Teaching objectives go through the process of average generation, understand the necessity of average learning, understand the meaning of average, and master the method of finding simple average.
teaching process
First, create situations and ask questions.
Teacher: The annual Sunshine Sports Festival in our school has started, and now it's a shooting competition for men and women 1 minute. Want to watch their game?
Courseware play: the shooting pictures of the first round of men's and women's competitions, and show the statistical data of the first round of shooting.
Women's team and men's team
Lily 3 Liangliang 6
Jiajia 5 Tian Tian 3
Jessica Hester Hsuan 4 Ding Ding 5
Wen Wen 2 Qiang Qiang 2
Total 14 total 16
The teacher concluded: By comparing the total, we know that the boys team won the first round.
Second, solve problems and explore new knowledge.
1. Feel the needs of an average generation.
Teacher: Do you want to watch the second round again? Now I want to join the second round of the women's team and show the statistics of the second round of shooting.
Women's team and men's team
Lily 4 Liang Liang 7
Jiajia 7 Tian Tian 3
Xuanxuan 5 Dingding 5
Wenwen 4 Qiang Qiang 9
Teacher Fan 5
25 in total, 24 in total
Think about it: Do you think this game is fair?
Let the students find a fair comparison method. Students report and exchange ideas. Finally, the method of comparing the average shots of each team is obtained.
Teacher: Yes, compare the average number of shots of each team, that is, the average. How can I get the average? Here are three ways to average:
2. Explore the method of averaging.
The first method: "more actions and less compensation" method.
Teacher: Change the basketball hit by girls into yellow discs and the basketball hit by boys into red discs. Let's look at the women's group first. Obviously, Jia Jia threw seven balls, while Lily and Wen Wen threw four balls, which was the least. Let's move these seven to Lili, which has the least supply, and then to Wenwen, which has the least supply, so that everyone has the same number. Look at the men's team, the top nine are the most, and Tian Tian is the least. If we move three of the nine to Tian Tian, their shots will be the same, and then move the bright one to Tintin, so that all four of them will have even shots. In this way, the method of turning different things into the same amount by turning more and less is called "moving more and making up less" The same number, we call it "average". The average number of women's teams here is five, and the average number of men's teams is six. So it is concluded that the boys team won the second round.
The second method: "combine first and then divide" method.
Women's team and men's team
Teacher: This is the total number of 25 shots made by the women's team. We divide it into five equal parts, five for each.
Teacher: This is the total number of 24 shots made by the men's team. Divide into four parts on average, six parts each.
The third method: column calculation method.
Girl group: (4+7+5+4+5)÷5=5 (each)
Boys team: (7+3+5+9)÷4=6 (each)
Teacher: The first formula, in brackets, represents the total number of shots made by all girls. The number 5 after division indicates that the average number of copies is 5, and the number 5 after the equal sign indicates that the average number of girls is 5. The second formula is to find the average number of shots of the men's team. Similarly, the total number divided by the number of copies is equal to the average, and the average number of shots of the men's team is 6.
3. Understand the meaning of the average.
Teacher: Through the above three methods, we got the average value. Look closely, what else did you find?
Take the average of girls' teams as an example to ask: How do you know and understand the number 5? Let the children describe their understanding of the meaning of the average according to their own experience.
Teacher's summary: The number 5 is the average of four, seven, five, four and five, which refers to the same number after a group of numbers are scored on average, and it is always smaller than the largest number and greater than the smallest number.
4. Communicate the connection between average and life.
Teacher: Have you ever seen the average in your daily life? There are many ways to find the average value, and each method has its own characteristics. In life, we should combine reality, analyze comprehensively, choose appropriate methods and solve problems flexibly.
blackboard-writing design
On the basis of "total number of copies/number of copies = number of copies", the average value is obtained.
The other two methods:
Make-before-break method and column calculation method
Total quantity/total number of copies = average value