The second volume of the fourth grade mathematics teaching plan "Average and Bar Chart" (1) 1. Unit teaching content
Average and bar chart
Second, the unit teaching objectives
1, understand the meaning of the average, learn the simple method of finding the average and understand the statistical significance of the average.
2. Know the composite bar chart, ask and answer questions according to the chart, find information and conduct simple data analysis.
3. In the process of collecting, sorting, describing and analyzing empirical data, we will find information, conduct simple data analysis and think methodically.
4. Experience the role of statistics in real life, and use the knowledge to solve simple mathematical problems in life.
5. Experience the close connection between mathematics knowledge and real life, stimulate learning interest and cultivate good study habits of careful observation.
6. Develop statistical concepts and cultivate independent inquiry ability and cooperative consciousness.
Third, unit teaching is heavy and difficult.
Understand the meaning of average, learn the simple method of finding average, and understand the statistical significance of average. Know the composite bar chart, answer questions according to the chart, find information and analyze simple data.
Fourth, the unit teaching arrangement
Average and bar chart 3 class hours
Average 1 class hour
First, the teaching content: general
Second, the teaching objectives
1, by exploring the process of average, learn how to find the average, move more and make up less, sum first and then divide, and understand the meaning of average.
2. In the process of using average knowledge to explain simple life phenomena and solve simple practical problems, we will further accumulate methods for analyzing and processing data and develop statistical concepts.
Third, teaching focuses on difficulties.
Key point: understand the meaning of average. Difficulty: I can simply average.
Fourth, multimedia courseware teaching preparation
Teaching process of verbs (abbreviation of verb)
(A) the introduction of new grants
1, courseware display: 8 upper bookshelves and 4 lower bookshelves in the class corner.
Ask a question: Can students help to rearrange it so that there are as many books on each shelf?
2. Students think and discuss.
After the communication between teachers and students, the teacher used courseware to operate and asked: Now there are 6 books on each floor. What are their numbers? (Average) How do we get the average of 6?
After communication between teachers and students, it was clear that the two books were moved from the upper level to the lower level, and the same number was obtained. Today, let's learn more about the friend "Average". Blackboard: just so-so.
(2) Exploration and discovery
? 1, teaching example 1.
(1) Courseware shows page 90 of the textbook. Example 1 Statistics: Four students of the environmental protection team collected the following mineral water bottles (courseware shows statistics).
Teacher: What mathematical information can you get from the statistical chart?
Feedback from students after communication: According to the statistics, Xiaohong collected 14, Xiaolan collected 12, Liang Xiao collected 1 1, and Xiaoming collected 15.
Teacher: According to the math information, what math questions can you ask? The teacher chooses the average question from the questions raised by the students.
(2) Solve the problem: How many mineral water bottles did each person collect on average?
Teacher: What do you mean by "how much do you charge per person"? Will you solve this problem? How to solve it? Discuss in groups. Teachers' patrol guidance.
(3) presentation.
Report and forecast: Method 1: Make more moves and make up less, students report, and demonstrate the process of making more moves and making up less with multimedia.
Teacher: Like this, tear down more mineral water bottles and replenish less mineral water bottles, so that everyone has the same number of mineral water bottles. This method is called removing more and making up less, and the equivalent number obtained is called the average value of these numbers. 13 is the average of 14, 12, 1 1, 15.
Method 2: According to the total quantity ÷ total number of copies = average value, get. (14+12+115) ÷ 4 = 52 ÷ 4 =13 (pieces).
(4) Summary: The average value can be obtained by shifting more and supplementing less. You can also calculate the average by dividing the total number of data by the number of data. When there is less data, you can use the method of shifting more to make up less. When there are a lot of data, it is easier to calculate the total first and then the average.
(5) The teacher asked: Average income per person 13. Has everyone really gathered 13? How to understand the sentence "each person receives 13"?
After communication between teachers and students, it is clear that "average collection per person 13" means that the number collected by each person can be greater than 13, less than 13, or exactly 13.
(6) Distinguish between "average score" and "average score".
① Distribute 52 mineral water bottles to 4 people on average. How much will each person get?
② Everyone gets 13, and the average person gets 13. Do these two "13" have the same meaning? After the communication between teachers and students, it is concluded that the average score is real and the average is imaginary. 2. Teaching example 2.
(1) Create a problem situation.
Class 4 (1) The men's and women's teams in Group 4 are kicking shuttlecock. Let's take a look at their games. The courseware shows the situation map and two statistical tables on page 9 1 of the textbook.
Teacher: These two statistics show their performance in kicking shuttlecock. Look at these two watches. What can you learn from them? (Number of participants, number of keys kicked by each person, etc. )
(2) Explore and solve problems.
Ask a question: Do you think the boys' team is better or the girls' team is better? Tell me your reasons. Let the students fully analyze and express the football situation of men's and women's teams from many angles. In my attempt, I realized that using the average can better explain the problem.
Student hands-on column calculation:
Boys team: (19+15+16+20+15) ÷ 5 = 85 ÷ 5 =17.
Women's group: (18+20+19+19) ÷ 4 = 76 ÷ 4 =19?
(3) the whole class reports and exchanges.
Teacher: Why is the men's team divided by 5 and the women's team divided by 4? Do you think the men's team or the women's team performed better? After communication between teachers and students, it is clear that the boys' team has five men, so it should be divided by five, while the girls' team has only four men, so it should be divided by four. The average kick of men's team is 17, and that of women's team is 19. The female team scored higher.
Teacher: Has the problem been solved? What did you get?
Through the communication between teachers and students, it is clear that analyzing the average data can often reflect the general situation and help us solve problems.
(3) Consolidate differences
1. Guide students to complete the "doing" on page 92 of the textbook.
Students work independently and discuss collectively how to get the average value.
2. Students from Class Four (1) took part in tree planting activities. The first group planted 180 trees, the second group planted 166 trees, and the third group planted 149 trees. How many trees were planted in each group on average?
3. Think about it: the average depth of swimming pool 120cm, and Xiaoming's height 130cm. Is it dangerous for him to learn swimming in the swimming pool? Why?
(4) Evaluation feedback
What did you learn from today's class?
After the communication between teachers and students, it is concluded that the average can be calculated by the method of "shifting more to make up less", or the sum of several data can be calculated first and then divided by the number of these numbers, and the result is the average.
(5) Blackboard design
Six, teaching postscript
average number
Method of averaging:
1. Less data: common methods of shifting more and supplementing less: total number ÷ number of copies = average value.
The second kind of composite bar chart
I. Teaching content
Composite bar graph
Second, the teaching objectives
1, in the process of data collection, collation, description and analysis, further understand the role of statistics in life and the close relationship between mathematics and life.
2, know the two forms of composite bar chart, can ask and answer questions according to the chart, can find information and simple data analysis.
3, through the investigation of life cases, stimulate interest in learning, cultivate students' good habits of careful observation, as well as cooperation awareness and practical ability.
Third, teaching focuses on difficulties.
Key points: Draw the composite bar chart correctly.
Difficulties: finding and analyzing information according to statistical charts, simple and practical questions and answers.
Fourth, teaching preparation.
Multimedia courseware, marker, ruler, triangle.
Teaching process of verbs (abbreviation of verb)
(A) the introduction of new grants
Do you know how many people there are in China? Do you know how many people are in your constituency? (Student answers) Let's sort out and analyze the collected information together.
(2) Exploration and discovery
1, teaching vertical single bar chart.
(1) The courseware shows the statistics of urban and rural population in a certain area on page 95 of the textbook.
Question: How can we clearly show the changes in the population of villages and towns in this area in recent years? After the students communicate, they can make a statistical chart to show it. According to the statistical data provided by the teacher, ask the students to complete the vertical single bar chart of urban and rural population in a certain area respectively.
(2) Show the statistical chart drawn by students.
Question: What information can we get from these two statistical charts?
Teacher: If I want to know the changes of urban population and rural population in 1980 and 20 10 quickly? So what should we do? Students discuss and report. Guide students to compare two statistical charts side by side and think about how to combine them.
2. Teaching vertical composite bar chart.
(1) Question: How to combine two simple bar charts into one statistical chart? Students discuss in groups and try to draw a statistical chart. Teachers' patrol guidance.
(2) Show the composite bar graph drawn by students.
Discuss and communicate: What are the differences and connections between double bar charts and single bar charts? Let the students think independently first, and then exchange ideas with other students in the group.
(3) the whole class exchanges and reports.
Through group cooperation to exchange the connection and difference between double and single bar charts, students realize that in order to distinguish the two contents, rectangles with different colors are used to represent them.
(4) Analyze the composite bar chart.
What information do you get from this statistical chart?
To sum up, students can be guided to observe the statistical chart and find that the urban population in this area has increased year by year, the rural population has decreased year by year, and the total population has increased year by year. At the same time, students should be educated in population.
3. Teaching horizontal composite bar chart.
(1) Show the incomplete horizontal composite bar chart on page 96 of the textbook. Ask the students to supplement the horizontal composite bar chart independently.
(2) display works.
How to draw a horizontal composite bar chart?
Through the communication between teachers and students, it is clear that the horizontal axis represents the number of people and the vertical axis represents the year in this statistical chart, so the horizontal bars drawn are horizontal.
(3) Analyze the horizontal composite bar graph.
What information do you get from this statistical chart? Let the students talk about it separately and then communicate in groups.
(4) Compare vertical and horizontal composite bar charts.
Teacher: We already know two kinds of composite bar charts, namely vertical composite bar charts and horizontal composite bar charts. Please compare these two charts and think: what are the differences and connections between C-type composite bar charts?
After the communication between teachers and students, it is concluded that these two composite bar charts are only different in form. When there are not many kinds of data, but each kind of data is relatively large, it is more convenient to express it with a bar chart.
4. Practice in real time.
Instruct students to complete the "doing" on page 97 of the textbook.
Students complete the statistics table according to the statistics table. Answer the questions according to the chart.
(3) Consolidate differences
The market sales of juice drinks of brands A and B in 1 month, February and March are as follows. Please draw a statistical chart and answer the following questions.
If you are the manager of a supermarket, how should you purchase the goods for next month?
(4) Evaluation feedback
What did you learn from today's class?
Summary after the communication between teachers and students: This lesson has learned and mastered the drawing methods of two forms of composite bar chart statistics.
(5) the blackboard design composite bar chart.
Six, teaching postscript
Nutritional lunch in the third classroom
I. Teaching content
nutritious lunch
Second, the teaching objectives
1, understand the common sense of nutrition and health, and cultivate the ability to solve problems by using simple permutation and combination and statistical knowledge.
2, according to the advice of nutrition experts, using the correct mathematical thinking method, analysis and distribution of scientific and reasonable lunch dishes.
3. Make clear the importance of scientific and reasonable diet and develop good eating habits.
Third, teaching focuses on difficulties.
Emphasis: Cultivate students' ability to analyze and sort out data and use data to solve problems. Difficulties: scientifically analyze the results and arrange the collocation scheme reasonably.
Fourth, multimedia courseware teaching preparation
Teaching process of verbs (abbreviation of verb)
(A) the introduction of new grants
What dishes do you usually like to eat? Are these dishes reasonable? Today we will study this problem together. The blackboard says: nutritious lunch.
(2) Exploration and discovery
1, independent catering.
(1) Show the situational diagram on page 10 1 of the textbook. Let the students choose recipes according to their own requirements.
(2) Communicate with the whole class and show the students' collocation scheme.
2. Scientific evaluation.
(1) Introduce the requirements of scientific catering: Does the food we ordered meet the nutritional standards? What do you mean by "not less than" and "not more than"? How to express it with mathematical symbols?
(2) Understand the calorie, fat and protein content of each dish. Show the calorie, fat and protein content table of each dish.
3. summary.
When we judge the nutrition of lunch, we should look at both calories and fat. Only if the two indicators are not excessive can it be considered as a nutritious lunch.
(3) Consolidate differences
1, learn to match reasonably.
If you were asked to match the recipe, would you? Just one set for each person. Requirements: Choose three of these ten dishes together, and the nutrition must be reasonable. Discuss in groups and report collectively. Each group sends representatives to report the matching scheme of the group.
2. summary.
Teachers and students jointly analyze and summarize the requirements of nutrition collocation: meat and vegetable collocation, nutrition balance.
3. Count the recipes that the whole class likes.
(1) Choose one representative for each boy and one representative for each girl to collect data, and the teacher will record it.
(2) Students complete the composite bar chart according to the statistical table.
(4) Evaluation feedback
What did you learn from today's class?
(5) blackboard design nutritious lunch
The calorie is not less than 2926 kilojoules, the fat is not more than 50 grams, and the nutrition is balanced.
Six, teaching postscript
The teaching plan of the second volume of fourth grade mathematics "Average and Histogram" (2) teaching objectives;
1, let students know the average and bar chart, and answer simple questions according to the chart to understand the significance and function of the average and bar chart in life.
2. The average can be calculated according to the known conditions, and simple bar statistical charts can be drawn according to the relevant data, so as to cultivate students' ability of applying knowledge and drawing.
3. Through the statistics of all kinds of information in real life, stimulate students' interest in learning mathematics and cultivate students' ability of analysis, comparison and imagination.
Key points and difficulties:
The significance and application of 1 and average.
2. Draw a bar chart.
3. Analyze according to the statistical chart.
Teaching guidance:
1, on the basis of students' existing knowledge and experience, let students actively construct a new cognitive structure.
Before that, students have mastered the knowledge of simple average, compound statistics, horizontal single statistics and vertical single statistics, which is an important basis for students to learn the content of this unit. Teachers should grasp the starting point of teaching on the basis of reviewing existing knowledge and activating students' existing life experience. Let students further experience the process of data collection, sorting, description and analysis, understand the average and composite bar charts, further teach with practical problems, and make reasonable judgments and decisions by using average knowledge and simple data analysis according to charts. In this way, data analysis and problem solving are combined, so that students can better understand the role of statistics in problem solving and gradually form the concept of statistics.
At the same time, the teaching of this part of the content should give full play to the students' main role, and find the difference and connection between composite bar chart and single bar chart through students' independent drawing of statistical charts and communication with their peers. Cultivate students' practical ability, cooperative spirit and innovative consciousness. In addition to using the materials provided by textbooks, teachers can also flexibly choose materials for teaching according to the actual situation of local students and students in this class.
2. Pay attention to train students to further understand the average and statistical charts, and understand the role of statistics.
In the first stage, students have learned to make reasonable judgments, predictions and decisions by using statistical results, and can initially understand the application of statistics in real life. In the teaching of this unit, we should pay attention to the actual situation, so that students can understand why composite bar charts are used in daily life and further understand the significance of statistics.
Class arrangement:
It is suggested to divide it into 4 class hours+activity classes:
The average class hours are1(1) ...............................................................................................................1class hours.
Average class hours in the second class (2) ...................................................1class hour.
The third kind of comprehensive bar chart (1) ............................................................................................................................................................
The fourth kind of comprehensive bar chart (2) ...............................................1class.
Nutritional lunch for the activity class-.............................................. 1 class in the second canteen.
Knowledge structure:
The average class hours are 1( 1)
Teaching content:
Example 1 on page 90, 1 on page 92 of "doing", and 1-3 on page 93 of exercise 22.
Teaching objectives:
1, combined with the specific situation, in the hands-on operation, observation, discussion and other activities to understand the meaning of the average, know the method of finding the average.
2. Learn simple data analysis initially, flexibly use relevant knowledge of averages to solve simple practical problems, and further understand the role of statistics in real life.
3. Experience the fun of using knowledge to solve problems successfully in relaxed and happy activities, and enhance students' interest in learning mathematics and self-confidence in learning mathematics well.
Key points and difficulties:
1, understand the meaning of the average, understand and master the method of finding the average.
2. Understand and master the method of averaging.
Teaching preparation:
Multimedia courseware, average data statistics table.
Scene import:
Teacher: Students, I brought some information about our life and study today. Look at the screen. (Courseware presents information)
Four shuttlecock players in Class 4 (1) play 50 shuttlecocks per minute on average.
(2) The average height of the three boys in the first group of Senior One is 120cm.
(3) In the third grade, each class carries out three recess activities on average.
(Show the materials in turn and ask three students to read the questions separately. The other students looked at the screen carefully and listened. )
Teacher: Students, the same word is used in all this information. Did you find it?
Health: Everyone has the word "average". (The courseware shows the "average" in the information in red again)
Teacher: Yes, (pointing to 50 items, 120 cm, 3 items, and the courseware shows these data in pink at the same time) These data are all "average values". (Blackboard Title: General)
Teacher: What do you want to know through today's study after seeing this topic?
Student: What's the average?
Student: What is the relationship between average score and average score?
Student: How to calculate the average?
Student: Where do you usually use averages in your life?
……
Teacher: Let's learn today's knowledge with these questions.
[Design Intention: Select mathematical information that students are familiar with, so that students can perceive the average, stimulate their interest in learning, cultivate their awareness of problems, and feel the close connection between mathematics and life. ]
New course teaching:
(A) the meaning of the average
Through the introduction before class, let's talk about what is the average. Students communicate after discussion. Teacher's induction: Average refers to the average of a set of data.
(2) Average method
Teaching example: give an example of 1 scene diagram.
1, analyze the problem
Teacher: This month, our school has carried out activities to protect the environment and strive to be the best environmental guardian. Let's take a look at this mineral water bottle collected by a small group of students in our class. Courseware shows related scenes and statistics, and students read questions.
Teacher: What information did you see?
Student: I see there are four students in this team.
I know Xiaohong received 14, Xiaolan 12, Liang Xiao 1 1, Xiaoming 15.
Health: How many mineral water bottles do you need to collect on average?
Teacher: What is average?
Health: Everyone has the same amount on average.
Teacher: Then let's think about it. How can you ask this team to collect an average of how many bottles per person?
Student: It can be solved by drawing a chart. Everyone draws 1 1 first, and then divides the remaining 8 equally, so everyone is 13.
Student: Put each bottle in a circle and move it so that everyone has the same number of bottles.
Health: You can add up all the bottles and divide them into four parts equally. Each part is the average number of bottles collected by everyone.
2. Overview of methods
Teacher: Please look at the screen (the courseware shows the theme map). This is a simple statistical chart of the four of them collecting bottles. Can you find any mathematical information?
Health: Not so much.
Teacher: What should we do?
Health: It can be solved by moving the bottle.
Teacher: How to move?
Health: Give Xiaohong 1 to Xiaolan, Xiaoming 2 to Xiao Liang, and everyone will be the same in the end. At the same time, use books and other equipment for simple operation and communication methods.
Teacher: through the operation just now, think about it: why did you move Xiaohong's bottle to Xiaolan?
Health: There are many little reds, but few little red riding hoods.
Teacher: He transferred the more to the less. What about the number of bottles collected by everyone?
Health: Just as much.
Teacher: Just now, these students have moved out more bottles, but fewer students have replaced them, so the number of bottles for each student is the same. This method is called "move more and make up less".
(blackboard writing "more moves and less supplements")
Teacher: Is there any other way? Please say something.
Student: Yes, it can be solved by average integral.
Teacher: How to calculate?
Health: Count it first, and then divide it by 4.
Teacher: Can you tell everyone what you think and write the formula on the blackboard?
Health: (14+12+115) ÷ 4 = 52 ÷ 4 =13 (pieces)
Teacher: Pointing to the formula (14+12+1+15) ÷ 4. Let's take a look at this classmate's method? Please tell me what you think.
Health: I first add up the total number of bottles collected by the four of them, and then divide them into four parts on average. Or I'll calculate how many bottles they received first, and then calculate how many bottles each person received on average.
Teacher: Do you understand? Who has the same method as him? Tell you again. (student exchange)
Teacher: Please raise your hand if you can use this method. Let's solve it together. What is the result? Students calculate in their exercise books.
Teacher: What does 52 mean?
Health: Four people collect the total number of bottles.
Teacher: Yes, just make it clear that the total number of bottles collected by Xiaohong and the four of them is 52. (Teacher writes "Total" on the blackboard)
Teacher: Why divide by 4 again?
Student: Distribute the total to four people equally, which means everyone has collected 13.
Student: It is divided into 4 shares on average, and 4 represents the total number of shares.
Teacher: Four is the total number of bottles. Divided by four is divided into four parts on average. This 13 is the average number of bottles collected by each of them. (blackboard "average")
Teacher: Then how to express it by formula?
Student: Average = total quantity ÷ total number of copies.
Teacher: Great. Let's encourage him and learn from him. Teacher's summary: We obtained the average of 13 through the method and calculation method of "shifting more to make up less". On the blackboard: the solution of the average: (1) move more and make up less. (2) Average = total quantity/total number of copies.
[Design Intention: Connecting with the reality of school life, using activity classes to create problem situations and stimulate students' interest in inquiry. On the basis of students' understanding of the meaning of the average, through hands-on calculation, let students find the method of finding the average, and go through the process of forming mathematical concepts and methods, so that students can initially understand two different methods of finding the average. ]
Class assignments:
1, complete the "doing" question on page 92 of the textbook 1. To know how to make the flowers in each vase equal is to average them. Students communicate independently.
2. Complete the question 1 in Exercise 22 on page 93 of the textbook. Students will revise collectively after independence.
Course summary:
What did you learn from today's class? Summary: the average value is the representative of the average level of a group of data. We can calculate the average through the method of "shifting more to make up less".
Homework after class:
1, complete exercise 22 on page 93 of the textbook, questions 2-3.
2. Complete the exercises in the workbook.