新课标高中数学必修4教案12篇 高中数学选修4-4教案
下面是范文网小编收集的新课标高中数学必修4教案12篇 高中数学选修4-4教案，以供参考。
教学目标
(1)掌握 与 ( )型的绝对值不等式的解法.
(2)掌握 与 ( )型的绝对值不等式的解法.
(3)通过用数轴来表示含绝对值不等式的解集，培养学生数形结合的能力;
(4)通过将含绝对值的不等式同解变形为不含绝对值的不等式，培养学生化归的思想和转化的能力;
教学重点： 型的不等式的解法;
教学难点：利用绝对值的意义分析、解决问题.
教学过程设计
教师活动
学生活动
设计意图
一、导入新课
【提问】正数的绝对值什么？负数的绝对值是什么？零的绝对值是什么？举例说明？
【概括】
口答
绝对值的概念是解?与?（?）型绝对值不等值的概念，为解这种类型的绝对值不等式做好铺垫．
二、新课
【导入】2的绝对值等于几？－2的绝对值等于几？绝对值等于2的数是谁？在数轴上表示出来．
【讲述】求绝对值等于2的数可以用方程来表示，这样的方程叫做绝对值方程．显然，它的解有二个，一个是2，另一个是－2．
【提问】如何解绝对值方程?．
【设问】解绝对值不等式?，由绝对值的意义你能在数轴上画出它的解吗？这个绝对值不等式的解集怎样表示？
【讲述】根据绝对值的意义，由右面的数轴可以看出，不等式?的解集就是表示数轴上到原点的距离小于2的点的集合．
【设问】解绝对值不等式?，由绝对值的意义你能在数轴上画出它的解吗？这个绝对值不等式的解集怎样表示？
【质疑】?的解集有几部分？为什么?也是它的解集？
【讲述】?这个集合中的数都比－2小，从数轴上可以明显看出它们的绝对值都比2大，所以?是?解集的一部分．在解?时容易出现只求出?这部分解集，而丢掉?这部解集的错误．
【练习】解下列不等式：
（1）?；
（2）
【设问】如果在?中的?，也就是?怎样解？
【点拨】可以把?看成一个整体，也就是把?看成?，按照?的解法来解．
所以，原不等式的解集是
【设问】如果?中的?是?，也就是?怎样解？
【点拨】可以把?看成一个整体，也就是把?看成?，按照?的解法来解．
，或?，
由?得
由?得
所以，原不等式的解集是
口答．画出数轴后在数轴上表示绝对值等于2的数．
画出数轴，思考答案
不等式?的解集表示为
画出数轴
思考答案
不等式?的解集为
或表示为?，或
笔答
（1）
（2）?，或
笔答
笔答
根据绝对值的意义自然引出绝对值方程?（?）的解法．
由浅入深，循序渐进，在?型绝对值方程的基础上引出（?）型绝对值方程的解法．
针对解?（?）绝对值不等式学生常出现的情况，运用数轴质疑、解惑．
落实会正确解出?与?（?）绝对值不等式的教学目标．
在将?看成一个整体的关键处点拨、启发，使学生主动地进行练习．
继续强化将?看成一个整体继续强化解?不等式时不要犯丢掉这部分解的错误．
三、课堂练习
解下列不等式：
（1）?；
（2）
笔答
（1）?；
（2）
检查教学目标落实情况．
四、小结
的解集是?；?的解集是
解?绝对值不等式注意不要丢掉?这部分解集．
或?型的绝对值不等式，若把?看成一个整体一个字母，就可以归结为?或?型绝对值不等式的解法．
五、作业
1．阅读课本?含绝对值不等式解法．
2．习题?2、3、4
课堂教学设计说明
1.抓住解 型绝对值不等式的关键是绝对值的意义，为此首先通过复习让学生掌握好绝对值的意义，为解绝对值不等式打下牢固的基础.
2.在解 与 绝对值不等式中的关键处设问、质疑、点拨，让学生融会贯通的掌握它们解法之间的内在联系，以达到提高学生解题能力的目的.
3.针对学生解 ( )绝对值不等式容易出现丢掉 这部分解集的错误，在教学中应根据绝对值的意义从数轴进行突破，并在练习中纠正这个错误，以提高学生的运算能力.
【学习目标】
知识与技能：理解两角差的余弦公式的推导过程及其结构特征并能灵活运用。
过程与方法：应用已学知识和方法思考问题，分析问题，解决问题的能力。
情感态度价值观： 通过公式推导引导学生发现数学规律，培养学生的创新意识和学习数学的兴趣。
.【重点】通过探索得到两角差的余弦公式以及公式的灵活运用
【难点】两角差余弦公式的推导过程
预习自学案
一、知识链接
1. 写出 的三角函数线 ：
2. 向量 , 的数量积,
①定义：
②坐标运算法则：
3. ， ，那么 是否等于 呢?
下面我们就探讨两角差的余弦公式
二、教材导读
1.、两角差的余弦公式的推导思路
如图,建立单位圆O
(1)利用单位圆上的三角函数线
设
则
又OM=OB+BM
=OB+CP
=OA_____ +AP_____
=
从而得到两角差的余弦公式：
____________________________________
(2)利用两点间距离公式
如图，角 的终边与单位圆交于A( )
角 的终边与单位圆交于B( )
角 的终边与单位圆交于P( )
点T( )
AB与PT关系如何?
从而得到两角差的余弦公式：
____________________________________
(3) 利用平面向量的知识
用 表示向量 ，
=( , ) =( , )
则 . =
设 与 的夹角为
①当 时:
=
从而得出
②当 时显然此时 已经不是向量 的夹角，在 范围内，是向量夹角的补角.我们设夹角为 ，则 + =
此时 =
从而得出
2、两角差的余弦公式
____________________________
三、预习检测
1. 利用余弦公式计算 的值.
2. 怎样求 的值
你的疑惑是什么?
________________________________________________________
______________________________________________________
探究案
例1. 利用差角余弦公式求 的值.
例2.已知 ， 是第三象限角，求 的值.
训练案
一、 基础训练题
1、
2、 ???????????
3、
二、综合题
--------------------------------------------------
新课标高中数学必修5教案
教学目标
(1)掌握一元二次不等式的解法;
(2)知道一元二次不等式可以转化为一元一次不等式组;
(3)了解简单的分式不等式的解法;
(4)能利用二次函数与一元二次方程来求解一元二次不等式，理解它们三者之间的内在联系;
(5)能够进行较简单的分类讨论，借助于数轴的直观，求解简单的含字母的一元二次不等式;
(6)通过利用二次函数的图象来求解一元二次不等式的解集，培养学生的数形结合的数学思想;
(7)通过研究函数、方程与不等式之间的内在联系，使学生认识到事物是相互联系、相互转化的，树立辨证的世界观.
教学重点：一元二次不等式的解法;
教学难点：弄清一元二次不等式与一元二次方程、二次函数的关系.
教与学过程设计
第一课时
Ⅰ.设置情境
问题：
①解方程
②作函数 的图像
③解不等式
【置疑】在解决上述三问题的基础上分析，一元一次函数、一元一次方程、一元一次不等式之间的关系。能通过观察一次函数的图像求得一元一次不等式的解集吗?
【回答】函数图像与x轴的交点横坐标为方程的根，不等式 的解集为函数图像落在x轴上方部分对应的横坐标。能。
通过多媒体或其他载体给出下列表格。扼要讲解怎样通过观察一次函数的图像求得一元一次不等式的解集。注意色彩或彩色粉笔的运用
在这里我们发现一元一次方程，一次不等式与一次函数三者之间有着密切的联系。利用这种联系(集中反映在相应一次函数的图像上!)我们可以快速准确地求出一元一次不等式的解集，类似地，我们能不能将现在要求解的一元二次不等式与二次函数联系起来讨论找到其求解方法呢?
Ⅱ.探索与研究
我们现在就结合不等式 的求解来试一试。(师生共同活动用“特殊点法”而非课本上的“列表描点”的方法作出 的图像，然后请一位程度中下的同学写出相应一元二次方程及一元二次不等式的解集。)
【答】方程 的解集为
不等式 的解集为
【置疑】哪位同学还能写出 的解法?(请一程度差的同学回答)
【答】不等式 的解集为
我们通过二次函数 的图像，不仅求得了开始上课时我们还不知如何求解的那个第(5)小题 的解集，还求出了 的解集，可见利用二次函数的图像来解一元二次不等式是个十分有效的方法。
下面我们再对一般的一元二次不等式 与 来进行讨论。为简便起见，暂只考虑 的情形。请同学们思考下列问题：
如果相应的一元二次方程 分别有两实根、惟一实根，无实根的话，其对应的二次函数 的图像与x轴的位置关系如何?(提问程度较好的学生)
【答】二次函数 的图像开口向上且分别与x轴交于两点，一点及无交点。
现在请同学们观察表中的二次函数图，并写出相应一元二次不等式的解集。(通过多媒体或其他载体给出以下表格)
【答】 的解集依次是
的解集依次是
它是我们今后求解一元二次不等式的主要工具。应尽快将表中的结果记住。其关键就是抓住相应二次函数 的图像。
课本第19页上的例1.例2.例3.它们均是求解二次项系数 的一元二次不等式，却都没有给出相应二次函数的图像。其解答过程虽很简练，却不太直观。现在我们在课本预留的位置上分别给它们补上相应二次函数图像。
(教师巡视，重点关注程度稍差的同学。)
Ⅲ.演练反馈
1.解下列不等式：
(1) (2)
(3) (4)
2.若代数式 的值恒取非负实数，则实数x的取值范围是 。
3.解不等式
(1) (2)
参考答案：
1.(1) ;(2) ;(3) ;(4)R
2.
3.(1)
(2)当 或 时， ，当 时，
当 或 时， 。
Ⅳ.总结提炼
这节课我们学习了二次项系数 的一元二次不等式的解法，其关键是抓住相应二次函数的图像与x轴的交点，再对照课本第39页上表格中的结论给出所求一元二次不等式的解集。
(五)、课时作业
(P20.练习等3、4两题)
(六)、板书设计
第二课时
Ⅰ.设置情境
(通过讲评上一节课课后作业中出现的问题，复习利用“三个二次”间的关系求解一元二次不等式的主要操作过程。)
上节课我们只讨论了二次项系数 的一元二次不等式的求解问题。肯定有同学会问，那么二次项系数 的一元二次不等式如何来求解?咱们班上有谁能解答这个疑问呢?
Ⅱ.探索研究
(学生议论纷纷.有的说仍然利用二次函数的图像，有的说将二次项的系数变为正数后再求解，…….教师分别请持上述见解的学生代表进一步说明各自的见解.)
生甲：只要将课本第39页上表中的二次函数图像次依关于x轴翻转变成开口向下的抛物线，再根据可得的图像便可求得二次项系数 的一元二次不等式的解集.
生乙：我觉得先在不等式两边同乘以-1将二次项系数变为正数后直接运用上节课所学的方法求解就可以了.
师：首先，这两种见解都是合乎逻辑和可行的.不过按前一见解来操作的话，同学们则需再记住一张类似于第39页上的表格中的各结论.这不但加重了记忆负担，而且两表中的结论容易搞混导致错误.而按后一种见解来操作时则不存在这个问题，请同学们阅读第19页例4.
(待学生阅读完毕，教师再简要讲解一遍.)
[知识运用与解题研究]
由此例可知，对于二次项系数的一元二次不等式是将其通过同解变形化为 的一元二次不等式来求解的，因此只要掌握了上一节课所学过的方法。我们就能求
解任意一个一元二次不等式了，请同学们求解以下两不等式.(调两位程度中等的学生演板)
(1) (2)
(分别为课本P21习题1.5中1大题(2)、(4)两小题.教师讲评两位同学的解答，注意纠正表述方面存在的问题.)
训练二 可化为一元一次不等式组来求解的不等式.
目前我们熟悉了利用“三个二次”间的关系求解一元二次不等式的方法虽然对任意一元二次不等式都适用，但具体操作起来还是让我们感到有点麻烦.故在求解形如 (或 )的一元二次不等式时则根据(有理数)乘(除)运算的“符号法则”化为同学们更加熟悉的一元一次不等式组来求解.现在清同学们阅读课本P20上关于不等式 求解的内容并思考：原不等式的解集为什么是两个一次不等式组解集的并集?(待学生阅读完毕，请一程度较好，表达能力较强的学生回答该问题.)
【答】因为满足不等式组 或 的x都能使原不等式 成立，且反过来也是对的，故原不等式的解集是两个一元二次不等式组解集的并集.
这个回答说明了原不等式的解集A与两个一次不等式组解集的并集B是互为子集的关系，故它们必相等，现在请同学们求解以下各不等式.(调三位程度各异的学生演板.教师巡视，重点关注程度较差的学生).
(1) [P20练习中第1大题]
(2) [P20练习中第1大题]
(3) [P20练习中第2大题]
(老师扼要讲评三位同学的解答.尤其要注意纠正表述方面存在的问题.然后讲解P21例5).
例5 解不等式
因为(有理数)积与商运算的“符号法则”是一致的，故求解此类不等式时，也可像求解 (或 )之类的不等式一样，将其化为一元一次不等式组来求解。具体解答过程如下。
解：(略)
现在请同学们完成课本P21练习中第3、4两大题。
(等学生完成后教师给出答案，如有学生对不上答案，由其本人追查原因，自行纠正。)
[训练三]用“符号法则”解不等式的复式训练。
(通过多媒体或其他载体给出下列各题)
1.不等式 与 的解集相同此说法对吗?为什么[补充]
2.解下列不等式：
(1) [课本P22第8大题(2)小题]
(2) [补充]
(3) [课本P43第4大题(1)小题]
(4) [课本P43第5大题(1)小题]
(5) [补充]
(每题均先由学生说出解题思路，教师扼要板书求解过程)
参考答案：
1.不对。同 时前者无意义而后者却能成立，所以它们的解集是不同的。
2.(1)
(2)原不等式可化为： ，即
解集为 。
(3)原不等式可化为
解集为
(4)原不等式可化为 或
解集为
(5)原不等式可化为： 或 解集为
Ⅲ.总结提炼
这节课我们重点讲解了利用(有理数)乘除法的符号法则求解左式为若干一次因式的积或商而右式为0的不等式。值得注意的是，这一方法对符合上述形状的高次不等式也是有效的，同学们应掌握好这一方法。
(五)布置作业
(P22.2(2)、(4);4;5;6。)
(六)板书设计
新课标高中数学必修2教案
一、向量的概念
1、既有又有的量叫做向量。用有向线段表示向量时，有向线段的长度表示向量的，有向线段的箭头所指的方向表示向量的
2、叫做单位向量
3、的向量叫做平行向量，因为任一组平行向量都可以平移到同一条直线上，所以平行向量也叫做。零向量与任一向量平行
4、且的向量叫做相等向量
5、叫做相反向量
二、向量的表示方法：几何表示法、字母表示法、坐标表示法
三、向量的加减法及其坐标运算
四、实数与向量的乘积
定义：实数 λ 与向量 的积是一个向量，记作λ
五、平面向量基本定理
如果e1、e2是同一个平面内的两个不共线向量，那么对于这一平面内的任一向量a，有且只有一对实数λ1,λ2，使a=λ1e1+λ2e2 ,其中e1，e2叫基底
六、向量共线/平行的充要条件
七、非零向量垂直的充要条件
八、线段的定比分点
设是上的 两点，P是上_________的任意一点，则存在实数，使_______________，则为点P分有向线段所成的比，同时，称P为有向线段的定比分点
定比分点坐标公式及向量式
九、平面向量的数量积
(1)设两个非零向量a和b，作OA=a，OB=b，则∠AOB=θ叫a与b的夹角，其范围是[0，π]，|b|cosθ叫b在a上的投影
(2)|a||b|cosθ叫a与b的数量积，记作a·b，即 a·b=|a||b|cosθ
(3)平面向量的数量积的坐标表示
十、平移
典例解读
1、给出下列命题：①若|a|=|b|，则a=b;②若A，B，C，D是不共线的四点，则AB= DC是四边形ABCD为平行四边形的充要条件;③若a=b,b=c，则a=c;④a=b的充要条件是|a|=|b|且a∥b;⑤若a∥b,b∥c，则a∥c
其中，正确命题的序号是______
2、已知a,b方向相同，且|a|=3，|b|=7，则|2a-b|=____
3、若将向量a=(2，1)绕原点按逆时针方向旋转 得到向量b，则向量b的坐标为_____
4、下列算式中不正确的是( )
(A) AB+BC+CA=0 (B) AB-AC=BC
(C) 0·AB=0 (D)λ(μa)=(λμ)a
5、若向量a=(1,1),b=(1,-1),c=(-1,2)，则c=( )
、函数y=x2的图象按向量a=(2,1)平移后得到的图象的函数表达式为( )
(A)y=(x-2)2-1 (B)y=(x+2)2-1 (C)y=(x-2)2+1 (D)y=(x+2)2+1
7、平面直角坐标系中，O为坐标原点，已知两点A(3，1)，B(-1，3)，若点C满足OC=αOA+βOB，其中a、β∈R，且α+β=1,则点C的轨迹方程为( )
(A)3x+2y-11=0 (B)(x-1)2+(y-2)2=5
(C)2x-y=0 (D)x+2y-5=0
8、设P、Q是四边形ABCD对角线AC、BD中点，BC=a,DA=b，则 PQ=_________
9、已知A(5,-1) B(-1,7) C(1,2)，求△ABC中∠A平分线长
10、若向量a、b的坐标满足a+b=(-2,-1),a-b=(4,-3)，则a·b等于( )
(A)-5 (B)5 (C)7 (D)-1
11、若a、b、c是非零的平面向量，其中任意两个向量都不共线，则( )
(A)(a)2·(b)2=(a·b)2 (B)|a+b|>|a-b|
(C)(a·b)·c-(b·c)·a与b垂直 (D)(a·b)·c-(b·c)·a=0
12、设a=(1,0),b=(1,1)，且(a+λb)⊥b，则实数λ的值是( )
(A)2 (B)0 (C)1 (D)-1/2
16、利用向量证明：△ABC中，M为BC的中点，则 AB2+AC2=2(AM2+MB2)
17、在三角形ABC中， =(2，3)， =(1，k)，且三角形ABC的一个内角为直角，求实数k的值
18、已知△ABC中，A(2,-1)，B(3,2)，C(-3,-1)，BC边上的高为AD，求点D和向量
《化学1必修》新课标人教版教案
摘 ?要：本文以我自己（刚毕业的新教师）对新出炉不久的高中新课标实验教科书《化学1必修》为教材的任教经历为依据 ，从不同的角度来审视与思考新课改和《化学1必修》，提出自己的理解。
关键词：新课改实验；化学1；浅析；展望
一、引言
9月起，在广东、山东、宁夏、海南等4省（自治区），开始新课改实验，而我有幸在这时走上教坛，“走近新课程”。可以说是机遇与挑战并存，如何理解好新课改的理念，如何用好新教材，是我教学工作起步优劣的关键，是我以何种姿态站在新课改的浪潮的关键。下面，谈谈对普通高中课程标准实验教科书化学1必修（以下简称“化学1必修”）的一些理解和思考。
二、对化学1的浅析课本体现了鲜明的时代性与人文性
该课本中多次出现了与现代生活相关的图片，如：海水淡化工厂、检测尿糖用的试纸、煤气灶火焰、壮观的烟花、微机与手机芯片、三峡大坝、火箭升空、光纤、记忆合金等；体现人文性的如：危险化学品标志、沙里淘金原理、“白马非马”论、青铜奔马（马踏飞燕）、司母戊鼎、各种矿物、人面鱼纹条陶、万里长城、网络搜索、英汉对照等等，这些让学生能在耳濡目染中无形的潜移默化。同时都能很好的体现出编者的初衷——体现时代性与人文性。
突出“着眼于提高21世纪公民的科学素养”这一主题
本册课本所涉及的内容是作为21世纪中国公民所必备的化学知识的部分，是将原来高中三册化学课本里的部分知识有机的融为一体，显得贴切而自然，但其要求不高，与后续模块之间形成一定的梯度，如：“第一章：《从实验学化学》，介绍的一些实验基本方法、物质的量相关的知识等是贯穿于整个化学学科的一条主线，承上启下，抛砖引玉的作用，在后续课程中会加深与巩固的，不求一步到位。又如：第二章《化学物质及其变化》，从基本原理上揭示了化学物质及其变化的角度而引入分散系，胶体（以前高三内容）、离子反应、氧化还原反应等，及后面两章介绍的几种常见金属和非金属等，均是取材于实际的，与生活、社会有紧密的联系，让学生易于入手，能够解释生活中常见现象，有学以致用的成就感，对于过于复杂的理论知识不做过多的阐述……这些都是留有余地的，兼顾各类学生，是学生毕业与继续深造所必需的。
三、对教师教学的展望
当我手里拿着这本不足一百页（连附录共94页）的课本，要用一学期的课时来教授完，确实有点不自信，一种茫然之感（在网上化学论坛也看到不少一线化学教师也如此说过）油然而生……那么，究竟怎样面对新课本呢？在使用了化学1必修，我以为，我们教师可以从以下几个方面尝试：
1.自己身体力行，做好表率
从新课本不难看出，作为化学教师光具备化学专业相关的知识，只囿于化学领域，没有与任教学科相关的科学有较宽广的知识与技能，则很难高屋建瓴，厚积薄发，只能穷于一时的应付，难免会捉襟见肘，更不用说驾驭教材了！因此，化学教师必须积极进取，不断的充实新知识、新思想、新方法，时刻把自己摆在课改的行动架构之中，努力构建自己的`教学风格。对于那些营造宽松的教学环境、自由的讨论、画龙点睛、恰到好处的点拨等，看似是妙手偶得，实际上这些都是优秀教师综合素质的自然流露和体现。当有了学识、风格、经验、思想，具备了亲和力、感染力、影响力，有一种气质和魅力，自然会是当之无愧的好教师了。
2.从实际出发，培养学生终生学习的意识和能力
高中学生会接触到很多与化学有关的生活问题，教师在教学中要注意联系实际（教师平时积累的教学素材这时能够派上用场！），帮助学生拓宽视野，开阔思路，综合运用化学及其他学科的知识分析解决有关问题。教师应注意领会每个课程模块在课程中的地位、作用和教育价值，把握课程模块的内容特点，考虑学生的学习情况和具体的教学条件，采取有针对性的教学方式，优化教学策略，提高教学质量（化学教师要认真学习化学新课标，理解其实质！并多参加各种新课改的研讨会议，多与其他教师讨论、交流）。在教学中，教师要结合课程内容，充分利用当地各种条件，组织学生开展参观、讨论、观看影像、听报告等实践活动，使学生有机会接触实际问题，综合运用所学的知识来认识生产生活中与化学有关的技术问题（灵活处理，体现教师的个性与风格）。在实践中增强学生的社会责任感，培养学生热爱祖国、热爱生活、热爱集体的情操；引导学生认识化学对促进社会进步和提高人类生活质量方面的重要影响，理解科学、技术与社会的相互作用，形成科学的价值观和实事求是的科学态度；培养学生的合作精神，激发学生的创新潜能，提高学生的实践能力。
3.重视实验教学和探究学习活动的功能
关于化学实验教学的功能在此不多赘述，这里主要谈谈实验探究活动：教师要根据学生在义务教育阶段以有的探究能力的基础上，制订高中阶段学生探究能力培养的具体方案，并认真加以实施。教师应充分调动学生的主观能动性，设法让他们主动参与探究学习的积极性，引导学生通过实验、观察、调查、资料收集、阅读、讨论、辩论等多种方式，在提出问题、猜想与假设、制定计划、进行实验、收集证据、解释与结论、反思与评价、表达与交流等活动中，增进对科学探究的理解，发展科学探究能力。
四、结束语
以上所列举种种只是我作为一个新教师初次使用《化学1必修》的一家之言，在实际的操作中当然会有很多不确定因素，这些要靠奋战在一线的广大同仁去创造性的解决。但是，有一个先决条件必需满足——高考指挥棒的功能与方向得改变。否则，编得再好的课本实施起来都会变质，编者的编书指导思想得不到实质性体现。高考的改革和新教材的推广将有何归宿，我们还是让事实说话吧！
参考文献：
[2]人民教育出版社化学室、全日制普通高级中学教科书（必修加选修） 化学（第一至三册）.北京：人民教育出版社，.6[4]中华人民共和国教育部制订.普通高中化学课程标准（实验）.北京：人民教育出版社，2003.4
[5]刘知新主编.化学教学论（第三版）.北京：高等教育出版社，.6
教学准备
教学目标
一、知识与技能
(1)理解并掌握弧度制的定义;(2)领会弧度制定义的合理性;(3)掌握并运用弧度制表示的弧长公式、扇形面积公式;(4)熟练地进行角度制与弧度制的换算;(5)角的集合与实数集 之间建立的一一对应关系.(6) 使学生通过弧度制的学习，理解并认识到角度制与弧度制都是对角度量的方法，二者是辨证统一的，而不是孤立、割裂的关系.
二、过程与方法
创设情境,引入弧度制度量角的大小,通过探究理解并掌握弧度制的定义,领会定义的合理性.根据弧度制的定义推导并运用弧长公式和扇形面积公式.以具体的实例学习角度制与弧度制的互化,能正确使用计算器.
三、情态与价值
通过本节的学习，使同学们掌握另一种度量角的单位制---弧度制，理解并认识到角度制与弧度制都是对角度量的方法，二者是辨证统一的，而不是孤立、割裂的关系.角的概念推广以后,在弧度制下,角的集合与实数集 之间建立了一一对应关系:即每一个角都有唯一的一个实数(即这个角的弧度数)与它对应;反过来，每一个实数也都有唯一的一个角(即弧度数等于这个实数的角)与它对应，为下一节学习三角函数做好准备.
教学重难点
重点: 理解并掌握弧度制定义;熟练地进行角度制与弧度制地互化换算;弧度制的运用.
难点: 理解弧度制定义，弧度制的运用.
教学工具
投影仪等
教学过程
一、 创设情境，引入新课
师：有人问：海口到三亚有多远时，有人回答约250公里，但也有人回答约160英里，请问那一种回答是正确的?(已知1英里=1.6公里)
显然，两种回答都是正确的，但为什么会有不同的数值呢?那是因为所采用的度量制不同，一个是公里制，一个是英里制.他们的长度单位是不同的，但是，他们之间可以换算：1英里=1.6公里.
在角度的度量里面，也有类似的情况，一个是角度制，我们已经不再陌生,另外一个就是我们这节课要研究的角的另外一种度量制---弧度制.
二、讲解新课
1.角度制规定：将一个圆周分成360份，每一份叫做1度，故一周等于360度，平角等于180度，直角等于90度等等.
弧度制是什么呢?1弧度是什么意思?一周是多少弧度?半周呢?直角等于多少弧度?弧度制与角度制之间如何换算?请看课本，自行解决上述问题.
2.弧度制的定义
长度等于半径长的圆弧所对的圆心角叫做1弧度角，记作1，或1弧度，或1(单位可以省略不写).
(师生共同活动)探究:如图,半径为的圆的圆心与原点重合,角的终边与轴的正半轴重合,交圆于点,终边与圆交于点.请完成表格.
我们知道，角有正负零角之分，它的弧度数也应该有正负零之分，如-π，-2π等等，一般地, 正角的弧度数是一个正数，负角的弧度数是一个负数，零角的弧度数是0,角的正负主要由角的旋转方向来决定.
角的概念推广以后,在弧度制下,角的集合与实数集R之间建立了一一对应关系:即每一个角都有唯一的一个实数(即这个角的弧度数)与它对应;反过来，每一个实数也都有唯一的一个角(即弧度数等于这个实数的角)与它对应.
四、课堂小结
度数与弧度数的换算也可借助“计算器”《中学数学用表》进行;在具体运算时，“弧度”二字和单位符号“rad”可以省略 如：3表示3rad sinp表示prad角的正弦应确立如下的概念：角的概念推广之后，无论用角度制还是弧度制都能在角的集合与实数的集合之间建立一种一一对应的关系。
五、作业布置
作业：习题1.1 A组第7,8,9题.
课后小结
度数与弧度数的换算也可借助“计算器”《中学数学用表》进行;在具体运算时，“弧度”二字和单位符号“rad”可以省略 如：3表示3rad sinp表示prad角的正弦应确立如下的概念：角的概念推广之后，无论用角度制还是弧度制都能在角的集合与实数的集合之间建立一种一一对应的关系。
课后习题
作业：习题1.1 A组第7,8,9题.
板书
教学准备
教学目标
1、 知识与技能
(1)进一步理解表达式y=Asin(ωx+φ)，掌握A、φ、ωx+φ的含义;(2)熟练掌握由 的图象得到函数 的图象的方法;(3)会由函数y=Asin(ωx+φ)的图像讨论其性质;(4)能解决一些综合性的问题。
2、 过程与方法
通过具体例题和学生练习，使学生能正确作出函数y=Asin(ωx+φ)的图像;并根据图像求解关系性质的问题;讲解例题，总结方法，巩固练习。
3、 情感态度与价值观
通过本节的学习，渗透数形结合的思想;通过学生的亲身实践，引发学生学习兴趣;创设问题情景，激发学生分析、探求的学习态度;让学生感受数学的严谨性，培养学生逻辑思维的缜密性。
教学重难点
重点:函数y=Asin(ωx+φ)的图像，函数y=Asin(ωx+φ)的性质。
难点: 各种性质的应用。
教学工具
投影仪
教学过程
【创设情境，揭示课题】
函数y=Asin(ωx+φ)的性质问题，是三角函数中的重要问题，是高中数学的重点内容，也是高考的热点，因为，函数y=Asin(ωx+φ)在我们的实际生活中可以找到很多模型，与我们的生活息息相关。
五、归纳整理，整体认识
(1)请学生回顾本节课所学过的知识内容有哪些?所涉及到主要数学思想方法有那些?
(2)在本节课的学习过程中，还有那些不太明白的地方，请向老师提出。
(3)你在这节课中的表现怎样?你的体会是什么?
六、布置作业: 习题1-7第4，5，6题.
课后小结
归纳整理，整体认识
(1)请学生回顾本节课所学过的知识内容有哪些?所涉及到主要数学思想方法有那些?
(2)在本节课的学习过程中，还有那些不太明白的地方，请向老师提出。
(3)你在这节课中的表现怎样?你的体会是什么?
课后习题
作业: 习题1-7第4，5，6题.
板书
略
一、教材分析
1.《指数函数》在教材中的地位、作用和特点
《指数函数》是人教版高中数学(必修)第一册第二章“函数”的第六节内容，是在学习了《指数》一节内容之后编排的。通过本节课的学习，既可以对指数和函数的概念等知识进一步巩固和深化，又可以为后面进一步学习对数、对数函数尤其是利用互为反函数的图象间的关系来研究对数函数的性质打下坚实的概念和图象基础，又因为《指数函数》是进入高中以后学生遇到的第一个系统研究的函数，对高中阶段研究对数函数、三角函数等完整的函数知识，初步培养函数的应用意识打下了良好的学习基础，所以《指数函数》不仅是本章《函数》的重点内容，也是高中学段的主要研究内容之一，有着不可替代的重要作用。
此外，《指数函数》的知识与我们的日常生产、生活和科学研究有着紧密的联系，尤其体现在细胞分裂、贷款利率的计算和考古中的年代测算等方面，因此学习这部分知识还有着广泛的现实意义。本节内容的特点之一是概念性强，特点之二是凸显了数学图形在研究函数性质时的重要作用。
2.教学目标、重点和难点
通过初中学段的学习和高中对集合、函数等知识的系统学习，学生对函数和图象的关系已经构建了一定的认知结构，主要体现在三个方面：
知识维度：对正比例函数、反比例函数、一次函数，二次函数等最简单的函数概念和性质已有了初步认识，能够从初中运动变化的角度认识函数初步转化到从集合与对应的观点来认识函数。
技能维度：学生对采用“描点法”描绘函数图象的方法已基本掌握，能够为研究《指数函数》的性质做好准备。
素质维度：由观察到抽象的数学活动过程已有一定的体会，已初步了解了数形结合的思想。
鉴于对学生已有的知识基础和认知能力的分析，根据《教学大纲》的要求，我确定本节课的教学目标、教学重点和难点如下：
(1)知识目标：①掌握指数函数的概念;②掌握指数函数的图象和性质;③能初步利用指数函数的概念解决实际问题;
(2)技能目标：①渗透数形结合的基本数学思想方法②培养学生观察、联想、类比、猜测、归纳的能力;
(3)情感目标：①体验从特殊到一般的学习规律，认识事物之间的普遍联系与相互转化，培养学生用联系的观点看问题②通过教学互动促进师生情感，激发学生的学习兴趣，提高学生抽象、概括、分析、综合的能力③领会数学科学的应用价值。
(4)教学重点：指数函数的图象和性质。
(5)教学难点：指数函数的图象性质与底数a的关系。
突破难点的关键：寻找新知生长点，建立新旧知识的联系，在理解概念的基础上充分结合图象，利用数形结合来扫清障碍。
二、教法设计
由于《指数函数》这节课的特殊地位，在本节课的教法设计中，我力图通过这一节课的教学达到不仅使学生初步理解并能简单应用指数函数的知识，更期望能引领学生掌握研究初等函数图象性质的一般思路和方法，为今后研究其它的函数做好准备，从而达到培养学生学习能力的目的，我根据自己对“诱思探究”教学模式和“情景式”教学模式的认识，将二者结合起来，主要突出了几个方面：
1.创设问题情景.按照指数函数的在生活中的实际背景给出两个实例，充分调动学生的学习兴趣，激发学生的探究心理，顺利引入课题，而这两个例子又恰好为研究指数函数中底数大于1和底数大于0小于1的图象做好了准备。
2.强化“指数函数”概念.引导学生结合指数的有关概念来归纳出指数函数的定义，并向学生指出指数函数的形式特点，请学生思考对于底数a是否需要限制，如不限制会有什么问题出现，这样避免了学生对于底数a范围分类的不清楚，也为研究指数函数的图象做了“分类讨论”的铺垫。
3.突出图象的作用.在数学学习过程中，图形始终使我们需要借助的重要辅助手段。一位数学家曾经说过“数离形时少直观，形离数时难入微”，而在研究指数函数的性质时，更是直接由图象观察得出性质，因此图象发挥了主要的作用。
教师活动：①引导学生对课堂知识进行归纳，完成对分类讨论、数形结合等数学方法的归纳;②布置课后及拓展作业
学生活动：完成对指数函数的概念和性质的课内小结并通过课后作业进一步深化学习目标，有能力的同学完成网上调研并在下节课与同学交流我国在利用14C进行考古所取得的成果。
设计意图：教师在本环节引导学生对指数函数的知识进行梳理，深化知识与技能目标，并通过作业实现目标的巩固。
5.板书设计
考虑到板书在教学过程中发挥的功能，本节课我设计了由三个板块构成的板书，板面分配比例为2：1：1，第一大板块包含了两部分，一是指数函数的定义，二是课前准备的画有坐标系和表格的小黑板;第二板块书写了例1和例2的第一问;第三板块由学生完成例2的后两问、练习和课堂小结组成。
五、教学评价
教学评价的及时有效能调动课堂的气氛、感染学生的情绪，对课堂教学发挥着积极的推动作用，因此，我将教学评价将贯穿于本节课的每个教学环节中。例如情景导入的表达式评价、回忆指数知识的记忆评价、得出指数函数概念的归纳评价、作图时的准确性评价、解题时的规范性评价、小结时的表述性评价等。在学生交流、讨论、探究等环节注意启发学生完成知识互评、能力互评，通过多种评价方式让更多的学生获得学习的自信，在轻松融洽的课堂评价氛围中完成本节课的教学和学习任务。
当然教师会通过对学生作业的批改获得更全面的对学生知识掌握的评价和课堂效果的反思，并在后续的时间里修订课堂设计方案，达到预期的教学效果，实现学生的能力发展。以上是我对指数函数这节课的设计和思考，敬请批评指正!
人教版新课标高一必修2 Unit 3 Computer―教案4
人教版新课标高一必修2?Unit?3 Computer―教案4 Unit?3?Computer??教?4 TITLE=人教版新课标高一必修2?Unit?3? ? The 3rd?period: learning about Language ---the Present Perfect Passive Voice Goals:?1. Learn the Present Perfect Passive Voice. 2. Help the students master the way of using the correct voice, telling the differences between the active voice and the passive voice.? Teaching Procedures: Step 1: Revision and lead-in 1.?Check the homework first Ex1: 1 totally? 2 revolution? 3 artificial intelligence?4 birth ?5 simple-minded ?6 go by?? 7 deal with? 8 network? 9 truly?10 anyway Ex2: revolution; network;?went by; totally; truly; simple-minded; Anyway; deal with Ex3: 1? totally??2 amazed??3 exciting??4 excited? 5 cheaply?6 unlucky 2. Lead-in Say: Are you familiar with these computers? Can you call them? (ask the Ss to distinguish different types of computers.) Do you know these new inventions of computer ? A wrist-worn PChas been invented?recently. A pen-like computer?has?already?been developed. (show them some pictures and ask them to make some sentences , using the Present Perfect Passive Voice.) Eg: It’s rather a hot day today! Would you like to have a swim after school ? Have you ever swum in the Blue Water World（蓝色水世界）?in the Oriental Suntown (东方太阳城) which has been set up in Taizhou? There a beautiful swimming pool has been built . Many high buildings have been set up. Lots of flowers and trees have been planted. A new bridge has been completed…. Step2: Discovering Ask the Ss to discover whether these sentences have something in common.. Help them to learn the useful structure : the Present Perfect Passive Voice.? Step3: Discussion : learning the structure Give some explanations 1构成： ?主动语态?被动语态 现在完成时?have/has done----------àhave/has been done He has been sent to study the new technology in the company. The dirty clothes have not been washed. Have the windows been cleaned? How many shopping centers have been built in this city? 2.?只有及物动词才有被动语态，不及物动词（词组）没有被动语态,?如:happen, take place, die, appear, disappear, fail, remain, lie, last, sit ,stand, break out, come true, belong to等．如： What has happened to your brother? 3．但许多不及物动词加介词或副词构成的.短语动词，相当于及物动词，也可以有被动语态。 但短语动词是一个不可分割的整体，变为被动语态时，不可丢掉构成短语的介词或副词。如： The child?has been taken good care of?by Grandma Wang all these years. A notice?has been put up?on the wall Step4: Practice and exercises 1.Change the following sentences into the Present Perfect Passive Voice. !). We have completed all the preparations for the task, and we’re ready to start. 2). This company has producednew types of computers. 3). They have interviewed several teachers for the job. 4). George has sent some texts and pictures to his friend’s cellphone. 5). They have developed some programmes for the human resource department of their company. 2.Change the following sentences into the Present Perfect Passive Voice. Put the verbs into correct form. Recently we have bought a new personal computer. We have used the computer every day since we bought it. We have just joined our computer to the Internet. However, we have found many problems with it. So we have decided to ask a professional man to fix it.Soon he has fixed the computer. He has built a PC way we wanted . How excited we are! These days we have written a lot of E-mails on the computer. We have decided to write a report about the positive and the negative effects of using computers. 3. Do some exercises: choice Step5: Using the structure : Play a game―What has been decided. 1. Give The Ss the situation :?Get into groups of four. Your task is to decide what has been decided for the class .Take turns to make the ideas as interesting or as lively as you can. 2. Give the Ss some examples: S1: It has been decided that those who do not do heir homework will be asked to return to school on Saturday. S2:It has been decided that those who keep the classroom tidy should be allowed to go home early everyday. S3:It has been decided …?S4:…??? 3. Ask them to collect the ones they all like best and be prepared to tell them to the class. Step6: Further Study:高考链接(This step can be done according to teaching needs.) 1. ---How long _____ at this job?B --- Since 1990. ?A. were you employedB. have you been employed ?C. had you been employed???D. will you be employed 2. When and where to go for the on-salary holiday ___yet. (2003?上海春季)?D A. are not decided?B. have not been decided C. is not being decided?D. has not been decided 3．All the preparations for the task ___, and we are ready to start. (?北京春季)?D Step 7: Homework 1.Finish Exercise 1 on P57. 2.Revise the Present Perfect Passive Voice.高中数学必修4教案学案
教学目标
1.理解平面向量的基本概念和几何表示、向量相等的含义；掌握向量加减法和数乘运算，掌握其几何意义；理解向量共线定理
2.了解向量的线性运算性质及其几何意义；会用向量的几何表示及其代数运算、三角形法则、平行四边形法则解决有关问题
教学重难点向量的有关概念与线性运算
教学过程设计（教法、学法、课练、作业）个人主页
一、知识回顾
1．下列算式中不正确的是（ ）
A. B
C D
2．已知正方形ABCD边长为1， , , 则 + + 的模=（ ）
A.0 B.3 C. D.
3．已知向量 , 满足： ，则 =（ ）
A.1 B. C. D.
4．在平行四边形ABCD中， , , ,M为BC的中点，则 = （用 , 表示）
二、例题讲解
例1设 是两个不共线的向量，已知 =2 + , = +3 , =2 - .若A,B,D三点共线,
求的值.
例2在梯形ABCD中,E,F分别是腰AB,DC的.三等分点,且 , 求
例3设O是平面上一定点,A,B,C是平面上不共线的三点,动点P满足 , .求点P的轨迹,并判断P的轨迹通过下述哪一定点:
①△ABC的外心; ②△ABC的内心;
③△ABC的重心; ④△ABC的垂心.
三、小结
四、训练练习
见练习纸
教后感
教学准备
教学目标
掌握三角函数模型应用基本步骤:
(1)根据图象建立解析式;
(2)根据解析式作出图象;
(3)将实际问题抽象为与三角函数有关的简单函数模型.
教学重难点
.利用收集到的数据作出散点图，并根据散点图进行函数拟合，从而得到函数模型.
教学过程
一、练习讲解：《习案》作业十三的第3、4题
3、一根为Lcm的线，一端固定，另一端悬挂一个小球，组成一个单摆，小球摆动时，离开平衡位置的位移s(单位：cm)与时间t(单位：s)的函数关系是
(1)求小球摆动的周期和频率;(2)已知g=24500px/s2，要使小球摆动的周期恰好是1秒，线的长度l应当是多少?
(1) 选用一个函数来近似描述这个港口的水深与时间的函数关系，并给出整点时的水深的近似数值
(精确到0.001).
(2) 一条货船的吃水深度(船底与水面的距离)为4米，安全条例规定至少要有1.5米的安全间隙(船底与洋底的距离) ，该船何时能进入港口?在港口能呆多久?
(3) 若某船的吃水深度为4米，安全间隙为1.5米，该船在2:00开始卸货，吃水深度以每小时0.3
米的速度减少，那么该船在什么时间必须停止卸货，将船驶向较深的水域?
本题的解答中，给出货船的进、出港时间，一方面要注意利用周期性以及问题的条件，另一方面还要注意考虑实际意义。关于课本第64页的 “思考”问题，实际上，在货船的安全水深正好与港口水深相等时停止卸货将船驶向较深的水域是不行的，因为这样不能保证船有足够的时间发动螺旋桨。
练习：教材P65面3题
三、小结：1、三角函数模型应用基本步骤:
(1)根据图象建立解析式;
(2)根据解析式作出图象;
(3)将实际问题抽象为与三角函数有关的简单函数模型.
2、利用收集到的数据作出散点图，并根据散点图进行函数拟合，从而得到函数模型.
四、作业《习案》作业十四及十五。
Unit 4 Earthquakes
Part One: Teaching Design (第一部分：教学设计)
Period 1: A sample lesson plan for reading
(A NIGHT THE EARTH DIDN’T SLEEP)
Aims
To listen and talk about natural disasters
To read about earthquakes
Procedures
I. Warming up
Warming up by looking
Good morning class. Have you ever experienced any natural disasters? Look at the pictures, can you name all the disasters?
volcano fire sandstorm
Typhoon hailstone thunderstorm
flood hurricane earthquake
Have you ever experienced an earthquake? Can you describe how terrible an earthquake is?
(The earth is shaking; all the buildings will fall down; many people will die; many children will become orphans.)
Warming up by discussing
Now, look at the pictures of Tangshan and San Francisco in warming up and describe what you see in the pictures. (beautiful cities; broad roads; tall building; large population.)
What will happen if there has been a big earthquake in these two cities?
As we all know, earthquakes are disasters to everyone. But can we avoid or at least reduce the loss caused by earthquakes? Can we foretell earthquakes? Now let’s come to Pre-reading and decide what may happen before an earthquake comes.
II. Pre-reading
1.Talking and sharing
What are the signs of an earthquake? (e.g. Cows, pigs and dogs become too nervous too eat. The mice will run out of the fields looking for places to hide. The water in the wells will rise and fall. Walls of the wells in village will have deep cracks. There will be bright light in the sky….)
2. Imaging and sharing
Imagine there is an earthquake now, your home begins to shake and you must leave it right away. You have time to take only one thing. What will you take? Why?
III. Reading
1. Listening and fast reading
Now let’s come to the text “A NIGHT THE EARTH DIDN’T SLEEP” and see what it tells us.
Please listen to the text and get the general idea of the passage. You should pay attention to the first sentences of each paragraph. In what order is the text written? (The text is written in time order. The general idea is the mixture of the first sentences of each paragraph, that is, the text tells us something that happened before the earthquake, during the earthquake and after the earthquake.)
2. Reading and underlining
Next you are to read and underline all the useful expressions or collocations in the passage. Copy them in your notebook after class as homework.
Collocations from A NIGHT THE EARTH DIDN’T SLEEP
A smelly gas, come out of, in the farmyards, too nervous to eat, run out of, look
for place to hide, water pipes, think little of sth., as usual, it seemed that, at an
end, one hundred kilometers away, one-third, eight kilometers long, thirty meters
Wide, cut across, in ruins, be injury, the number of, reach more than 400, 000,
everywhere, everything was destroyed, be gone, blow away, sth. be not safe for, tens of thousands of, give milk, half a million, instead of, be shocked, later that afternoon,
be trapped under the ruins, fall down, all…is/was not…,hundreds of thousands of,
dig out, the dead, to the north of, coal mines, built shelters, fresh water
3. Reading aloud and translating
Next we are going to read aloud the text and translate it into Chinese.
4. Reading and transforming information
Read the text again and answer the following questions.
1. What natural signs of coming disaster were there?
2. Can you think of some reasons why these signs weren’t noticed?
3. Can you describe the disaster caused by the earthquake?
4. What events and situations probably made the disaster worse?
5. How were the survivors helped?
6. Could anything more have been done to help the survivors? Why or why not?
Answers: 1, 3, 4, 5 are easy to answer.
2. Maybe at that time people didn’t have knowledge of an earthquake.
6. The students have their own answers.
4. Discussing writing style
As you have understood the general idea of the text, I still put more questions to you.
1. From whose point of view are events described? How do you know? (A writer
Who didn’t see the quake uses the third person “they” when he writes.)
2.Why do you think the writer chose to express her feelings about the quake rather than simply report what happened? (Although the writer was not there he felt sad for the people of Tang Shan. He knows that giving some feelings will make the reading more interesting.)
3.Why is the title “A NIGHT THE EARTH DIDN’T SLEEP”? (As usual, night is the time to sleep, and night should be quiet and safe. But that night everything changed. The writer used it as a title to show how terrible and how unusual that night is.)
5. Reading and understanding difficult sentences.
If you have some difficult sentences to understand, come to me for help.
IV. Closing down
Closing down by doing exercises
Now please do the comprehending Exercises 1, 2 and 3 on page 27.
Closing down by discussing
by now you’ve known that earthquakes are terrible natural disasters and that China is unlucky enough to have a lot of them. Now imagine that your group lives in the city that has a lot of earthquakes, what should you do during an earthquake? Look at the given situation and discuss in pairs.
(1) If you are OUTDOORS, …
(2) If you are in a HIGH BUILDING, …
(3) If you are DRIVING, …
(4) If you are HAVING CLASS, …
(5) If you are in a CINEMA, …
What should you do during the earthquake?
Situation:
(1) how to rescue those still trapped in the ruins;
(2) how to take care of the survivors;
(3) how to repair buildings that survived the earthquake;
(4) what to do with the buildings that survived the earthquake;
(5) where to find people to help build a new city;
(6) how to teach children about earthquake safety;
(7) where to put information for survivors and their families;
(8) how to plan for further disasters.
Period 2: A sample lesson plan for Learning about Language
(The Attributive Clause: that, which, who, whose)
Aims
To learn about the usage of who, which, that and whose in the Attributive Clause
To discover useful words and expressions
Procedures
I. Warming up
Warming up by discovering useful words and expressions
Hello everyone. After reading the passage, we have got to know the usage of the words and expressions, but we should do more practice. Now turn to page 27 to find the correct words and expressions from the passage to finish the sentences. You are given two minutes to finish them. Of course, you can discuss with your partners. Two minutes later, check in pairs and then check with the whole class.
II. Learning about language
1. Reading and finding
Turn to page 26 and read the text A NIGHT THE EARTH DIDN’T SLEEP. Tick out the attributive clauses in the reading passage and translate them into Chinese.
2. Doing Exercises 2 on page 28
Turn to page 28 and do Exercise 2 in pairs.
III. Ready used materials for Relative Pronouns: which, that, who whom whose
What are Relative Pronouns?
Relative pronouns are special pronouns which can connect the antecedent and the
Attributive clause. Also they can be used as a part of the attributive clause. Here
Are some important differences:
1． which/ that: referring to things, can be used as a subject or an object in the
Attributive clause; when they are used as an object, they can be omitted:
The plane is a machine that/which can fly.
The school (that/which) he visited last week is to the south of the city.
2. that/ who/whom: referring to a person, can be used as subject or object in the
Attributive clause; whom can be used as an object:
The girl (that/whom/who) we saw yesterday was Jim’s sister.
The man that/who is talking to my father is my maths teacher.
3. whose: referring to a person or a thing, can be used as an attribute in the
Attributive clause:
This is the writer whose name is known all over the world.
The room whose window faces south is mine.
4.Before everything, anything, everybody, anybody, all, the best +n, the
fifth +n, we use that instead of which:
All (that) I need is time.
This is the largest factory (that) I have ever visited
The sixth lesson (that) we are learning is the most difficult in Book Two.
5. We can’t use that in a Non-Defining Attributive Clause:
I have lost the pen, which I like very much.
I have two sisters, who are both teachers.
IV. Closing down by doing a quiz
Now you are going to take a quiz on Relative Pronouns.
fill in the blanks, using which, that, who, whom, whose.
(1) The force ( ) causes everything to fall towards the ground is called gravity.
(2) A friend ( ) helps you in time of need is a friend indeed.
(3) Do you know the girl ( ) parents are teachers in our school?
(4)The woman ( ) I spoke to just now is my English teacher.
(5) He saw a house ( ) windows were all broken.
(6)Everything ( ) can be done today mustn’t be done tomorrow.
(7)Can you think of anyone ( ) could look after him?
(8)This is the best hotel ( ) I know.
(9)The man ( ) I saw told me to come back today.
(10)Those ( ) want to go to the Great Wall write down your names here.
(11) He talked a lot about the teachers and the schools ( ) he had visited.
(12)The ninth lesson ( ) we are learning is the most difficult in Book One.
(13)Mount Blanc(勃朗峰), ( ) they visited last month, is the highest mountain in Europe.
(14)We know all the teacher ( ) work in our school.
(15)The house in ( ) Lu Xun once lived is a museum now.
(16)The house ( ) Lu Xun once lived is a museum now.
(17)The house ( ) Lu Xun once lived in is a museum now.
(18)You can take any room ( ) you like.
(19) He showed a machine ( ) parts are too small to be seen.
(20)The sports meet was put off, ( ) was exactly what we wanted.
Answers to the exercises: (1)which/that (2)who/that (3)whose (4)whom/that/who (5)whose (6)that (7)that (8)that (9)that/whom/who (10)who (11)that (12)that (13)which (14)that (15)which (16)in which/where (17)which/that (18)that (19)whose (20)which
Period 3:A sample lesson plan for Using Language
(A letter from Zhang Sha)
Aims
To read and speak about traveling
To write a letter describing feeling about traveling
Procedures
I. Warming up
Warming up by discussing
Have you ever written a speech? What is a speech? Speech means an act of speaking formally to a group of listeners. What do you have to consider when you are writing a speech? Please discuss it in pairs. (1. Who is the audience? 2. How can we express ourselves clearly?)
Warming up by reading
What should you include in your speech when you try to write one? Read the letter on page 29 and imagine you are the student who was invited to give a speech. Now write a short speech, in which you should follow the points in exercise 3 on page 29.
II. Reading and underlining
Read the letter and exercises again and underline all the useful expressions or collocations in the letter. Copy them in your notebook after class as homework.
Collocations from the letter
Congratulations, be pleased to do sth., win the high school speaking competition, a
Group of five judges, all of whom, agree, be proud of, open a new park, honour those who died in the terrible disaster, would like to do, have you do sth., as you know, invite sb.
To do sth., on that special day, at the beginning of, thank sb, for doing sth.,
Honour sb. for sth., be known as, encourage sb. to do sth., be happy to do sth.,
Collect stamps, lose one’s life
III. Listening
Turn on your books at page 30. We’ll listen to a story about a person who experienced the 1906 San Francisco earthquake. I’ll play the tape three times. First listen and try to get some details that exercises 1 and 2 request. Second listen again and try to finish the exercises. Third listen and check your answers.
IV. Guided writing (SB. page 31)
1. Making a introduction
Have you ever read a newspaper story? Now turn on your books to page 31 and look at Writing. Read the brief description about how to write a newspaper story. Compare a newspaper story to a short story and answer the following questions.
1) What should you write before writing a newspaper story? (outline)
2) What should a newspaper outline have? (a headline; a list of main ideas; a list of important details)
3) Why a headline is needed? (It can tell the readers what the topic is; it can also attract the readers’ attention)
4) How can you finish a newspaper story? (First, you should write a headline, then organize your main ideas into paragraphs, and then put some details into each paragraph.)
5) Have you found out the difference between a newspaper story and a short story?
(Usually a short story begins with small details and includes big details later. A newspaper story does just the opposite. Both kinds of stories use paragraphs with main ideas. In a good newspaper story, the point-of-view is objective (i.e. it has no point-of-view) while a short story is subjective (i.e. it has a point-of-view). A newspaper story has no conclusion; a short story generally does.)
Now I’ll show you a newspaper story to find out the headline, main idea and details of each paragraph.
THE WASHINGTON POST
SEATTLE-A powerful earthquake with a magnitude of 6.8 hit Washington State last week. The quake, the biggest in 50 years, caused billions of dollars in damage. But miraculously, only one person died and more than 100 people were injured in the quake.
Authorities said one reason there wasn’t greater destruction is that the region spent millions of dollars in the last decade designing earthquake----proof facilities and improving existing buildings, schools and homes.
earthquake expert said the event illustrated(说明) the growing gap between rich and poor nations in the ability to mitigate(减轻) natural disasters. Only a handful of people were seriously injured here, a slight number compared with the devastation(破坏) in countries like Turkey, India and El Salvador, where quakes have buried thousands under poorly constructed buildings.
2. Writing
Now prepare the outline for a short newspaper story for China Daily. You can use the example in exercise 1 to help you organize your outline.
3. Underling
Read the outline and the newspaper story in Writing and underline all the useful expressions or collocations in them. Copy them to your notebook after class as homework.
Collocations from Writing
A list of, put some details into each paragraph, a team of, raise money, thousands of,
Plan to do sth., in early June, hope to do sth., be interested to do sth.
IV. Closing Down
Closing down by summary
We have learned a lot about earthquakes. Now let’s have a summary about what we have learned. Look at the following questions.
(1) Have you ever experienced an earthquake?
(2) Can you describe an earthquake in English?
(3) What do you know about the cause of an earthquake?
(4) What new information about earthquakes have you learned now?
(5) What words and expressions can you use to describe an earthquake?
Closing down by finding information
Go to the library to read or get online to search in order to find more in formation about natural disasters.
Part Two: Teaching Resources (第二部分：教学资源)
Section1: A text structure analysis of A NIGHT THE EARTH DIDN’T SLEEP
I. Type of writing and summary of the main idea
Type of writing This is a piece of descriptive writing
Main idea of the passage The article describes the cause, the course and the
Result of Tang Shan earthquake in 1976. It
Shows us the terrible image of earthquake. At the
Same time it hits us that we must realize that
We can do something to minimize the damage
Caused by earthquake.
Topic sentence of 1st paragraph Strange things were happening in the countryside in
Northeast Hebei.
Topic sentence of 2nd paragraph Everything began to shake and it seemed that the
World was at an end.
Topic sentence of 3rd paragraph Everywhere they looked nearly everything was
destroyed.
Topic sentence of 4th paragraph All hope was not lost.
II. A text structure analysis
Read the text “A NIGHT THE EARTH DIDN’T SLEEP”, and then complete the following chart.
Time/ order What happened Result
Three days before the earthquake
At about 3:00 am Saw: cracks
Water in the wells--- rose and fell,
Animals--- too nervous , hide
fish jumped out of bowls & ponds
bright light in the sky
Water pipes---cracked and burst
Heard: sound of planes
Smelt: smelly gas in the cracks of the wells People thought little of the
events and went to bed
As usual
At 3:42 am
felt: everything shook
one-third nation felt it
Heard in Beijing 100 kilometers away
A huge crack cut across houses,
Roads…
Saw: steam burst from holes in the ground
Hard hills of rock-rivers of dirt
City lay in ruins
4 400,000 people
killed/injured
75% factories
90% home were gone
bricks covered
dams/bridges fell
Not safe railway tracks
Useless
Cows never milk
Pigs/chickens died
Wells filled with sand
Rescue workers and doctors trapped under the ruins
buildings fell down
Water/food/electricity
Hard to get
After that hope not lost
Army sent 150,000 soldiers
Workers built shelters for survivors
fresh water was taken to the city the city began to breathe again
III. A retold version of the text
one possible version
Strange things happened in Tang Shan. For three days the water in the village wells rose and fell. The well walls had deep cracks and a smelly gas came out the cracks. The chickens, pigs and mice were too nervous. Fish jumped out of bowls and ponds. Bright light appeared in the sky. People heard the sound of planes even when no planes were in the sky. The water pipes in some buildings cracked and burst.
At 3:42 am everything began to shake. It seemed that the world was at the end! One-third of the nation felt it. A huge crack cut across the city. In fifteen terrible seconds a large city lay in ruins. Two-thirds of the people died or were injured. Nearly everything was destroyed in the city. 75% of its factories and 90% of its homes were gone. Then later that afternoon, another big earthquake shook Tangshan. People began to wonder how long the disaster would last.
but all hope was not lost. The army sent 150,000 soldiers to help them. Workers built shelters for survivors. Slowly, the city began to breathe again.
Section 2: Background information on EARTHQUAKES
I. Zhang Heng
Zhang Heng (张衡) (78AD-139AD) was an astronomer, mathematician, artist and literary scholar（文学学者）in the Eastern Han Dynasty of China.
born in today’s Nangyang County, Henan, he was a good writer at age 12. At the age of 16, he left home to pursue(从事) his studying the capital city. He spent at least 10 years of his youth in literary studies and writing. He published several well-recognized literary writings. He switched to(转向) astronomy after age 30.
In the year 123 he corrected the calendar to bring it into line with the seasons.
In 132 Zhang Heng invented the first seismograph(地震仪) for measuring earthquakes. His device was in the shape of a cylinder(圆柱体) with eight dragon heads around the top, each with a ball in its mouth. Around the bottom were eight frogs, each directly under a dragon head. When an earthquake occurred, a ball fell out of the dragon’s mouth into a frog’s mouth, making a noise. He also invented the odometer(里程表)
Zhang Heng was the first person in China to construct a rotating celestial globe.
In one of his publications he also proposed π= 730/232 (or about 3.1466) .
II. Earthquake Survival Tips
Would you know what to do during a really big earthquake? Experts have looked into matter carefully. It may be worth you while to look over the following tips they have for us.
If the ground begins shaking while you are driving, pull over and stay in your car. If you are in a building, try to get near a strong wall. The corner of the room or the space under a big doorway is the safest. As soon as the quake is over, check the gas pipe in the building. Gas fires often result from earthquakes. These tips may prove to be lifesavers. We should, therefore, keep them in mind. Remember to always hope for the best but prepare for the worst.
escape in the School
If it has an earthquake when having classes, the students should listen to the teacher’s instruction, protect their heads and hide under the desks.
If it has an earthquake when the students are in the sports ground, they can crouch on the spot and protect their heads with hands. Be sure to keep away with high building and dangerous objects.
don’t go back to the classroom.
Retreat in order after the earthquake.
escape in Public Places
Listen to the command of the site workers. Don’t be scared and don’t rush towards the exits. Try to avoid crowds. Avoid to be squeezed to the wall or barriers.
At theaters and gyms: crouch down or slip under the chairs; avoid suspending lights and electric fans; protect the head with schoolbags; after the earthquake, listen to the command of the workers, retreat in an organized way.
In department stores, bookstores, museums or subway: find firm counters, commodities (low furniture etc.) or a pillar, or the corner of a wall to crouch down on the spot, protect the heads with hands or other objects; keep away from glass windows, glass counters or show counters; keep away from tall cupboards; keep away from advertisement boards and other suspending objects.
on buses or trolley buses: Grasp the handles to avoid being injured; lower the center of gravity; hide near the seats; get off after the earthquake passed.
Section3: Words and expressions
I. Words for reading
1. imagine vt. form a picture of in the mind；think of (sth.) as probable：想象；认为（某事）可能发生或存在。宾语为名词、代词、动名词、从句。宾语从句为否定意义时，要用否定转移，与think, believe, suppose, expect用法相同，成为I/ We don’t imagine…,意为“我（们）认为……不……如：We can imagine her sadness.我们可以想象她的悲伤。I didn’t imagine (my) becoming a teacher in my childhood.在童年时代，我并未想象能成为一名教师。Can you imagine how much I was surprised to hear the news?你能想象我听见这个消息有多惊讶吗？I don’t imagine so. = I imagine not.我认为不是这样。
Cf. imagine, guess, suppose
Imagine意为“想象，幻想”，指在脑海中形成一个清晰明确的印象，或认为某事物可能发生或存在;
Guess： form an opinion, give an answer, make a statement, based on supposition, not on careful thought, calculation, or definite knowledge: “猜测，臆测”，指未知道前的猜测;
Suppose: let it be though that; take it as a fact that:认定，假定； guess; think: “想象，推测”，意指“假定或假设中的情形”。
2. cf. shake, tremble
Shake: move, be moved, quickly or violently up and down, forwards and backwards: 最普通用词，可指人或物 “摇动，发抖”。指人时常用于感情激动、寒冷、惧怕引起的身体颤动。在表示 “因……而颤抖”时，多用with。在表示 “使受震撼，使（信念等）动摇”，常用于be shaken by/with/at中。
Tremble: shake involuntarily ( with fear, anger, cold, physical weakness, etc.) 颤栗,震颤,发抖(因恐惧,愤怒,寒冷,体弱等)，常常与shake相互替换，但指握手，摇头或捧腹大笑时用shake, tremble只用作不及物动词。如：The poor boy was shaking with cold.这个孩子正冻的发抖。They were badly shaken by the news.他们对这个消息大为震惊。The host shook hands with all the guests.主人跟所有的客人握手。Her voice was trembling with anger.她气的声音发抖。
3. cf. rise, raise
Rise vi. ( of the sun, moon, stars, river, price, temperature, etc.) appear above the horizon:指自然“上升”，常用于日、月、云、霞、烟、水蒸气、物价、温度、河水、潮水及人的职位等：He rose from his chair and began his speech.他从椅子上站起来开始了他的演说。Her temperature is still rising.他的体温还在上升。He has risen in rank.他已经升职了。
Raise vt. 1. lift up; move from a low(er) to a high(er) level; cause to rise: 外部的力量，“举起、提高”： The people’s living standard has greatly been raised.人民的生活水平已大大的提高了。 2．grow or produce (crops); breed (sheep, etc.); bring up a family: 饲养、种植”、养育、抚育： They can raise rice here.他们这儿能种水稻。
4. burst into / burst out : send out suddenly; break out into; suddenly begin to ……
burst into + doing: She burst into tears. = She burst out crying.她突然哭起来了。
burst out + n.：All of them burst into laughter = All of them burst out laughing.他们全都大笑起来了。
5. cf. destroy, ruin, damage
destroy: break to pieces; make useless; put an end to: 毁灭；摧毁；毁坏；破坏。表示在肉体上、精神上或道义上彻底摧毁，使之无法复原，也可以表示对某物体进行完全的毁坏: All his hopes were destroyed.他所有的希望都毁灭了。An atom bomb would destroy a city. 一颗原子弹可以摧毁一座城市。
Ruin: sth. which has decayed, been destroyed, etc.:败坏，毁坏，崩溃的状态。 指对物体或生命彻底的破坏，但往往是非暴力的，也往往不是一次的打击结果，常指对美好的或希望中的事物的破坏: Smoking ruined his health.吸烟毁了他的健康。She ruined his prospects.她毁了他的前途。
damage: harm or injury that causes loss of value: 损害；损毁（使失去价值）。一般指对物体或生命的局部损坏：Their houses were damaged by the enemy’s shellfire.他们的房屋被敌人的炮火击毁了。
6.cf. hurt, wound, injure
Hurt: cause bodily injury or pain to; damage; pain ( a person, his feeling): 使受伤；使疼痛；伤害； 使伤心。一般用语，即可指肉体上的伤害，也可指精神上的伤害，还可用作不及物动词，意为“疼痛、惹起痛苦”: What he said hurt me deeply.他说的话使我非常伤心。
Wound: hurt or injury to the living tissue of the body, caused by cutting, shooting, tearing, etc., esp. as the result of attack: 指外伤，如枪伤、刀伤、剑伤，尤指在战争中，战斗中受伤: He got wounded in the fighting.他在战斗中受了伤。
Injure: hurt; damage, esp. for result of an accident;一般指由于意外或事故而受伤。如：He was badly injured in the accident.他在这次事故中受了重伤。Smoking will injure your health.吸烟会毁了你的健康。
7. cf. shock, astonish, surprise
Shock vt./n: to cause usually unpleasant or angry surprise to (sb.): 震惊，打击，吃惊程度最大，后面常跟介词at/by构成词组be shocked at/by，表示“对……吃惊”，或接不定式表示原因，也可作名词，意为“震动，打击”: He was shocked by what you said.他对你说的话感到震惊。He was shocked to know his son playing all day.他知道他的儿子整天玩大为震惊。The news gave me a great shock.这个消息给了我很大的打击。
Astonish vt./n: surprise greatly. 语气比surprise要强，含有令人难以置信: I was astonished to see him in Tibet.在西藏见到他，真感到惊异。The news astonished everyone.这个消息使每个人都很震惊。
Surprise vt./n: (feeling caused by) sth. sudden or unexpected: 最普通用词，意为“使惊讶，使吃惊”，含有“意想不到”之意。如： I was surprised to see the great changes in my hometown.看到家乡的巨大变化他惊讶不已。His failure didn’t cause much surprise (was not a great surprise.)他的失败未引起很大的惊奇（并非很意外的事）。
II. Words for using language
1.congratulation n 1）（with on）an expression of joy for sb.’ success, good fortune, luck, etc. : 庆贺，祝贺，常用复述形式，并与介词on搭配，构成短语congratulations on sth. /doing …. 2）Congratulations ( on your winning the races)！恭喜（你获得了胜利）！I offered my congratulations on his success. 我对他的成功表示了祝贺。3）congratulate v. (with on.) to speak to ( a person) with praise and admiration for a happy event or sth. successfully done: 意为“向某人表示祝贺，向某人道贺”，构成短语congratulate sb. on sth. /dong…. congratulate oneself that结构中：We congratulated him on having passed the examination.我们祝贺他通过了考试。He congratulates himself on having chosen a good woman to be his wife.他暗自庆幸自己挑选了一位贤惠的女子作妻子。
2. cf. especially, specially
especially: to an exceptional degree; in particular: 特殊地，尤其，常用于正式文体中: This is a very common word, especially in spoken English.这是一个很普通的词，尤其在英语口语中。She likes the country, especially in spring.她喜欢这个国家，尤其是春天。
Specially: for a particular purpose: 特别地，专门地，表示“为了特别的目的”：This cake was specially made for you. 这个蛋糕是专门为你做的。
3. cf. be known as, be known for, be known to sb.
be known as作为……而闻名；be known for以/因……而闻名；be known to sb.为……而熟悉。如：He was known as a excellent singer.他作为一名优秀的歌手而闻名。The city is known for its long history.这座城市以它的悠久的历史闻名。 He is known to the police as a thief. 警察都知道他是个小偷。
III. Explanation of difficult sentences
1. It seemed that the world was at an end.似乎世界末日来临。
Seem连系动词，似乎，好象
1）seem + (to be ) + adj./n.
2）seem + to do
3）seem + like + n.
4）It seems/seemed (to sb.) + that-clause如：Our English teacher seems to be a kind man. He seems to know everything = It seems that he knows everything. It seems like years since we last met. It seems that I have seen her before. = I seem to have seen her before.
2. Everywhere they looked nearly everything was destroyed.人们无论朝哪里看，几乎一切都被毁了。
everywhere 用作连词，等于wherever, no matter where，引起让步状语从句。如：Everywhere I go, I find the same thing.无论我去哪儿，我都看到一样的东西。You see it everywhere you look.无论你往哪儿看，你都会看到它。
3. …90% of its homes were gone.90%的家都不存在了。
是过去分词作表语，意为“不在”“走了”“丢了”“用完了”，或指人“死了”。分数、百分数作主语，谓语动词要根据分数、百分数代表的量是可数名词还是不可数名词而定。如：His job was gone.他的工作丢了。My watch was gone.我的表不见了。He’ll be gone for quite a little while.他要离开很长一段时间。50% of the students in our class are girls.我们班50%的学生是女生。Two-thirds of the earth surface is covered with water.地球表面的三分之二是水。
4. The army organized teams to dig out those who were trapped and to bury the dead.救援人员组成小分队，将被困的人挖出来，将死者掩埋。
Those who相当于意为“凡……的人”，表示的是两者以上的不定数量，who引导的定语从句用复数，不能用that代替。（注意：anybody who, he who中谓语动词用单数。）
The dead意为“死难者”。形容词或分词前加表示同一类人或物，谓语动词常用复数形式。如：Those who want to see the film write your names on the paper.想看电影的人把你们的名字写在这张纸上。Anybody who breaks the law will be punished.任何人犯法都要受到惩罚。He who laughs last laughs best.谁笑在最后，谁笑的最好。The rich are not always happy.有钱人并不总是幸福的。
5. To the north of the city, most of the 10,000 miners were rescued from the coal mines. 在城市的北部，一万矿工中的大多数从矿井中被救出。
In the north, to the north与on the north
In表示“在其中”，在境界内；to表示在境外，不接壤；on表示接壤。如：China lies in the east of Asia.中国位于亚洲东部。Japan lies to the east of China.日本位于中国的东面。（指在中国境外）China faces the Pacific on the east.中国东临太平洋。（指东部境界与太平洋相接）