Model essay on "seeking average" teaching plan in the second volume of fifth grade mathematics of People's Education Press.

First, the teaching objectives:

1, initially establish the basic idea of average (that is, the statistical idea of shifting more and supplementing less) and understand the concept of average.

2, master the simple method of averaging, and can flexibly choose the method to answer according to the specific situation.

3. Cultivate students' ability to estimate and apply mathematical knowledge to solve practical problems.

Second, the teaching focus:

Flexible choice of average method to solve practical problems.

Third, the teaching difficulties:

The meaning of the average.

Fourth, the teaching process:

(a) the story import:

Courseware demonstration; An old monkey picked 12 peaches in the forest. After returning home, he called three little monkeys to give them peaches, including seven monkeys, four monkeys and six monkeys.

Teacher: Do you have anything to say about the old monkey sharing peaches?

Health: Three monkeys share different peaches.

Health: Three monkeys should get the same amount.

According to the students' answers, write on the blackboard: no more, no less.

(2) Explore new knowledge:

1, use small magnetic disks instead of peaches (the teacher arranges small magnetic disks on the blackboard according to 7, 4 and 1 respectively).

Please observe carefully and discuss in groups of four. What method can you use to make each group have the same number?

Step 2 exchange feedback

(1) leads to more shifts and less supplementary shifts, (2)(7+4+ 1)÷3.

Teacher: Observe the small disk after moving and think: What has changed and what has not?

Blackboard: The total number remains the same.

Just as much, not as much.

3. Summarize and reveal the topic.

Teacher: Just now, by shifting calculation, we got the same number 4, which is called the average.

(blackboard writing topic)

4. Just now, some students used the method of (7+4+ 1)÷3=4 to calculate their average. Now the teacher sets the other group to 8. What's the average? Will it?

Health: Yes. (do it yourself)

Feedback (7+4+ 1+8)÷4=5.

By comparison, it can be concluded that the total number of copies = average.

(3) Applied Mathematics

The teacher's courseware shows the average problems in life, and the students read the materials themselves.

1. Announcement of the National Tourism Administration on the Tourism Information of the "Eleventh" Tourism Golden Week in 2004

(1) The daily average ticket income of Shanghai Oriental Pearl is 1.3 million yuan, and the Forbidden City in Beijing is 2 million yuan.

(2) The Sun Yat-sen Mausoleum in Nanjing receives an average of 70,000 tourists every day, and the Forbidden City in Beijing receives an average of 50,000 tourists every day.

2. The daily average temperature in Beijing has exceeded 10℃ for five consecutive days.

3. Grade three 1 class average height 136 cm.

(4) Study the average height.

1, just said the average height, and find the average height of the whole class. What should I do?

Show the height statistics of a class in Grade Three (unit: cm)

① 140 14 1 139 143 142 145

② 135 134 136 13 1 132 134

③ 130 13 1 132 130 128 127

④ 128 129 128 127 127 125

⑤ 124 127 124 125 124 123

⑥ 123 122 120 123 124 122

2. Teacher: How many centimeters is the average height of the class estimated? What should I do? There are three options, which one do you choose?

A, choose the shortest one in the first row

B, choose the sixth row

C, choose the tall and short first group.

Teacher: Why did you choose this way?

3. Students' trial calculation

4. Teacher: What do you think of this average height? Are there any bolder ideas about this average height, and what other ranges can it represent?

Student feedback

(5) Consolidate development.

Select (by gesture)

1. The Third Squadron of the Young Pioneers mobilized its members to plant trees. Plant 180 plants on the first day, and plant 3 15 plants on the second and third days. How many trees are planted on average every day? ( )

2、( 180+3 15)÷2 2、( 180+3 15)÷3

3. At 1 hour, 7: 00, 13 and 19 in a day, the temperatures measured by the weather station are 8 degrees Celsius, 15 degrees, 24 degrees and 17 degrees respectively. Please work out the average temperature of this day. ( )

4、(8+ 15+24+ 17)÷4 2、(8+ 15+24+ 17)÷( 1+7+ 13+ 19)

(6), expand the exercise

1, guess the average monthly expenditure of teachers.

2. The teachers wrote on the blackboard: monthly average cost 1000 yuan. Do you know the meaning of this sentence?

The teacher made a rough statistics on the expenditure in the first three months of this year.

Display: Mr. Chen's monthly expenditure statistics from 1 to March 2005.

Month 1 February, March and April

Amount108010201050

Can you help the teacher work out the average monthly expenditure in the first three months of this year?

3. Student feedback

Can you predict the teacher's expenditure in April?

5. If the average monthly expenditure in the first four months does not exceed 1000 yuan, how much money can the teacher spend in April at most?

Verb (abbreviation of verb) summary:

"Averaging" is a part of the new textbook Statistics and Probability. It is closely related to our real life, and the public media in modern society use statistical charts to express information, so understanding statistical charts is an essential mathematical literacy for modern citizens. Based on this, the teaching focus of this course is to use the concept of average to analyze data and understand the meaning of data, and make necessary inferences according to the data.

extreme

First, create situations and ask questions.

Talk: Let's play a little racket game. Next, we invite XXX (3 people) from Team A and XXX (4 people) from Team B to come to the front, each with a ball. Note: the rule of the game is that the team with the most balls wins within the specified time, understand? (understand)

The teacher controls the time (5 seconds) and writes it on the blackboard according to the number of strokes, such as:

Team A: 6+7+8=2 1 (each)

Group B: 10+4+3+6=24 (unit)

After that, let the students put the ball here gently and walk back to their seats slowly.

Teacher: The following two teams find out the total number of rackets in your team as quickly as possible. According to the students' answers, the teacher completes the blackboard above.

Teacher: Let me think. Within the specified time, Team A made 2 1 and Team B made 24. Which team won? Or can you say that team B won? )

Life can't find its way!

Teacher: Why did you say no?

Health: We were taken by three people, and they were taken by four people. What do you mean? ) That would be unfair.

Teacher: After hearing what he said, all the members of Team A felt unfair, didn't they? In the case of unequal quantities, it is unfair to compare the total, but we will encounter such a situation in our life. For example, we just had a mid-term exam. How do we compare the results of three classes? (compare the average), can we compare how many pictures everyone here has taken?

Second, solve problems and explore new knowledge.

1, the initial perceptual average needs to be generated.

Health 1: 2 1÷3= respectively.

24÷4=

Find things that are equal to each other.

Teacher: How many times did you take pictures on average? Help team a calculate first. Why "∫3"? Let's help team b calculate it again. Why is it "⊙ ⊙" ?

Teacher: Let's take Team B as an example. What does this "six" mean? (Maybe some students just took six pictures.) Do you have any different opinions? (6 shots per person on average)

2, understand the meaning of the average

Teacher: Not 1. You obviously shot 10. How did it become six? Where did more people go (more supplies make fewer people)? Then how did the number two that was shot less shoot four, and how did it become six? Give me a few more injections, and gradually more. )

Teacher: The more the supply, the less the slow supply, and the less the slow supply, and finally the four are gradually equal. This 6 is the average of four people. (blackboard writing: general)

Q: How is this average calculated? (Add first and then divide)

Teacher: Let's take a look again. The extra 10 is given to the less, and the less is gradually increased. To what extent?

Health: Everyone is equal.

Teacher: So this 6 is what the students said. Is the average of the group numbers of10,4,3,6. This average reflects the overall level of this group in the south. Team a and team b, the average level of team a is 7, and the average level of team b is 6. Which team has a higher overall level? Students directly say team a.

Summary: Question, when we compared the total number just now, many students felt that it was unfair to compare the total number. So what should we compare when the number of people is not equal? (average)

3. The connection between communication average and life

Teacher: Students, the average comes when we need it. In our life and study, the average is used in many places. (Examples of students)

Third, the strategy of estimating the average.

1. Displays the statistics of tourists in Nantong Children's Park during May Day.

Dialogue: Did the students travel during May Day? Where have you been?

(1) estimated value

Q: When you see this chart, tell me what information you read. Students who haven't spoken yet say something.

Students: 1, 1 100, No.2 1300, No.3 1000, No.4 900, No.5 700.

Teacher: So what else do you want to know? How many people come every day on average? ) Let me see the question: How many people have come every day in the past five days?

Requirements: calculation is not allowed, only estimation is allowed. (The estimated life is 1000, 1200, as long as it is between 700 and 1300. )

If some students estimate 500,600,2000 and so on. Ask the students to discuss: Could it be 500,600,2000? Why?

Summary: Give less and get more, give more and get less. The average can't exceed the maximum. A few will increase, and the average will not be less than the least. In other words, who should the average be less than and greater than?

(2) calculate it.

Teacher: OK, each student estimates another number and keeps it in his heart. We can only work it out if the estimate is accurate. Next, please carefully calculate in your exercise books and introduce them to us in different ways later.

Report: All of them are 1000. How to calculate it? Introduce your method to us.

Simply put: find out the total number of people these days and divide by 5. That is, first, then. Is there any different way? I introduced them in my life through more activities and less supplements, and I also got 1000. This is called doing more and making up less. (The blackboard moves more and makes up less)

(3) Reveal the estimation method

Teacher: Hey, please raise your hand if the second estimate is close to 1000. The teacher also secretly estimated it just now. The teacher estimated that it was 2000. Do you think it's possible? Why? Tell me about it!

Health: the average value is less than the maximum value and greater than the minimum value. Our estimate should be well-founded.

Teacher: According to statistics, there are fewer and fewer people coming from the 2nd. If you are the manager of Nantong Children's Park, do you have any tricks to attract tourists? This is a good move (to reduce prices and improve the environment). After class, Mr. Wang will send our classmates' suggestions to the administrator of Nantong Children's Park online, okay?

3. Show the math scores of four students in the mid-term exam of this class.

Dialogue: We made a test paper the day before yesterday, which was the result of four students.

Q: What's the difference between the best and the least? How must their average scores be compared? How about at least?

Q: What method do you want to use to calculate their average score?

Two methods for calculating the average value are introduced respectively. (90 points)

4. Show three pictures respectively.

Talk: Water is the source of life. China is rich in water resources, but the distribution is uneven.

(1) Severe water shortage areas in China.

Introduction: This is a serious water shortage area in China. They consume an average of 30 kilograms of water per month for eating, washing clothes and washing vegetables.

(2) Show the statistical chart of household water consumption in Xiaofang.

Teacher: This is the statistical table of water consumption of small household surveyed by the teacher. Water consumption in the first quarter 16 ton, in the second quarter, 24 tons, in the third quarter, 35 tons and in the fourth quarter, 2 1 ton. Do you know how many tons of water are used on average every month?

Some students may choose 1 and 2. Arrange a representative of 1 and a representative of 2 to come to the front. Please ask the students who choose 2 to ask the students who choose 1? Q: What are the requirements of the topic? So how many months are there in a year? Then why did you choose 1? The other person may not answer the third question.

Teacher: The key point of this question depends on the average monthly water consumption. What do 1 and 3 ask for respectively? How many tons of water does his family use on average every month? (16+24+35+21) ÷ 4 = 24 (ton)

(3) The average monthly water consumption of Xiaofang is about 24 tons.

Display (1) and (3) two pictures at the same time. What do you want to say most at this moment? Save water from yourself. ?

8. Consolidate exercises

Tisso

Teaching objectives

1. Make students understand the meaning of "average" and master the simple method of finding the average. They can find the average value according to simple statistics.

2. Cultivate students' comprehensive analytical ability and operational ability.

3. Make students realize that mathematics knowledge is closely related to life and enhance their interest in mathematics.

Teaching focus

Make clear the difference between "average" and "average score" and master the method of "average"

Teaching difficulties

Understand the concept of average and make clear the difference between "average" and "average score"

Teaching step

First, pave the way for pregnancy.

1. Xiaohua read 60 pages in 4 days. How many pages does she read on average every day?

2. A cup with the same thickness from top to bottom contains 16 cm of water. Pour all these horizontally into four cups of the same thickness. How many centimeters is the water depth of each cup?

The sum of the weights of Xiao Ming and Xiao Gang is 160 kg. What is the average weight?

Teacher: The above two questions (1, 2) divide a number into several parts on average, and actually each part is the same, while the third question divides the sum of two numbers into two parts on average, and each part is not necessarily an actual number. So there is a difference between "finding the average of several numbers" and "dividing a number into several parts on average"

Second, explore new knowledge.

1. Introduce new courses.

Before, we studied the application problem of "dividing a number into several parts and finding out how much each part is", that is, the problem of "average score"

Today we will study the problem of "averaging".

2. Teaching example 2.

(1) Example 2. Use four identical cups to hold water with water levels of 6 cm, 3 cm, 5 cm and 2 cm respectively. What is the average water level of these four cups?

(2) Organize discussion: How to understand "average height of water surface"?

(3) The students reported the discussion results, and the teacher further clarified that the so-called "average height" is not the actual height of each cup, but the same height value of the water surface height under the condition that the total water volume remains unchanged.

(4) student operation.

Please take out the prepared building blocks and use the height of each building block to represent 1 cm. First, according to the height requirements of the example, four piles of wood are stacked to represent the height of four glasses of water, and then use your brains to make the water levels of these four glasses equal.

(5) There are generally two methods for students to report the operation results.

The first type: count how many building blocks there are * * *, or pile all the building blocks together, *** 16 cm, and then use them.

16 ÷ 4 = 4 cm, and the average height of each glass of water is 4 cm.

Second, move more directly and make up less. Take 2cm from 6cm and put it into 2cm cup, and take 1cm from 5cm and put it into 3cm cup, and you can directly get four glasses of water, all with the same water level, which are 4cm. This shows that the average water level of the original four cups is 4cm.

(6) Teacher: Through students' calculation, we get that the average height of these four cups is 4cm. But there is a problem here. During the operation, we changed the actual water height of the cups and got the average height, while the original water height of the four cups changed. In real life, it is not allowed to change the original value in many cases of averaging. For example, height 180cm. The short man's height is 140 cm, and the average height of the two men is 160 cm. It is not to cut off a part of the tall man and stick it on the short man to make them equal in height. It can be seen that it is not feasible to calculate the average height of these four glasses of water by direct operation in many cases. If you don't operate, can you directly calculate the average height? How to calculate easily?

(7) Guide students to calculate in tabular form.

(6+3+5+2)÷4

= 16÷4

= 4 cm

Answer: The average height of these four cups is 4 cm.

Summary: Through the calculation of the above questions, it is further clear that the sum of heights should be calculated first, and then the average height can be obtained by dividing the sum of heights by the number of cups.

(8) Look at Example 2 and review questions. The result of both questions is 4 cm. Do they mean the same thing?

Clear: in the review questions, 4 cm is the result of average score, that is, the actual height of each cup of water is 4 cm; Example 2 is the average value, and 4cm represents the average value of the water level in each cup, but the actual height of the water level in each cup is not necessarily 4cm, and their actual heights do not need to be changed.

(9) feedback exercises.

Xiao Qiang threw softball three times, and his scores were 28m, 29m and 27m respectively.