Mathematics lecture notes on finding averages

The average is an important concept in statistics. Next, I have compiled a mathematical lecture on finding averages for you. Let’s take a look.

Mathematics lesson notes on finding averages

1. Teaching materials

1. Teaching content: Compulsory education Six-year primary school mathematics "Average".

2. Textbook analysis:

With the development of science, technology and mathematics itself, statistics has become an important part of modern mathematical methods and an important field of applied mathematics. From scientific research to students' daily lives, statistics are everywhere. The new "Mathematics Curriculum Standards" also arranges "Statistics and Probability" as an important learning area, emphasizing the development of students' statistical concepts. It is on this basis that this unit introduces students to the preliminary knowledge of statistics. This course is taught after students have a preliminary understanding of statistics. It consists of two parts, namely understanding the meaning of average and the method of averaging.

3. Important and difficult points in teaching:

The average is a characteristic number commonly used in statistical work. It can reflect the general level of statistical objects and has a wide range of uses. Therefore, understanding the meaning of average and mastering the calculation method of average are the focus of teaching. And the meaning of "average" is different from the "average score" that we have learned in the past. Correctly understanding the actual meaning and application of average is the difficulty of teaching.

4. Teaching objectives:

Based on this understanding, we cannot just stop at "simply giving some data and asking students to calculate their averages" in teaching. , but should fully guide students to understand the rich and profound background of statistics and probability contained in the concept of "average", help them realize the practical significance and wide application of average in real life, and be able to use it in new situations It solves real problems and achieves necessary development. To this end, I have formulated the following three teaching objectives:

Knowledge objectives: enable students to understand the meaning of averages, explain the actual meaning of averages, and master the method of finding averages.

Ability goal: to be able to discover problems from real life, collect useful information as needed, and cultivate students' strategic awareness and ability to apply mathematics to solve practical problems.

Emotional goals: Cultivate students' cooperative spirit and innovative qualities through group learning activities, experience the close connection between mathematics and life, and promote the harmonious development of students' personalities.

2. Teaching method:

Since the meaning of "average" is relatively abstract and difficult to understand, it is easy for students to feel fearful of difficulties. "Finding the average" is a type of application questions, but the application questions in current textbooks are often divorced from the reality of life, making students feel boring. Therefore, I actively create real problem situations originating from life based on the students' cognitive rules of perception, representation, and abstraction and the teaching principles of inspiration, intuitiveness, and teaching students in accordance with their aptitude. "Activities are the main line and innovation is the purpose", using effective means such as multimedia teaching, focusing on the guidance method, supplemented by intuitive demonstration methods, question-provoking methods, and discussion methods to provide students with opportunities to fully engage in mathematical activities and stimulate Students' learning enthusiasm enables students to actively participate in the whole process of learning, give full play to the leading role of teachers, and play the role of organizer, guide and collaborator.

3. Talking about learning methods:

In terms of guidance on learning methods, I strive to create an equal, democratic, harmonious and safe teaching atmosphere, give full play to students’ subjectivity, and through observation and operation , comparison, analysis and other activities, allowing each student to actively participate and actively explore according to their own experience and their own way of thinking to discover and construct mathematical knowledge. Through mutual discussions and exchanges in group cooperation, students learn to interact with others, share the success of their peers, explain their own ideas, listen to other people's opinions, and gain positive emotional experiences. Teachers also need to allow students to conduct self-reflection and independent evaluation to improve their ability to solve problems and comprehensively summarize.

4. Teaching process:

(1) Creating situations and preliminary perceptions

At the beginning of the class, I used multimedia to show this scene: "Sunday, Three good friends went fishing together. They caught 6, 11, and 4 fish respectively. Please think of a way to make them catch the same number of fish.

"[Introduced by familiar life situations, students can realize that mathematics is around them and that mathematics is inseparable from everything in life, thus creating a sense of intimacy with mathematical knowledge and better stimulating students' interest in loving and learning mathematics.]< /p>

Then let the students operate the match sticks and display the results as quickly as possible. Then let the students close their eyes and reflect on the previous operation process, and then outline the method of "moving more to make up for less", and then using multimedia. Continue to demonstrate "Another classmate came and he caught 11 fish" and let students imagine the "moving" process in their minds and communicate [We know that "average" and "average score" are different concepts. The result is a real quantity, but the average is just an abstract quantity that represents an intermediate state. Therefore, when teaching, I do not let students perform operations, but let students feel the "average" through communication and imagination. The actual meaning of "number" was prepared for subsequent deepening.]

The students' understanding had just been balanced, and I used multimedia to cleverly set up conflicts: "Four more students came, and they caught 10 fish respectively. Article, 7, 9, 8" still allows students to imagine in their minds. Students feel that it is too troublesome to use the method of "moving more to make up for less". What should they do? [Forcing them to consciously break through their thinking stereotypes and change Seek strategies for solving problems from different angles to obtain the general method of finding averages, that is, "first combine and then divide equally" and require column calculations. [This process is actually a "mathematicalization" process, which is very important for cultivating students' ability to use mathematics Observation and thinking about problems have practical significance. ]

Finally, let students give a name to the result "7" obtained after the operation, thereby eliciting the meaning of "average"

< p> (2) Contact life and ask questions

After the students initially understood the meaning of "average", I contacted the familiar "buy half ticket" topic to bring up the topic of height and asked the students to introduce themselves. Then, I asked the students in the first row and the last row to stand up, compare their heights and tell them how they compared. Students would find this question too easy, because the students sitting at the end would They tend to be taller. I asked the students in the 3rd and 4th groups to stand up and compare again. The students found that the heights were different and it was difficult to compare. I thought of adding up the heights of each person and then found that the two groups had different numbers. Still unable to compare.

The student was suddenly in suspense, and his thoughts were in a state of indignation. I seized the opportunity to ask: "Is there a better way to accurately compare the two groups of students? Taller?" Encourage students to fully express their opinions and guide them to conclude that the best way is to compare by finding their average height. ["Learning starts from thinking, and thinking starts from doubt. "Through the creation of problem situations, it provides motivation for exploratory activities and clarifies the direction, allowing students to enter the realm of "their hearts seek to communicate but fail to get it, and their mouths to express their opinions but fail", stimulating their desire to explore.]

(3) Independent exploration, cooperation and communication

After clarifying the direction of inquiry, which is to find the average height of each group, I organized students to discuss: "Require the average height of each group, and What kind of preparation work should be done?" Let students know that they must first collect the height of each classmate before calculating. [The real mathematics problems around the students just stimulated the students' interest in conducting research and prompted them to actively cooperate to obtain the results of the group The victory of the competition. ]

With the sound of music, the activity began in student groups. Students were allowed to leave their seats and independently collect the height of each student in the group to fill in the statistics table to calculate the average height. , and then communicate the calculation methods within the group and unify the results, and the group leader will fill in the summary table. [Here, the teacher gives full play to the main role of the students and lets them explore and solve problems independently in an open activity space. Integrate the identities of participants and collaborators into their activities, get along with them as equals, enthusiastically help them deal with emergencies, and obtain feedback information in a timely manner. Display and exchange various calculation methods on the projector, affirm and encourage them one by one. Simple algorithm and summarize the basic method: total number/number of copies = average. Then stimulate students to think: "The average height of group 1 is 138 cm, so the height of each student in their group must be 138 cm. Right?" [Further understand the meaning of averages through analysis, and cultivate students' ability to see problems from multiple perspectives.]

Finally, guide students to observe the table and compare Group 3 and Group 4, which group is higher? Allow students to experience success in solving problems through their own exploration.

On this basis, let students continue to explore the information hidden in the table, exchange experiences, and ask new questions "What is the average height of the whole class?" Let students estimate, and then verify it through written calculations to cultivate students' estimation ability. After knowing the average height of the whole class, I took the opportunity to show the average height statistics of fourth grade primary school students across the country 10 years ago and now, so that students can compare with their own actual conditions, and educate students to exercise actively and cherish a happy life!

(4) Practical application and experience life

Mathematics comes from life and must be applied to life to reflect its value and charm. After the students understood the meaning of "average" and learned the method of finding "average", I introduced the following realistic situation:

1. The average height of the students in Xiaoming's class is 140 centimeters, so His height must be 140 centimeters. Is that correct?

2. The average height of the students in Ming’s class is 140 cm and the average height of Xiaoqiang’s class is 137 cm. Can we say that Xiao Ming is definitely taller than Xiao Qiang?

3 , The average water depth of the swimming pool is 130 centimeters, and Xiao Ming is 140 centimeters tall. Is it dangerous for him to learn swimming in the swimming pool? Why?

4. The teacher found that our home’s electricity consumption in the second quarter was like this (Projecting electricity bills), can you use the skills you just learned to help me predict my home’s electricity consumption this month, okay? Why do you think so?

[Through the analysis of the situation, the question The solution not only deepens students' understanding of the concept of "average" and realizes the practical significance of "finding average" in daily life, but also creates opportunities for students to express freely and communicate extensively, improving their "mathematical communication". "ability. ]

In order to let students experience the wide range of uses of averages, I also let students freely communicate about averages they have seen in life, and then expanded students' horizons through newspapers and periodicals, and experienced the use of averages in all walks of life. wide range of uses in the industry.

(5) Evaluation summary, expansion and extension

At the end of the class, I asked the students to act as judges to score this class. When the students argued endlessly about the final score, I promptly raised questions: " Whose score should be used as the standard? What score is the most fair?" Guide students to actively use the knowledge they have learned to solve problems. [It seems like a random stroke, but it shows the teacher’s ingenuity. Through "rating the teacher" and calculating the average score, it not only strengthens the new knowledge of this lesson, reproduces the practical application of "finding the average" in life, but also allows the teacher to get real information feedback, and at the same time provides a summary for the subsequent class. With clever presets, it can be described as "killing three birds with one stone". ]

Finally, let students talk about what they learned from this lesson and how they plan to use it. [Let students self-evaluate and enhance students’ self-confidence in mathematics learning; expand and extend the classroom to further stimulate students’ interest in continuing to explore. ]

Reflection on mathematics teaching for finding averages

The average is an important concept in statistics, and it is very abstract for third-grade students. In the past, when teaching the concept of average, teachers often focused on how to find the average. The new textbooks place more emphasis on allowing students to understand the meaning of averages. Based on this understanding, I highlighted in the design that students should understand why they should learn average in specific situations, and focused on guiding students to understand the meaning of average in the background of statistics, and to grasp the characteristics of average in comparison and observation. , and then use averages to solve problems and understand its value. In this lesson, I focused on the following aspects:

1. Introducing concepts into real life situations to stimulate students' interest in learning.

Based on practical problems (a ring competition between boys and girls), which team will win? Guide students to communicate and think. Let students feel that mathematics is around us, so as to deeply understand the value and charm of mathematics. In the discussion of students' activities, under the cognitive conflict, it is obviously unfair to compare the total number of people when the number of people is different; and the average can represent their overall situation, so an "average" is produced, and the feeling average is The needs of real life also create the need to learn "averages". Only by organizing this process in teaching can students have a deeper understanding of the statistical significance and role of the average, and can they independently think of using the average as a representative of a set of data to make comparisons and comparisons when faced with similar problems. analyze.

2. Create an effective way to learn mathematics, understand the meaning of averages and learn the algorithm of averages

I use group cooperation and independent inquiry to allow students to explore and find solutions on their own. average method. One is to combine first and then divide, and the other is to move more to make up for the less. Then guide students to feel that the essence of these two methods is to make originally different numbers the same, thus introducing the concept of average. While explaining the method, he lost no opportunity to penetrate: the average is between the maximum and minimum values ??of a set of data, which can reflect the overall level, but cannot represent the situation of each individual. In this way, students' understanding of the concept of average becomes more profound and comprehensive.

3. Mathematical ideas and methods of penetration estimation.

In teaching, I combined the characteristics of averages. First, I asked students to guess how many girls each girl got on average, and then actually calculated, not only to find the range of the average, but also to find the method of finding the average ( (Move more and make up for less), which cultivates students' ability to use estimation methods for inspection.

4. Mathematics is closely related to life.

In teaching, I also combine the content of the teaching materials, follow the students' cognitive rules, integrate students' life experience into the classroom, guide students to understand the connection between mathematics and life, and explore mathematical materials in real life. Use the effective mathematics resources around you to learn mathematics knowledge. The four exercises I selected are from the shallower to the deeper, and the selected content is close to the students’ life. For example: the first question is the understanding of averages; the second question is the application of averages. , the third question is an in-depth understanding of averages. These three consolidation exercises are closely related to students' lives, so that students can truly feel that there is mathematics in life and mathematics is used everywhere in life, so they will have great interest in mathematics and take the initiative to learn mathematics and use mathematics. math. In addition, in a river with an average water depth of 110 centimeters, is it dangerous for Xiao Ming to swim in the river? In this discussion, students received safety education. This kind of teaching realizes the multiple values ??of mathematics education and enables various disciplines to play an effective integration role.

Generally speaking, this class achieved the teaching objectives, the key and difficult points were highlighted, and the students' enthusiasm was high. However, there are also shortcomings in the teaching process. First, the time arrangement is not very good, and there is not enough time for practice, resulting in some exercises that have not been completed. The main reason is that the new class takes a long time. If students are asked to observe statistical graphs and talk about what they know, they can ask a few less students to answer. This is not the focus of this class. 2. At the beginning of the class, because the courseware suddenly had no sound, I was a little nervous and wasted time. In fact, this does not affect the teaching of this class. Be flexible in dealing with emergencies!

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