Chickens and rabbits in the same cage is one of the famous typical anecdotes in ancient China. About 65,438+0,500 years ago, this interesting question was recorded in Sun Tzu's calculation. Today, there are pheasant rabbits in the same cage, with 35 heads above and 94 feet below. Pheasant rabbit geometry?
These four sentences mean that there are several chickens and rabbits in a cage. From the top, there are 35 heads, and from the bottom, there are 94 feet. How many chickens and rabbits are there in each cage?
The essence of this problem is a binary equation. If the teaching method is proper, primary school students can understand the concepts of unknowns and equations and exercise their ability to abstract numbers from application problems. Generally, in the fourth to sixth grades of primary school, the content of one-dimensional linear equation is used to teach.
There is another change in the same book: there are beasts today, and there are 64 feet; Birds, four feet, seventy-six on the top and forty-six on the bottom. Q: What are the geometric shapes of birds and animals? A: Eight animals and seven birds. The subject conditions include different heads and different feet.
Methods and skills of raising chickens and rabbits in the same cage;
I enumeration method (list method)
The method is very simple, and the process is very complicated. According to the ever-changing number of chickens and rabbits, the number of legs of chickens and rabbits is filled in the table respectively until the correct answer is found. This method is only applicable to the exploration in classroom teaching and the guidance of other methods. Because this method is too clumsy and consumes a lot of time, it is generally not suitable for daily exercises and exams.
Second, the hypothesis method (contradiction method)
One of the main methods to solve the problem of "chickens and rabbits in the same cage" is to make some assumptions about the topic according to the known conditions, then make reasoning according to the conditions, find out the contradiction with the number of topics, and finally make reasonable modifications and draw correct conclusions.
At the same time, the hypothesis method is also a method often encountered in Olympic math problems (only the chicken and rabbit are in the same cage here, and the hypothesis methods of other problems are not described here for the time being). The key of this method is to find the contradiction with the mean in the problem through hypothesis.