高一数学教案大全，接下来随着小编一起来看看吧!(组图)(2)

教学建议

(1）根据教科书，关于它的定义是形式化的定义，即解析特征必须长得像，不能有区别，比如，等等。

(2）对基数的限制的理解和理解也是理解的重要部分。如果可能的话，让学生自己学习基数和索引的限制，老师将提供补充或使用具体的例子来说明，因为对这个条件的理解不仅关系到对的理解及其性质的分类和讨论，也关系到后面对基数的理解学习对数函数，一定要真正了解它的由来。

对于图像的绘制，虽然采用了在列表中绘制点的方法，但在具体的教学中，要避免点之前的盲列表计算，避免点的盲连。表中应列出要点。将点连接到合适的地方，所以在追踪列表中的点之前，应该先对函数的性质做一些简单的讨论，对要绘制的图像的存在范围、一般特征和变化趋势有一个大致的了解。绘制，然后以此为指导。列出计算，跟踪点以获取图像。

教学设计实例

主题

教学目标

1.理解的定义、形象的初步把握、本质及其简单应用。

2.通过图像和属性的学习，培养学生观察、分析、归纳的能力，进一步体验数形结合的思维方法。

3.通过正确的研究，学生可以掌握函数研究的基本方法，激发学习兴趣。

教学重点和难点

重点是理解定义，把握形象，把握本质。

难点在于理解基数对函数值的影响。

教学设备

投影仪

教学方法

鼓舞人心的讨论研究风格

教学过程

一个。介绍一个新班级

我们学习了指数计算，在此基础上，今天我们要学习一类新的常用函数—————————。

1.6。 （在黑板上写字）

之所以引入这种类型的功能，是因为它是现实生活中的需要。例如，让我们看看以下问题：

问题1：当某种细胞分裂时，一个分裂成两个，两个分裂成四个，...这样的一个细胞分裂几次后，分裂的次数和得到的细胞数形成一个函数关系，你能写出和之间的函数关系吗？

学生回答： 和 之间的关系可以表示为。

问题 2：有一根 1 米长的绳子。第一次砍是绳长的一半，第二次砍是剩下绳子的一半....第二次砍后绳子的剩余长度是米，试着写出和之间的函数关系。

学生的回答：.

在上面的两个例子中，我们可以看到这两个函数与我们之前研究的函数不同。从求幂的形式来看，自变量都在指数的位置，那么形式就是这样一个函数被调用。

一个。概念（在黑板上）

1.定义：调用窗体的函数。 （在黑板上写字）

给出定义后，老师会对定义做一些解释。

2.一些笔记（写在黑板上）

(1） 关于 :

老师先问一个问题：为什么底数要大于0而不等于1？ （如果学生觉得困难，可以把问题分解成如果有问题会发生什么？例如，此时对应的函数值在实数范围内不存在。

如果它没有意义，如果那么无论取什么值，它总是1，没有必要研究它。为避免上述各种情况的发生，特规定和。

(2）关于定义域（板书）

老师引导学生复习指标范围，发现指标可以合理。此时，老师可以指出，当指数是一个无理数时，它也是某个实数。对于无理指数幂，学习到的有理指数的性质和运算规则是适用的，所以指数范围扩大到实数范围，所以定义域是。扩展的另一个原因是为了使其更具代表性和实用性。

(3）判断是不是（黑板上）

刚才我们分别了解了midbase和exponent的要求。让我们从整体的角度来看待它。根据定义，我们知道是什么样的函数。看看下面的功能是不是。

(1）, (2）, (3）

(4）, (5） .

学生回答并说明原因。老师根据情况做了点评，指出只有(1）和(3）是肯定的，其中(3）可以写成索引图。

最后提醒学生，定义是形式化的定义，形式上一定要完全一样，然后再将问题引向更深层次。有了初步研究的定义领域和功能的性质，此时研究的关键是绘制其形象，可以进行详细总结。

3.电感性

是用什么方法画的。用列表追查，发现老师准备讲清楚性质，然后学生回答。

功能

1.定义域：

2.取值范围：

3. Parity：既不是奇函数也不是偶函数

4.截距：不在轴上，在轴上为1。

对于属性1和2，你可以把它们放在一起，问问它们起到什么作用。 （确定图像存在的大致位置）第3条也应证明。对于单调性，我建议找到一些特殊点。 ，先看看，再下结论。最后一个也是绘制引导函数图形的基础。 (The image is located above the axis and does not intersect the axis.)

On this basis, the teacher can guide the students to list and trace points. When picking points, students should also be reminded that because there is no symmetry, the value of should be positive or negative, and due to unclear monotonicity, the number of points should not be too small.

Here, the teacher can use the computer list to trace points and give ten sets of data, while the students list the points on their own, with at least six sets of data. When connecting the dots into a line, the students must be reminded of the changing trend of the image (when the smaller is, the closer the image is to the axis, the larger is, the faster the image rises), and a smooth curve is connected.

两个。 Image and Nature (Blackboard)

1. Image drawing method: list drawing point method under the guidance of nature.

2. Sketch:

After drawing the first image, ask students if they need to draw the second image?有代表性吗？ (The condition for the teacher to prompt the base number is and, the value can be divided into two paragraphs) Let the students understand that they need to draw the second one, you might as well take it as an example.

At this time, students should choose the method of drawing its image. Students should be made aware that list tracing is not the only method, and the method of image transformation is simpler. That is, = and the image are symmetric about the axis, and the image at this time already exists and has the conditions for transformation. Let the students do the symmetry by themselves, the teacher draws the picture with the help of the computer, and the image obtained in the same coordinate system.

Finally, ask students if they need to draw again. (There may be two possibilities. If the students think there is no need to draw anymore, they will ask the reason and ask them to tell the nature. If they think they still need to draw, the teacher can use the computer to draw pictures like this and compare them together, and then find the commonality. )

Since images are features of shapes, let’s first look at them from a geometric point of view. Teachers can make a table as follows:

If the students say that the above content is not complete, the teacher can appropriately put forward the observation angle for the students to describe, and then ask the students to translate the geometric characteristics into the properties of the function, that is, the description from the algebraic point of view, fill in the other part of the table Full.

After filling in, ask students to make another table following this example and fill in the corresponding content. In order to further sort out the properties, teachers can propose to classify from another angle and sort out the properties of functions.

3. nature.

(1） Regardless of the value, there is a definition domain of, and the value domain is, which is too late.

(2）, it is an increasing function in the domain of definition, when is a decreasing function.

(3） Hour,, Hour,

After the summary, students are especially reminded to remember the image of the function. With the image, the properties can be read out from the image.

三个。 Simple application (board writing)

1. Use monotonicity than size. (Writing on the blackboard)

After studying its concept, image and nature of a class of functions, the most important thing is to use it to solve some simple problems. First, let's look at the following questions.

Example 1. Compare the sizes of the following groups

(1） and; (2） and ;

(3） and 1. (writing on the blackboard)

First, let the students observe the characteristics of the two numbers. What are the similarities? The students point out that they have the same base but different exponents. According to this feature, what method should be used to compare their sizes? Let the students think about it and propose a method of constructing a function, that is, to treat these two numbers as the function value of a certain function, and use its monotonicity to compare the magnitude. Then take the (1） question as an example to give the answering process.

Solution: is an increasing function on, and

Finally, the teacher emphasizes that the process must write three sentences clearly:

(1） Construct a function and specify the monotonic interval of the function and the corresponding monotonicity.

(2） Comparison of the size of independent variables.

(3） The size comparison of function values.

The process of the last two questions is omitted. Students are required to imitate the (1）question) to describe the process.

Example 2. Compare the sizes of the following groups

(1） and; (2） and ;

(3） and. (Blackboard)

First let the students observe the difference between the number of groups in Example 2 and Example 1, and then think about the solution. Guide students to discover that it can be written as for (1）, so that it can be transformed into a problem with the same base, and then solved by the method in Example 1, it can be written as for (2）, can also be transformed into the same base Yes, and (3）The previous method is not applicable. Consider a new conversion method and let the students think about the solution. (The teacher can remind students that the function value is related to 1, and 1 can be used as a bridge)

Finally, the students say >1,.

After the solution, the teacher will summarize the method of comparing the size

(1） Method of Constructing Function: Numbers are characterized by the same base but different meanings (including those that can be converted to the same base)

(2） Bridging comparison method: Use a special number 1 or 0.

三个。 Consolidation exercises

Exercise: Compare the sizes of the following groups (writing on the blackboard)

(1） and (2） and ;

(3） and; (4） and. The answering process is omitted

四个。 Summary

1. The concept of

2. Image and nature of

3. Simple application

五个。 Blackboard design

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