I. teaching material analysis

1. Teaching content: One of the teaching contents of Unit 1, Section 2, Book 9 of Nine-year Compulsory Education Primary School Mathematics published by People's Education Press. In this lesson, we will teach examples 4 and 5 of P20-P2 1, and the "doing while doing" problem on page 2 1, exercise 5, Question 1-4.

2. The position, function and significance of teaching content.

"Dividing a number into decimals" is widely used in production and life, which plays an important role in primary school mathematics learning and is also one of the key contents of this textbook. It is taught on the basis of students' knowledge of "divisor is fractional division of integers" and "invariance of quotient" Learning the teaching content of this course well aims to enable students to understand the arithmetic of "division is division of fractions", master the calculation law, infiltrate the mathematical method of reduction, and cultivate interrelated dialectical views. The teaching material uses the list method and transformation method to help students understand the calculation method, so as to establish the division law that divisor is fraction.

2. Teaching objectives

Knowledge goal: to understand the division operation with decimal divisor and master the calculation rules.

Ability goal: through learning, improve computing ability and solve practical problems.

Emotional goal: infiltrating the "transformed" mathematical thought and the dialectical view of the relationship between things.

Second, teaching ideas

1, using migration, clarify the conversion principle.

Understanding the principle of division calculation with divisor as decimal is "the property of constant quotient" and "the law of decimal size change caused by decimal position movement" After the division with decimal divisor is converted into the division with integer divisor, the calculation principle of "fractional division with integer divisor" is used. First, review the divisor and dividend with a 20-page table, and at the same time expand the invariable property of the same multiple quotient, which will help pave the way for the division of "dividing divisor into decimals", and then lead to questions, arouse students' cognitive conflicts, stimulate students' interest and generate the impulse to explore.

2. Try to do examples and master the transformation method.

After making clear the principle of transformation, let the students try examples. On the basis of experiments, guide students to observe and compare, abstract the shift method of decimal point during conversion, and finally summarize the shift law. The specific methods are as follows: ① Students try to do Example 4 and tell the method of decimal point shift. ② Students try to do Example 5. (3) Guide students to summarize the methods of shifting during transformation, and on this basis, summarize the calculation rules of division with divisor as decimal. After obtaining the calculation rules, it should also be emphasized that:

The right shift of (1) decimal places depends on the decimal places of the divisor, not the decimal places of the dividend.

⑵ In integer division, the quotient of dividing two numbers will not be greater than the dividend, while in fractional division, when the divisor is less than 1, the quotient will be greater than the dividend.

⑶ Pay attention to the numerical problem of remainder in fractional division. This problem can be illustrated by examples. For example: 57.4÷24, let the students understand that the remainder is 2.2, not 22.

3. Special training to improve "transformation" skills.

A divider is the division of decimals. After the divisor is converted into an integer, the dividend may appear as follows: the dividend is still a decimal; The dividend happens to be an integer; "0" should be added at the end of the dividend. In view of the above situation, special training can be carried out:

① Vertical displacement movement. When practicing moving the decimal point vertically, students are required to write clearly the marked decimal point and the moved decimal point, and the decimal point on the new point should be clear, so that the decimal point is marked first, then moved, and then clicked. This method of decimal point shift is concrete and impressed students deeply.

② Horizontal shift learning. When practicing moving the decimal point in the horizontal direction, because "stroke, shift and point" are only reflected in the mind, it is necessary for students to establish the equations before and after the transformation, which makes people clear at a glance.

Third, the embodiment of new ideas in teaching

How to succeed in teaching: Teachers' "teaching" is based on students' "learning".

1. Inspire students' desire to explore knowledge based on their thinking reality. Students in different stages of development have differences in cognitive level, cognitive style and development trend, and different students in the same stage also have differences in cognitive level, cognitive style and development trend. People's intellectual structure is diverse. Some people are good at thinking in images, some are good at calculation, and some are good at logical thinking. This is the reality of students. The closer teaching is to students' reality, the more students need to explore knowledge by themselves, including finding problems, analyzing problems and solving problems. In the process of guiding students to feel arithmetic and algorithms, let them try, let them actively participate in the formation of new knowledge, and promptly mobilize students to speak their own methods boldly, and then let them compare the correctness and simplicity of the methods themselves. In this way, students think about arithmetic and algorithms in their own way of thinking, which is clear in their hearts and mouths.

2. When students make mistakes when analyzing or solving problems in class, especially some "regular mistakes" influenced by thinking set, such as students being influenced by decimal addition and subtraction when dealing with quotient decimal points. In view of this situation, should teachers criticize and simply deny or encourage them to speak boldly and express their views, and then let students find and verify their mistakes themselves? Of course, it should encourage students to express their views, opinions and ideas boldly. Students' self-denial of their own methods is tantamount to self-denial. In this way, the understanding of teaching knowledge is more profound, not only knowing why, but also knowing why. Moreover, students' questioning and self-denial of the problems raised, analyzed or solved by themselves is conducive to students' self-reflection ability and self-monitoring ability.

Mathematics teaching activities should abstract mathematics problems from concrete problems, analyze them in various mathematical languages, solve them by mathematical methods, acquire relevant knowledge and methods, form good thinking habits and consciousness of applied mathematics, feel the joy of teaching creation, enhance students' confidence in learning mathematics, and gain a more comprehensive experience and understanding of mathematics. Therefore, students are the masters of mathematics learning, and teachers should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematics activities, help them master basic mathematics knowledge, skills, ideas and methods, and gain rich experience in mathematics activities.

Fourth, the teaching process

(a) review of imports

1. How many times must each of the following decimals be enlarged to become an integer? How to move the decimal point? 0.3 1.330.8750.009

2. What are the following figures expanded by 10 times, 100 times and 1000 times respectively?

1.582 130.63.95

3. Fill in the table below.

Bonus 15 150 1500

Separator 5505

business

According to the above table, talk about the changing law among dividend, divisor and quotient. (Dividend and divisor expand or shrink by the same multiple at the same time, and the quotient remains unchanged. )

4. Fill in the blanks according to the unchangeable nature of quotient and explain the reasons.

( 1)5628÷28=20 1; (2)56280÷280=();

(3)562800÷()=20 1; (4)562.8÷2.8=()。

(Emphasize the reason of (4). (4) Compared with the formula (1), the dividend and divisor are reduced by 10 times, so the quotient remains unchanged, or 20 1, that is, 562.8÷2.8=5628÷28=20 1. )

(B) explore mathematical induction

1, learning example 4: How many pairs of shorts can a piece of 0.67m cloth and a piece of 56.28m cloth make?

(1) formula for students to examine questions: 56.28÷0.67.

(2) Reveal the topic:

What's the difference between this formula and the division we learned before? Divider is the division of decimals. )

Today we are going to learn "a number divided by a decimal". Divide a number by a decimal number.

(3) Explore arithmetic.

① Thinking: We have learned fractional division with divisor as integer. How to calculate the divisor if it is a decimal now? Converts a divisor to an integer. How to convert a divisor into an integer? )

② Students try to do:

Act out the students' results and explain them by the students:

Solution 1: Convert the unit name "meter" into centimeters for calculation.

56.28m ÷ 0.67m = 5628cm ÷ 67cm =84 (strips)

Solution 2: Divider and divisor are simultaneously expanded by 100 times, and then calculated. 5628÷67=84 (strips)

A: It can be cut into 84 pieces.

Be reasonable: (Why enlarge the dividend and divisor by 100 times respectively? )

Divider 0.67 is converted into integer 67, which is 100 times larger. According to the invariability of quotient, the dividend of 56.28 should be expanded by 100 times, that is, 5628.

Summary: What methods can be used to convert divisors into integers?

(1) Rewrite the company name; (2) Invariance of utilization quotient. )

(4) Exercise: Finish the exercise191.2 ÷ 3.80.756 ÷ 0.18.

Thinking: How do you transform it? Why?

Talk to each other at the same table about the methods and reasons of transformation. After independent calculation, it is revised. Key points: Using the invariant property of quotient, how many times can dividend and divisor be expanded at the same time, and which number is determined by its decimal places?

(determined by the number of decimal places of the divisor. Because all we have to do is convert the divisor into an integer, which is fractional division. Such as: 0.756 ÷ 0.18 = 75.6 ÷18. )

(Design intention: On the basis of trial operation, guide students to feel the shift method of decimal point in the process of conversion, and pave the way for the law of independent generalization. )

2. Study Example 5: It takes 10.5 yuan to buy 0.75kg of oil. What's the price per kilogram of oil?

Student formula: 10.5÷0.75.

① How to convert the divisor 0.75 into an integer? (Enlarge the divisor by 0.75 times 100, and convert it into 75. To keep the quotient unchanged, the dividend should also be expanded by 100 times. )

② What is the dividend 10.5 times 100 times? (10.5 magnification 100 times is 1050, and the decimal places are not enough, and finally it is "0". )

3. What is the difference between Comparative Example 4 and Example 5? (When the dividend moves to the decimal point, the number of digits is not enough, and "0" is added at the end. )

4. Exercise: Exercise the textbook P2 1 Question 2. After the students finish independently, make a summary.

(Design intent: Teachers can properly explain the method of adding "0" to the dividend shifted after the decimal point. Students are in no hurry to comment after trying. Let them compare two examples in the textbook and inspire students to observe and compare the differences between the two examples and the matters needing attention in calculation. Guide students to analyze and compare, and gradually abstract the displacement method. Let students sum up the division calculation rules with divisor as decimal on the basis of fully accumulating experience, which will receive the effect of waterway. )

(3) Review and summary

Thinking: How to calculate the division with the divisor as a decimal? Draw a conclusion from the discussion (fill in the blanks): divisor is a small selection division. The calculation rule is: divisor is fractional division. First, move the decimal point of () to (); The decimal point of the divisor is shifted to the right by several digits, and the decimal point of the dividend is also shifted to the right () (if the digits are not enough, the () of the dividend should be supplemented with "0"); Then use the divisor () for fractional division calculation. Read P 19-20 and underline the key words.