新概念77课

新概念77课（精选8篇）

新概念77课 篇1

考点解说

了解空间线线平行、线面平行、面面平行的概念;能正确利用有关定理解决平行问题的证明题和探索性问题.一、基础自测 1.已知直线a//平面,平面//平面,则a,的位置关系为.2.已知m,n是两条不同的直线,,是两个不同的平面,有下列4个命题:

(1)若m//n,n,则m//;(2)若mn,m,n,则n//;

(3)若,m,n,则mn;(4)若m,n是异面直线,m,n,m//,则n//.其中正确的命题的序号是.3.已知m,n是两条不同的直线,,,是三个不同的平面.给出下列四个命题:

(1)若m,m,则//;(2)若,,则//;

(3)若m,n,m//n,则//;

(4)若m,n是异面直线,m,m//,n,n//,则//.其中真命题是.4.设x,y,z表示空间不同的直线或平面,且直线不在平面内,给出下列五个命题:

(1)x为直线y,z为平面;(2)x,y,z为平面;(3)x,y为直线,z为平面;

(4)x,y为平面,z为直线;(5)x,y,z为直线.则其中能保证“若xz且yz,则x//y”.其中真命题是.5.对于不重合的两个平面与,给定下列条件:

①存在平面,使得、都垂直于;②存在平面,使得、都平行于;③内有不共线的三点到的距离相等;

④存在异面直线l,m,使得l//,l//,m//,m//.其中可使//的有个.6.给出下列关于互不相同的直线m,n,l和平面,的四个命题:

(1)m,lA,点Am,则l与m不共面;

(2)l、m是异面直线,l//,m//,且nl,nm,则n;

(3)若l//,m//,//,则l//m;

(4)若l,m,lm点A,l//,m//,则//.其中为假命题的是.7.已知m,n是不同的直线,,是不重合的平面,给出下列命题:

(1)若m//,则m平行于内的任一条直线;(2)若//,m,n,则m//n;

(3)若m,n,m//n,则//;(4)若//,m,则m//;

(5)若,m,n//,则mn.其中,真命题的序号是.8.下列命题中,是假命题的是.(1)三角形的两条边平行于一个平面,则第三边也平行于这个平面;

(2)//,a,过内的一点B有唯一的一条直线b,使b//a;(3)//,//,,分别与,的交线为a,b,c,d,则a//b//c//d;

(4)一条直线与两个平面成等角是这两个平面平行的充要条件.二、例题讲解

例1.如图,四棱锥PABCD中,底面ABCD为菱形,BAD

60,ABPB

, PCPA,E为CD的中点.(1)证明:BEPA;(2)在PC上找一点F,使得PA//平面BEF.例2.如图,四棱锥PABCD中,PA底面ABCD,ACCD,DAC60, ABBCAC,E是PD的中点,F为ED的中点.(1)求证:平面PAC平面PCD;(2)求证:CF//平面BAE

.AB,BCPC.2(1)求证:PABC;(2)试在线段PB上找一点M,使CM//平面PAD,并说明理由.例3.如图,在四棱锥PABCD中,CD//AB,ADAB,ADDC

例4.如图,在多面体ABEDC中,AB平面ACD,ACADCDDE2,AB1,F为CE的中点,DE平面ACD.求证:BF//平面ACD.板书设计

教后感

三、课后作业

班级姓名学号等第1.已知,,是三个不同的平面,a,b是两条不同的直线,有下列三个条件:

(1)a//,b;(2)a//,b//;(3)b//,a.如果命题“a,b,且,则a//b”为真命题,则可以在横线上填入的条件为.(正确的序号)

2.已知m、n是不同的直线,、是不重合的平面,给出下列命题:

①若//,m,n,则m//n;②若m,n,m//,n//则//;

③若m,n,m//n，则//;

④m,n是两条异面直线,若m//,m//,n//,n//，则//.上面的命题中,真命题的序号是.3.设,,为两两不重合的平面,l,m,n为两两不重合的直线,给出下列四个命题:①若,,则||;②若m,n,m||,n||,则||,③若||,l,则l||;④若l,m,n,l||,则m||n.其中真命题的个数是.4.已知a,b,c是直线,是平面，给出下列命题:

①若ab,bc,则a//c;②若a//b,bc,则ac;

③若a//,b,则a//b;④若a与b异面,且a//,则b与相交;

⑤若a与b异面,则至多有一条直线与a,b都垂直.其中真命题的个数是.5.,为平面,m为直线,如果//,那么“m//”是“m//”的条件.6.已知m,n是两条不同直线,,,是三个不同平面,下列命题中正确的是.(1)若m‖,n‖,则m‖n;

(3)若m‖,m‖,则‖;(2)若,,则‖;(4)若m,n,则m‖n.7.设有直线m,n和平面,.下列四个命题中,正确的是.(1)若m//,n//,则m//n;(2)若m,n,m//,n//,则∥;

(3)若,m,则m;(4)若,m,m,则m//.8.下列命题中正确的是.(1)直线a,b与直线l所成角相等,则a//b;

(2)直线a,b与平面所成角相等,则a//b;

(3)平面,与平面所成角均为直二面角,则//;

(4)直线a,b在平面外,且a,ab,则b//.9.如图,在长方体ABCDA1B1C1D1中,ABAD2.(1)证明:面BDD1B1面ACD1;

(2)若E是BC1的中点,P是AC的中点,F是

AC11上的点,C1FmFA1,试求m的值,使得

EF//D1P.10.在菱形ABCD中,DAB60,PA面ABCD,且PAAB2,E是AB的中点.(1)求证PCBD;(2)设F是PD上一点,试确定F的位置,使AF//平面PEC.

11.直棱柱ABCDA1B1C1D1中,底面ABCD是直角梯形,BADADC90, AB2AD2CD2.(1)求证:AC面BB1C1C;

(2)在A1B1上是否存在点P,使DP与面BCB1和面ACB1都平行?

12.如图,在直四棱柱ABCDA1B1C1D1中,已知DCDD12AD2AB,ADDC,AB//DC.(1)求证:DCAC1;(2)设E是DC上一点,试确定E的位置,使D1E//面A1BD.1

13.（选做题）如图,ABCD为直角梯形,CCDA90,AD2BC2CD,P为平

面ABCD外一点,且PBBD.(1)求证:PABD;

(2)若直线l过点P,且l//BC,试在直线l上找一点E,使得PC//

新概念77课 篇2

关键词：思维活动,概念,判断,推理,演绎性,发展性,严密性,思维能力

《普通高中数学课程标准》指出:教学中应加强对基本概念和基本思想的理解和掌握, 对一些核心概念和基本思想要贯穿高中数学教学的始终, 帮助学生逐步加深理解。数学中的思维活动就是概念、判断和推理, 而判断和推理的基础就是概念。概念是思维的细胞, 只有对概念理解透彻, 才能掌握运算的技能和技巧, 才会有合理快捷的逻辑论证。在教学中, 常发现部分学生数学概念模糊不清: (1) 认为学数学只要会解题就行, 不必花时间、精力去注意那些枯燥的概念; (2) 认为只要能熟练背诵概念就行, 并没有深刻地去理解。结果运用起来似是而非, 解答问题则错误百出。因此, 上好数学概念课是使学生学好数学的首要一环。如何搞好新课程下的数学概念课教学?笔者结合教学实践, 谈几点看法。

一、揭示数学概念的演绎性

数学概念的演绎性主要指:概念的意义不是通过客体抽象、归纳, 而是通过概念对概念的演绎来确定的, 即通过公理或已知概念对新概念的约定。概念所指的对象还是概念。例如, 立体几何中的第一个基本概念——平面。它是通过一组公理来揭示其意义的, 并未给出定义。对于平面的概念, 教材中简明写道:“常见的桌面、黑板面、平静的水面以及纸板等, 都给我们以平面的形象。几何里所说的平面就是从这样一些物体抽象出来的。但是, 几何里的平面是无限延展的。”

事实上这一段话并不揭示几何中平面概念的任何意义, 几何中的平面与上述种种“形象”毫不相干, 我们由此并不能得出几何中关于“平面”概念的任何意义。通过生活中形形色色“很平的形象”也抽象不出能够用之于几何中严密逻辑推理的平面概念。那么, 平面概念的真谛何在呢?它的准确意义存在于三个公理和三个推论之中, 或者说, 平面是具有性质公理和推理的一种“对象”, “平面”这两个字只是具有这种性质的“对象”的一个代名词。因此, 教师在教学中应该让学生从三个公理中去领会平面的意义, 即平面的确定 (有且仅有一个) 这一平面概念的核心。

例1.在四面体ABCD中, 若有两条高相交, 则另外两条高也必相交。

分析:意识到“两条高相交”意味着过这两条高有平面, 这是解决该题的关键。

证明:设ABCD的两条高AP、BQ交于H, 则过AP、BQ必有平面, 记作ABH, 它与棱CD交于E。则CD⊥平面ABH (即ABE) 。所以CD⊥AB。

在△ABC内作CF⊥AB于F, 连结FD, 则AB⊥平面FCD。

因为AB奂平面ABC, 平面ABD,

所以ABC⊥FCD, 平面ABD⊥平面FCD。

则过C和D的四面体ABCD的两条高线必在平面FCD内, 从而它们相交。

证明过程表明:在题设中的“两条高相交”暗示我们过这两条高“有平面” (即平面ABE) , 而要求证另外两条高也相交, 暗示我们去证明另外两条高共面, 从而启发我们得到平面FCD。

这里用“平面”的概念去演绎“两条相交直线”。

二、揭示数学概念的发展性

任何事物都是发展的, 数学概念亦如此。概念随着推理发展, 在不同问题的推理中对概念作出不同的表述, 这是概念发展的基本渠道。承认并接受这一点十分重要。只有这样才能摆脱概念的僵化状态, 才能在应用中把握概念的本质, 丰富概念的内涵, 理解概念的用法。

如定义:“以二面角的棱上任意一点为端点, 在两个面内分别作垂直于棱的两条射线, 这两条射线所成的角叫二面角的平面角”。在基本问题中, 二面角的概念就是以定义的叙述方式来理解的, 这在解题中常用。但在许多解题中用以下方法更为简便:

例2.若一个平面垂直于二面角的棱, 那么, 这个平面与二面角两个面的交线所夹的角就是二面角的平面角。

分析:设平面γ与二面角α-l-β棱交成∠ABC,

因为β⊥γ, 所以l⊥AB, l⊥BC,

从而, ∠ABC为α-l-β的二面角。

又如定义:一个数列从第二项起, 每一项与它的前一项的差等于同一个常数, 这个数列就叫做等差数列。

例如命题: (1) 如果一个数列的通项an=an+b (a, b为常数, n∈N) , 那么这个数列叫等差数列。

(2) 如果一个数列的前n项和Sn=an2+bn (a, b为常数, n∈N) , 那么这个数列叫等差数列。

可以证明以上两个命题与等差数列的定义是等价的, 所以, 用它们来进行判断也是等效的。

因此, 在教学中, 教师要揭示概念的发展性, 从中发掘一些定义的概念的等价命题, 这样无疑能帮助学生迅速、准确地进行判断和解题。

三、揭示数学概念的严密性

概念的严密性是概念的演绎性的必然结果, 也是概念用于逻辑推理的要求。学生每接触一个新概念, 往往会疏忽了某一些本质, 忽略了概念的严密性, 从而导致不能很好地掌握这个新概念, 教师在教学中, 除严格地讲清这个概念的所有本质属性外, 宜通过实际例子, 尤其是典型性例子, 强化学生对新概念严密性的认识。

如, 在讲授奇、偶函数的概念时, 用f (-x) 与f (x) 的关系判断函数的奇偶性, 学生容易记住, 但往往忽略了这个概念的前提条件:奇、偶函数的定义域必定是关于原点对称的区域。透彻地说, 就是没有真正弄清概念中的任一实数x与-x均必须保证在其定义域中, 这一严密的定义。所以, 教师可适时地举一些例子, 如函数y=sinx, x∈ (0, π) ;y=-3x2, x∈ (-5, 5) 等。

再如, 讲授“两个平面互相垂直, 过其中一个平面内作一直线垂直于这两个平面的交线, 则此直线必垂直于另一个平面”定理时, 构造了一个命题:两个平面互相垂直, 过其中一个平面内一点作一直线垂直于这两个平面的交线, 则此直线必垂直于另一个平面, 让学生判断其真假, 不少粗心的学生立即回答是真命题, 细心的学生就会推敲概念中“平面内作一直线”, 变为“平面内一点作一直线”的区别, 得出假命题的结论。如α⊥β, A∈β, α∩β=l, AC奂β, AC⊥l于C点, 过A点可作无数条直线垂直于交线l, 但这些直线并非都垂直于α, 而过A的直线中有且仅有直线AC垂直于平面。

因此, 教师可通过紧扣概念严密性的例子来加深学生对概念的理解和掌握。

四、善于灵活运用概念去解决问题

任何一门学科都是由一系列的概念体系组成的, 所以, 概念既是最基础的知识, 又是最重要的知识。灵活运用概念去解决问题, 提高思维能力, 则是我们进行数学概念教学的目的。为此, 在教学中应通过实例加强该方面能力的培养和训练。

例3.设F1 (-c, 0) , F2 (c, 0) 是椭圆上的两焦点, P是以F1F2为直径的圆与椭圆的一个交点, 且∠PF1F2=5∠PF2F1, 求椭圆的离心率。

解:设∠PF1F2=α, 在△PF1F2中

由椭圆定义得:

解题过程中应用了椭圆概念的定义, 简化了解题过程, 取得了事半功倍的效果。

数学概念的演绎性和严密性揭示了数学概念特点及在概念的发展中必须严守概念的本质, 而概念的发展又告诉我们:数学概念绝不能死背定义, 必须结合解题进一步领会概念的各种表述形式, 掌握反映概念本质的种种侧面, 真正使学生悟出隐藏在形式后面的概念的无限真谛。以上提到的几个方面, 应当在新授课、复习课、习题课等不同课型中根据需要而得到重视。

道可道, 非常道;名可名, 非常名。如果我们教师在施教的过程中, 能抓住学生掌握知识的薄弱环节, 采取相应对策, 就能对提高课堂教学质量起到重要的作用。

参考文献

[1]陈旭远.新课程推进中的问题与反思.首都师范大学出版社, 2009-06.

[2]章建跃, 陶维林.概念教学必须体现概念的形成过程.数学通报, 2010 (01) .

[3]岑燕斌.在自主学习中重视概念教学.中学数学教学, 2005 (06) .

数学概念课教学与微课设计 篇3

【关键词】数学概念 数学概念课 微课

【中图分类号】G434；G633.6【文献标识码】A 【文章编号】2095-3089（2016）09-0106-02

由于数学概念本身具有严密性、抽象性和高度概括性，教师在教学中往往更注重培养学生思维的逻辑性和精确性：给出定义、名称和符号，字字推敲，处处斟酌，揭示概念的内涵与外延。要求熟读、熟记定义，死记硬背结论，然后转入巩固应用。这种忽视概念产生背景及生成过程的教学方式，太过重视定义的叙述与记忆，强调概念的应用，虽然能节省时间但不能掲示数学概念的本质，无法让学生经历概念的产生、探究的思维过程，缺乏从感性到理性的认识，学生只注重掌握应试题型与具体的解题技能、技巧，难以形成真正的数学思维能力，更难以体会其中所蕴含的数学思想和方法。

一、引入概念时创设情境

概念是抽象的、高度概括的，每一个概念的产生都有丰富的知识背景，形成概念的首要条件是要让学生获得十分丰富和合乎实际的感性材料，而合理创设情境，利用学生在日常生活中熟悉的具体事例，通过学生的观察、分析、探索，发现规律、作出归纳，对概念的形成有直观感受，有利于学生完成从感性认识到理性认识的过渡，培养学生的观察能力和探索能力。课前让学生利用微课对“椭圆的概念”作情境引入，自学并动手操作，去探究发现。

（1）请同学们把印有定圆F1 的圆形纸片拿出来，按照以下步骤操作：第一步，在圆内部任取不同于圆心的一点F2；第二步，在圆F1上任取一点P1，然后将纸片对折，使得点P1与点F2重合，然后将纸片展开，用铅笔把折痕L画出来 ；第三步，再在圆F1上任取其他点，按照步骤二多操作几次，就可以画出一系列折痕，观察、猜想这是一种什么图形？

（2）要想取遍圆周上所有的点，这个工作量非常大，接下来我们就借助《几何画板》工具，让电脑来帮助我们演示作图。

（3）研究其中的一条折痕，我们在圆F1上任取一点P1，然后把折痕L加粗显示出来 ，P1F1与L交于点P，思考折痕L与线段P1F2之间是什么关系？为什么？（因为沿着折痕L对折后，点P1与点F2重合，故折痕L是线段P1F2的垂直平分线，即|PP1|=|PF2|）

（4）能否求出|PF1|+|PF2|的值？这个结果是否是定值呢？ （|PF1|+|PF2|=|PF1|+|PP1|= |F1P1|，而|F1P1|是圆F1的半径，是一个常数）

（5）如果我另换一条其他的折痕，这个结果会改变吗？（不变）

（6）如果在折痕L上除点P外任取点Q，将|QF1|+|QF2|的值与|PF1|+|PF2|的值进行比较，你有何发现？（由三角形任意两边之和大于第三边可知，|QF1|+|QF2|=|QF1|+|QP1|>|F1P1|）

二、表述概念时必须准确

由于数学概念是用科学的，精练的数学语言概括表达出来的，它所揭示事物的本质属性必须准确，用准确的文字语言给出定义，符号表示，对概念中每一词、句进行仔细推敲，培养学生正确的表述概念，有利于深化对概念的理解.教学过程中可利用微课辅助对“椭圆的概念”的准确表述。

（1）“到两定点的距离的和为定值的点的轨迹一定是椭圆吗”（动画演示可能是空间的椭球形，而不是平面图形，使学生认识到必须限制：“在平面内”，以加深对概念的印象）。

（2）这里的常数2a为什么要大于2c？若常数2a=2c，2a<2c呢 ？（边演示边让学生归纳，2a>2c得到的图形为椭圆，2a=2c得到的图形为一条线段，2a<2c不存在图形，因为三角形的任意两边之和应大于第三边）。

（3）表述椭圆的概念：平面内与两个定点F1、F2的距离之和等于常数2a（且2a>|F1F2|）的点的轨迹叫作椭圆，这两个定点叫作椭圆的焦点，两焦点间的距离叫作椭圆的焦距，记法：|PF1 | +|PF2| =2a（2a>2c=|F1F2|）。

让学生知道如果漏掉其中一句甚至一个字，如“平面内” “2a>2c=|F1F2|”等，都会引起椭圆概念的错误，抓住问题的本质，用恰当、简洁的文字准确表达概念。

三、巩固概念应用变式

学生在认识和形成、理解和掌握概念之后，巩固概念是一个不可缺少的环节， 巩固的主要手段是多练习、多运用，适时利用变式训练，让学生在应用中巩固概念，从而确保概念课教学的高效，课后利用微课对“椭圆的概念”的变式巩固。

总之，在数学概念课中利用微课辅助教学的方式可以很好处理概念的引入、表述、理解以及巩固，充分发挥微课的优势，抓住概念的本质，在探索、辨析、感悟和运用中真正掌握数学概念，充分提高数学概念课的教学效率。

参考文献：

[1]周友良.椭圆第一定义的教学.中学数学教学参考，1999 （9）.

[2]郭冬梅. 对新课改下高中数学概念教学再思考.科技创新导报，2011 （3）.

[3]陈燕锋.高中数学概念教学的现状分析及对策研究.现代教育科学，2013 （6）.

新概念第三册29课教案 篇4

I.New words and expression 生词和短语 a.Largely adv.在很大程度上

--His success was largely due to luck.b.Universal adj.普遍的universal agent n.全权代理人;universal time n.(= Greenwich Time)世界时间,格林尼治时 universal joint n.[机]万向接头

万向接头：一种接头或连轴节，能使互相不在一条线上的机械零件在传输旋转运动时在任意方向上具有有限的运动自由度。Universality n.普遍性, 一般性, 多方面性, 广泛性 Universally adv.普遍地, 全体地, 到处

It’s universally acknowledged(adj.公认的)that English is get more and more important.Universe n.宇宙, 世界, 万物

c.Comic adj.喜剧的, 可笑的；Comedian n.滑稽演员, 喜剧演员； Comedy n.喜剧, 喜剧性的事情

--Tragic adj.悲惨的, 悲剧的；--Tragedy n.悲剧, 惨案, 悲惨, 灾难--Tragedian n.悲剧演员, 悲剧作家 d.Distasteful adj。avastefully）Unpleasant adj.使人不愉快的, 讨厌的 Displeasing adj.使人不愉快的, 令人发火的--The idea is distasteful to me.e.Pester v.一再要求, 纠缠（assail vt.攻击, 困扰）

pester sb.to do sth.以某事烦扰某人;缠住某人讨取某物;麻烦某人做某事 pester sb.with sth.以某事烦扰某人;缠住某人讨取某物;麻烦某人做某事--He continually pesters his boss with demands.pester sb.for sth.以某事烦扰某人;缠住某人讨取某物;麻烦某人做某事--Don’t pester me for the trifle.（n.小事, 琐事, 微不足道的东西）

f.Dread v.惧怕；Dread + 名词, 动名词, 动词不定式--We were dreading his arrival.我们正担心他来呢！--He dreaded having to meet his parents.--I dread to think what will happen if he finds out.Dreadful adj.令人恐惧的, 令人不快的；--a dreadful disaster 可怕的灾难 dreaded adj.感到恐惧的；

in dread of….害怕某人[某事]--We are in dread of insects.（insect n.昆虫）terrify vt.使恐怖, 恐吓

horrify v.使恐怖, 使极度厌恶, 惊骇 fear v.害怕, 畏惧, 为...担心 g.Grief n.悲痛, 伤心事, 不幸, 忧伤

He is consoling his friend in grief for the loss of child.h.hobble v.瘸着腿走

--I hurt my foot while getting off the bus, and had to hobble home.我在下公共汽车时脚受了伤, 只好一拐一拐地走回家。Hobble n.困难, 窘惑；--be in(get into)a hobble 陷于窘境 i.compensate v.补偿；to compensate sb.For 为…向某人赔偿

Nothing can compensate the young mother for the loss of her favrourite daughter.年轻的妈妈丧失了自己心爱的女儿是任何东西也弥补不了的。Compensate v.酬报（for）

The company compensates her for extra work.公司因她的额外工作而给她报酬。

mumble v.喃喃而语；mumbler n.说话含糊的人 j.He mumbled sth.to me but I could not hear what he said.他对我咕哝了几句，可是我没听清他说的什么。k.basis n.基础, 基本, 根据

basic adj.基本的 n.基本, 要素, 基础 n.[计]BASIC语言, 基本高级语言 l.bind vt.vi.（bound, bound, binding）缚, 绑--be bound up with 与...有密切关系

Situation n.情形, 境遇；--Comic situation 喜剧情节 violent adj.猛烈的, 狂暴的, 剧烈的；--a violent death 横死, 暴死 eve n.前夕, 前日 n.节日的前夜（--New Year‘s Eve除夕）n.（重大事件的）前夕（--on the eve of the great war 大战前夕）

brought up: raise, educated;

mysteriously bound up with: strangely connected to make: force;

universal appeal: international attraction stems: comes;

come into fashion: become popular distasteful: unpleasant tasteless;TEXT What is the basis of ‘sick’ humour?

1.Most funny stories are based on comic situations.be based upon… 基于…

This news report is based entirely on fact.这篇新闻报导是完全根据实际情况写成的。

2.stem from 源自, 起源于

--His feeling of hate stem from envy.（n.羡慕, 妒嫉）

--Her interest in flowers stemmed from her childhood in the country.= come from 出身于, 由...引起, 是...的结果, 是在...生长大的 = arise from 由...而引起, 由...而产生 = originate from 由某人发起(首创)The quarrel originated in a misunderstanding.争吵是由于误解而引起的。The film originated from a short story.这部电影取材于一篇短篇小说。Originate vt.使产生, 创始, 创办, 发明, 发起, 引起 They originated the plan.他们首先提出这一计划。

3.come into fashion 流行起来, 开始风行;come into power(开始)掌权, 上台 4.call into being 使产生, 使出现, 建立, 成立

5.Chance在表达机会这个概念的时候, 经常采用复数形式。One’s chances of doing sth are good 某人做某事的可能性很大--My chances of passing the examination are good.--His chances of being dismissed are good.One’s chances of doing sth are remote/ slight 某人做某事的可能性很小--His chances of arriving here by bicycle are remote.6.take heart 鼓起勇气, 打起精神--He took heart when he got the good news.lose heart 灰心, 泄气

If they knew how difficult it was to drill through the hard rock they will lose heart.7.More than… 超出…范围--The cake is more than I can eat.More than后面可以引导省略主语的比较从句, 从句中常见的形容词有：necessary, good, Possible, anticipate, expect, feel, suggest, report, require, think.--The man drank a little more than was good for him.= The man drank a little more than what was good for him.There were more accidents than(what)was reported.He eats more than(what/it)is good for him.As后面可以引导省略主语的比较从句

He arrived as I expected.= He arrived as(what)was expected.He eats as much as(what/it)is good for him.The man drank as much as(what)was good for him.比较：

1>--He eats more than is good for him.他总是吃的正好。--He eats as much as is good for him.他总是吃的过多。2>--The man drank a little more than was good for him.--The man drank as much as was good for him.委婉的表达方式：

The man drank a little more than was good for him.She is quite fat.= She isn’t right fat.（Right adv.正确的, 合适的, 恰当的）8.in the process of… 在...的过程中

In the process = during the party（上文中的party）27-04 9.How much = To what extent--How much can I trust him? = To what extend can I trust him? II.Read the passage two or three time.Make sure you understand it.And then in not more than 80 words discribe what happened from the time when the car got past the boulders to the moment it stopped in the shallow pool(Para3).Use your own words as far as possible.1.Write a list of points(in note form).2.Connect your points to write a rough draft of the summary.Try to use your own words as far as possible, not only making extracts(摘抄)from the passage.Don’t count the number of the words until you have finished the rough draft.3.In the rough draft, you are likely to go well over the words limit.Correct your draft carefully, bringing the number of words down to the set limit.III.Summary-writing points 1.Man broke right leg---before Christmas---taken to hospital 2.When---go home?---didn’t want---spend Christmas there 3.Christmas Day---still right leg in plaster---day in hospital 4.Next day---good chance of leaving hospotal---New Year 5.Next Year’s Eve---party---drank too much 6.End of party---slipped on piece of ice---broke left leg Summary

A man broke his right leg just before Christmas and was taken to hospital.He wanted to know when he could go home.On Christmas Day he was still in hospital with his keg in plaster, but there was a good chance of leaving hospital for the New Year.In fact, he was out in time to go to a New Year’s Eve party where he drank too much, slipped on a piece of ice and broke his left leg.IV.Letter writing

新概念2册94课介词填空翻译 篇5

5.不让他和别人吵架是不可能的。6.对他的治疗有效，它很快就会痊愈的。7.尽管他已经35岁了，他还是和母亲住一起，依靠他的母亲。8.我试着劝他，但是他对我很无礼。

9.很感激你对我这样耐心。10.他干得不错，但是你还是不能依赖他。11.我这在考虑换个工作。12.如果你干涉别人的事情，你会后悔的。13.你相信那些废话吗？ 14.很明显的是如果你一直骚扰他，他会和你发脾气的。15.你对他的要求太过分了，你还不能胜任那份工作。16.不要盲目自信。17.他已经做好了各种应急准备。18.我不敢向他提及那件事情。19.别因为这件事责备他，我会对所发生的事情负责。20.你喜欢学习，你应该多鼓励他。21.你应该留意和那些对你的成功特别感兴趣的人。22.我请求他给予帮助。23.我很后悔求他，对于他的拒绝，没我感到很震惊。24.你对戏剧感兴趣吗?25.你一时到你面前的困难了吗? 26.他已经有权领取退休金，但是他还想过退休。27.谁来对损坏进行赔付？ 28.这辆车不如我去年买的那辆。29.恐怕我还不能对你的工作进行评价。30.她对自己的工作能力引以为傲，但是她不会抚养孩子。31.我们已习惯了恶劣的天气。32.当你还不了解基本情况的时候，你怎么能同意这样的主意呢？ 33.他向我坦白说他已经信别的宗教了。34.她想向我借唱片，但是她还不好意思。35.如果你的尝试失败了，别指望我会帮助你。

1.of2.of … to3.to…from4.on…on5.from…with6.to…of7.with…on8.with…to9.to…with10.at…on11.of…for12.in/with13.in1 4.to…in…with

15.of…to16.of17.for18.of…to19.for…for20.on …in21.of…about

22.to23.for/about…at/by24.in25.of…of26.to…of27.for28.to29.on

新概念二76到96课摘要写作 篇6

A boy played truant and travelled 1,600 miles.After hitchhiking to Dover, he slept in a boat.Next morning, he found himself in Calais where a lorry drive gave him a lift and something to eat.On getting off near Paris, he stopped another car which didn’t take him to Perpignan but to Paris.There he was picked up by a policeman and sent home by authorities.Lesson74

（一）After a bus stopped by a river bed, film stars descended, they dressed in dark glasses and old clothes so as not to be recognized.They carried picnic things to a shady spot and sat down.Just then, Jeriff appeared and said rudely: ‘You must leave here because camping is not allowed there.Even when they told him who they were, Jeriff didn’t believe them.（二）

A bus stopped by a river bed, a party of film stars descended, they dressed in dark glasses

and old clothes, in order that they wouldn’t be recognized.They carried the picnic things to a shady spot, everyone had sat down when Sheriff appeared and asked them rudely to leave, as camping is not allowed there.They told him who they were but Jeriff didn’t believe them.Lesson75

（一）A plane crashed in the mountains but the only passengers, a woman and baby daughters didn’t hurt, and it was extremely cold in midwinter, so she put the children in a case and covered them with clothes.When the planes passed next morning, she stamped ‘SOS’ in the snow.This was seen by a pilot who sent a message to the nearest town and they were rescued by a helicopter.（二）

When a plane crashed in mountains, the only passengers, a woman and her baby daughters didn’t hurt.However, it was in midwinter and extremely cold, the woman kept close all night.On hearing planes next morning, the woman stamped ‘SOS’ in the snow which was seen by a pilot, he sent a message and they were rescued by a helicopter.Lesson76

（一）In the end of news bulletin, the television announcer showed viewers fields of Calabria when grew Macaroni for six hundred years.Harvesting began earlier this year and the whole village were working hard before September rains.The crops were processed in

the factory.After the harvest, there was a famous competition which Signor Fratelli has won since 1991.That was the end of bulletin on April 1st.（二）

In the end of news bulletin, the television announcer showed viewers fields of Calabria.Here Macorroli grew for six hundred years.This year, harvesting began earlier, the whole village were working hard before the September rains so that the crop was processed in the factory.After the harvest, there was a famous competition.This Signor Fratelli has won it since 1991.With that end of bulletin, it was April 1st.Lesson77

（一）Doctors operated a mummy: an Egyptian woman who died in 800B.C..Doctors wanted to find out whether she died of a rare disease.After removing a section, doctors sent it to a laboratory.During the operation, they unexpectedly found a small wax figure of the god Duamutef which was inside the mummy.Though they were afraid that the mummy would fall to pieces, the mummy survived the operation.（二）

Doctors operated on a mummy: an Egyptian woman who died in 800 B.C..In order that they could find out if she died of a rare disease, they removed a section of the mummy which was sent to a laboratory.Inside the mummy, they unexpectedly found a figure of the god Duamutef.They were afraid that the mummy would fall to pieces, but it survived the operation.Lesson78

（一）Having read an article about smoking, the writer decided to smoke last cigarette.He didn’t smoke for a week and his wife suffered terribly, because he had a bad temper and a large appetite.Meanwhile, his friends kept on offering him cigarettes and they were amused to see his sweets.When he went to a party, he accepted a cigarette which was offered by his friend and since then things returned to normal.(二)The writer read an article about smoking and he decided to smoke last cigarette.He didn’t smoke for a week and his wife suffered terribly because of her husband’s bad temper and large appetite.Whenever his friends offered cigarettes, they were amused because he produced sweets.However, at a party, he accepted a cigarette from his friend.Now, things returned to normal.Lesson79(一)The plane took off and flew over the city.When gaining height, the plane had to return to the airport.Meanwhile, a flight attendant told them to keep clam.After disembarking, they learnt that there was a very important person on board.The police had been told that a bomb had been planted on the plane.The plane was searched thoroughly, nothing was found, the plane took off five hours later.(二)After having taken off, the plane flew low over the city.Although it gained height, it had

to return to the airport.During this time, a flight attendant told them to keep calm until it disembarked.They learned that there was an important person on board.Because the police had been told that a bomb had been planted on the plane, they searched the plane thoroughly.However, they found nothing, so the plane took off five hours later.Lesson80(一)The Crystal Palace which was built for the exhibition was different from others, because it was made of iron and glass, a great many goods were sent from the world as well as the machinery.So many visitors were taken to the Palace by boat or train that it was possible to build colleges and museums from the profits.After the exhibition, it was moved to South London where remained one of the most famous buildings in the world until it was burnt down in 1936.(二)The Crystal Palace was built for the exhibition，made of iron and glass, it was different from others.Not only the goods but also the machinery was sent from the world.This attracted the visitors who went there by boat or train.Later, the colleges and museums were built from the profits.The Crystal Palace was moved to South London and remained one of the most famous buildings in the world until 1936 when it was burnt down.Lesson81

(一)After having killed the guard, the prisoner of war dragged him into the bushes and changed into the man’s clothes.Then he put a rifle over his shoulder and marched in front of the camp.A short time afterwards, four officers got off a car and stopped at the camp gates, so the prisoner stood to attention and saluted.When they had gone, the driver of the car came towards him and after the prisoner knocked him out, he jumped into the car and drove away.(二)As soon as he had killed the guard, dragged the dead man into the bushes and changed into the dead man’s clothes, with a rifle over his shoulder, he marched in front of camp.Four officers got out of the car and he stood to attention and saluted.When the driver came towards him, he knocked the driver out.Then jumping into the car, he drove away.Lesson82(一)A strange fish was caught near Madagascar after having pulled the fishing boat out at sea.Making effort not to damage it, the fisherman brought it to shore.The fish, which was thirteen feet long with a head like horse, was sent to a museum.It is being examined by a scientist who said that it is an oarfish and they live at a depth of six hundred feet.(二)A strange fish was caught near Madagascar.Though the fishing boat was pulled out to sea, the fisherman made effort not to damage it.On being brought to shore by the fisherman, the fish was found to be over thirteen feet long and was sent to a museum.Now that is being examined by a scientist.It is called oarfish and lives at a depth of six hundred feet.Lesson 83(一)After having been defeated in the recent elections, Prime Minister retired and has gone abroad, Patrick, who has been a fanatical opponent of Mr.Lane’s Radical Progressive Party, went to the former Prime Minister’s house three times and asked the policeman whether it was Mr.Lane’s house.When it was third time, the angry policeman told him that Mr.Lane was defeated and had his retirement abroad.Patrick said that it was something he loved to hear.(二)Since the former Prime Minister was defeated in the recent elections, he has retired and gone abroad.As Patrick has been a fanatical opponent of Mr.Lane’s Party, he went to Mr.Lane’s house three times.Each time he asked the policeman if it was Mr.Lane’s house.The third time, he was told that Mr.Lane was defeated and had his retirement abroad by the angry policeman.Patrick said that he knew it, but it was something he loved to hear.Lesson84(一)Busmen’s strike begins on Tuesday which may last for a week.Because of this, car owners offer free rides to people who are going to work, university students have volunteered to drive buses too, but they will have to pass a special test.Though it is difficult to get to work, the public has expressed that they are grateful.Only one or two

people have objected that the students will drive too fast.(二)Because busmen’s strike begins on Tuesday, which may last a week.Car owners offer free rides to people going to work.University students who have volunteered to drive buses will have to pass a special test.Despite the fact that it is difficult to get to work, the public feels grateful, except for one or two who have objected that the students will drive too fast.Lesson 85(一)Now that the former headmaster Mr.Page will be retiring, pupils of the school will be sending him a gift and a large album of students’ signatures.After having attended a farewell dinner in his honor, he completed as a teacher for forty years.He will devote himself to gardening which is a new hobby for him but he has often remarked one is never too old to learn.(二)After twenty eight years as a teacher, former headmaster, Mr.Page will be retiring, pupils will sent him not only a gift but also an album of their signatures.He will attend a farewell dinner in the honor of a man who completed as a teacher for forty years.Now he will devote himself to gardening.Though it is a new hobby, it doesn’t matter because he always remarks that one is never too old to learn.Lesson86(一)The moment the speedboat had struck a buoy, both men jumped into the water.As it moved off, both men had just begun to swim towards the shore.Turning in a circle, it came straight towards them.After it just missed them, they swam as quickly as they could until they swam out of danger.When the boat returned, it lost speed.Soon the petrol was used up, it floated.(二)Because the speedboat struck a buoy, both men fell into the water.It moved off and while the men swam to the shore.Moving in a circle, it roared towards them and only just missed them, they had no sooner swum out of danger than the boat returned.This time, however, the boat lost speed, because the petrol was used up and floated.Lesson87(一)At the time of the murder that the man claimed that he was travelling on the 8 o’clock train to London and arrived to work on time.When the inspector asked if a later train would get him to work on time, the man agreed it would, but he always travelled early.The inspector suggested that he was lying because the 8 o’clock train broke down, so the man caught the 8.25.(二)When the murder happened, the man claimed that he was travelling on the 8 o’clock train to London.He said that he arrived to work on time.Then the inspector asked if a later

train would get him to work on time.Though the man agreed it would, he always travelled early.In reply, the inspector suggested he was lying as the 8 o’clock train broke down ,therefore the man caught the 8.25.Lesson 88(一)Six men who have been trapped for seventeen hours may lose lives, because the rescue operations are difficult.Since the explosives are used, vibrations will cause the roof of the mine to collapse.The rescues workers are drilling a hard rock but the progress is slow.Two hours ago, a microphone was lowered and has enabled the men to keep in touch with their relatives, they are running short of food, but they are in good spirits.(二)Six men have been trapped for seventeen hours and may lose lives.The rescue operations are difficult, as the explosives are used, it will cause the roof of the mine to collapse.Because of this, they are drilling a hard rock，yet the progress is slow.Now that, a microphone was lowered, it has enabled the men to keep in touch with their relatives.Though they are running short of food, they are in good spirits.Lesson89(一)The writer’s local cinema packed a lot of people because a comedy show would be

presented by the P.&U.Bird Seed Co.As many artists who should have appeared failed to turn up.The show was very dull, the funniest thing was the advertiser who introduced program said that ‘ This is the Poo and Ee Seed Bird Company.Good ladies, evening and gentlemen!’(二)The local cinema packed lots of people, because the P.&U.Bird Seed Co.would present free comedy show but many artists who should have appeared failed to turn up.Because of this, the show was very dull, the funniest thing was that the advertiser who introduce at the beginning of the program said that ‘This is the Poo and Ee Seed Bird Company.Good ladies, evening and gentlemen!’

Lesson 90(一)Divers working on North Sea oil rigs were terrified by a giant fish that bumped into them when they worked in deep water.The fish are not sharks or whales.On the contrary, they are favourite eating varieties that grow to unnatural sizes.There are three factors to cause the fish to grow so large.The first is the warmth from hot oil-pipes.The seconds is the plentiful food, the third is the absence of fishing.(二)Divers who worked on North Sea oil rigs were terrified by a giant fish bumping into them while they were working in deep water but the fish are not sharks or whaled, they are favorite eating varieties which grow to unnatural sizes.Three factors have caused the fish to grow so large: warmth from the oil-pipes, plentiful food and the absence of

fishing.Lesson 91(一)While circling the balloon for some time, the pilot saw three men in a basket，one of them was holding a pair of binoculars.When the balloon flew over the station, they took photographs.Then the balloon landed near an airfield but the police didn’t arrest anyone, because the basket contained two members of Parliament and Commanding officer.Afterwards, the officer explained that one half of the station didn’t know what the other half was doing.(二)A pilot circled the balloon under which there were three men in the basket containing one of them with a pair of binoculars.Before landing on, it flew over the station and took photos.It landed near an airfield.As two of the men were two members of Parliament and the other was the Commanding Officer, the police didn’t arrest them.The mystery was explained that one half of the station didn’t know what the other half was doing.Lesson92(一)The writer returned home about two a.m.and rang the doorbell.Having failed to wake up his wife, he put a ladder against the wall and climbed towards the bedroom window.Suddenly a policeman called out, the writer answered rudely, he told the policeman that he had forgotten his key, the shouting woke up his wife and she opened the window just

新概念77课 篇7

数学教育理论认为数学概念教学应该注重概念产生的背景、提出(引入)过程等环节[1];数学概念学习APOS理论模型认为学生学习数学概念进行心理建构的第一阶段就是操作或活动阶段[2],即在一定背景下引入概念;在教科书的演变过程中,因式分解内容也从讲解式发展到启发式,尤其注重从实际的例子引入,以便学生理解[3]。不难看到,概念的背景和引入是概念教学非常重要的起步。至此,笔者将因式分解概念的背景介绍和引入作为备课的重点之一,让学生通过这节课体会因式分解概念学习的必要性和重要性。

一、基于概念背景的因式分解教学设计

为更好地引入因式分解这一概念的背景,笔者进行了如下的教学设计片段:

二、基于概念背景的因式分解思考

笔者将课程的引入设计为以上三重思考,通过一些例子来渗透因式分解这一概念的必要性和重要性,让学生在一个大的背景下学习因式分解概念。

1.因式分解与学科内容的逻辑关系

因式分解是对整式的一种变形,是把一个多项式转化成几个整式乘积的形式,它与整式乘法是互逆变形的关系。因式分解是后续学习分式、二次根式、一元二次方程、二次函数等知识的基础,是解决整式恒等变形和简便运算问题的重要工具。因此,“思考1”的设计是想让学生体会到因式分解和后续学习的密切关系。笔者选择从分式化简的角度来引导学生思考,学生通过很容易想到了要想化简只需要将分子a2 a写成乘积的形式。

2.因式分解与实际应用

“思考2”展示了长方形草坪和长方体纸盒的设计问题:当长方形草坪的面积一定时,如何设计它的长和宽,当长方体包装盒的体积一定时,如何设计它的长、宽、高。尽管这样的设计不唯一,但学生通过12=4×3和ab=a × b也容易想到将a2-b2写成两个式子乘积的形式,将a3+2a2b+ab2写成三个式子乘积的形式,这样的问题让学生切实感受到生活中的一些实际问题也需要用到“将某个式子写成乘积的形式”,同时让学生感受因式分解有其几何背景。

3.因式分解与思维训练

在评课活动中,老师们曾提到,“思考1”和“思考2”的设计是在他们意料之中的, 但“思考3”的设计在他们意料之外。有老师问到,这样的问题学生在学完本课之后能解决吗?笔者认为“思考3”的设计目的并不是让学生一定会对n4+4进行因式分解,而是想让学生感受因式分解在数学史中的地位和作用,同时用这样一个数学史的问题引起学生的兴趣和思考,带着这个问题学完本章,在章节结束时顺其自然地解决这个问题。在实际授课过程中,笔者感受到学生对“思考1”和“思考2”的回答很流畅,而对“思考3”的回答就没那么顺畅了。笔者提示学生从具体的数入手计算,学生们行动起来,并把得到的数进行质因数分解,说明它是合数,也由此想到了是否能把n4+4也写成一些式子乘积的形式。

三、小结

至此,学生已经对“把某个式子写成乘积形式”这一变形的印象非常深刻了,此时提出因式分解的概念便水到渠成。后续教学过程就是围绕因式分解与整式乘法是互逆变形的关系归纳概括因式分解的概念,然后辨析概念,最后讲解了一种因式分解的基本方法—提公因式法。在本课的最后,笔者又回到了课程起始的三个思考,学生恍然大悟,要解决这三个问题,其实就是对a2-b2、a3+2a2b+ab2和n4+4进行因式分解。

整堂课下来,学生给笔者的感觉是他们多多少少体会到了学习因式分解概念的必要性,概念的产生也没有那么突兀。这使笔者感到这样的思考和备课是很有意义的。回顾已有学者、研究者对数学概念教学的研究,我们看到,概念的背景和引入虽然只是概念教学的一部分,但它却是概念教学非常重要的起步。在数学教科书的演变过程中,我们洞察到因式分解概念教学越来越注重从实际例子引入,从大的背景出发,启发学生思考,使概念在课堂中的产生顺理成章。

数学概念课教学的反思 篇8

关键词:氛围 探索性 掌握 开拓

一、概念习得过程分析

概念教学涉及到概念的起源,要让学生感受到引进这一概念的必要性,理解概念的内涵与外延即概念的本质属性,这一过程必须通过学生归纳,猜想,类比,分析等方法体现概念的形成过程得出正确的定义,成为再创造、再发现的过程。这样不仅深刻领会了概念的本质,培养了学生的思维能力,使学生产生了创新的欲望,不断探索发明,在学到了知识的同时,掌握学习、思考和解决问题的方法,在受到科学精神、科学思维的能力训练后能力得以提升。课堂的设计必须由此引发而构建的一种新的教学模式,称为“课堂交流教学模式”进行概念课教学。学生讨论交流是概念教学的基本要求,使学生在交流中获取知识,提升能力,在交流探讨中发现新知,提高学生学习的积极性,发散思维,敢于创新。教师肩负起教书育人的责任,培养出高素质人才。但概念的习得必须有一个反复认识的过程,特别是一些需要经过反复训练的解题方法,技巧等。尤其对基础比较差的学生,知识点落实要到位,如,求反函数的定义域问题。

二、概念教学中必须遵循的原则

(一)发展性原则概念教学中必须是两方面的发展相吻合。一是学生个体心志的自然发展即学生本身具备了学习其一内容的能力;二是教学本身的发展,所要教学的这一概念是已有知识的自然发展,即必须将知识的发展序列化,使教材知识的逻辑展开与学生认知规律相结合,两者的有机整合才能达到最佳效果。首先是教学内容本身体现为一个人认识的自然发展,而不是静止的,僵死的,现成认识成果。其次,必须使整个教学过程充分遵循这种人类认识的自然发展过程,并由此而实观学生个人认识的自然发展。例如,“反函数”的教学。学生已具备了判断函数的能力,学习反函数是对函数认识的延伸。而从函数知识的逻辑发展来看,要更深层次研究函数,必须引出反函数。两者有机结合,使得两方面都能得以发展,设计恰到好处。

(二)探索性原则概念教学要体现为一种探索性活动,每一个定义的呈现都必须体现一种过程,经历了这一过程不仅使学生学会怎样来定义一个数学概念,对定义的必要性与作用会有更深的体会,而且可以使学生感受到发明创造的艰辛与快乐,感受出该概念的本质属性,例如:“等比数列”的教学,课前布置问题:根据等差数列的定义,你能猜想什么是等比数列吗?试举出一两个例子。你能给等比数列一个定义吗?对照等差数列,猜想等差数列有什么性质?这一过程伴随民主平等,宽松的学习氛围,展示的是学生勇于探索,求异创新的活动。这一原则必须渗透在教学的每一环节之中,教师应有意识地设计探索性问题、开放性问题,使学生主动地置身于一种探索研究的氛围之中。

(三)深刻性原则让学生参与教学活动的目的在于建立一种平等、和谐、热烈的教学气氛,让不同层次的学生认知结构、个性品质在参与中都得到发展,所以应着眼于学生实质性的参与、深层次的思维活动,立足于展开学生的思维活动,铺之以必要的讨论和总结,使学生在参与过程中展现个性、展现能力、展现成果,使学生在展现的满足中认识自我。

三、必须解决的问题

(一)如何设计恰到好处的探索性问题。所设计的问题必须建立在学生已有认识基础之上,并且能体现研究本节课的概念的必要性,既能揭示概念的本质内涵,又不高深莫测,必须设立在认知与教学内容的生长点上,在实际操作中是有困难的。

(二)在同一班级中如何兼顾到不同层次的学生。在同一教室里每位个体的认知结构、思维方式、领悟能力各不相同,并且差距很大,如何才能充分调动每位学生的积极性,最大限度的发挥其主观能动性,这是教学组织中的难点所在,可以小组讨论,以这种学习方式达到掌握概念,并提高应用的技能。

(三)如何使知识点的落实与综合能力的提高两全其美。在平时的课后反馈可以发现,设计问题情景,使学生置身于探索之中,主动发现知识,这对于培养学生的综合能力,提高整体素质是非常有益的,那么知识点的落实、基本技能的训练如何才能得以加强?而小步快近、多练习、勤反馈正是解决问题的好方法,这种方法容易将可供探索的问题分解为较认知水平的“结构性问题”有利于扫除教学障碍。但它不利于学生学习主动性、研究探索精神的培养。由此看来,教学中必须设计两者优势互补的最佳方案,既能使知识点落到实处,又能使其它方面的能力得到较大的发展,使每位学生的收益最大化。

四、理解概念,开拓思维