1, hypothesis method
The total number of chickens and rabbits is a known, and the total number of feet is b known. There are X chickens and Y rabbits. Because each chicken has two feet and each rabbit has four feet, the following two equations can be listed: x+y = the total number of a heads 2x+4y = the total number of b feet. By solving this system of equations, the values of x and y can be obtained. According to the assumed number of chickens and rabbits, we can calculate the actual number of chickens and rabbits.
2. Foot cutting method
Foot amputation is a relatively intuitive method. Its basic idea is to cut off both feet of all chickens and rabbits, so the total number of feet of chickens and rabbits will be changed from 38 to 19. If there is a rabbit in the cage, the total number of feet will be more than the total number of heads 1, so the total number of feet is 19 and the total number of heads is 14.
3. Whistling method
Blowing a whistle is a faster method. Its basic idea is to make all rabbits stand on their front feet and lift their rear feet, so that each rabbit has two feet left. At this time, if you whistle for each rabbit, then the rabbit will lift its hind feet, so the total number of feet you see on the ground is the number of rabbits. Because the number of feet of a chicken is equal to the number of heads, the total number of feet left is the number of chickens.
Chickens and rabbits in the same cage is one of the famous typical interesting topics in ancient China. About 65,438+0,500 years ago, this interesting question was recorded in Sun Tzu's mathematical classics. Due to the limitation of primary school mathematics curriculum standards, it will be difficult to explain the solution of this problem to primary school students with binary equations. So we need to prepare some solutions that only involve the appearance of the problem. All the representation solutions are related to the essence of this problem.
Historical background
Chicken and rabbit in the same cage is one of the famous mathematical problems in ancient China. About 1500 years ago, this interesting question was recorded in Sun Tzu's calculation. It is described in the book that there are pheasant rabbits in the same cage, with 35 heads on the top and 94 feet on the bottom. What are the geometric shapes of pheasant rabbits?
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.