"Mathematics Wide Angle" is a new attempt made by the new textbook in infiltrating mathematical thinking methods into students. The textbook is based on students' familiar and interesting life scenes, and pays attention to infiltrating these mathematical thinking methods into students, putting learning activities in simulated scenes, providing students with opportunities for operation and activities, initially cultivating students' awareness of orderly and comprehensive thinking, and laying the foundation for students to learn combinatorial mathematics and probability statistics in the future.

1, chickens and rabbits in the same cage

Chickens and rabbits caged together is one of the famous anecdotes in ancient China, which was recorded in Sun Tzu's Art of War. The problem of chickens and rabbits in the same cage is a common problem in primary school Olympic mathematics. Many elementary school arithmetic application problems can be transformed into such problems, or solved by a typical solution-"hypothesis method". So we should learn its solutions and ideas. Usually the hypothesis method is simpler and easier to understand.

2. The principle of pigeon nest

There are ten apples on the table. If we put these ten apples in nine drawers, no matter how we put them, we will find at least two apples in at least one drawer. This phenomenon is what we call the "pigeon hole principle".

The pigeon hole principle roughly means: "If each drawer represents a collection, then each apple can represent an element. If there are n+ 1 elements in n sets, there must be at least two elements in a set. " The pigeon coop principle is sometimes called the pigeon coop principle. This is an important principle in combinatorial mathematics.