First, the equation:

1, an equation with unknown numbers is called an equation.

2. The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.

3. Principle of solving equations: balance.

4. Add, subtract, multiply and divide the same numbers (except 0) on the left and right sides of the equation at the same time, and the result is still an equation. This is the essence of the equation.

Second, solving simple practical problems with column equations:

1, the general steps of solving practical problems by equation: examine the meaning of the question, set the unknown, find out the equation with equal relationship, solve the equation, find the answer, and test whether it is in line with reality.

2. Sum and multiple problem: the application problem of knowing the sum of two numbers and the multiple relationship between them and finding out what these two numbers are. When solving, we can set one of the numbers as x, then express the other number with a formula containing x, and then list the equations as sum or difference.

Three, cuboids and cubes:

1. Features of cuboids and cubes: Cuboids have six faces, which are generally rectangular (in special cases, two opposite faces are square), and the areas of the opposite faces are equal; There are 8 vertices, 12 edges, and 12 edges can be divided into 3 groups: 4 long, 4 wide and 4 high. A cube has six faces, all of which are squares with equal areas; There are 8 vertices, 12 sides, and each side has the same length.

2. The sum of the sides of a cuboid = (length+width+height) × 4; Sum of cube sides = side length × 12.

The six faces and the total area of a cuboid or cube are called its surface area. Surface area of cuboid = (length× width+length× height+width× height) × 2; Surface area of cube = side length × side length ×6.

Characteristics of knowledge point summary

1, systematization: the primary feature of knowledge point summary is to systematize scattered knowledge points and form a logical and hierarchical knowledge system. This helps students to master the knowledge they have learned more comprehensively and understand the relationship between knowledge points.

2. Highlight the key points: When summarizing the knowledge points, we usually emphasize the key points, difficulties and test sites, so that students can clearly understand the learning direction, grasp the key contents and improve the learning efficiency.

3. Concise and clear: Summary of knowledge points describes complex concepts and principles in concise language, which is convenient for students to remember and review quickly. At the same time, by using auxiliary tools such as charts and mind maps, knowledge points are more intuitive and easy to understand.