Teaching design of the average of people's education edition
Teaching content: pages 42~45 of the second volume of third grade mathematics published by People's Education Press.
Teaching material analysis:
Average is an important concept in statistics, which is very abstract for junior three students. In the past, when teaching the concept of average, teachers often focused on the solution of average. The new textbook pays more attention to making students understand the meaning of average. Based on this understanding, in my design, I emphasize that students should understand why they should learn averages in specific situations, pay attention to guiding students to understand the significance of averages in the statistical background, grasp the characteristics of averages in comparison and observation, and then use averages to solve problems and understand their values.
Teaching objectives:
1. Know the meaning and solution of the average.
2. Strengthen students' understanding of the statistical significance of the average.
3. Use mathematical thinking to solve the average problem in life and enhance the awareness of mathematical application.
Teaching focus:
Understand the practical significance of the average and master the method of finding the average.
Teaching difficulties:
Understand the practical significance of the average.
Teaching method: enlightenment teaching method
Teaching process:
First, preview thinking: (moving, feeling)
Small research before class
1. Organize the bookshelves at home. How to make the number of bookshelves on each floor the same?
2.2 people 1 group jump rope, and record the number of times each person jumps. Compared with the other group, which group won?
Second, problem discussion: communication report of small research before class (feeling)
Teacher: Yesterday, Mr. Meng arranged a small study for everyone before class and asked each group to take it out and communicate in the group.
Teacher: Which group will report these two small questions?
Design intention: "Heuristic teaching" emphasizes the importance of students' preview and report exchange before class, so that we can fully trust students' ability and rely on them completely. Therefore, in close contact with students' real life, starting from students' life experience and existing knowledge, I created a small research link before class, so that students can enrich the relevant knowledge of averages through their own hands, perceive the important role of averages in life, and stimulate students' desire to explore. And experience the joy of success through communication and reporting.
Third, teaching material analysis: (Feeling)
(A) create a situation to stimulate interest in the introduction
1. Introduction to the dialogue: (Showing the bookcase of the slide teacher's house) At present, there are 12 books on the upper floor and 10 books on the lower floor. I want to ask my classmates to help me rearrange it so that there are as many books on each shelf.
feeling
(1) The process of students' thinking and imagination transfer.
(2) Teacher's operation, Q: Now there are 1 1 books on each floor. What are their numbers?
(3) Teacher: In this way, shift several different numbers, add more and make up less, combine them first and then divide them equally. The same number is the average of these numbers.
Today, let's meet our new friend "Average", shall we?
(blackboard writing: general)
Design intention: The concept of average is naturally introduced from real life, and the range of average is ingeniously infiltrated, so that students can initially feel that average is a general situation of a group of data, not an actual quantity, and make a good preset for deepening their understanding and grasp of the meaning of "average" in the future.
(2) Explore new knowledge
1. Understand the meaning and explore the methods.
Question: the group cooperated to stack wafers as required, with 2 wafers in the first row and 7 wafers in the second row; Three in the third row.
Teacher: Looking at the chip in front of you, what questions can you ask?
Health: I think the number of discs in each row is the same?
Teacher: That's a good question! Let's study how to make three rows of wafers equal. Do activities first, then communicate with each other.
Group activity discussion.
Design intention: Let students ask their own questions and then solve them, which greatly stimulates students' enthusiasm for exploration.
Report and communicate.
Health 1: We take out 1 from 7 to 3, and then take out 2 from 7 to 2, so that there are as many wafers in each row.
Health 2: We take 2 with the least number of rows as the standard. Take five from seven, take five again and again, and then put these six evenly in three rows, two in each row, and combine them with the original two, four in each row, the same.
Teacher: No matter how we move, we always move big numbers to small numbers.
Please think about it: what are the same rules in the process of moving just now?
Write on the blackboard according to the students' answers: from inequality to equality.
Summary: In this way, under the premise that the total number remains unchanged, several different numbers become the same number by shifting more and supplementing less, and the same number is the average value of the original number.
Design intention: "average" and "average sharing results" are different concepts. The result of average share is a real quantity, and average is only an abstract quantity representing the intermediate state, which once again makes students really feel the practical significance of "average".
2. Initial application, internalization and expansion.
Teacher: Just now, the students expressed the average value in various ways. Please choose your favorite method and tell me what you think. (Show: What is the average of 7, 3, 6 and 4? )
Health 1: I think so (7+3+6+4)+4=5, so the average of 7, 3, 6 and 4 is 5, and the method of ten is also used when adding.
Health 2: I take out 2 from 7 and give it to 3; 6 take out 1 give 4. Move more and make up less. The average of 7, 3, 6 and 4 is 5.
Slide show: height situation
Let's estimate the average height first. (148, 147, 149, & amphellip& amphellip) Do a calculation and compare the estimates. Whoever counts himself first will write on the blackboard.
Health 1: I think so. 152 gives three to one 146,15/kloc-0 gives two to one 147, so the average value of this set of data is 149.
Health 2: I think so. The number of this column ranges from 146 to 153, in which 148 and 150 are missing, and the middle number of 148 and 150 is 149, so these averages are/kloc.
Design intention: Create a learning situation closely related to students' living environment and knowledge background, so that students can actively carry out teaching activities such as observation, estimation, verification, reasoning and communication, internalize various methods of averaging in time, and encourage diversification of problem-solving strategies.
(3) Expanding exercises
1. Application 1.
Group activity: Take out the prepared questionnaire, first calculate the average value with a calculator, and then exchange opinions with each other. The contents of the questionnaire include the weight and height of the players, the telephone and electricity charges at home in recent months, and the temperature last week. )
Exchange feedback.
Design intention: Collect and sort out data from life, and calculate the average, so that students can make representative data reflected by the "average" in a certain period of time, and people can use it to predict the future development trend in real life and work. With the introduction of calculators, students are willing and have more energy to devote to practical and exploratory mathematics activities.
2. Application 2.
Please use the calculator to help the young players calculate the final score.
Health 1: final score (84+70+88+94+82+86)&; Points; 6=84 (points). (Most students agree)
Health 2: I disagree. I think the highest score and the lowest score should be removed. Final score (84+88+82+86)&; Points; 4=85 (points), fair and reasonable.
Teacher: Have you ever seen this method of averaging? Olympic Games, TV competitions, etc. ) In order to make the game more fair, this method is usually used to get the average value in the game.
Design intention: guide students to communicate and think in combination with practical problems. Let students feel that mathematics is around us, so as to deeply understand the value and charm of mathematics.
3. application 3.
Teacher: On Sunday, Xiaoli went to learn swimming happily. She met a problem. The average depth of the swimming pool is 126 cm, and the height of Xiaoli is 134 cm. Is it dangerous for her to learn to swim in this swimming pool?
□ Yes □ No □ Maybe □ Maybe not.
(1) Communicate your thoughts with your deskmate.
(2) Name (3)
(3) student evaluation.
Teacher: The average water depth is only a representative figure. His actual depth is unknown. It may be higher than 65,438+026 cm, deeper than 65,438+026 cm, or just 65,438+026 cm. Practical problems should be treated separately according to the actual situation.
Design intention: deepen students' understanding of the concept of "average", make students experience the possibility of events and improve their mathematical communication ability.
(D) class summary
Teacher: What did you learn from this class? Is there a problem?
Extracurricular development
Recommended homework: 1. Now you ask the teacher, "What is the average height of our class?"
Can it be solved? This problem is left to everyone to solve after class.
Design intention: echo the beginning and extend it through extracurricular practical activities to further improve students' ability to use what they have learned to solve practical problems.
Teaching reflection:
The enlightenment concept puts forward that the learning goal should be changed from "paying attention to knowledge" to "paying attention to students' learning process", and points out that "five senses" is a cyclic process. Classroom design should change from "imparting knowledge" to "initiating activities" in order to get "moving, feeling, feeling and gratitude". From the teaching of this class, we can know that students have accumulated "average" knowledge in their lives, so I need to design all aspects of teaching according to the actual situation of students, pay attention to students' small research before class, and let students use various resources &; Mdash& ampmdash; Students should help each other, carry out independent inquiry learning, and actively construct a knowledge system about averages, so that students can gain self-confidence, scientific attitude and rational spirit in learning, and realize the development effect of teaching and the essential function of educating people.
The concept of enlightenment holds that students must be taught to participate in various practical activities in order to gain knowledge, experience and development. The new curriculum reform also regards learning as a process of "doing" and "experiencing", which highlights the practical characteristics of students' learning. In the teaching of this class, I didn't transplant and copy the content of the textbook, but created and processed it, turning the content of the textbook into an activity for students to study, study and feel, and organizing it into a "life world" for students. This is an important principle that we must follow in the current design teaching.
Average knowledge points of people's education edition
Basic formula: ① average = total amount &; Points; Total shares
Total amount = average &; Times; Total shares
Total copies = total quantity &; Points; average number
② Average value = benchmark number+sum of differences between each number and benchmark number &; Points; Total shares
Basic algorithm:
① Find out the total quantity and total number of copies, and calculate with the basic formula ①.
② Benchmark number method: according to the relationship between given numbers, determine a benchmark number; Generally, the number or intermediate number close to all numbers is selected as the reference number; Taking the reference number as the standard, find the difference between all given numbers and the reference number; Then find the sum of all differences; Then find the average of these differences; Finally, the sum of this difference and the average value of the reference number is the average value, and the specific relationship is shown in the basic formula ②.