Phase I (1 ~ 3), Phase II (4 ~ 6) and Phase III (7 ~ 9)

Knowledge and skills ● Experience the process of abstracting numbers from daily life, and know numbers, decimals, simple fractions and common quantities within thousands of miles; Understand the meaning of four operations and master the necessary operation skills (including estimation).

Experience the process of intuitive understanding of simple geometry and plane graphics, understand simple geometry and plane graphics, feel the phenomena of translation, rotation and symmetry, initially describe the relative position of objects, and acquire the skills of preliminary measurement (including estimation), map recognition and drawing.

● Experience in data collection, sorting, description and analysis, and master some simple data processing skills; The initial sense of uncertainty

● Experience the process of abstracting the relationship between numbers and simple numbers from real life, know the numbers within 100 million, understand the meanings of fractions, percentages and negative numbers, and master the necessary operation skills (including estimation); To explore the hidden laws in a given thing, a simple quantitative relationship can be expressed by a formula and a simple equation can be solved.

By exploring the relationship between the shape, size, movement, position and figure of an object, I learned the basic characteristics of simple geometry and plane figure, transformed simple figure, preliminarily determined the position of the object, and developed skills such as measurement (including estimation), map recognition and drawing.

● Experience the process of collecting, sorting, describing and analyzing data, and master some data processing skills; Experience the equal possibility of events and the fairness of game rules, and you can calculate the possibility of some simple events.

● Go through the process of abstracting symbols from specific situations and know rational numbers, real numbers, algebraic expressions, equations, inequalities and functions; Master the necessary calculation (including estimation) skills; Exploring the quantitative relationship and changing law in specific problems can be described by algebra, equations, inequalities and functions.

Experience the process of exploring the basic properties, transformation and positional relationship of objects and figures, master the basic properties of triangles, quadrilaterals and circles, as well as the basic properties of translation, rotation, axial symmetry and similarity, initially understand projections and views, and master basic skills such as map reading and drawing; Knowing the necessity of proof can prove the basic properties of triangles and quadrangles and master the basic reasoning skills.

● Engaged in the activities of collecting, describing, analyzing data, making judgments and communicating, feeling the necessity of sampling, understanding the idea of using samples to estimate the population, and mastering the necessary data processing skills; If we further enrich the understanding of probability and know the relationship between frequency and probability, we will calculate the probability of some events.

Mathematical thinking ● Be able to use life experience to explain relevant digital information, and initially learn to describe simple phenomena in the real world with specific numbers.

● Develop the concept of space in the process of exploring the shape, size, positional relationship and movement of simple objects and figures.

● With the help of the teacher, initially learn to select useful information for simple induction and analogy.

● Be able to think simply and methodically in the process of solving problems.

● Be able to reasonably explain the digital information in real life, and describe and solve simple problems in the real world with numbers, letters and charts.

● Further develop the concept of space in the process of exploring the position relationship of objects, the characteristics of graphics, the transformation of graphics and the design of patterns.

● Be able to collect useful information according to the needs of solving problems, conduct induction, analogy and speculation, and develop initial rational reasoning ability.

● In the process of solving problems, be able to think methodically and make a convincing explanation for the rationality of the conclusion.

● Be able to reasonably explain and infer large digital information in specific situations, and describe the relationship between things with algebraic expressions, equations, inequalities and functions.

● In the process of exploring the essence of graphics, the transformation of graphics and the mutual transformation between plane graphics and space geometry, the concept of space is initially established and geometric intuition is developed.

● Ability to collect, select and process mathematical information, and make reasonable inferences or bold guesses.

● Some mathematical conjectures can be tested by examples, so as to increase the credibility of conjectures or turn over conjectures.

● Understand the necessity of proof and develop the preliminary deductive reasoning ability.

Solve problems ● Be able to find and ask simple math problems from daily life under the guidance of teachers.

There are different solutions to understand the same problem.

● Experience in solving problems in cooperation with peers.

● Initially learn to express the general process and results of solving problems.

● Be able to find and put forward simple mathematical problems from real life.

● Be able to explore effective methods to solve problems and try to find other methods.

● Can solve problems with the help of a calculator.

● Initially learn to cooperate with others in problem-solving activities.

Can express the process of solving problems and try to explain the results.

● Have the consciousness of reviewing and analyzing the problem-solving process.

● Be able to find and put forward mathematical problems in combination with specific situations.

Try to find solutions to problems from different angles, and effectively solve problems, and try to evaluate the differences between different methods.

● Understand the importance of cooperation with others in solving problems.

● Be able to clearly express the problem-solving process with words, letters or charts, and explain the rationality of the results.

● Gain experience in solving problems through reflection on the process of solving problems.

Emotion and attitude ● With the encouragement and help of others, I am curious about some math-related things around me and can actively participate in vivid and direct math activities.

With the encouragement and help of others, I can overcome some difficulties in math activities, gain successful experience, and have the confidence to learn math well.

Understand that some phenomena can be described by numbers and shapes, and feel the close connection between mathematics and daily life.

Experience the process of learning mathematics such as observation, operation and induction, and feel the rationality of mathematical thinking process.

● Under the guidance of others, be able to find mistakes in mathematics activities and correct them in time.

I am curious about some things related to mathematics in the surrounding environment and can actively participate in mathematics activities organized by teachers.

With the encouragement and guidance of others, I can actively overcome the difficulties encountered in mathematics activities, have successful experience in overcoming difficulties and using knowledge to solve problems, have a certain grasp of whether the results I get are correct, and believe that I can make continuous progress in my study.

● Experiencing mathematics is closely related to daily life. I realize that many practical problems can be solved by mathematical methods and expressed and communicated in mathematical language.

Through observation, operation, induction, analogy, reasoning and other mathematical activities, we can experience the exploration and challenge of mathematical problems and feel the order of mathematical thinking process and the certainty of mathematical conclusions.

● Be conscious of asking questions about places you don't understand or different viewpoints, be willing to discuss mathematical problems, and correct mistakes in time when found.

● Willing to contact with mathematical information in the social environment, willing to talk about some mathematical topics, and able to play an active role in mathematical activities.

Dare to face the difficulties in mathematics activities, have successful experience in overcoming difficulties independently and solving problems with knowledge, and have confidence in learning mathematics well.

Experiencing numbers, symbols and graphics is an important means to effectively describe the real world. We realize that mathematics is an important tool to solve practical problems and communicate, and understand the role of mathematics in promoting social progress and developing human rational spirit.

Knowing that mathematical conjecture can be obtained through observation, experiment, induction, analogy and reasoning, experiencing mathematical activities is full of exploration and creativity, and feeling the necessity of proof, the rigor of proof process and the certainty of conclusion.

On the basis of independent thinking, actively participate in the discussion of mathematical problems, dare to express their own views, respect and understand the opinions of others; Can benefit from communication.