1. Concepts: natural numbers, integers, decimals, infinite decimals, cyclic decimals, pure cyclic decimals, numbers, counting units, integers and decimals, properties of decimals, rewriting and ellipsis of numbers, rounding, divisibility, divisor, multiple, greatest common divisor, least common multiple, prime number, composite number and factorization prime factor.

2. Methods: Algorithm, operation sequence and operation rule of addition, subtraction, multiplication and division (simple calculation).

Solve the problem:

(1) Analyze the meaning of the question and find out the known conditions and problems.

(2) Determine the quantitative relationship between conditions and problems

(3) Formula calculation.

(2) Simple equation

1. Concept: equation, unknown number, equation, addition, subtraction, multiplication and division.

2. Use letters to represent numbers, solve equations and solve problems (quantitative relationship).

(3) Scores and percentages

1. Concepts: Fraction, Fraction Unit, True Fraction, False Fraction, Relationship between Fraction and Division, Basic Properties of Fraction, Simplest Fraction, General Fraction, Reduced Fraction, Percentage (Percent), Fraction and Multiple.

2. Application: reciprocity among fractions, decimals and percentages, four operations of addition, subtraction, multiplication and division of fractions, and simple operations.

Solve the problem:

(1) Find the fraction or percentage of one quantity relative to another.

(2) Find out the fraction or percentage that one quantity is more or less than another quantity.

(3) Find the fraction or percentage of a quantity-unit 1 known.

(4) Given the fraction or percentage of a quantity, find this quantity-unit 1 unknown.

(4) Measurement of quantity

1. Concepts: commonly used length units, area units, unit of volume, mass (weight) units, time units, forward speed between two adjacent units, number of names, single numbers and compound numbers.

2. Application: name number rewriting-the high-level unit is changed to the low-level unit, multiplied by the forward speed; From low-level units to high-level units, divided by the forward speed.

(5) Preliminary knowledge of geometry

1. Concepts: straight line, ray, line segment, angle and angle classification, vertical line, parallel line, triangle classification, triangle internal angle sum, parallelogram, trapezoid, height, circle, diameter, radius, pi, sector, axisymmetric figure and axis of symmetry.

2. Operation: measure angle, draw angle, draw vertical line, draw parallel line, draw height (triangle-trapezoid-parallelogram), draw rectangle, square, circle, semicircle and symmetry axis.

3. Calculation: area (triangle-trapezoid-parallelogram-rectangle-square-circle),

Perimeter (rectangle-square-circle-semicircle),

Surface area (cube-cuboid-cylinder),

Volume (cuboid-cube-cylinder-cone).

(6) Proportion and specific gravity

1. Concepts: ratio, the relationship between ratio and division and fraction, ratio, basic properties of ratio, simplest ratio, proportion, basic properties of proportion, scale, positive proportion and inverse proportion.

2. Calculation: Find the ratio, simplify the ratio and solve the ratio.

3. Solve the problem: distribution in proportion, proportion, positive proportion and inverse proportion.

(7) Simple statistics

1. Can draw statistics or charts (bar charts and line charts).

2. Analyze the problem according to the chart and solve the problem-for example, find the average value, increase or decrease one quantity by a few percent compared with another, and so on.