First, the chicken and the rabbit are 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.
Second, the principle of filing.
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.
Third, classification
Classification refers to classification according to category, grade or nature.
Fourth, find the law.
Discovery mode is a basic skill in mathematics teaching in primary and secondary schools. The purpose is to let students discover, experience and explore the simple arrangement rules of figures and numbers. Through comparison, we can understand and master the method of finding patterns, and cultivate students' preliminary observation, operation and reasoning ability.
Five, simple arrangement and combination
The thinking method of permutation and combination is not only widely used, but also the knowledge base for students to learn probability and statistics, and it is also a good material for developing students' abstract ability and logical thinking ability. We have made some efforts and explorations in infiltrating mathematical thinking methods, and presented important mathematical thinking methods through the simplest examples in students' daily life.
Six, logical reasoning
Deductive reasoning is the process of drawing specific statements or individual conclusions from general premises through deduction, that is, the logical form of deductive reasoning is of great significance to rationality, because it plays an irreplaceable role in correcting the rigor and consistency of human thinking.
Seven. Overlapping problem
In daily life or mathematical problems, when some data are classified according to a certain standard, it often happens that some data belong to two or more different categories at the same time, so there will be repeated calculations when calculating the total. This kind of problem is called overlapping problem. The common method to solve the overlapping problem is to add several counting parts with repeated inclusion, and then exclude the number of repeated elements from their sum, so that the calculated results are neither missing nor repeated. This principle is called inclusion and exclusion principle, also known as inclusion and exclusion principle.
Eight, pancake problem
By discussing how to arrange homework reasonably to save the most time, let students know how to optimize the use of ideas in solving problems. Because grade five students have a certain ability and foundation to solve problems, it can be said that in daily study and life, students can easily find solutions to problems and different strategies to solve problems, but the key here is to let students understand the idea of optimization, form the consciousness of finding the optimal solution from various schemes, and improve their ability to solve problems.
Nine, planting trees
In order to be more intuitive, it is illustrated by graphic method. Trees are represented by points, and the lines along which trees follow are represented by lines, thus transforming the problem of planting trees into the problem of the relationship between "points" on an unclosed or closed line and the number of line segments between two adjacent points.
Ten, looking for defective products
There are many different situations of "defective products" in real life production, some are different in appearance from qualified products, and some are made of substandard materials. The defective products we are looking for in this class have the same appearance as the qualified products, but the quality is different, and we know in advance that the defective products are lighter (or heavier) than the qualified products, and there is only one defective product in all the items to be tested.