Knowledge and skills:

1, which enables students to estimate by fractional multiplication.

2, can apply the knowledge of decimal multiplication to solve practical problems in daily life.

3, master some ways and methods to solve the problem.

Process and method:

1, the process of solving problems in different ways, improving the ability of analysis, synthesis and judgment.

Emotional attitudes and values:

1, let students realize the close relationship between mathematics and practical problems.

2. Enhance the awareness of independent exploration and improve the ability of cooperation and communication.

Emphasis and difficulty in teaching

Teaching focus

Be able to explain the estimation process and choose a reasonable estimation method according to the meaning of the problem.

Teaching difficulties

Be able to explain the estimation process and choose a reasonable estimation method according to the meaning of the problem.

teaching tool

Multimedia courseware exercise paper

teaching process

Teaching process design

1 review strategy

1, estimated value (the number is reserved as an integer)

34.6? 56.4? 47.8?

23. 1+34.3? 43+54.8?

Teacher: Today we continue to learn and estimate related knowledge.

2 Explore new knowledge

1. Solving problems with estimation

(1) courseware gives the theme diagram of Example 8.

Teacher: Mom went to the supermarket to buy things today, but there is a problem that students need to help her solve.

Courseware presentation problem

(2) Organize information and understand the meaning of the question.

Teacher: What mathematical information do you find from the picture? Fill in the information you found in the form prepared before class.

Ask students to analyze carefully, understand the meaning of the question and fill in the form.

Teacher: What are the advantages of writing this information in the form?

Health: You can see more clearly, and it is easier to clarify the meaning of the topic.

(3) Solve problems independently.

A, discuss the problem-solving methods.

Teacher: What do we need to know first in order to know whether the money left by my mother is enough to buy a box of eggs1from 0 yuan or 20 yuan?

Health: First of all, you need to know how much money is left after buying rice and meat.

Health: Take the remaining money and 10 yuan, and compare it with 20 yuan, and you will know whether the money is enough.

Try to solve this problem.

Teacher: Then how do you calculate how much money is left? Please use your own method to calculate.

Students' autonomous computing

Report your own calculation method

The default student is 1: I calculated with my calculator that there is 17.6 yuan left, which is enough for 10 yuan to buy a box of eggs, but not enough for 20 yuan to buy a box of eggs.

Health 2: I calculated it in column and column, and the result is the same as that of health 1.

Health 3: I judge by estimation. 1 bag of rice is less than 3 1 yuan, two bags of rice are less than 62 yuan, and 0.8 kg of meat is less than 27 yuan. 100 yuan minus 62 yuan, minus 27 yuan, and 1 1 yuan, enough to buy a box of 10 yuan.

Health 4: I also use the estimation method to judge that one bag of rice surpasses 30 yuan and two bags of rice surpass 60 yuan. 1 kg meat 25 yuan more, 0.8 kg meat more than 25? 0.8=20 (yuan). If 20 yuan buys another box of eggs from now on, the total * * * exceeds 100 yuan, then it is not enough to buy a box of eggs from 20 yuan.

Teacher: The meat in the title is 26.5 yuan per kilogram. Why is it estimated to surpass 25 yuan? Isn't it closer to an accurate result to surpass 26 yuan?

Health: Because my mother bought 0.8 Jin of pork, what is the price of pork at 25? 0.8=20 (yuan) is convenient for calculation, but what if it is estimated to be 26? If it is 0.8, it will be more troublesome to calculate.

Teacher: Isn't the estimated 30+30+20+20 in that question exactly equal to 100? Why is it not enough?

Health: Because the first 30, 30 and 20 are all exceeded, the final total will exceed 100.

(4) Choose a suitable calculation method.

Teacher: Students have so many algorithms! Then which method do you think is better?

Health: It's probably easier to solve.

Teacher: Who can tell me the difference between the estimation methods of the third and fourth students?

Students discuss the differences between the two evaluation methods.

Report:

Health: One is that the estimation method is too big, and the other is too small.

Teacher: Why use two different estimation methods?

Students think, communicate and summarize

Health: Overestimation is used to explain enough, and underestimation is used to explain not enough. These two estimation methods should be used according to different situations.

Summary: In the face of different situations, we should choose different methods to solve them.

2. Solve the problem of segmentation

(1) courseware gives the theme diagram of Example 9.

Teacher: Students, what mathematical information do you get from the situation diagram?

Students observe and exchange information.

Health: The car drove 6.3 kilometers.

The charging standard is: pay 7 yuan within 3 kilometers; If it is more than 3km, in addition to 7 yuan, it is required to pay 1.5 yuan every kilometer. If it is less than 1km, it will be calculated as 1km.

(2) Interpret the charging standard.

Teacher: Who can tell me what the taxi fare is? How to understand it?

Health: Take a taxi to 7 yuan within 3 kilometers; If it is more than 3km, in addition to 7 yuan, 1.5 yuan shall be paid for each kilometer. If it is less than 1 km, it shall be calculated as 1 km.

The students expressed their understanding of the charging standard.

Teacher: Uncle Wang's mileage is 6.3 kilometers. How many kilometers should it be?

Health: 0.3 km is calculated as 1 km, so 6.3 km should be counted as 7 km according to the charging standard.

(3) Discuss the charging method of 7 kilometers to solve the problem.

Think about it, according to the charging standard, how much is uncle Wang's travel expenses?

Health: It should be calculated in two parts, the amount payable within 3 kilometers and the amount payable beyond 3 kilometers.

Try to solve this problem.

Students answer independently,

Teachers patrol and report the results.

Report the solution to the problem.

Method 1: The first 3 kilometers are collected in 7 yuan, and the last 4 kilometers are calculated as 65438+ 0.5 yuan per kilometer.

7+ 1.5? (7-3)

=7+ 1.5? four

=7+6

= 13 (yuan)

② Think about it: If all the mileage is calculated as per kilometer 1.5 yuan, will there be more or less normal charges? Why?

Health: If the distance per kilometer is 1.5 5 yuan, the first 3 kilometers are 1.5? 3=4.5 (yuan), but actually received 7 yuan, so the charge will be less than the normal charge.

Then how should this be formulated?

Method 2: First, calculate 7 kilometers according to 65438+ 0.5 yuan per kilometer, plus the first 3 kilometers less.

1.5? 7= 10.5 (yuan)

The first 3km is underestimated: 7- 1.5? 3=2.5 (yuan)

Payable amount: 10.5+2.5= 13 (RMB)

(4) Contrast deepens cognition.

Teacher: Do you have anything to say by comparing these two methods of solving problems?

Health: He used two different methods to interpret the teacher, but the final result was the same.

Student: There are two or more different ways to solve the same problem.

The teacher concluded: Some problems may have more than one solution. We should be good at finding problems in daily life and learn to solve them in different ways.

(5) Check the calculation results.

Teacher: Is our answer right? Can you complete the following form according to the above charging standard?

Courseware presentation, students try to complete it independently.

Teacher: What did you find?

Health: 7 kilometers is exactly 13 yuan, and our answer is correct.

Step 3 consolidate the exercise

1.30 yuan is enough to buy the following things? Tell your deskmate how you worked it out.

Answer:

Calculation:

1.25+ 1.60+3.70? 4+6.60+2.40

= 1.25+ 1.60+ 14.8+6.60+2.40

=2.85+ 14.8+9

=26.65 yuan < 30 yuan

30 yuan is enough.

Estimate:

1.25 & lt； 2 1.60 & lt； 2

3.70? 4 & lt4? four

6.60 & lt7 2.40 & lt 3

2+2+4? 4+7+3=30 (yuan)

30 yuan is enough.

2. In order to encourage water conservation, a water supply company in a city collects water charges on a monthly basis. /kloc-less than 0/2 tons per ton of 2.5 yuan, and more than 12 tons per ton of 3.8 yuan.

(1) Water consumption of Xiaoyun's home last month 1 1 ton. How much should the water fee be?

(2) Xiaoke's water consumption last month was 17 tons. How much should he pay for water?

Answer:

( 1)2.5? 1 1=27.5 (yuan)

A: The water fee is 27.5 yuan.

(2)2.5? 12=30 (yuan)

3.8? 5 = 19 (yuan)

30+ 19= 49 (yuan)

Answer: 49 yuan should pay the water fee.

Summary after class

Teacher: What new knowledge have you gained through today's study?

Write on the blackboard.

solve problems

62+27+ 10=99 (yuan) 7+ 1.5? (7-3) 7? 1.5= 10.5 (yuan)

60+20+20= 100 (yuan) =7+ 1.5? 4 7-3? 1.5=2.5 (yuan)

=7+6 10.5+2.5= 13 (yuan)

For different problems, = 13 (yuan)

Select the appropriate estimation method.

There are different solutions to the same problem.

Teaching plan to solve problems (2) Teaching objectives

Knowledge and skills

1. Through the characteristics of taxi fare charging in real life? Piecemeal billing? What do you mean by learning to use it? Piecewise calculation? And then what? Suppose first and then adjust? To solve the problem? Piecemeal billing? Practical problems.

2. Through review and reflection, guide students to establish general methods to solve such problems and improve their ability to solve problems.

3. In the process of solving problems, let students have a preliminary understanding of the function thought.

Process and method

Let students go through the process of solving problems;

1. On the basis of students' existing experience, closely combine the situation, use function images, and combine numbers and shapes to help students understand the meaning of the problem.

2. Through analysis, inspire students to solve problems with different ideas and methods.

3. Through review and reflection, guide students to establish general methods to solve such problems. Accumulate experience in solving problems.

Emotional attitudes and values

Feel the application value of mathematics, improve the interest in learning mathematics, and enhance the confidence in learning mathematics well.

Emphasis and difficulty in teaching

Teaching emphasis: understanding? Piecemeal billing? The meaning of; Master and solve? Piecemeal billing? Two calculation methods of the problem.

Teaching difficulty: right? Suppose first and then adjust? Understanding and flexible application of basic calculation methods.

teaching tool

Ppt courseware

teaching process

(1) Create situations and introduce new lessons.

Teacher: Did all the students take taxis? Have you noticed how the taxi is charged? (Let the students say)

Teacher: It seems that although the students have had the experience of taking a taxi, they are not clear about the taxi charging method. Let's discuss and solve the practical problems of taxi charging together. (blackboard writing topic: solving problems)

Design concept: attach importance to students' existing experience, so that students can find mathematical problems from real life and experience the value of mathematics.

Second, cooperate and exchange, and explore new knowledge.

1. Show the picture of Example 9 on page 16 of the textbook and understand the meaning of the question.

Teacher: What's the practical problem for us to solve in this situation?

Health: How much does it cost to drive 6.3 kilometers?

Teacher: What information is needed to solve this problem?

The student said.

Teacher: That is to know the taxi fare standard.

Gift fee: 7 yuan within 3 kilometers; More than 3 kilometers, per kilometer 1.5 yuan (less than 1 kilometer is calculated as 1 kilometer).

Teacher: How to understand the taxi charging standard? To make it easier for students to understand, let's draw a picture to demonstrate. Draw first

The horizontal axis represents the mileage traveled by taxi, and the vertical axis represents the expenses paid by car. ? 7 yuan within 3 kilometers? What does this mean? (Students say they understand. )

Teacher: (Dynamic demonstration) Very good. For example, how much will it cost to open 1 km? What about driving 2 kilometers? What about driving 2.7 kilometers? Does 7 yuan include 3 kilometers within 3 kilometers? (Students think and answer)

Teacher: That is to say, from the beginning, as long as it doesn't exceed 3 kilometers, you have to pay 7 yuan.

Teacher: How much does it cost to drive 4 kilometers? Why? What about 5 kilometers?

(Students think and answer)

The passenger in the topic has traveled 6.3 kilometers. How many kilometers should he pay? (Students think and answer)

Teacher: Great! Less than 1 km is calculated as 1 km, which means to adopt? Become law? Take? A whole kilometer? Count.

Teacher: The students have understood the meaning of this question. Can you answer the passengers' questions in your own way?

2. Column calculation. Students think independently, list formulas and work out the results. Teachers patrol and coach, call students to report, and ask students to talk about their own algorithms when reporting. The teacher writes on the blackboard according to the students' answers.

Solution 1: piecewise calculation

Within 3 kilometers: 7 yuan.

Cost over 3 kilometers: 1.5? (7-3)=6 yuan.

Total cost to be paid: 7+(7-3)? 1.5

=7+4? 1.5

=7+6

= 13 (yuan)

A: The passenger should pay the fare of 13 yuan.

(Focus on asking students to talk about the meaning of each step)

Teacher's summary: the fee paid = the first fee+the second fee. We call it an algorithm? Piecewise calculation? (blackboard writing)

Teacher: Let's verify that this classmate did it right. (Dynamic demonstration process) It seems that this classmate's calculation is correct.

Teacher: Please look at the picture carefully. Do you find any connection between taxi fare and mileage? How do they change?

Teacher's summary: Taxi fare changes with taxi mileage. The more miles a taxi travels, the higher the fare. 7 yuan remains unchanged within 3 kilometers; For those exceeding 3km, 1.5 yuan will be charged for each kilometer. What does this image look like to students? (Student answers) It shows us a price ladder. What do we call a charging method like taxi? Piecemeal billing? . (blackboard writing: charging by sections)

Teacher: Do students use it? Piecewise calculation? Is there any other way to solve the passenger problem? (Students think)

Teacher: Can you calculate the whole journey according to 1.5 yuan? Students think and presuppose that students may or may not answer. )

Teacher: Why not? Show the pictures according to the students' answers. )

Teacher: Assuming the whole journey is calculated as 1.5 yuan/km, 7 km is 10.5 yuan, which is less than the original 2.5 yuan. Please observe the image with keen eyes. What's the problem? (Students found the root of the problem through the comparison of two images: 7 yuan is charged within 3km, if calculated by 1.5 yuan/km, only 4.5 yuan, the first 3km, is charged, and 2.5 yuan is charged less. )

Teacher: What should I do if I charge less?

Write on the blackboard according to the students' answers:

Suppose: 1.5? 7= 10.5 (yuan)

Insufficient calculation: 7- 1.5? 3=2.5 (yuan)

Adjustment: 10.5+2.5= 13 (yuan)

A: The passenger should pay the fare of 13 yuan.

Teacher: We call this method:? Suppose first and then adjust? (blackboard writing solution 2: assume first, then adjust) Can students understand this method of solving problems?

Design concept: guide students to collect and sort out information, the teacher gradually draws function images according to the information, and the combination of numbers and shapes makes students understand? Piecemeal billing? The meaning of. Let students use it through analysis? Piecewise calculation? A solution to the problem. Through verification, the function image is completely supplemented to guide students to observe the image, and the relationship and change between taxi fare and mileage are considered, and the idea of piecewise function is initially realized. (3) Teaching by comparing two images? Suppose first and then adjust? The method. Let the students find the connection between knowledge and the root of the problem: the problem appears in the charge within the first 3 kilometers. If it is calculated by 1.5 yuan/km, only 4.5 yuan will be charged for the first 3 km, and 2.5 yuan will be charged less, and if it is charged less, it will be added. In this way, we can understand and analyze the meaning of the problem more intuitively.

Third, consolidate application and improve internalization.

1. Basic exercises to consolidate new knowledge.

(1) Teacher: Students, if the charging standard is unchanged and the mileage is changed to 8.6 kilometers, will you use the method just now? (Students do it independently, teachers patrol and help students with difficulties)

(2) Report the calculation results.

Show students homework, let them reason, communicate with the whole class and share ideas.

Teacher: Apart from the fact that taxi fares are charged in stages, are there any similar problems in life?

2. Use expansion to improve cognition.

(1) Show Exercise 4, Question 8. Students read the questions, understand the meaning of the questions and answer them independently.

(2) Report the answer results, communicate with the whole class and share ideas. Image demonstration and comparative thinking.

3. Review and reflect, and establish methods.

(1), explore? Piecewise calculation? Law of solving problems.

Teacher: Retrospectively? Piecewise calculation? What laws did you find in the process of solving problems?

According to the students' answers, the payable expenses = front desk expenses+background expenses.

(2) explore and use? Suppose first and then adjust? Methods the law of solving problems.

Teacher: Retrospectively? Suppose first and then adjust? What laws did you find in the process of solving problems?

According to the students' answers, the summary is as follows: ① First, suppose that all the fees are calculated according to the later charging standards.

(2) Look at this calculation, whether the previous paragraph is more or less.

3 what is less should be added, and what is more should be reduced.

4. Show Exercise 4, Question 7 (Adaptation).

(1) Ask the students to sort out the information by themselves, understand the meaning of the question and make it clear? Piecewise calculation? Which two paragraphs should I count? It should be divided into two parts: the price in the price list and the money for printing 40 photos later.

(2) Report the calculation results and let the students reason. The whole class communicates with each other and shares ideas.

Design concept: As students have different abilities, starting design is a basic exercise. The purpose is to let students consolidate the problem-solving methods of this kind of problems. The eighth question behind is different from the example and the first exercise, and it has depth. Is this question in use? Piecewise calculation? There is no difference between the method and the first two questions. But in use? Suppose first and then adjust? There are obstacles in the method. The difficulty is that the first three minutes are not less, but more. What if the first three minutes are too much? Add something. Show the images step by step according to the students' calculation process, and find the differences from the first two questions, so as to improve the cognition of such questions.

Through review and reflection again, guide students to establish general methods to solve such problems. Accumulate problem-solving experience and further improve students' problem-solving ability.

5. Show the ninth question in Exercise 4 and let the students finish it after class.

Create a situation of mailing letters, so that students can form a good habit of saving resources.

Fourth, class summary, combing internalization.

Teacher: Students, what have you learned from this class? (Students talk about harvest)

Summarize according to the students' speeches: Through the study just now, we found that? Piecemeal billing? The law contained in the problem has been found and solved? Piecemeal billing? Two general methods of the problem, one is? Piecewise calculation? And the other one? Suppose first and then adjust? . The students did a good job.

Design concept: combing knowledge and internalizing knowledge through summary. Accumulate problem-solving experience and further improve students' problem-solving ability.