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1、“平面向量数量积的物理背景及其含义”说课稿尊敬的各位评委，各位老师大家好，我是来自项城市一高的王瑞琪。今天，我说课的题目是 平面向量数量积的物理背景及其含义，敬请各位老师予以指导。平面向量数量积的物理背景及其含义是新课标人教A版数学必修 4第二章第四节第一课时的内容。下面，我从背景分析、教学目标设计、课堂结构设计、教学媒体设计、教学过程设计及教学评价设计六个方面对本节课的思考进行说明。一、背景分析1、学习任务分析平面向量的数量积是继向量的线性运算之后的又一重要运算，也是高中数学的一个重要概念，在数学、物理等学科中应用十分广泛。本节内容教材共安排两课时，其中第一课时主要研究数量积的概念，第二课时
2、主要研究数量积的坐标运算，本节课是第一课时。本节课的主要学习任务是通过物理中“功”的事例抽象出平面向量数量积的概念，在此基础上探究数量积的性质，使学生体会类比的思想方法，进一步培养学生的抽象概括和推理论证的能力。其中数量积的概念既是对物理背景的抽象，又是研究性质的基础。同时也因为在这个概念中，既有长度又有角度，既有形又有数，是代数、几何与三角的最佳结合点，不仅应用广泛，而且很好的体现了数形结合的数学思想，使得数量积的概念成为本节课的核心概念，自然也是本节课教学的重点。2、学生情况分析学生在学习本节内容之前，已熟知了实数的运算体系，掌握了向量的概念及其线性运算，具备了功等物理知识，并且初步体会了
3、研究向量运算的一般方法：即先由特殊模型（主要是物理模型）抽象出概念，然后再从概念出发，在与实数运算类比的基础上研究性质和运算律。这为学生学习数量积做了很好的铺垫，使学生倍感亲切。但也正是这些干扰了学生对数量积概念的理解，一方面，相对于线性运算而言，数量积的结果发生了本质的变化，两个有形有数的向量经过数量积运算后，形却消失了，学生对这一点是很难接受的；另一方面，由于受实数乘法运算的影响，也会造成学生对数量积理解上的偏差，特别是对性质的理解。因而本节课教学的难点数量积的概念。二、教学目标设计普通高中数学课程标准（实验）对本节课的要求有以下三条：（1）通过物理中“功”等事例，理解平面向量数量积的含义
4、及其物理意义。（2）体会平面向量的数量积与向量投影的关系。（3）能用运数量积表示两个向量的夹角，会用数量积判断两个平面向量的垂直关系。从以上的背景分析可以看出，数量积的概念既是本节课的重点，也是难点。为了突破这一难点，首先无论是在概念的引入还是应用过程中，物理中“功”的实例都发挥了重要作用。其次，作为数量积概念延伸的性质和运算律，不仅能够使学生更加全面深刻地理解概念，同时也是进行相关计算和判断的理论依据。最后，无论是数量积的性质还是运算律，都希望学生在类比的基础上，通过主动探究来发现，因而对培养学生的抽象概括能力、推理论证能力和类比思想都无疑是很好的载体。综上所述，结合“课标”要求和学生实际，
5、我将本节课的教学目标定为：1、了解平面向量数量积的物理背景，理解数量积的含义及其物理意义；2、体会平面向量的数量积与向量投影的关系，掌握数量积的性质，并能运用性质进行相关的运算和判断；文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编
6、码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T
7、5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7
8、 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文
9、档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A1
10、0T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5
11、F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J13、体会类比的数学思想和方法，进一步培养学生抽象概括、推理论证的能力。三、课堂结
12、构设计本节课从总体上讲是一节概念教学，依据数学课程改革应关注知识的发生和发展过程的理念，结合本节课的知识的逻辑关系，我按照以下顺序安排本节课的教学：即先从数学和物理两个角度创设问题情景，通过归纳和抽象得到数量积的概念，在此基础上研究数量积的性质，使学生进一步加深对概念的理解，然后通过例题和练习使学生巩固概念，加深印象，最后通过课堂小结提高学生认识，形成知识体系。四、教学媒体设计文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F
13、7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1
14、文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A
15、10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P
16、5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2
17、J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M
18、8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L
19、7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1和“大纲”教材相比，“课标”教材在本节课的内容安排上，虽然将向量的夹角在“平面向量基本定理”一节提前做了介绍，但却将原来分两节课完成的内容合并成一节，相比较而言本节课的教学任务加重了许多。为了保证教学任务的完成，顺利实现本节课的教学目标，考虑到本节课的实际特点，在教学媒体的使用上，我的设想主要有以下两点：1、制作高效实用的电脑多媒体课件，主要作用是改变相关内容的呈现方式，以此来节约课时，增加课堂容量。2、设计科学合理的板书，一方面使学生加深对主要知识的印象，另一方面使学生清楚本节
20、内容知识间的逻辑关系，形成知识网络。五、教学过程设计课标指出：数学教学过程是教师引导学生进行学习活动的过程，是教师和学生间互动的过程，是师生共同发展的过程。为有序、有效地进行教学，本节课我主要安排以下四个活动：活动一：创设问题情景，激发学习兴趣文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A1
21、0T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5
22、F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J
23、1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8
24、A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7
25、P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M
26、2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1正如教材主编寄语所言
27、，数学是自然的，而不是强加于人的。平面向量的数量积这一重要概念，和向量的线性运算一样，也有其数学背景和物理背景，为了体现这一点，我特意设计了物理学中一物体在力F 的作用下产生位移S，力 F所做的功 W=|F|S|cos，并分析，力做功的公式中涉及到哪些量？猜想：功可以看成力与位移之间进行的一种运算的结果。这样设计的意图在于使学生了解数量积的物理背景，让学生知道，我们研究数量积绝不仅仅是为了数学自身的完善，而是有其客观背景和现实意义的，从而产生了进一步研究这种新运算的愿望。同时，也为抽象数量积的概念做好铺垫。活动二：探究数量积的含义1、概念的抽象在分析“功”的计算公式的基础上提出问题1 问题 1
28、：你能用文字语言来表述功的计算公式吗?如果我们将公式中的力与位移推广到一般向量，其结果又该如何表述？学生通过思考不难回答：功是力与位移的大小及其夹角余弦的乘积；两个向量的大小及其夹角余弦的乘积。这样，学生事实上已经得到数量积概念的文字表述了，在此基础上，我进一步明晰数量积的概念。（视频）2、概念的明晰已知两个非零向量与，它们的夹角为，我们把数量 cos叫做与的数量积（或内积），记作：，即：=cos在强调记法和“规定”后，为了让学生进一步认识这一概念，提出问题 2 问题 2：向量的数量积运算与线性运算的结果有什么不同？影响数量积大小的因素有哪些？并完成下表：文档编码:CT6W2M8A10T5 H
29、M8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA
30、2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码
31、:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5
32、 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7
33、ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档
34、编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10
35、T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1角的范围090=900180的符号通过此环节不仅使学生认识到数量积的结果与线性运算的结果有着本质的不同，而且认识到向量的夹角是决定数量积结果的重要因素，为下面更好地理解数量积的性质做好铺垫。（视频）3、探究数量积的几何意义这个问题教材是这样安排的：在给出向量数量积的概念后，只介绍了向量投影的定义，直到
36、讲完例 1 后，为了证明运算律的第三条才直接以结论的形式呈现给学生，我觉得这样安排似乎不太自然，还不如在给出向量投影的概念后，直接由学生自己归纳得出，所以做了调整。为此，我首先给出给出向量投影的概念，然后提出问题 3。如图，我们把cos（cos）叫做向量在方向上（在方向上）的投影，记做：OB1=cos问题 3：数量积的几何意义是什么？这样做不仅让学生从“形”的角度重新认识数量积的概念，从中体会数量积与向量投影的关系，同时也更符合知识的连贯性。文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J
37、6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6
38、W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8
39、Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X
40、5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:C
41、T6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 H
42、M8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA
43、2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J14、研究数量积的物理意义数量积的概念是由物理中功的概念引出的，学习了数量积的概念后，学生就会明白功的数学本质就是力与位移的数量积。这样就回归到标题，数量积的物理背景也即问题 4 功的数学本质是什么？活动三：探究数量积的运算性质1、性质的发现教材中关于数量积的三条性质是以探究的形式出现的，为了很好地完成这一探究活动，我特意设计成填空形式。让学生分组做并讨论你所填的空有什么用途，在学生讨论交流的基础上，教师进一步明晰数
44、量积的性质，然后再由学生利用数量积的定义给予证明，完成探究活动。2、明晰数量积的性质这样设计体现了教师只是教学活动的引领者，而学生才是学习活动的主体，让学生成为学习的研究者，不断地体验到成功的喜悦，激发学生参与学习活动的热情，不仅使学生获得了知识，更培养了学生由一般到特殊的思维品质。（视频）应用与提高文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P
45、5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2
46、J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M
47、8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L
48、7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6
49、M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W
50、2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q3L7P5F7 ZA2X5J6M2J1文档编码:CT6W2M8A10T5 HM8Q