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1、整体思想解题策略（一）一、教学目标：1、通过学习掌握数学解决问题的基本方式之一，整体代入法；2、让学生掌握将要解决的问题看作一个整体，通过对问题的整体形式、整体结构、已知条件和所求综合考虑后代入的方法?二、教学重点与难点整体思想方法在代数式的化简与求值、解方程（组）等方面都有广泛的应用，整体代入、叠加叠乘处理、整体运算、整体设元、整体处理等都是整体思想方法在解数学问题中的具体运用三、教学过程（一）数与式中的整体思想【例 1】已知代数式3x24x+6 的值为 9，则2463xx的值为()A18 B12 C9 D7 相应练习：1.若代数式2425xx的值为7，那么代数式221xx的值等于（）A2
2、B3 C2 D4 2.若 3a2-a-2=0,则 5+2a-6a2=3.先化简，再求值222142442aaaaaaaa，其中 a 满足 a22a1=0总结：此类题是灵活运用数学方法解题技巧求值的问题，首先要观察精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 1 页，共 4 页已知条件和需要求解的代数式，然后将已知条件变换成适合所求代数式的形式，运用主题带入法即可得解。【例 2】.已知114ab，则2227aabbabab的值等于（）A.6B.6C.125D.27分析：根据条件显然无法计算出a，b的值，只能考虑在所求代数式中构造出11ab的形式，再整体代入求解【例 3】已知2
3、002007ax，2002008bx，2002009cx，求多项式222abcabbcac的值总结：在进行条件求值时，我们可以根据条件的结构特征，合理变形，构造出条件中含有的模型，然后整体代入，从整体上把握解的方向和策略，从而使复杂问题简单化【例 4】逐步降次代入求值：已知 m2-m-1=0，求代数式 m3-2m+2005的值相 应 练 习：1、已 知m是 方 程2250 xx的 一 个 根，求32259mmm的值.2、已知m是方程2310 xx的根，求代数式10214mm的值.总结：此类题目通常为初中阶段很少接触到得三次方程甚至更高次的方程，那么用初中阶段的知识直接解题时肯定行不通的，所以这
4、个时候我们就要考虑如何降次的问题。通常来讲技巧性还是蛮强的。（二）几何与图形中的整体思想【例 5】如图，123456分析：由于本题出无任何条件，因而单个角是无法求出的利用三角形的性质，我们将12视为一个整体，那么应与 ABC中BAC精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 2 页，共 4 页文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ
5、9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL1
6、0M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码
7、:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4
8、HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 Z
9、L10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档
10、编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V
11、4 HJ9N1C3K8I7 ZL10M6Z1X7R9的外角相等，同理34，56分别与ABC，ACB的外角相等，利用三角形外角和定理，本题就迎刃而解了用整体思想解题不仅解题过程简捷明快，而且富有创造性，有了整体思维的意识，在思考问题时，才能使复杂问题简单化，提高解题速度，优化解题过程同时，强化整体思想观念，灵活选择恰当的整体思想方法，常常能帮助我们走出困境，走向成功课堂练习：1当代数式a-b 的值为 3 时，代数式 2a-2b+1的值是()A5 B6 C7 D8 2用换元法解方程(x2+x)2+2(x2+x)1=0，若设 y=x2+x，则原方程可变形为()Ay2+2y+1=0 By22y+1=0
12、 Cy2+2y1=0 Dy22y1=0 3 当 x=1时，代数式ax3+bx+7的值为 4，则当 x=l 时，代数式ax3+bx+7的值为()A7 B10 C11 D12 4(08 芜湖)已知113xy，则代数式21422xxyyxxyy的值为 _ 5已知 x22x1=0，且 x0，则1xx=_布置作业：1如果(a2+b2)22(a2+b2)3=0，那么a2+b2=_2(07泰州)先化简，再求值：2224124422aaaaaa，其中a是方程x2+3x+1=0的根3、已知a是方程2200910 xx一个根，求22200920081aaa的值.4 附加题：阅读材料，解答问题为了解方程(x21)2
13、5(x21)+4=0我们可以将 x21 视为一个精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 3 页，共 4 页文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7
14、ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文
15、档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3
16、V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I
17、7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R
18、9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6
19、M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9整体，然后设 x21=y，则原方程可化为 y25y+4=0 解得 y1=1，y2=4当 y=1 时，x21=1，x2=2，2x；当
20、y=4 时，x21=4，x2=5，5x12x，22x，35x，45x解答问题：(1)填空：在由原方程得到方程 的过程中，利用_法达到了降次的目的，体现了 _ 的数学思想；(2)用上述方法解方程：x4x26=0四、教学反思精品w o r d 学习资料 可编辑资料-精心整理-欢迎下载-第 4 页，共 4 页文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K
21、8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X
22、7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5
23、C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C
24、3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z
25、1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6
26、I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9文档编码:CC6I5C6M3V4 HJ9N1C3K8I7 ZL10M6Z1X7R9