Divide a number by decimal number 1 1, teaching materials and teaching objectives
Dividing a number into decimals is one of the important contents of the four decimal operations. The focus of teaching is to enable students to master the deduction process of dividing into decimals and integers, and to skillfully use the law of quotient invariance to calculate.
When a number is divided into decimals, the teaching materials are arranged in two levels: first, the decimal places of divisor and dividend are the same (Example 5);
Second, the divisor and dividend have different decimal places (Example 6). In these two examples, the divisor should be converted into an integer by using the constant law of quotient, and then calculated.
When the decimal places of the divisor and the dividend are the same, we only need to use the quotient invariance law to expand the divisor and the dividend by the same multiple, and then we can convert the divisor into an integer and calculate it. When the divisor and the divisor have different decimal places, how many times the dividend should be expanded depends on the divisor's decimal places (for example, if the divisor has two decimal places, then the dividend and the divisor can only be expanded by 100 times, no matter how many decimal places or integers the dividend has). These two kinds of questions have a law, which is based on the same law of quotient.
Teaching objectives:
(1) enables students to understand and master the calculation law of "divisor is the division of fraction", and use the law of quotient invariance to transform the division of divisor into the deduction process of division in which divisor is an integer.
(2) Apply the invariable law of quotient to guide students to understand that things are interrelated and changing, thus cultivating students' mathematical thinking methods of transformation.
(3) Cultivate students' ability to actively participate in learning and cooperation through group exchange learning.
Second, teaching methods and learning methods.
Teachers should arrange teaching materials according to the teaching concept of the new curriculum. They should not only respect the teaching materials, but also insist on them. It is necessary to present the contents of teaching materials in combination with the life cases around students, so as to facilitate students' independent inquiry and cooperative learning and cultivate their awareness and ability of applying mathematics. The essentials of teaching are: attaching importance to the foundation, making a good transition and mastering the law. Teachers should concentrate on teaching and let students fully participate in mathematics activities in order to promote students' ability of independent inquiry and independent thinking.
(1) Strengthen basic training. Decimals are learned on the basis of integer division, so when teaching this unit, several basic trainings should be serious and timely. For example, look at the vertical oral calculation of two or three-digit subtraction; Do fractional division, the divisor is an integer; Memorize the law of decimal point movement and so on. Different forms of training should be taken with the progress of teaching to effectively improve the accuracy and speed of students' calculation.
(2) Guide students to explore actively. When teaching examples with different decimal places of divisor and dividend, in order to cultivate students' interest in exploration and discussion, teachers should proceed from the whole and appropriately increase the capacity and density of questions, so that students can explore and summarize the calculation methods of laws independently in practical calculus in various situations. In the process of students' calculus, teachers should be good at guiding students to understand that when the decimal places of divisor and dividend are different, the decimal places of divisor should prevail.
(3) Practice in time to improve accuracy. Whether in the way of training or in the time of training, it should be carefully designed to improve the pertinence and effectiveness of exercises, among which classroom exercises are the most important. Practice has proved that doing well in classroom exercises is not only a reliable guarantee to improve the quality and efficiency of exercises, but also an effective measure to reduce students' academic burden. Therefore, in class, teachers must have enough time for students to practice, and give feedback and correction in time.
Third, the teaching process
Examination of a communication
What is the nature of 1. quotient invariance?
2. Calculation: 108÷3656x28÷27
(2) Explore new knowledge
1, Example 5: Grandma weaves a "Chinese knot" and weaves a silk rope that needs 0,85 meters. This is 765 meters of silk rope. How much can you knit?
Question: How can I convert to the integer division I learned before?
Discuss at the same table (according to the law of quotient invariance, the dividend and divisor are expanded at the same time 100 times)
2. Example 6: 12.6 ÷ 0.28
Question: Is this the same as the above example? If not, how to expand dividend and divisor?
Discussion at the same table: the derivation should be based on the decimal places of divisor, in which divisor and divisor should be expanded by 100 times before they can be converted into fractional division with divisor as integer; At the same time, teachers should give instructions in time: when the dividend number is not enough, use "0" to make up; The decimal point of quotient should be aligned with the decimal point of dividend.
3. Group calculus, discussion and refining methods
Group A: 6.4÷0.857, 6÷4.246, 8÷ 1.2.
Group B:16.1÷ 0.460,093 ÷ 0.319,0 ÷ 0.06.
When students do calculus in class, teachers patrol, guide and guide them, so that students can gradually understand the main points of these knowledge.
Classroom exercises: (omitted)
(4) class summary:
1. What did we learn today?
2. How to calculate the division in which the divisor is a decimal?
(5) Homework: (omitted)
Divide a number by a decimal. 2. teaching material analysis
1, the position and function of teaching materials
Dividing a number by decimals is the content of "Decimal Division" in Unit 2, Book 1, Experimental Textbook for Grade 5 of Nine-year Compulsory Education Curriculum Standard.
There are two kinds of fractional division: one is fractional division with integer divisor; The other is the division in which the divisor is a decimal. "Dividing a number into decimals" is taught on the basis of learning that "dividing a number into decimals is an integer", which is the focus of decimal division teaching and an important basis for learning decimal elementary arithmetic in the future.
2. Education and teaching objectives
According to the above teaching material analysis, considering the existing cognitive structure of students, the teaching objectives of this course are determined as follows:
(1) Knowledge goal: Through teaching, let students understand that the division with decimal divisor can be converted into decimal division with integer divisor for calculation; Master the calculation rules of division with divisor as decimal, and can apply the rules to calculate.
(2) Ability goal: to cultivate students' ability to analyze, reason, summarize, generalize, try and innovate, and improve their computing ability and ability to solve practical problems.
(3) Emotional goal: infiltrating the "transformed" mathematical thought and the dialectical materialist view of the relationship between things.
3. Emphasis and difficulty in teaching
Among them, it is the teaching focus of this lesson to master the calculation rules of division with divisor as decimal and use the rules to calculate. However, due to the limited analytical reasoning ability of fifth-grade students, it is difficult to understand the calculation principle of the division with decimal divisor into the division with integer divisor.
In order to highlight key points, break through difficulties and enable students to achieve the teaching objectives set in this section, I will talk about teaching methods and learning methods again.
Second, teaching strategies (speaking and learning)
Because the division of divisor in this lesson should be converted into division of divisor into integer according to quotient invariance, it is obvious that quotient invariance means that the new knowledge divisor is the connection point of decimal division and the old knowledge divisor is the integer division. Therefore, before teaching a new lesson, we should first check students' mastery of quotient invariance, and then guide students to use quotient invariance to convert division of divisor into division of divisor into integer, so as to transform new knowledge into old knowledge, integrate old and new knowledge, and facilitate students to incorporate new knowledge into existing cognitive structure. According to the above analysis, it can be seen that this teaching material belongs to progressive teaching material and is suitable for "trying teaching method". On the basis that students have mastered that divisor is integer division and fully reviewed the invariance of quotient, they are guided to try to learn Example 5 and Example 6 for the second time, and finally achieve the purpose of understanding arithmetic and mastering algorithms.
Students' independent inquiry is the main line of teaching. For all students, starting from students' life experience and existing knowledge, the boring calculation teaching is put into familiar and interesting real situations, so that students can experience the whole process of finding problems from real situations and solving problems through calculation. Pay attention to students' learning process and learning methods, and try to experience the process of transforming the division of divisor into fractional division of divisor into integer, so that students can use old knowledge to migrate, explore independently, cooperate and communicate, and develop their innovative consciousness and practical ability. Let students collide their thoughts and exchange their feelings in group cooperative learning activities, and enhance their confidence in learning mathematics well.
Third, talk about the teaching process
According to the American educator Bloom's "Mastering Learning" strategy theory, the vertical and horizontal relationship between old and new knowledge in this course textbook, and the teaching principles of "step by step" and "teaching students in accordance with their aptitude", the following teaching procedures are specially designed for implementing quality education:
(A) to promote knowledge transfer
Mathematics learning is characterized by gradual and spiral rise, just like taking stairs. With a foundation, we can continue to move to a higher level. Divider is the division of decimals, and the key point is the division into integers. So the calculation of division with integer divisor is the basis of learning division with decimal divisor, so it is very necessary to review before class.
The key to understand the calculation law of division with divisor as decimal is to use "the property of constant quotient" and "the law of decimal size change caused by decimal position movement" to convert division with divisor as decimal into division with divisor as integer, and then use the law of "fractional division with divisor as integer" to calculate.
First, review the changing law of dividend, divisor and quotient with a 20-page table, that is, the invariable nature of quotient, which paves the way for "transforming" the division of divisor into decimal, and then leads to questions, arouses students' cognitive conflicts, stimulates students' interest in learning, and produces hunger and thirst for knowledge.
(B) the perception of the surrounding mathematics
Scene: The "Book Scroll and Little Sheep" Reading Festival in Yangzi Township Primary School is in full swing. The students in Class 5 (2) bought some colored cardboard and prepared to make reading cards. Courseware display: The school campus is full of exquisite reading cards made by students themselves, and then there is a dialogue: the wholesale of colored cardboard is only 0 per card. 85 yuan, it costs 7.65 yuan to buy colored cardboard. Ask a math question: How many pieces of cardboard did a * * * buy?
Curriculum standards point out that students should be familiar with the background or reality of hunger life and provide them with rich learning resources. Combining the school's reading festival activities in teaching, the scene in the textbook is reasonably adapted, which not only educates students in reading, but also conforms to the reality of students' campus activities, closely links mathematics with life, makes students feel familiar and cordial, produces enthusiasm and impulse to solve problems, and puts them in the best state of actively exploring knowledge. )
(3) Enjoy the fun of inquiry
Step one: study hard and make the arithmetic clear.
First of all, ask the way: this is the division of divisor into decimals. Think about it and see if you can solve it with what you have learned. Please think independently, and then communicate your thoughts with the group. After the students finish speaking, teachers and students discuss and explain the truth. At this time, students may come up with two methods.
The first method is to change "7.65 and 0.85" into "minutes" for calculation. The second method is to enlarge the divisor and dividend by 100 times according to the invariant property of quotient. Here, students are mainly guided to understand why divisor and dividend should be enlarged by 100 times at the same time, so as to convert divisor 0.85 into an integer, and in addition, students are mainly guided to understand why divisor and dividend should be enlarged by the same multiple, so as not to change the original quotient. After the students understand arithmetic, the teacher explains the vertical writing format to the students. Under the guidance of the teacher, let students try to complete the vertical supplement, so that students can not only understand the transformation process; And mastered the standard vertical writing format. Finally, complete the first "do" question.
Step 2: Try again and be rational.
On the basis of students' efforts to complete Example 4, let students continue to study Example 6 with the joy of success. In order to help students successfully try to learn Example 6, before trying, students can contact the method of Example 5 and think about how to calculate. What's the problem? When students find that the number of digits of dividend is not enough when dividend and divisor are expanded to the same multiple at the same time, let them discuss the solution around this problem. In the discussion, guide the students to recall: "What should I do if the original decimal place is not enough when the decimal point changes in the past?" After discussion and exchange, the teacher told the students about the vertical style of blackboard writing, emphasizing that the decimal point in the divisor should be crossed out to make the divisor an integer. Note that the decimal point of the divisor moves to the right, and the decimal point in the dividend should also move to the right accordingly. If there are not enough digits, add a few zeros.
Finish the second question, "Do the problem, do the problem", and let the students know the problems that should be paid attention to in calculating the division of fractions by correcting mistakes.
The third step is to actively guide the summarization algorithm.
After students try to complete Examples 5 and 6, guide students to summarize the calculation method of fractional division.
Design intention: Give full play to students' initiative and guide students to actively explore.
It is better to teach people to fish than to teach them to fish. When exploring new knowledge, we should first provide students with the direction of thinking, that is, whether they can solve it with what they have learned, and then provide students with sufficient thinking space, give full play to their initiative, guide students to constantly try different mathematical activities through observation, comparison and contact with old knowledge, organize and guide students to use old knowledge to acquire new knowledge, and infiltrate "transformed" mathematical ideas into teaching.
(D) Experience the joy of success
Practice is easy before it is difficult, and pay attention to communication, display and evaluation in feedback. Students taste the joy of success in the evaluation, further cultivate students' awareness of applying mathematics, and better promote the understanding and application of the difficulties in this lesson.
(5) Share your gains and mine.
At the end of the class, ask the students what you got from today's study.
Design intention: To cultivate students' inductive ability and language expression ability, students should sum up and complement each other. Teachers only give proper guidance, cultivate students' ability of induction and generalization, and encourage students to evaluate themselves from the aspects of mathematical knowledge, mathematical methods and mathematical emotions.
Fourthly, reflection on teaching design.
1, implement a principle-the principle of taking students as the main body
2. Highlight an idea-transformed mathematical thought.
3. Infiltrate a kind of consciousness-the consciousness of applied mathematics.
Divide a number by a decimal number. 3. teaching material analysis
Dividing a number into decimals, that is, dividing a number into decimals, is one of the key knowledge in the ninth book of nine-year compulsory education and six-year primary school mathematics. The focus of this section of the textbook is: the shift law of decimal point when the division with decimal divisor is converted into the division with integer divisor. The key is to transform the division of divisor into a division of divisor into an integer according to the fact that divisor and dividend are expanded by the same multiple at the same time and the quotient is unchanged.
Second, the analysis of learning situation
1, students have a good grasp of the basis of integer division, and they also have a good grasp of dividing fractions by integers.
2. There are obvious differences in students' ability to use new knowledge to solve practical problems, but different students have different potentials.
3. Excellent students and students with learning difficulties have great differences in their understanding of arithmetic. But it can basically pass.
Another point is that I have been taking these two classes. I have always attached great importance to the guidance of learning methods in my usual teaching, especially when teaching fractional multiplication.
Third, teaching methods.
Because primary school students' learning is always based on the original knowledge framework or the original life experience, I mainly use migration to clarify the principle of transformation in this class, and guide students to explore independently and find their own ways to solve new knowledge. I would like to add here that transfer includes the transfer of knowledge and the transfer of learning methods.
Fourth, study law.
This lesson is mainly to let students master the problem-solving strategy of transforming one problem into another, which is what we call "transformation" learning method. Through the transfer of learning methods and knowledge, students' analytical ability, analogy ability and abstract generalization ability are cultivated.
Fifth, teaching ideas
The key of this lesson is to convert the division with decimal divisor into the division with integer divisor. In order to understand that the arithmetic of this calculation rule is "the property of constant quotient" and "the law of the change of decimal size caused by the movement of decimal point position", it is necessary to convert the division of divisor into the division of divisor into integer, and then use the calculation rule of "fractional division of divisor into integer" to calculate. In order to promote migration and clarify the principle of transformation and replacement, I am going to design the following links:
1. In order to promote the transfer of learning methods, let me first recall how decimal multiplication is calculated. Let the students recall that decimal multiplication is to calculate integer multiplication first, that is, to convert new knowledge into old knowledge to solve it. After the students answer, the blackboard is 8.4÷ 1.4. In order to save calculation time, I only reduced the data of the topic by mastering the method. Can the teacher ask the students to compare this division formula with what they have learned before? Then discuss in groups and see if we can find a calculation method.
Feedback students' discussion, clarify the principle of transformation, and ask students to explain what their ideas and basis are. Ask the students to clarify the transformation principle in the mutual debate. It also achieved the purpose of highlighting key points and solving difficulties.
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. Specific practices are as follows:
① Students try to do Example 4 and tell the method and reason of decimal point shift.
② Students try to do Example 5. As mentioned above, the decimal point should be treated, and then the difference between Comparative Example 4 and Example 5 should be noted that the number of emphasized digits is not enough, and 0 should be added.
(3) Let the students observe the three questions on the blackboard, find out the calculation rules, guide the 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 scale of the right shift depends on the scale of the divisor, not the scale of the dividend.
3, special training, strengthen the "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 exercise. 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.
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Based on the students' existing foundation and the design of this course, it is expected that they can basically master the transformation method and the teaching effect should be ideal.
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