Teaching content: People's Education Press, the second volume of fourth-grade mathematics, and the wide-angle mathematics "chicken and rabbit in the same cage"
The problem of keeping chickens and rabbits in the same cage is one of the famous and interesting topics in ancient China. By learning to solve the problem of chickens and rabbits in the same cage, the ability to analyze and solve problems is improved.
Example: About 1500 years ago, an interesting mathematical problem was recorded in Sun Tzu's Art of War, that is, the famous problem of "chickens and rabbits in the same cage". The book describes it like this: "There are chickens and rabbits in the same cage, with 35 heads above and 94 feet below. Chicken and rabbit geometry? "
There are some chickens and rabbits in the cage. There are 35 heads at the top and 94 feet at the bottom. How many chickens and rabbits are there?
Method 1: list enumeration method
List enumeration method is to let us list the tables, and solve this problem step by step by listing them in turn. The detailed process is shown in the following table:
chicken (as food)
35
34
33
32
……
26
25
24
23
rabbit
1
2
three
……
nine
10
1 1
12
foot
70
Seventy two
74
76
……
88
90
92
94
This method is simple and easy to understand, but the process is too clumsy and cumbersome.
Method 2: Leg lifting method
This is the method used by the ancients to solve problems, which is also the method used in Sun Tzu's calculation.
1, leg lift, that is, the chicken is "golden rooster independent", the rabbit has two hind legs touching the ground and its front legs raised, so the number of legs is half of the original. 94÷2=47 feet.
Now the chicken has one foot and the rabbit has two feet. As long as there is a rabbit in the cage, its feet are more than its head 1.
3. Then the difference between the number of feet and the number of heads is 47-35 = 12, which is the number of rabbits.
4. Finally, the number of chickens is obtained by subtracting the number of rabbits from the number of heads 35- 12 = 23.
So we can sum up the formula: the number of rabbits = the total number of legs ÷2- the total number.