When solving mathematical problems, according to the background and possibility of the problem, the problem of numbers is borrowed.

Help shape to observe, shape problems, think with numbers, and adopt this "combination of numbers and shapes"

Solving problems, we call it "the thinking method of combining numbers and shapes"

Its main characteristics: number? Shape? Solve problems; Or shape? Count? Problem solved. also

In other words, there are two ways to deal with problems: "helping numbers with shapes" and "shaping them with numbers".

Now changing ideas, changing ideas. The basic idea of the combination of numbers and shapes is: according to numbers

Structural characteristics, construct corresponding geometric figures, and use the characteristics and laws of figures

Method to solve the problem of number; Or convert all or all formal information into algebraic information, weaken or

Eliminate the formal reasoning part, so that the formal problem to be solved can be transformed into the discussion of quantitative relationship.

But the combination of numbers and shapes is easy to make mistakes, so according to the characteristics of the topic, after finishing the topic,

I always tell my classmates that we should "not only read books, not only books, not only authority, not only eyes."

Eyes. At the same time, quoting Mr. Hua's poems in time shows that we should pay attention to the combination of numbers and shapes

What? "Numbers are interdependent, how can you split in two? When counting missing shapes, there is no intuition and no shape.

Time is hard to be nuanced. Numbers and shapes are well combined, and everything is separated. Geometric algebra unification

Body, always separated from Mo. "

Let me talk about how to combine the contents of the five modules required by the People's Education Edition B.

Cultivate students' ability to combine numbers with shapes.

Compulsory (1) Chapter 1 Set: If it is an abstract set, venn diagram is often used, if it is a number.

Set the common number axis, if it is the common coordinate system of the point set, concretize the abstract problem.

Auxiliary number

Chapter 2 Functions: The first function and the second function are familiar to students. Through this chapter,

Learn the idea of further strengthening the combination of numbers and shapes, and stand out through the image of functions and the five properties of functions (definition range, value range, monotonicity, parity and periodicity). get through

The image of the function further clarifies that the root of the equation, that is, the zero point of the function, is the image and seat of the function.

The intersection of axes.

The third chapter, when studying the function of reference, right and power, we should remember their images in order to solve problems. Besides,

Transcendental inequalities often appear in practice, and the combination of numbers and shapes is often used to solve transcendental equation inequalities.

Methods, here we have to understand that under the idea of combining numbers with shapes, the methods are different and feasible.

Operability, personal memory and thoughts are universal and permeate every corner of every chapter.

Fall down. For example, the textbook P 13 1 First.

8 questions, P 132 question 7, all need to be drawn and said.

Ming.

Compulsory (2) The first chapter is a preliminary study of solid geometry, which is mainly intuitive through ordinary geometry.

Confirm the spatial position relationship, and implement it in the measurement calculation, and further use logical reasoning.

The relationship between points, lines and surfaces. From concrete to abstract, it conforms to human cognitive law, just like

Children play with toys first, and then break them into eight pieces to understand their mechanism.

The second chapter is plane analytic geometry. Lines and circles are the best combination of numbers and shapes.

Point, because the circle has good geometric properties, is both a central symmetric figure and an axisymmetric figure.

Shape, so the combination of number and shape is often used to solve the problem of circle.

Compulsory (3) The first chapter is the preliminary algorithm, which is represented by block diagram and written language.

Graphic language to express, intuitive and concise, a picture is worth a thousand words. This reminds me of ince.

Tan, when he gave a speech, he used thousands of words of speeches and paper only the size of a palm to draw charts.

Display, thus strengthening memory. This shows how important the diagram is.

The second chapter is statistics, which uses stem leaf diagram and frequency distribution histogram to represent the characteristics of data, and uses

Scatter chart and regression line are the classic 4 norms of the combination of numbers and shapes that represent the correlation degree of two variables.

The third chapter is probability, and it is easy to understand to explain Wang's reprimand with Westergue. Classic

In the probability model, the coordinate system is used to find the basic event part, such as P 1 13 cases.

5. Find the foundation with the tree diagram

Total number of events, such as P 1 14 cases.

6. Geometric probability is inseparable from graphics, no matter the area ratio,

The geometric probability of volume ratio or length ratio should be calculated graphically.

Compulsory (4) Chapter 1, trigonometric function lines and triangles in trigonometric function unit circle.

The image of function is often used to solve problems.

Chapter 2 Plane vector is the bridge between geometry, algebra and triangle, so this chapter is always

Explain related algorithms and operation rules around graphics.

Compulsory (5) Chapter 1 To solve the triangle, we must grasp the triangle and analyze the quantitative relationship.

In order to make good use of the knowledge of sine and cosine theorem and trigonometric function.

Chapter 2: Sequence is a special function, and arithmetic progression's general term formula is a linear function.

Number, which represents an isolated point on the image of a linear function. The sum formula of the first few terms is a quadratic function.

It represents an isolated point on the quadratic function image, and the general term formula of geometric series is non-zero.

The product of a constant and an exponential function, whose image is the curve of an exponential function image. Chapter III Inequality: The derivation of mean inequality is proved by geometry, and at the same time, the mean value is used.

Value inequality, with the help of the image of double hook function, further strengthens its application, and one-dimensional quadratic inequality with the help of function.

Several images to illustrate: "Find the middle less than zero and the two sides greater than zero." Linear programs are our reinforcement numbers.

Good materials with combination of shape and shape should be accurately drawn, feasible areas should be found, and graphics should be used well.

In short, in the five modules of the compulsory course (new textbook), each chapter is permeated with the idea of combining numbers with shapes, and also

It requires us to further summarize this way of thinking, find out the rules and points for attention, and strengthen the combination of numbers and shapes.

It also strengthens the interaction between the left and right brains and sets off a "brain storm", which is conducive to the cultivation of creative thinking and innovation ability.

Talent cultivation.