This textbook sets two examples for teaching. Example 4 is a common problem in teaching. Firstly, the distance between Wang Hong and other three people is represented by histogram, so that students can not only know how many kilometers each person runs, but also recall old knowledge and intuitively feel the numbers related to scores in the diagram, providing experience for solving the problem that "what percentage of one number is another"; Then guide students to link the question "How far Li Fang runs is Wang Hong's" and "How far Li Fang runs is Wang Hong's", so that students can transfer their existing problem-solving experience to new problem situations; Finally, the textbook guides the calculation skills of percentage. Write the quotient in decimal form first, and then rewrite the decimal into percentage, so that students can understand the simplicity of expressing the result of division with decimal. Example 5: Practical problem of finding percentage in teaching. First, the textbook helps students understand that "attendance is the percentage of actual attendance to the number of people who should attend" and interprets percentage as the percentage of one number to another. After calculating the attendance of the track and field team on Monday, students can choose two days' data to calculate the attendance, thus consolidating their understanding of attendance. On this basis, the textbook requires students to find the survival rate of saplings through "practice" and tell examples of percentage in life, so that students can further understand the significance of percentage and feel the wide application of percentage in life and production.
The teaching focus of this lesson is to understand and master the idea and method of "what percentage of one number is another number". The difficulty is to analyze the quantitative relationship and find the correct unit "1".
[Teaching objectives]
1. Through the transfer of knowledge, let students understand the idea of solving the application problem of "What percentage is a number" and master the calculation method of percentage.
2. In the process of solving practical problems, we can further understand the internal relationship between mathematical knowledge, thus being inspired by the dialectical materialism view that there is a universal relationship between things.
3. Understand the application of percentage in specific life problems, stimulate students' enthusiasm for learning, and further establish confidence in learning mathematics well.
[Teaching process]
First, pave the way for pregnancy
1. What is a percentage?
2. Rewrite the following figures into percentages.
0.6 7/ 10 3.5 5/8 1
3. Give the statistical chart of Example 4, and observe carefully to get information.
(1) Compare the multiple relation of any two quantities, and put forward the question "A fraction of one number is a fraction of another number". How should I ask this question?
How far does Li Fang run than Wang Hong?
How far does Wang Hong run than Lin Xiaogang?
……
(2) Free oral answers and timely questions: Who is better than who? Who is this unit "1"?
(3) Summary: How to find the score of one number to another?
4. These questions all use scores to express the multiple relationship between two people's running distances. Percentages also represent multiples. Can you change "what percentage of a number is another number" to "what percentage of a number is another number"?
5. Introduction: In this lesson, we will learn to solve a simple practical problem: what percentage of one number is another?
[Comment: According to the law of knowledge transfer, we should review the meaning of percentage at the beginning of class, and the method of converting fractions and decimals into percentages, focusing on the problem-solving method of "the fraction of one number is a fraction of another number", paving the way for the smooth exploration of new knowledge and the transition to new courses. ]
2. Explore new knowledge
(1) Teaching Example 4: Find what percentage of one number is another.
1. Change the review question "What percentage of the distance Li Fang runs is Wang Hong" to "What percentage of the distance Li Fang runs is Wang Hong"?
2. Try to answer and find the question:
Dialogue: Do you want to try to find out for yourself?
The students try to do it and say their names.
Dialogue: What problems did the students meet that need to be discussed?
3. Students communicate freely, and teachers guide their thinking in a timely manner:
(1) Discuss how to formulate
Thinking: Why? what do you think?
Introduction: Which two quantities are being compared and which quantity is regarded as the unit "1"? What percentage of the distance Li Fang runs is that of Wang Hong?
Summary: This question takes the distance run by Wang Hong as "1", and the distance run by Li Fang is a few percent of that of Wang Hong. In fact, this is equivalent to asking Li Fang to occupy only a few percent of Wang Hong.
(2) Explore how to calculate
Thinking: How to calculate?
Guidance: First, find out how far Li Fang has run than Wang Hong, and then convert it into percentage. (blackboard writing: 4÷5=4/5=80%)
The calculation results are expressed in decimals and then converted into percentages. (blackboard writing: 4÷5=0.8=80%)
Summary: After the division formula is listed, the quotient is usually expressed as a decimal and then rewritten as a percentage.
(3) Summary:
Thinking: What did you understand?
Guide: Compared with the review questions, what hasn't changed? (known conditions and quantitative relations)
what has changed? (The expression of the multiple relationship between two numbers changes from fraction to percentage)
So have the ideas and methods to solve these two problems changed?
Summary: How many percent of the distance run by Li Fang is that of Wang Hong? Or take the distance run by Wang Hong as the unit "1" and divide the distance run by Li Fang by the distance run by Wang Hong. The formula is the same, but the result is expressed as a percentage.
"give it a try"
How to answer "What percentage is the distance between Wang Hong and Lin Xiaogang?"?
(1) Students answer independently and think at the same time: What problems did you encounter in the calculation process?
(2) communication:
What if we can't separate? The quotient of (5÷7) is an infinite decimal. Without divisor, the quotient should retain three decimal places, that is, the decimal place before the percent sign. )
5. Reflection and induction: (First discuss the following two questions in groups, and then organize the whole class to communicate)
(1) Why is the distance Wang Hong runs divided in Example 4 and divided in "Try it"?
Example 4 is the ratio of the distance run by Li Fang to that run by Wang Hong, and the distance run by Wang Hong is regarded as "1"; "Try it" is the ratio of the distance run by Wang Hong to that run by Lin Xiaogang, and the distance run by Lin Xiaogang is regarded as "1", so the kilometers run by Wang Hong are the divisor in the former formula and the dividend in the latter formula.
(2) What do you usually think when you answer the question "What percentage of one number is another number"?
"What percentage of a number is another number" is actually the same as "What percentage of another number is a number" and can be directly calculated by division. Note that the unit "1" will change with different comparison standards, so we must find the correct unit "1" to solve this kind of problem.
6. Complete the exercise 1.
[Comment: This level of teaching leads to examples by changing the questions, communicates the connection between the review questions and the examples with questions, and highlights two problems by using the transfer law: first, it highlights the calculation method of the percentage when the quotient is an infinite decimal, and second, it highlights the quantitative relationship of a few percent problems through comparative reflection, so that students can master the ideas and methods for solving practical problems that how many percent of one number is another. ]
(B) Teaching Example 5: The problem of finding percentage
1, Example 5: The school track and field team consists of 40 people. The following table is the statistics of the number of people attending the training every morning for a week. (Display statistical chart)
2. Guide analysis:
(1) What is attendance? What's the actual attendance percentage? )
(2) What is the attendance rate? (Percentage)
(3) So how to get attendance? When the attendance rate is estimated to be high. (actual attendance directly divided by attendance)
3. Calculate:
What is the attendance rate of the track and field team on Monday? (blackboard writing: 39÷40=0.975=97.5%)
Select the data of two days from the above table and calculate the corresponding attendance rate respectively. (Students are free to choose solutions)
4. Feedback communication:
(1) When is the highest attendance rate? When is the lowest attendance rate?
(2) The actual attendance on Wednesday and Thursday is the same as the attendance, and the formula is 40÷40= 1. How to rewrite it as a percentage? (Instruct students to rewrite 1 as 100%)
(3) Why is the attendance rate on Monday, Tuesday and Friday not 100%? Can the attendance rate be higher than 100%?
5. Compare and find out the * * * similarity of each attendance rate:
(1) Meaning: The quantity of all parts is compared with the total.
(2) Meaning: "1" in total.
(3) Representation: take the sum of "1" as the denominator or divisor, and the number implied by the ratio of ××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
[Comment: This layer of teaching first helps students understand the meaning of attendance, then encourages students to choose two days' data to calculate attendance, and finally guides students to reflect on whether attendance can be higher than 100%, so that students can further understand attendance and become the basis for understanding other percentages. ]
Three. Expansion and extension
1. Finish the second question of "practice": first talk about the meaning of "survival rate" and then answer it independently.
2. Complete the third question "Practice"
(1) What percentage have you heard in your daily life? What do they mean?
Peanut oil-oil yield student exam-excellent rate
Product inspection-qualified rate-salt content of brine.
Seed Test-Shooting Test of Germination Rate-Hit Rate
(2) Discussion: What are the advantages of finding these percentages?
Pointing out the percentage can facilitate the analysis and comparison of data. (blackboard writing: easy to analyze and compare)
(3) Communication: Choose your favorite percentage and tell the calculation method.
[Comment: Let students tell the percentage in life, understand and tell the meaning of these percentages, so as to further understand the meaning of percentage, effectively broaden their knowledge and feel the wide application of percentage in life. ]
Four. Class summary
1. In this lesson, we learned the practical problem "How many percent does a number have", and the ideas and methods to solve the practical problem of fractions are the same as "How many percent is another number?" , but the result is to be converted into a percentage. When doing the problem, we must accurately judge who the unit "1" is, which is the key to solving the problem.
2. Homework: Exercise 2 1, Question 1~3.
[General Comment: In the teaching design of this lesson, teachers have a better understanding of the intention of compiling textbooks and a better grasp of the internal relationship between the knowledge before and after. At the beginning of class, we should use the transfer law to find the connection point between old and new knowledge, and guide students to learn new knowledge based on the knowledge that one number is a fraction of another, so as to grasp the starting point of teaching well. In class, teachers provide sufficient time and space for independent exploration and communication, so that students can improve their thinking process in discussion and communication, and then guide students to review and reflect after solving problems, and * * * summarize problem-solving methods to improve students' understanding level. At the end of the class, teachers should closely connect with the reality of life, broaden students' knowledge, and let students feel that mathematics comes from life and is applied to life, and mathematics is around. ]