A percentage is a part of a whole expressed as a percentage. A number indicating that one number is a percentage of another number is called a percentage, which is usually used. %? To show. The following is a summary of the percentage of knowledge points in the sixth grade that I have compiled, for your reference!

course content

In the "Percent of Cognition" unit of Grade 6 (Volume 1), percentage is used to describe the significance of initial teaching percentage and the multiple relationship between part and whole or two similar quantities; Teach the rewriting of percentages, fractions and decimals, and solve the simple problem that one number is a few percent of another. On this basis, arrange this unit to apply percentage to solve practical problems, further understand the meaning of percentage and realize its wide application.

Percentages are often used in daily life and productive labor, such as expressing the relationship between one quantity and another, calculating interest and taxes, designing and calculating discounts, etc. Solving problems by percentage can be calculated by formula or solved by formula equation. These are the teaching contents of this unit.

There are many teaching contents in the whole unit, and six examples, four exercises and the arrangement and practice of the whole unit are arranged, which are roughly divided into five sections.

Example 1. Exercise 1: Find out how much one number is more than another. This paragraph is arranged after the sixth grade (the first volume), with a simple percentage.

Example 2, Example 3, Exercise 2: Calculate the tax payable and the available interest amount according to the tax rate and interest rate stipulated by the state. This paragraph applies percentage multiplication to solve practical problems.

Example 4, Exercise 3, solve the problems related to discounts, including designing discounts, and find the current price or original price according to discounts. In this paragraph, there are equation solutions and equation solutions. Finding the original price by equation is the key.

Example 5, Example 6 Exercise 4, the column equation solves a slightly complicated percentage problem or fraction problem. The sixth grade (the first volume) only teaches a slightly more complicated problem of finding the percentage of a number. What percentage of a number is known? The problem of finding this number is arranged in this unit, which is brought out by the percentage problem.

"Finishing and Exercise" synthesizes the knowledge content of the whole unit and further applies percentage to solve practical problems.

Teaching material analysis:

The sixth grade (the first volume) teaches the meaning of percentage, the latter is the ratio of 100, and the experience percentage is also called percentage or percentage; Teach the relationship between percentages, fractions and decimals, especially the mutual rewriting of percentages and decimals, and make necessary preparations for applying percentages to solve practical problems; It also taught a simple question, that is, what percentage one number is of another, and initially applied the percentage. On this basis, this unit continues to teach the application of percentage, including four contents, namely, the practical problem of finding a few percent more (or less) than another number, the practical problem of finding the tax payable according to the known tax rate and the interest due according to the known interest rate, and the practical problem related to discount, and the more complicated practical problem of finding a few percent of a number. Six examples and four exercises are arranged, and the whole unit content is divided into four teaching sections. Finally, arrange unit exercises.

1. Taking the meaning of percentage in the real question as a breakthrough, this paper analyzes the quantitative relationship through reasoning and explores the algorithm.

2. Transfer the experience of finding the fraction of a number to finding the percentage of a number.

3. The column equation solves the practical problem of knowing the percentage of a number and finding this number.

In teaching examples 4, 5 and 6, we should renew our ideas and change our customary teaching methods. First of all, students are not required to distinguish between fractional multiplication and fractional division, especially not to apply the so-called law of multiplication to the known unit "1" and the so-called law of division to the unknown unit "1". In the past, this way of solving problems had a good effect, but it seriously restricted students' thinking and turned the process of analyzing quantitative relations into a simple judgment based on individual words. To improve teaching methods, we should strengthen the understanding of the meaning of fractions and percentages, make full use of the quantitative relationship of fractions of a number, and reasonably choose formulas or equations to solve problems. Secondly, there is no need for association training about scores and percentages. If 25% is used, there is still (1-25%); I read 1/5 of the whole book on the first day, and 1/6 of the whole book on the second day. I thought of 1/5+ 1/6 of the whole book in two days. These associations serve the column partition formula. It is necessary to guide students to fully explore and make use of the most basic quantitative relations in practical problems such as combination and difference as the basis of equations or formulas, so as to link the teaching of primary schools with junior high schools and lay a good foundation for students' subsequent study.

Teaching objectives:

Class arrangement:

Percentage application 1 1 class hour

The first lesson: Find out how much one number is more (less) than the other.

Teaching content: textbook page 65438 +0, example 1, try to practice, exercise 1, question 1~3.

Teaching objectives:

1, so that students can understand and master the basic thinking method of "one number is more (less) than another number" in real situations and solve related practical problems correctly.

2. In the process of exploring the method of "how much more (how much less) one number is than another", students can further deepen their understanding of percentage, realize the close relationship between percentage and daily life, enhance their awareness of independent exploration and cooperation, and improve their ability to analyze and solve problems.

Teaching process:

I. Teaching examples 1

1, give two known conditions in the example 1, and ask students to draw a line segment to represent the relationship between these two quantities.

After the students finish drawing, discuss: how many lines are drawn to represent these two quantities? How many lines should be drawn longer? About how long? what do you think?

Make a request: according to these two known conditions, what problems can you solve?

Guide students to ask questions such as "how many hectares are actually planted", "how many hectares are actually planted", "how many percent of the actual afforestation area is equivalent to the original plan" and "how many percent of the original planned afforestation area is equivalent to the actual" from the perspective of difference ratio and double ratio.

On the basis of students' full communication, the question in the example 1 is put forward: What percentage is the actual afforestation more than the original plan?

2. Guide thinking: This question is which two quantities are compared? Which quantity is used as the unit of comparison? 1? What percentage of actual afforestation is required, that is, which quantity is what percentage?

Summary: To require the actual afforestation to be several percent more than the original plan means to require the actual afforestation to be several percent more than the original plan.

Revelation: According to the above discussion, how are you going to answer this question in the form of a table?

After continuous calculation, the students further asked: How is the number of hectares actually planted more than originally planned calculated? What percentage of 4 hectares is needed 16 hectares? How should the comprehensive formula be listed?

3. Further guidance: It was previously suggested that "according to two known conditions, it can be found out that the actual afforestation area is equivalent to a few percent of the planned area". Can you answer this question in detail?

After calculation, the students ask: What is the relationship between the two percentages of 125% obtained here and the 25% just obtained?

Discuss clearly with the students that removing the same part of 125% as the unit 1 means that the actual afforestation is more than originally planned.

Request: According to the above discussion, it is required that "the actual afforestation is several percent more than the original plan". How else can we make it?

Students ask: What does 125% in the formula "100%" mean? 100%?

Second, teach "give it a try"

1. Show me the question: What percentage is the original planned afforestation less than the actual afforestation?

Inspiration: guess according to the answers to the questions in the examples. What is the answer to this question?

After the students make a guess, they will not make an evaluation for the time being.

Question: Which two quantities are compared in this question? Which quantity is used as the unit of comparison? 1? The requirement that "the original planned afforestation is a few percent less than the actual afforestation" means asking which amount is a few percent of which amount. How are you going to solve this problem? Can you list different formulas?

2. Students discuss after calculation: Is this answer the same as your previous guess? Why is it different?

Summary: The problem in "try it" and the example is to compare the actual afforestation area with the original planned afforestation area, but the percentage is different because of the different number of units in the comparison.

Third, guide the completion of "exercises"

1, ask students to read the questions freely.

2. Question: How to understand the problem that the number of graduate students in 2005 increased by several percent compared with that in 2004?

After discussion, the students were asked to give their own solutions.

3. According to the students' performance in the process of answering questions, the camera asks: Have you encountered any new problems in the calculation?

After the students ask questions, guide them to read the bottom note of the textbook on this page independently and organize appropriate exchanges.

Fourth, guide the completion of the exercise 1, question type 1~3

1, do exercises 1, question 1.

Students can be encouraged to fill in the blanks independently. If some students find it difficult, they can be inspired to draw the corresponding line graph first, and then think according to the line graph.

2. Do exercises 1, question 2.

Let the students talk about their understanding of the question first, and then let the students answer it continuously. Remind students to keep the calculated quotient to three decimal places.

3. Do exercises 1, question 3.

Encourage students to answer independently first, and then let students explain the thinking process clearly through communication. Students can be reminded to use a calculator to calculate.

Verb (abbreviation of verb) class summary

What did you learn from this lesson? What do you usually think when you find that one number is less (more) than another? What else should I pay attention to in the calculation process?

The second category: find a few percent more (less) than the other party.

Teaching content: Complete 2-3 pages of exercises 1, questions 4-8.

Teaching objectives:

1, to help students consolidate the thinking method of solving the problem that "one number is more (less) than another number" in different problem situations.

2. Further clarify the connection and difference between "one number is a few percent more (less) than another number" and "one number is a few percent of another number", and deepen the thinking on the basic methods to solve related problems.

Teaching process:

First, review the introduction.

How to solve the practical problem of "how much more (less) one number is than another"? How did you solve it? Is there any other way?

2. Complete the exercise 1, questions 4-8.

1, complete the fourth question.

Students solve problems independently after reading.

Tell me, tell me how you answered. Is there any other answer to question (2)?

What's the difference between these two questions?

2. Complete question 5.

Let the students answer independently first, and then organize exchanges and comparisons.

Focus on comparing questions (2) and (3) with questions (1).

3. Complete question 6.

Read the questions and find out what the incubation period is. Then the students answer independently. Communicate the correct rate of inspection and help students with difficulties understand.

4. Complete question 7.

Read the question and say how you understand it.

Clear: "the price of chocolate is a few percent more expensive than toffee", which means "the price of chocolate is a few percent more expensive than toffee."

Students exchange views after answering the questions.

5. Complete question 8.

Students answer independently. You can use a calculator to calculate. Communicate after completion.

Third, read "Do you know"

Students read independently.

Communication: What do you think after reading it?

Thinking: Why can't we say that the GDP growth rate of China in 2006 was 0.3% higher than that of 2005?

Two different percentages with outstanding unit of 1 cannot be directly subtracted.

Can you give some examples about percentage points and negative growth?

Fourth, the class summarizes.

What have you gained from learning this lesson?

Teaching design of tax payment in the third classroom

Teaching content:

Example 2 and "try" and "practice" on pages 4-5 of the textbook. Exercise 2, Question 1-4.

Teaching objectives of class hours:

1, so that students have a preliminary understanding of tax payment and tax rate, and understand and master the calculation method of tax payable. Initially cultivate students' tax awareness, continue to feel that mathematics is around, and improve their knowledge application ability.

2. Cultivate and solve simple practical problems and realize that there is mathematics everywhere in life.

Teaching emphasis: mastering the application of percentage in real life.

Teaching difficulty: Infiltrating life is the teaching idea of mathematics.

Preview: Find out what is tax payment? How to pay taxes? What is the significance of paying taxes?

Difficulties: knowledge about paying taxes by installments. Clever use of percentage tax.

Teaching process:

I. Understanding and Understanding Tax Payment (Slide Projection)

According to the provisions of the national tax law, paying taxes is to pay a part of the collective or individual income to the state according to a certain proportion for the development of economy, national defense, science, culture, health, education and social welfare, so as to continuously improve people's material and cultural living standards and safeguard national security. Therefore, any collective or individual has the obligation to pay taxes according to law.

Tax revenue is one of the main sources of national fiscal revenue. Taxes include value-added tax, consumption tax, business tax and income tax. China's tax revenue is increasing year by year. By 2005, the annual tax revenue had reached 3,086.6 billion yuan. (Carry out tax awareness education)

Question: Have you ever learned about paying taxes in the tax department in your life? So what exactly is tax payment and how should the tax amount be calculated? Today we will learn to pay taxes. It says on the blackboard: Pay taxes.

Second, the new curriculum teaching

1, teaching example 2.

Example 2: The turnover of Starlight Bookstore last year1February was about 500,000 yuan. If the business tax is paid at 6% of the turnover, how much should this bookstore pay last year1February? Students' reading problems.

Question: Think about it. Is it really necessary to pay business tax on the 6% turnover in the question? How to calculate in the form of columns? Can you do it? Give it a try!

Students try to practice and revise collectively, and the teacher writes the formula on the blackboard.

Key point: Calculating the tax payable is actually calculating the percentage of a number, that is, multiplying the total income of the taxable part by the percentage of a tax rate, and then calculating the tax payable.

2. How do we calculate?

Method 1: instruct students to calculate the percentage of components.

Method 2: Guide students to convert percentages into decimals for calculation.

3. Try it.

Question: What should I ask this question first? What else do you want?

Student: What is the 10% of 5200 yuan first? Plus 5200 yuan is the money paid for buying a motorcycle.

Students' blackboard writing performance and Qi training are carried out at the same time and revised collectively.

4. Students finish the exercises in the textbook.

Third, practice synchronously.

1, Exercise 2, Question 1

Assign students reading questions and ask them to explain the meaning of each data in the formula.

What do you mean by 1.8 million and 3.6 million respectively? Then how should I ask the business tax here?

Students discuss and practice.

Fourth, expand and upgrade.

Question 4 of exercise 2.

China's personal income tax collection standard published in June, 5438+October, 2005: 1600 yuan's personal income is not taxed. If the monthly income exceeds 1600 yuan, the excess shall be taxed according to the following standards. The excess part is within 5% of 500 yuan, the excess part is within 2,000 yuan, 500 yuan-10%, and the excess part is within 5,000 yuan, 200 1 yuan-15% * * *

Li Ming's mother's monthly income is 1800 yuan, and his father's monthly income is 2500 yuan. How much personal income tax should they pay?

In this question, is the taxable income of Li Ming's mother 1800 yuan? Why? How much should the class discuss Li Ming's mother's tax? How much is the tax rate? So dad's income is 2500 yuan, how much tax should he pay? What is his tax rate?

Introduce the tax payment in stages, and finally let the students calculate the personal income tax that Li Ming's parents should pay respectively.

Verb (abbreviation of verb) class review

Question: What did you learn from this lesson? Aware of what? Without taxes, the country will not be able to raise the necessary funds to do things for everyone. Therefore, China's Constitution stipulates that every collective and citizen has the obligation to pay taxes according to law. I hope that when students grow up, they will strive to be tax pioneers and contribute to the prosperity of the motherland!

Distribution of intransitive verbs

Class assignment: Exercise 2, Questions 2-3.

the fourth lesson

Teaching purpose:

1, understand the meaning of savings.

2. Understand the meaning of principal, interest rate and interest.

3. Mastering the calculation method of interest will correctly calculate the deposit interest.

Teaching preparation:

Physical projector, credit union deposit slip, relevant interest rate table

Teaching process:

First, create situations and introduce topics.

1, the teacher has 8,000 yuan at home for the time being, but it is not safe to leave the cash at home. Who can help the teacher find a way to deal with the money better?

This classmate's suggestion is good, so I will save this 8000 yuan. Before saving, the teacher also wants to know something about saving. Who would like to introduce it?

Second, contact life and understand concepts.

1. Ask students to introduce their savings knowledge.

2. That's right. Savings can support national construction, which is the advantage of savings. Let's take a look at the following information projection: In February 2006, Bank of China issued loans of 856.3 billion yuan, 2099.9 billion yuan and 576.5438 billion yuan to industry, commerce, construction and agriculture respectively. This money is all our usual savings. According to statistics, by the end of 2005, the total deposit of urban residents in China has exceeded 10 trillion, so it is good for the country and individuals to keep the temporarily unused money in the bank.

3. What should I do when saving? How many types of savings are there?

According to my own understanding, what are demand deposits and time deposits, and what are fixed deposits and fixed withdrawals?

Third, participate in practice and internalize experience.

1, the students know a lot of knowledge. The teacher first thanked everyone for sharing so much savings knowledge with each other. Now the teacher is going to deposit the money in our Taixing Town Credit Union. Before the deposit, the staff of the credit union gave the teacher some deposit slips and asked the teacher to fill them out completely. Now there is such a deposit slip on the students' desks. Do you know how to fill in all the parts? Give it a try! (Students discuss with each other and fill in)

2. Students show the completed form and introduce it accordingly.

Just now, all the students successfully deposited 8000 yuan into the credit union. Suppose a few years later, the deposit expires and the teacher goes to the credit union to take it out. The students all remember that the original deposit in the credit union was 8000 yuan. Is it only 8000 RMB now? Is it less or more? What is the proper name for this extra money?

4. What is interest? What is 8,000 yuan? How much interest is generally determined by what? What else do you know?

According to the economic development and changes of the country, the interest rate of bank deposits is sometimes adjusted. The domestic interest rates of bank demand and lump-sum deposit and withdrawal from 65438 to 0998 are as follows: (Forecast) Time demand.

Lump sum deposit and withdrawal 1 year lump sum deposit and withdrawal 2 years lump sum deposit and withdrawal 3 years lump sum deposit and withdrawal 5 years lump sum deposit and withdrawal 98.3.251.715.225.586.6698.711. 144.599.6. 100.992.252.432.72.882002.2.20.72 1.952.242.522.792006.8.30

What can you get from the table?

Information?

According to the communication just now, how do you think the interest should be calculated?

6. According to the certificate of deposit you just filled out, can you help the teacher figure out how much interest there will be when 8000 yuan expires?

Fourth, link examples to sublimate understanding.

1, can you help Liang Liang calculate how much interest he can get when it expires?

Students read the book after calculation and compare with it.

Name reading: According to the national tax law, the interest earned by individuals in bank deposits should be paid at the rate of 20%.

2. The deposit interest must be paid at the rate of 20%. Paying taxes is the duty of every citizen. Students here should pay taxes according to law when they grow up. So how much interest tax should Liangliang pay? How much interest did Liang Liang earn?

According to the certificate of deposit filled in your hand, can you help the teacher calculate how much interest tax the teacher should pay? What exactly did you get?

After the students calculate, report and communicate.

4. Pointing at a classmate, why can I not pay taxes?

If you buy government bonds and construction bonds, you can not only support the development of the country, but also not pay taxes. I hope the students will support the construction and development of the country in the future. Does anyone know what other forms of savings are tax-free?

Independent induction and practical application of verbs (abbreviation of verb)

1. What information did you get in this class? What skills have you mastered?

2. Use what you have learned to complete questions 5, 6, 7 and 8 in Exercise 2.

Lesson 5: Practical Problems about Discount

Teaching content: example 4 and "exercise" on page 8 of the textbook, exercise 3, question 1~4.

Teaching objectives:

1, so that students can know the meaning of discount, understand the application in daily life, and learn to do equations to answer "What is the percentage of a given number?" Find this number and other practical problems related to discount, further understand the internal relationship of percentage problem, and deepen the understanding of the quantitative relationship expressed by percentage.

2. In the process of exploring and solving problems, students can further cultivate the habit of independent thinking, active cooperation and communication with others, and conscious testing, experience the fun of success, and enhance their confidence in learning mathematics well.

Teaching process:

I. Teaching Examples 4

1, understand the discount.

Dialogue: When we are shopping, we often encounter the situation that stores sell goods at a discount.

Show the scene diagram of textbook example 4. Ask the students to talk about what information they get from the pictures.

Question: Do you know what "all books are 20% off" means?

According to the students' answers, it is pointed out that selling goods at reduced prices is usually called "discount". 20% off is 20% off the original price, and 20% off is 20% off the original price.

2. Explore solutions.

Question in Question 4: What is the original price of interesting mathematics?

Inspiration: How much did the child in the picture spend on an interesting math book? Is "12 yuan" here the current price or the original price of interesting mathematics? What is the relationship between the current price and the original price of a book in this question?

Follow-up: "The current price is 80% of the original price". Which two quantities compare 80%? Which quantity should be used for comparison? 1? Do you know the original price of this book? How are you going to answer this question?

Further enlightenment: according to the discussion just now, can you find out the equal relationship between the quantities in the problem?

Students communicate with each other in groups and then in the whole class. The teacher wrote on the blackboard according to the students' answers:

Original price? 80%= actual selling price

Question: Will you list the equations according to this equation relationship?

Write on the blackboard according to the students' answers.

Solution: Let the original price of interesting mathematics be RMB. ? 80%= 12= 12? 0.8= 15 A: original price of interesting mathematics 15 yuan.

3. Guide inspection and communication.

Revelation: Is the calculated result correct? Will you test this result?

Let the students check independently first, and then exchange inspection methods.

Inspire students to use different methods to test: you can find the percentage of the actual selling price to the original price to see if the result is 80%; You can also multiply the original price 15 yuan by 80% to see if the result is 12 yuan.

Second, guide the completion of "practice"

Let the students talk about the relationship between the current price and the original price of idiom stories, and know how to find the original price from the current price. Then ask the students to solve the equation according to the sentence order of Xiao Hong in the example. Students communicate after solving the problem: How did you come up with the solution of the equation? What kind of equality relation is the column equation based on? How did you test it?

Third, consolidate the practice.

1, do exercise 3, question 1.

After reading the questions, let the students talk about the meaning of discount for each commodity, and then let the students answer them separately.

After the students answer, ask: What can you think of when you find the actual selling price according to the original price and the corresponding discount?

2. Do Exercise 3, Question 2.

Let the students answer independently first, and then comment on the students' answers appropriately.

3. Do Exercise 3, Question 3.

Let the students talk to each other in the group first, and then call the roll.

4. Do Exercise 3, Question 4.

Let the students answer independently first, and then name the thinking process.

Fourth, the class summarizes.

Question: In retrospect, what does discount mean? What is the relationship between the current price, original price and discount of a commodity?

Requirements: After class, take time to go to a nearby shopping mall or supermarket to have a look, collect information about discounts on goods, and ask some questions to answer.

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