[[Preliminary Understanding of Decimals]] A preliminary understanding of decimals.

Lecture note on "Preliminary Understanding of Decimals"

First of all, talk about textbooks.

1, analysis textbook:

"A preliminary understanding of decimals" is the content of Unit 3 in the second volume of Grade Three. This lesson is taught on the basis of students' initial understanding of scores. Here, students are exposed to decimals for the first time. Learning this part well can lay a solid foundation for studying decimals systematically in the future.

The textbook first arranges to know that the integer part is one decimal place of 0, and then arranges to know that the integer part is two decimal places of 0. The decimal cognition of two examples is introduced from the practical problem of length measurement, and each example is presented from the specific life situation, so that students can learn mathematics more vividly, concretely and naturally.

2. Teaching objectives:

According to the requirements of curriculum standards and the present situation of teaching materials, I set the goal of this lesson as follows:

(1), understand the actual meaning of decimals in combination with specific situations, and understand the actual meaning of decimals in yuan and meters.

(2) A few tenths of the initial perception can be expressed by one decimal place, and a few percent can be expressed by two decimal places. Can read and write decimals

(3) Cultivate the consciousness of active exploration and the ability of cooperation and communication, and experience the connection between mathematics and real life. Preparation before class: multimedia courseware, physical projector, commodity price tag.

3. Emphasis and difficulty in teaching

The preliminary understanding of decimals is an abstract and difficult content in the concept of primary school mathematics. The decimal point is another representation of a fraction. Although students have a preliminary understanding of fractions and have learned the rate of progress between length units and monetary units, it is still difficult to understand the meaning of decimals. At the same time, many problems of decimals in students' later study are not clear. Therefore, understanding the meaning of decimals is not only the focus of this class, but also the difficulty of this class.

Second, talk about teaching methods and learning methods.

Teaching method is the sum of a series of activities taken by teachers and students to achieve their goals in the teaching process. According to the characteristics of teaching content and students' thinking, I chose the optimal combination of intuitive demonstration, supplemented by conversation inspiration, trial and error, guided discovery, student-student interaction and the combination of lectures and exercises. Give full play to the role of teachers, mobilize students' initiative, and guide students to find problems, analyze problems, solve problems and acquire knowledge, so as to achieve the purpose of training thinking and cultivating ability.

The strategy of "teaching methods according to textbooks and learning methods according to rules" tells us that learning methods and teaching methods are harmonious and inseparable. In order to better highlight students' dominant position, in the whole process, through various forms, fully mobilize students' various senses to participate in learning, induce students' internal potential, and make them not only learn, but also learn. Qian Xuesen once said: Science and humanistic spirit are two sides of the same coin, and they are indispensable. If the scientific nature of mathematics teaching is rigid, then humanity is its flexibility. What humanistic spirit needs is infiltration, and what it needs is "spring breeze melts rain", "moistening things silently" and "landing without trace", so that mathematics teaching can take off its rigid coat, show opportunities and overflow.

Interesting and full of wisdom, I create a peaceful and relaxed learning atmosphere in teaching, teachers and students talk and communicate equally, and position mathematics teaching between intentional and unintentional.

Third, the teaching process

(A), create a situation to stimulate interest

1. Create a "social investigation" situation in the supermarket.

Multimedia presentation: supermarket survey situation map

Teacher: Yesterday, the teacher went shopping in the supermarket and saw two children recording something with pens and notebooks. Out of curiosity, I went forward to ask, it turned out that they were doing a "small social survey"-understanding the prices of some commodities. I looked at it and found that they recorded it like this-

Multimedia presentation: two record sheets

Teacher: Can you understand? What kind of record sheet do you like? Tell me your opinion.

Teacher: Yes, these two kinds of records have their own advantages, but the little girl's record sheet is simpler, clearer and more convenient, which is worth learning.

Multimedia presentation: highlight the record sheet with "yuan" as the unit.

2, the first decimal, the introduction of new lessons.

Multimedia presentation: 5.98, 0.85 and 2.60.

Teacher: The teacher put forward these numbers, such as (5.98, 0.85, 2.60), which we call-(decimal) Teacher: What are the characteristics of these decimals?

Multimedia presentation: decimal point turns red

Teacher: It's called decimal point. Today we will learn about decimals together.

Writing on the blackboard: a preliminary understanding of decimals

Design intention: Mathematics curriculum standard points out that teachers should be good at discovering and excavating mathematics around students, reflecting the practical significance of learning mathematics and feeling the application value of mathematics. When I designed this course, I found that the prices of our textbooks were all presented in decimal form. Therefore, the teaching design takes the price of mathematics textbooks as the starting point of this course. Let the students guess and look at the table, introduce the decimals in life, and reveal the theme of this lesson: knowing decimals.

(2) Connecting with practice and exploring new knowledge.

1, decimal reading and writing learning

(1) read decimal

Teacher: Can you read these decimals? Read to your deskmate.

(where students call the roll and give directions while reading)

Multimedia display: display the pronunciation of three decimal places in real time.

(2) Write decimals

Teacher: We can already read these decimals, so how do you write them? Let's have a try. Blackboard: 5.98 yuan, 0.85 yuan, 2.60 yuan.

Design intention: Decimal reading and writing is relatively simple, and students can solve it directly with their own experience and knowledge. Don't drag your feet, focus your time and energy on the construction of the practical meaning of the following decimals.

2. The practical significance of constructing decimals with "yuan" as the unit.

Teacher: Who knows what the decimals of these yuan represent?

(Students answer, the teacher writes it on the blackboard)

Blackboard: 5 yuan 9.8, 0 yuan 8.5, 2 yuan 6.0.

Teacher: How do you know?

Design intention: students are not required to answer perfectly here. As long as students can raise points from top to bottom, it shows that they have some understanding of the practical significance of fractional price, but they should also pay attention to the logic of students' expression and cultivate accurate and complete expression ability. Summary: These decimals in yuan units, the left side of the decimal point represents several yuan, the first position on the right side of the decimal point represents several angles, and the second position on the right side of the decimal point represents several points.

practise

Teacher: From your speeches, I can see that you already know how to express prices in decimals, so I'm going to test you. Can you rewrite the following prices in RMB?

Multimedia presentation: a few dollars and cents, according to the students' answers to show the answers in time.

4. The construction of the practical meaning of decimals in rice.

(1) Examples of life

Teacher: Through the study of steel, children are very clear about the decimal notation of prices. Where else are decimals used in life?

Students speak freely and say where they have seen decimals, and the teacher is sure.

Teacher Zhuang also collected some decimal data of the animal kingdom. Let's read together.

Multimedia presentation: the second question on page 9 1 in the book.

Teacher: It seems that decimals can represent not only price, but also height, weight, speed and distance. Decimals in life are really everywhere! Speaking of height, do you know your height? Want to know the height of the teacher? My height is 1.60 cm.

Blackboard: 1 m 60 cm

Teacher: Guess the teacher's height 1.82 cm. How to express it in meters?

Teacher: The children have a good guess. Let's study why Mr. Zheng's height 1.82 cm can be expressed by1.82 m.

Design intention: Let the students find out the decimals in life and use decimals to indicate the method of guessing the teacher's height, which leads to another core link of this lesson-the meaning and writing method of one decimal point and two decimal points based on meters, decimeters and centimeters. The combination of meaningful acceptance learning and inquiry learning is adopted here to fully mobilize students' enthusiasm and initiative, which is in line with students' cognitive laws and constructivist learning theory.

(2) Perceived "several tenths" can be expressed by one decimal place.

Multimedia display: instrument scale marked with 1- 10.

Teacher: This is a ruler 1 meter long. Divide 1 meter into 10 parts. How many decimetres is each part? 1 meter is a fraction?

Multimedia demonstration: 1 decimeter long line segment and 1 decimeter word.

Teacher: 1 decimeter. What fraction of 1 meter?

1 1 1 division: Yes, 1 decimeter is 1 meter, that is, meter. The decimal of the meter is 0. 1 meter. 1 0 101multimedia presentation:1decimeter =0. 1 meter10 multimedia presentation: 3-meter long line segment.

Teacher: This section is 3 centimetres, and that 3 centimetres is a fraction of a few metres. What is the decimal number?

Multimedia demonstration: 3 minutes =0.3 meters Teacher: Can you still find 0.7 meters on the ruler? Point up. The design intention of 10 is to arouse students' memory of scores with vivid courseware. The relationship between fractions and decimals is established by units of length,

Let the students know that decimals are another manifestation of fractions. Moreover, the different presentation modes of 1 decimeter, 3 decimeters and 7 decimeters can avoid the monotony of the class and pave the way for the next link transition.

(3) Perceived "percentage" can be expressed by two decimal places.

Teacher: Children, faced with the same thing, we can make new discoveries from a different angle.

Multimedia display: instrument scale marked with1-100.

Teacher: How many shares is 1 meter divided equally now? What is the length of each serving? (1 cm)

1 division: 1 cm How many meters are expressed in fractions? () How many meters is the decimal system? (0.01m)1001multimedia presentation:1cm = 0.01m1003 Teacher: What is the score of 3 cm? How about decimal representation (meters)? (0.03 m) 1003 Multimedia presentation: 3 cm = m =0.03 m 100 Teacher: 18 cm How many meters is the decimal? (0.18m)

Blackboard: 18cm = 0. 18m.

Teacher: What do you think? (Students talk about their own ideas)

Summary: The number before the decimal point indicates how many meters, the first number to the right of the decimal point indicates how many decimeters, and the second number to the right of the decimal point indicates centimeters.

Blackboard writing: meter, decimeter, centimeter

Step 5 consolidate small exercises

Teacher: Now do you know why the teacher's height 1.82 cm can be written as 1.82 m?

Multimedia presentation: Lili measuring her height.

Teacher: A child is measuring his height. Let's go and have a look.

Teacher: Lili's height is1.20cm. What is the decimal number of meters?

Teacher: If the height of a child is 1.42 meters, how many meters and centimeters is it? (1.42 cm)

Design intention: This link responds to the previous conjecture and can make the classroom structure more integrated. Write down your height in decimal form, and let the students practice to consolidate their knowledge. Ask the students to think backwards, "1.42 meters equals several meters and centimeters?" Further deepen students' understanding of decimal meaning.

(C), the use of expansion

Comparison of ancient and modern representations of 1. decimals

Teacher: Children, do you know how to express decimals in ancient China? Let's have a look.

Multimedia Presentation: Ancient and Modern Decimals of p94

Teacher: Which method do you think is better for expressing decimal points?

2. Price quiz game

Teacher: Let's use the decimal counting method we learned today to play a "price quiz" game!

Multimedia demonstration: Toy car engineer: The price of toy cars ranges from 100 yuan to 120 yuan, with a fraction.

Design Intention: The first application of these two extensions is to let students know about the expression methods of decimals in ancient and modern times and the designers of decimals, so that students can understand the culture of mathematics while learning the meaning of constructing decimals. The second game design of "Wonderful Price" comprehensively uses the knowledge of decimals, not only designs the reading method of decimals, but also indirectly expands the comparison of decimals, which lays the foundation for studying the comparison of decimals in the future and cultivates students' sense of numbers.

(4) Summary and extension

Teacher: Today we know decimals. What have you gained? Is there a problem?

Teacher: Actually, there are many mysteries about decimals waiting for us to discover and explore. Let's observe more in life and dig more mysteries about decimals!

(5) Blackboard design

A preliminary understanding of decimals

Jiaoyuanfen

5.9 8 yuan 5 yuan 9.8 minutes1m82cm =1.82m.

0.8 5 yuan 0 yuan 8.5 decimeters cm.

2.6 0 yuan 2 yuan 6 Angle 0 18cm = 0. 18m。

Design intention: The curriculum standard points out that practice should enable students to consolidate knowledge, form skills and develop innovative thinking. In order to make classroom practice play a dual role in promoting knowledge mastery and training ability, I pay attention to the following two points when organizing practice: first, practice forms are diverse to keep students' interest in learning; Second, the difficulty of practice is gradually deepened, and students' cognitive level is constantly improved.

Lecture notes on decimal addition and subtraction

Rebecca Xiguan primary school

Textbook analysis

First, teaching content: Qingdao version of the third grade elementary school mathematics unit 3 information window 2.

Second, the status, role and significance of teaching content

Before learning this lesson, students have mastered the meaning and law of integer addition and subtraction, and just finished learning the meaning and nature of decimals, which has laid a solid foundation for solving the problem of integer reduction in this lesson. The content of this lesson lays the foundation for learning addition and subtraction of decimal system, addition and subtraction and addition and subtraction of fractions. Decimals are widely used in life, which is the concentration and refinement of life and has practical significance. They can quickly achieve the purpose of applying what they have learned, which is helpful for students to understand that mathematics is everywhere and integrate life lessons. The value of mathematics is fully reflected.

Third, the teaching objectives:

1, combined with the specific situation, understand the meaning of decimal addition and subtraction, learn the calculation method of decimal addition and subtraction, and really know how to calculate.

2. After exploring the calculation method of decimal addition and subtraction, we can understand the relationship between decimal addition and subtraction and integer addition and subtraction.

3. Get into the habit of looking at the questions carefully and checking them carefully.

4. Let students experience the connection between life and mathematics.

5. Feel the connection between mathematics and scientific knowledge, and cultivate the emotion of loving science.

Fourth, the characteristics, key points and difficulties of teaching content arrangement

The teaching content of this section is introduced from the integer addition and subtraction. Teach addition first and then subtraction, and understand the calculation law of decimals by comparing the law of integers. After one step calculation, learn to add and subtract, add and subtract, and simply calculate. This arrangement is in-depth and interlocking step by step, forming a unified knowledge chain.

Teaching Breakthrough: Integer Addition and Subtraction

Teaching emphasis: the exploration process of decimal addition and subtraction calculation method

Teaching difficulties: the calculation method of addition and subtraction of different digits (especially the reduction of digits with fewer digits)

V. Design of teaching methods and learning methods

Mathematics learning activities are based on students' existing knowledge and experience. Teachers mainly stimulate students' enthusiasm for learning, fully provide opportunities to engage in mathematics activities, and help students truly understand and master the basic knowledge and skills of mathematics in the process of independent exploration and cooperation. Based on this understanding, this course focuses on activating teaching materials, strengthening experience and deepening application. Adopt a three-stage teaching mode of "participation before class-exploration in class-extension after class". In essence, it is self-study guidance, inspection guidance, exploration of laws, and return to the whole construction system. Self-study before class to collect data and write decimal addition and subtraction formulas to enhance the ability to collect information, explore and discover new knowledge in class, build new knowledge, and experience the joy of competition and cooperation in learning; After-class expansion embodies the value of knowledge and encourages students to have the need to learn.

Six, teaching procedures:

First, check the import.

Write down the following questions and talk about what to pay attention to when calculating.

8+6= 28+5= 37-5= 12-6

(Three people perform, the other students do it in the exercise book) Second, explore new knowledge

1. Display information in information window 2:

(1) Students think: What information did you get from the pictures? What math questions would you ask?

(2) The math questions put forward by the teacher according to the information obtained by the students are written on the blackboard.

(3) Teachers choose an addition problem and a subtraction problem from students' numerous problems. Let's solve these two problems today: 0.7+0.6 0.7-0.3.

2. Teach 0.7+0.6

(1) The teacher first proposed that this formula is fractional addition. Decimal addition, like the previous addition, is also the operation of combining two numbers into one number.

(2) Teachers guide students to find solutions suitable for their knowledge level according to their actual learning situation. How to calculate the decimal addition? (Teacher writes on the blackboard: calculation)

(3) Guide students to compare two types:

One is the addition in meters, which is a fractional addition problem.

One is to rewrite meters into meters and turn the decimal addition problem into integer addition problem. Through observation and comparison, we know that when calculating integer addition, we should align the numbers on the same digit and then add them from the unit; Decimal addition is also the addition of the same digit. When the columns are vertical, as long as the decimal points are aligned, the numbers on the same bit can be aligned.

(4) Students try to calculate by writing 0.6+0.8.

Before the students make a written calculation, the teacher first discusses the problem of number alignment with the students. Teacher demonstration.

Guide the students to say, when calculating 0.6+0.8 vertically, what to do first, then what to do, and finally what to do?

(5) Guide students to sum up: What are the similarities between decimal addition and previous addition in calculation? How to calculate the fractional addition?

3. Teaching 0.7-0.3

(1) Can you solve this problem? How should it be formulated?

(2) Organize students to discuss: How to make a column and calculate the numbers correctly?

(3) Guide students to talk about why decimal points of decimal subtraction should be aligned.

(4) Students try: (one person performs on the board, others do it in this book), and teachers patrol and guide.

4. Guide students to discuss what to do first and then how to do it when calculating 1.2-0.6 verticality. What did you do in the end?

(1) According to the students' feedback, the teacher finally explained:

From the decimal point of view, like integer subtraction, 2 MINUS 6 is not enough. Subtract 1 to the previous place and add 2 to get 12.

(2) Exercise: 1.2-0.7 2.3- 1.8

5. Teaching 1-0.3

(1) student discussion

(2) Summary: 1 can be regarded as 1.0, 0 minus 3 is not enough, abdication minus 3.

Third, consolidate development:

(1) Independent exercise 1: Remind students to pay attention to decimal point alignment and number alignment. (2) Independent exercise 2

Fourth, the class summary

What did you learn from this course?