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1. Preliminary algorithm

The meaning of (1) algorithm, program block diagram.

(1) by analyzing the process and steps to solve specific problems (such as solving binary linear equations, etc.). ), we can understand the idea and significance of the algorithm.

② Through imitation, operation and exploration, experience the process of expressing and solving problems by designing program block diagram. In the process of solving specific problems (such as solving ternary linear equations, etc. ), understand the three basic logical structures of program block diagram: sequence, conditional branch and loop.

(2) Basic algorithm statements: Through the process of transforming the program block diagram of specific problems into program statements, we can understand several basic algorithm statements-input statements, output statements, assignment statements, conditional statements and loop statements, and further understand the basic idea of the algorithm.

(3) By reading the algorithm cases in ancient mathematics in China, we can understand the contribution of ancient mathematics in China to the development of mathematics in the world.

2. Statistics

(1) random sampling

(1) can raise some valuable statistical questions from real life or other disciplines.

② Understand the necessity and importance of random sampling in combination with specific practical problem situations.

③ In the process of solving statistical problems, learn to use simple random sampling method to extract samples from the population; Through case study, we can understand the methods of stratified sampling and systematic sampling.

④ Data can be collected through experiments, consulting materials and designing questionnaires.

(2) estimate the population with samples

① Understand the significance and function of distribution through examples. In the process of representing sample data, learn to list the frequency distribution table, draw the frequency distribution histogram, frequency line diagram and stem leaf diagram (see example 1), and understand their respective characteristics.

② Understand the significance and function of standard deviation of sample data through examples, and learn to calculate the standard deviation of data.

③ We can reasonably select samples according to the needs of practical problems, extract basic numerical features (such as mean and standard deviation) from sample data, and make reasonable explanations.

④ In the process of solving statistical problems, we will further understand the idea of estimating the population with samples. We will estimate the population distribution with the frequency distribution of samples and estimate the basic digital characteristics of the population with the basic digital characteristics of samples. Understand the randomness and numerical characteristics of sample frequency distribution.

⑤ We will use the basic method of random sampling and the idea of sample estimation to solve some simple practical problems; Through the analysis of data, we can provide some basis for rational decision-making, understand the role of statistics and understand the difference between statistical thinking and deterministic thinking.

⑥ Form a preliminary evaluation consciousness of data processing.

(3) Correlation of variables

① Make a scatter plot by collecting the data of two related variables in the real question, and use the scatter plot to intuitively understand the correlation between variables.

② Experiencing the process of describing the linear correlation of two variables with different estimation methods. Knowing the idea of least square method, we can establish a linear regression equation according to the given coefficient formula of linear regression equation (see Example 2).

3. Possibility

(1) Understand the uncertainty and frequency stability of random events in specific situations, and further understand the meaning of probability and the difference between frequency and probability.

(2) Understand two mutually exclusive events's probability addition formulas through examples.

(3) Through examples, we can understand the classical probability and its probability calculation formula, and use enumeration method to calculate the number of basic events and the probability of some random events.

(4) Knowing the meaning of random numbers, we can use simulation methods (including random numbers generated by calculators for simulation) to estimate the probability and get a preliminary understanding of the meaning of geometric probability (see Example 3).

(5) By reading the materials, we can understand the cognitive process of human beings to random phenomena.