What percentage of one number is another?

Find the percentage of one number to another.

Teaching content: From page106 to111in the textbook, how many percent of one number is another?

Teaching objectives:

1. Understand the practical significance of percentages in specific situations. Will answer some simple practical questions, such as what percentage of one number is another.

2. According to the method of finding the percentage of one number to another, and so on, master the method of finding the percentage.

3. In the process of solving problems, further understand the application value of percentage in real life and cultivate interest in learning mathematics.

Teaching process:

first kind

First, create situations to introduce new lessons.

Teacher: This year's National Day, the teacher went to Jinan to play, stayed in Tianlong Hotel near the square, and showed the information window 2 through multimedia (only the information data on the left).

The teacher introduced the picture background: During the Golden Week, the health and epidemic prevention department strengthened the inspection of hotel hygiene. * * * 200 hotels were randomly selected, of which 190 were qualified.

What questions can you ask after reading this information? (Observe the information window and ask questions)

Second, situational guidance, cooperative exploration

1. Courseware displays the first information window, and students' questions are written on the blackboard.

(1) How many rooms does Tianlong Hotel stay in every day?

(2) What is the daily occupancy rate of Tianlong Hotel rooms?

……

Students answer the teacher's patrol independently, and then communicate collectively.

First solve the first problem, sampling communication: 300÷400.

400÷300

Teachers ask students to sort out their own understanding ideas independently and compare which problem-solving ideas are correct. In the communication, remind students of the problem-solving ideas and methods of "how much is a fraction of another number" that they have learned before, so as to make knowledge transfer and pave the way for learning new knowledge in the next step.

Finally, it is concluded that 300÷400 is the correct method to solve the problem.

Solve the second question: What percentage of the total number of rooms in Tianlong Hotel every day?

300÷400

The students exchanged their reports and summed up the "total number of rooms in Tianlong Hotel" as the unit "1". Look at the number of rooms in Tianlong Hotel every day, which accounts for a few percent of the unit "1".

And compare the calculation process: 300 ÷ 400 ÷ 300 ÷ 400.

= =0.75

=75% =75%

Guide students to sum up the characteristics of the two methods independently and choose their favorite calculation method for calculation.

2. Teacher: What are the similarities and differences between students' ideas to solve these two problems?

Guide students to summarize independently: the algorithm of percentage application problem and fractional application problem is the same, but the result should be converted into percentage.

3. Consolidation exercise: What is the percentage of the total number of rooms in the Emerald Everest Welsh Hotel per day?

Emerald Everest Hotel:

279÷300

= 0.775

=77.5%

Hotels in Wales:

2 15 ÷ 227

≈ 0.947

= 94.7%

Students finish independently, report and communicate, explain the problem-solving ideas and consolidate the problem-solving methods.

Teachers guide students to consolidate: when solving percentage application problems, if the result is divided into infinite decimal places, keep three decimal places and one decimal place before the percent sign.

Teacher's summary: 77.5% and 94.7% are actually hotel occupancy rates. How to explain the occupancy rate?

Guide students to explain the full meaning of occupancy rate.

Students discuss and exchange: the room occupancy rate refers to the percentage of occupied rooms in the room to the total number of rooms, and whoever wants it will be divided.

Health report, teacher guidance, supplement.

Teacher: Which hotel has a high occupancy rate, the Emerald Everest Hotel or the Welsh Hotel?

Answer independently and explain the meaning.

Blackboard: 94.7% > 77.5%, so the occupancy rate of Welsh hotels is high.

Teachers and students summarize the ideas and methods to solve the problem of "what is the percentage of one number to another".

4. Add information data and red dot 2 to the right of the information window.

Question: What is the sanitary qualification rate of these hotels?

Teacher: How to understand this sentence? What's the pass rate?

Hygiene: What percentage of hotels are qualified in hygiene?

Teacher: Then how do you ask for it?

Health: 190÷200

And analyze the problem-solving ideas, the teacher affirmed, and questioned whether 190÷200 is a decimal or a fraction, how to reflect the percent of pass?

Students communicate in groups and report.

Teacher-student summary: Usually we write the qualified rate as follows:

Qualified rate = × 100%

× 100%

= 0.95 × 100%

=95%

Teacher: Why do you want to take 100%?

Further consolidate the significance and methods of solving percentage application problems, and exchange reports between students.

Teacher's summary: the formula qualification rate is a kind of percentage, and the formula itself should be expressed in the form of percentage (%). If the formula sheet is written as "qualified rate = qualified number/total number of spot checks", it is only a fraction, not a percentage. If you add "× 100%" after it (equivalent to × 1), you can keep the value unchanged and it is in the form of percentage.

Teacher: Just now, our hygiene quality was considered from the perspective of hygiene qualification. Think about it, from what angle can you think?

Health: From the point of view of unqualified hygiene, do you want to find unqualified rate?

Teacher: How to find the unqualified rate?

Students answer and give feedback.

5. Feedback:

A, let students know that the qualified rate and unqualified rate can't exceed 100%, and why.

B, the relationship between qualified rate and unqualified rate?

The teacher summed it up.

6. Where else can you find percentages in your life?

In real life, percentages are often used, such as germination rate, attendance rate, survival rate, oil yield rate, myopia rate, etc ... Can you tell what they mean respectively?

Group communication. Report.

And do the fourth exercise independently, report and correct it.

Third, consolidate the practice.

Do the problem by yourself 1 ~ 3.

Students finish independently, write reports on their behalf and correct them collectively.

Fourth, classroom review, exchange gains.

What did you gain from today's study?

Teacher: Percent and fraction application problems are the same in arithmetic.

Verb (abbreviation for verb) homework after class

1. Collect examples of the practical application of percentage in life.

2. Practice 5 ~ 9 questions by yourself.

Second lesson

First, review the old knowledge.

Teacher: Students, last class, we learned how to find the percentage of one number to another and the application of percentage in life, and put forward and solved many valuable math problems. Let's review the knowledge of last class first, and then do some exercises.

1. How to answer the question "What percentage is the difference between one number and another?"?

Comparative quantity ÷ standard quantity (quantity in 1) × 100%

2. What should we pay attention to when solving the application problem of "How many percent is one number from another"?

(1) It is necessary to correctly judge which quantity is regarded as the unit "1";

(2) When calculating in column form, divide the "comparison quantity" by the unit "1";

(3) Divide the results into percentages;

(4) The "qualified rate", "germination rate", "flour yield", "oil yield" and "survival rate" are all partial comparisons with the whole, and the percentage is less than or equal to 100% and cannot be greater than 100%.

3. Do you know where percentage is used in life? What do they all mean? How to calculate?

Blackboard: product qualification rate = number of qualified products/total number of products × 100%.

Employee attendance = actual attendance/attendance × 100%

Peanut oil yield = peanut oil weight/peanut weight × 100%.

Survival rate of planting trees = number of surviving plants/number of plants × 100%

Second, consolidate the practice.

1. Fill in the blanks and calculate.

(1) There are () students in this class, including () girls. The number of girls accounts for 80% of this class.

(2) There are () students in this class, and today's attendance is (). The attendance rate today is ()%.

(3) The hotel * * * has 400 rooms, and we stayed in 300 rooms today. Today, the hotel occupancy rate is ().

Students independently calculate and explain the calculation method.

2. True or false. (Tick "√" in brackets for correctness and "×" for error. )

(1)40 is 80% of 50.

(2) Fifty is 80% of forty.

(3) The germination rate of these seeds is as high as 120%.

(4) Seeds were used for germination test, and germinated 100. The germination rate of these seeds is 100%.

(5) self-exercise. The myopia rate of primary school students in Cai Ying is 6%, and that of bright primary school students is 6%. The number of nearsightedness in these two schools is the same.

3. Say, in the following questions, what quantity should be used as the unit "1" and how to present it.

(1) What percentage of the output in March is equivalent to that in April?

(2) What percentage of this road has been repaired?

(3) What percentage of the first half of the month's output accounted for that month's output?

(4) What percentage of Chinese cabbage is the weight of radish?

(5) What percentage of the train speed is the car speed?

4. Column calculation.

(1)5 kg is what percentage of 4 kg?

(2) What percentage of 5 kg is 4 kg?

Revision question: Why are the calculation results of these two small questions different?

[Design Intention] The above exercise is the basic exercise to find the percentage of one number to another. Teachers have designed a variety of practice forms and different types of questions, aiming at broadening students' practice breadth and enabling students to use what they have learned flexibly to solve problems. Teachers should pay attention to the correct rate of students' questions in teaching, so that most students can master this knowledge.

Third, comprehensive exercises.

1. Do exercises 6 and 8 by yourself. Students fill in independently and communicate with the whole class.

2. Practice Question 7 by yourself. After the students read the questions, the teacher asked: How do you get the pass rate? Students answer independently, and the whole class communicates.

3. Practice Question 9 by yourself. After reading the questions, the teacher asked: What's the salt content? How to ask? Students answer independently, and the whole class communicates.

Fourth, supplementary exercises

1. The seed germination test with wheat seeds showed that 490 seeds germinated and 10 seeds did not germinate. What is the germination rate of these wheat seeds?

A grain depot plans to import 800 tons of grain, and has imported 300 tons at present. What is the planned import ratio? What percentage was not brought in?

Qianjin Primary School planted 450 trees last year, and 420 survived. What is the survival rate? (The number before the percent sign is reserved for one decimal place. )

5. A flour mill grinds 34,000 tons of flour from 40,000 tons of wheat and calculates the flour output.

Fifth, the whole class summarizes and sublimates.

What are you most interested in today's study?

Through today's lesson, we have mastered the calculation method of how many percent of one number is another number, and can apply this knowledge to solve some practical problems. I hope that students can be as careful as this class in the future and work hard in their studies.

Sixth, homework

Do the problem by yourself 10.

Did I learn?

First, review knowledge and establish a cognitive structure.

Dialogue Introduction Review: This week, we learned something about percentages. Let's review what we have learned independently, and then communicate in groups.

When students report, focus on guiding students:

1. When summarizing the relationship among percentage, fraction and decimal, guide students to recall the exploration process and summarize the methods.

2. Summarize the simple practical problems that how many percent of one number is another number, and ask students to give examples to talk about what practical problems can be solved.

Second, organize exercises to consolidate what you have learned

1. Write down the following percentages and say what each percentage means.

(1) Almost 50% of the world's total population is under 25 years old.

(2)29% of children said that "the best friend at present" is a teacher.

(3) About 90% of colds are caused by viruses and about 10% by bacteria.

Combined with the meaning of the sentence, tell your understanding of the meaning of percentage.

Fill in the form exercise

The courseware shows the reciprocal table of percentage, fraction and decimal. Let the students fill in the form independently first, and then modify it all.

3. Solve practical problems:

The protein content in soybean is about 100%, the fat content is about 18%, and the carbohydrate content is about 0.25. Which component has the highest content?

Independent calculation and collective correction. Ask the students to talk about solving problems and compare which one is the best.

24. The following figures are arranged in chronological order from small to large.

a.75% 0.5 40%;

b.0. 12 127% ;

5. Solve the practical problems of teaching materials

Dialogue: The following are Li's monthly expenses.

project

food

waterpower

cultural education

other

Expenditure (yuan)

Eight hundred

100

500

200

What questions can I ask? And answer.

6. question 3.

Question after independent answer: Is the survival rate likely to exceed 100%? Why? What other percentages do you know?

Third, explore laws and develop mathematical thinking.

1. Expanding exercise (the teacher gives questions to explore the percentage law according to the students' practice)

Let the students explore independently first, and then give appropriate hints according to the situation.

2. quiz. (Combined with the teaching focus of this unit)

Fourth, reflect on evaluation and stimulate interest and self-confidence.

Take out the self-evaluation form, and the group will carry out reflective evaluation activities to evaluate the exchange feelings of the stars and talk more about their successful experiences.

Five, talk about harvest in the harvest garden

Looking back on your study in this unit, what do you think you have gained? Talk to each other in groups.

Conduct group communication first, and then conduct collective communication.

Teacher said: It seems that the students have gained a lot through the study of this unit. The teacher is really happy for you. I believe you will have more gains in your future study!