again feel that primary schools have a wide range of applications. This is a very important number and we should learn it well.
Step 3 Explore the meaning of decimals
The meaning of decimals can't just depend on teachers' explanations and students' reciting conclusions. Students must gain experience through activities. So in this link, I let the students do it themselves: fold and smear, first with fractions, and then with decimals, so that students can gradually understand the meaning of decimals in the experience. It is best to guide students to observe and discover, learn to sum up the meaning of decimals, cultivate students' good study habits, and teach students to learn to learn.
4. How to read decimals
Let the students try to read first, and then summarize.
5. Know the name of each number in the decimal part.
A, show the counter, the teacher introduces the name of each number in the decimal part.
B. What's the difference between the decimal part and the integer part? Why?
C. Pinball activities: Enhance students' interest through open game activities, so that students can strengthen their understanding of decimal places in the activities and realize that decimal parts are also decimals.
6, consolidate the use of preset action exercises according to the students' learning situation, in order to further strengthen training.
V. Indicating the expected effect
The design of the above-mentioned teaching procedures follows the students' cognitive rules and age characteristics. Students are the masters of learning, so students can explore and communicate independently and experience the joy of success. I try my best to create a life situation, make math problems come alive, and make students feel that there is math everywhere in life, and math is around. Pay attention to independent inquiry, cooperation and exchange, and let students experience the process of knowledge formation. Let students actively construct their own cognitive structure. Students operate, think and solve problems under the guidance of the classroom, so that students can acquire knowledge, develop intelligence, cultivate positive learning emotions and organically integrate three-dimensional goals.