(1) Through systematic arrangement and review, students can master the basic knowledge about integers, decimals, fractions, percentages, ratios and simple equations, have the ability to perform four operations on integers, decimals and fractions, use the simple algorithms they have learned, calculate rationally and flexibly, solve equations and proportions, and form the habit of checking duplicates and scores. Have estimation consciousness and preliminary estimation ability.

(2) enable students to consolidate the appearance of the size of some units of measurement they have learned, firmly grasp the progress between the units they have learned, and skillfully rewrite names and numbers simply.

(3) Make students firmly grasp the characteristics of the geometric shapes they have learned, skillfully calculate the perimeter, area and volume (volume) of some geometric shapes, and consolidate the simple drawing and measuring skills they have learned.

(4) Make students master the preliminary knowledge of statistics, understand and draw simple statistical charts, and calculate the average problem.

(5) Let students feel the close connection between mathematics and real life, and cultivate students' exploration consciousness through observation, operation and guess. On the basis of firmly mastering some common quantitative relations and solving methods of application problems, students can flexibly use what they have learned and solve some simple practical problems in their lives independently.

(6) To cultivate students' serious, strict and diligent learning attitude, the spirit of independent thinking and overcoming difficulties, and the study habits of careful calculation, neat handwriting and conscious inspection.

(7) Through practical activities, cultivate students to find mathematical problems from the surrounding situations, so that students can initially understand the relationship between mathematics and social life, cultivate students' mathematical consciousness and feel the role of mathematics.

(8) The strategy and skills of problem-solving are the focus of the topic selection and judgment.

Second, the specific requirements of each part of the knowledge and ability:

The concept of 1 number.

(1) The system firmly grasps the meanings of natural numbers, integers, decimals, fractions and percentages, and their relations and differences. Master decimal counting method, can read and write all kinds of numbers correctly and skillfully, can rewrite tens of thousands and hundreds of millions of digits, can round off and omit the mantissa of a number as required, and can write approximate values. Know numbers, digits, counting units and their differences. Firmly grasp the numerical sequence table of integers and decimals, find the approximate number of decimals, know the circulating decimals, and carry out the mutual transformation between fractions and pseudo-fractions, integers and fractions, decimals and percentages. Will compare the size of the numbers. You can get the approximate number of a number according to the specific situation. It can explain the meaning of the score.

(2) Understand and apply some basic properties of integers, decimals and fractions. The nature of divisibility mainly grasps the concepts of divisibility and division, divisor and multiple, prime number and composite number, odd number and even number, common divisor and common multiple, greatest common divisor and minimum common multiple, coprime number and prime factor, and understands their relations and differences. Master the characteristics of numbers divisible by 2, 5 and 3. Will decompose the prime factor (generally no more than two digits). Will find the greatest common divisor (limited to two numbers) and the least common multiple (limited to two or three numbers), and it is not required to comprehensively use the above concepts for the divisibility of numbers.

(3) Can explore simple laws and solve the laws of series or calculation.

(4) Numbers can be used for coding.

2. Four operations.

(1) Understand and master the meaning and laws of addition, subtraction, multiplication and division of integers, decimals and fractions, and master the relationship between the parts of the four operations.

(2) Be able to correctly calculate the four items of integer, decimal and fraction, and be proficient in some basic calculations. Four operations will be checked. In the four operations of integers, pen addition and subtraction are mainly three digits, generally not more than four digits; One multiplier does not exceed two digits, and the other multiplier generally does not exceed three digits; The divisor of written division shall not exceed two digits. In the four decimal operations, the restriction on the number of digits is the same as that in the four integer operations, and the approximate value of the product sum quotient will be rounded and truncated. The numerator and denominator are relatively simple, and most of them can be calculated orally. Will make an estimate. Don't use an abacus to calculate, use a calculator to calculate.

(3) Mastering the order of elementary arithmetic can correctly calculate elementary arithmetic problems. Elementary arithmetic is mainly in two steps, generally no more than three. (No scores, the topic of decimal elementary arithmetic).

(4) Master the operation rules and be able to apply them to some simple operations. Master the simple algorithm of continuous addition, subtraction, multiplication and division. Students should be encouraged to apply what they have learned, choose appropriate methods and conduct calculations and tests reasonably and flexibly.

(5) According to the narrative calculation (mainly divided into two steps, generally no more than three steps).

3. Algebra is preliminary.

(1) will use letters to represent numbers, common quantitative relations, operation rules, calculation rules, and formulas for calculating the perimeter, area and volume of geometric objects. Quantities can be expressed by algebraic expressions.

(2) Understand the meaning of the equation, solve the unary equation and test it (the content of the unary equation is only a χ b = c, a χ b χ = c). There is no decimal operation in the equation, and there is no mixed operation of decimal and fraction).

(3) The equations will be listed and solved according to the written description.

4. Ratio and proportion.

(1) Understand the meaning and nature of ratios and proportions, and be able to write ratios and proportions as required. You can find the ratio and simplify the ratio. Solution ratio. Make clear the connection and difference between ratio, fraction and division.

(2) The scale of the plan can be calculated, and the distance on the plan and the actual distance can be calculated according to the scale. Can use scale to measure and draw a plan.

(3) Understanding the meaning of positive-negative ratio will determine whether two quantities are positive or negative.

5. Measurement of quantity.

Master the commonly used units of measurement such as length, area, volume, volume, weight, time, etc., and rewrite singular and plural, high-level units and low-level units. Choose the appropriate unit name according to the actual situation.

6. Preliminary geometry.

(1) master the characteristics of plane graphics and their connections and differences. Know the sum of the angles inside the triangle. A preliminary understanding of axisymmetric graphics. Grasp the meaning of perimeter and area, understand the derivation process of perimeter and area calculation formula, and use the formula to calculate the perimeter and area of the learned figure. (Don't test rounded corners, fan shapes, combined figures, and the data of quadrature calculation should not be too complicated. )

(2) Master the characteristics of the learned three-dimensional graphics and their relationships. Understand the meaning of surface area, volume and volume of three-dimensional graphics, and calculate their surface area and volume without the knowledge of ball. Can solve practical problems according to the cutting, spelling and segmentation information of graphics.

(3) Strengthen operation training and cultivate students' practical ability. Ask the students to measure the length and angle of the line segment with a protractor. The angle will be drawn according to the specified degree, and the height will be drawn in triangle, parallelogram and trapezoid. The line segment is drawn to the specified length. Can draw vertical lines (including the distance from points to straight lines), parallel lines, rectangles, squares and circles. Measure the diameter of a circle without a center. The axis of symmetry of the axisymmetric figure will be drawn. Don't draw triangles, parallelograms, trapeziums, sectors and all three-dimensional figures. ) will be drawn to scale.

7. Preliminary statistics.

(1) Master some preliminary knowledge of statistics, collect and sort out data. Will fill in simple statistics. Will be averaged according to the data.

(2) Understand the characteristics and uses of various simple statistical charts, and understand and explain simple statistical charts (that is, look at charts to answer questions). Can obtain mathematical information from statistical charts, ask mathematical questions and answer them according to the information, make simple statistical tables and draw simple statistical charts. Will do some simple analysis on the statistical chart. Pay attention to neatness and beauty when drawing statistical charts. (Don't take an examination of fan-shaped statistical charts, and the requirements for drawing statistical charts should not be too high.

8. solve the problem.

(1) By reviewing simple application problems of integers, decimals, fractions and percentages (including simple fractional engineering problems, interest and tax payment problems), we can further master the structure of simple application problems, and correctly choose solutions according to the meaning of four operations and the quantitative relationship in the problems. You can fill in the mathematical information that should be collected to solve a mathematical problem.

(2) Further master the general steps of solving compound application problems of integers, decimals, fractions and percentages, and focus on the methods of analyzing the quantitative relations in problems. The presentation forms of application questions are diversified. In addition to text narration, forms such as tables, pictures and dialogues can also be designed. Students should be allowed to answer some questions with redundant conditions or openness (the conditions are open, the questions are open, the problem-solving strategies are open, and the answers are not unique). ) adapted from textbooks to provide students with opportunities for independent exploration. Integer and decimal application questions shall not exceed three steps at most, and fractional and percentage application questions shall not exceed two steps (comprehensive formula or step-by-step formula is allowed. )。

(3) Use equations to solve application problems (the restrictions of steps are the same as those of arithmetic solution, and the unknowns are generally set directly). Further understand the relationship and difference between solving application problems with equations and arithmetic methods. Will choose a simple solution according to the specific situation of the topic.

(4) Understand the relationship between average score and proportional distribution, and use the knowledge of ratio to solve the application problem of proportional distribution. Such as water, electricity, dividends.

(5) I can use the knowledge of proportion to solve the problem of easy application of positive and negative proportions.

(6) Using the preliminary knowledge of geometry, we can establish a mathematical model (related to length, area, volume or volume) and answer some simple practical questions (applying a formula is only a one-step calculation).