Knowledge point of "wide angle of mathematics"
First, the problem of planting trees.
1. Plant at both ends (both ends): the number of plants is equal to the number of intervals+1.
2. Planting one end (one end): the number of plants is equal to the number of intervals.
3. No planting at both ends: the number of plants is equal to the interval number-1.
Second, the number of chessboards:
1. Number of outermost chessboards: number of chessmen per side × number of sides-number of sides.
2. The total number of chessboards: the number of chessmen in each row × the number of chessmen in each column.
3. Number of people on the outermost layer of the phalanx: number of people on each side ×4-4.
4. Place flowerpots on polygons: the number of flowerpots placed on each side × the number of sides-the number of sides.
Third, the pigeon nest problem.
1. Put n+ 1(n is a natural number greater than) objects into n "pigeon coops". There is always a "pigeon coop" with at least 2 objects.
2. Put more than kn(k and n are natural numbers greater than) into n "pigeon coops", and there is always a "pigeon coop" with at least (k+ 1) objects.
3. If there are n (n is a natural number greater than) "pigeon coops", to ensure that there are at least two items in a "pigeon coop", there must be at least n+ 1 item.
4. If there are n pigeon coops (n is a natural number greater than), to ensure that at least (k+1) items are put in one pigeon coop (k is a natural number greater than), then at least (kn+ 1) items are needed.
5. (The total number of distributed objects is-1)÷ (The number of objects in a dovecote is at least-1) = A...B (b), where a is the number of pigeon coops required.
6. Ideas and methods to solve the problem by using "pigeon nest problem": constructing "pigeon nest" and establishing "mathematical model"; Put the object into the "pigeon cage" and make a comparative analysis; Explain the reasons and draw a conclusion. For example, there are four pigeons flying into three dovecotes, and there is always one pigeon flying into at least two pigeons.
Tip: The key to solving the problem of pigeon nest is to find out who is the "pigeon cage" and who is the "pigeon".
The main contents of the four major fields of primary school mathematics
Numbers and algebra: understanding, representation, size, operation and estimation of numbers;
Graphics and geometry: the basic graphics of space and plane, the nature and classification of graphics; Translation, rotation and axial symmetry of graphics;
Statistics and probability: collecting, sorting and describing data, and processing data;
Practice and comprehensive application: learning activities with a class of problems as the carrier and students' active participation are important ways to help students accumulate experience in mathematics activities.
General steps of solving application problems with mathematical equations
1. Find out the meaning of the problem, find out the unknown, and express it with X;
2. Find out the equal relationship between quantity and quantity in the application problem and make the equation;
3. Solve the equation;
4. Test and write the answers.