含绝对值不等式优秀教案.pdf
【课题】含绝对值的不等式【教学目标】知识目标：（1）理解含绝对值不等式xa或xa的解法；（2）了解axbc或axbc的解法能力目标：培养学生观察、分析、归纳、概括的能力，以及逻辑推理能力，考察学生思维的积极性和全面性，领悟分类讨论、化归和数形结合的数学思想方法，培养数学理解力，化归能力及运算能力，初步学会用数学思想指导数学思维。情感目标：激发学生学习兴趣，鼓励学生大胆探索，向学生渗透“具体抽象具体”、“未知已知未知”的辩证唯物主义的认识论观点，使学生形成良好的个性品质和学习习惯。【教学重点】（1）不等式xa或xa的解法（2）利用变量替换解不等式axbc或axbc【教学难点】利用变量替换解不等式axbc或axbc教学方法：主要采取启导式教学，通过对初中不等式知识及绝对值的含义和几何意义等相关知识的学习引入，在教师指导下由实例引出解绝对值不等式的实际意义，导出解决含绝对值不等式的解法这一研究主题。【教学设计】（1）从数形结合的认识绝对值入手，有助于学生对知识的理解；（2）观察图形得到不等式xa或xa的解集；（3）运用变量替换，化繁为简，培养学生的思维能力；（4）加强解题实践，讨论、探究，培养学生分析与解决问题的能力，培养团队精神【教学备品】教学课件【课时安排】1-2 课时(80 分钟)【安全教育：清点人数】教学过程教师行为学生行为教学意图时间*揭示课题含绝对值的不等式*回顾思考复习导入问题任意实数的绝对值是如何定义的其几何意义是什么解决对任意实数x，有,0,0,0,0.xxxxxx其几何意义是：数轴上表示实数x的点到原点的距离拓展不等式2x和2x的解集在数轴上如何表示根据绝对值的意义可知，方程2x的解是2x或2x，不等式2x的解集是(2,2)（如图（1）所示）；不等式2x的解集是(,2)(2,)U（如图（2）所示）介绍提问归 纳总结引导分析了解思考回答观察领会复习相关知识点为进一步学习做准备充分借助图像进行分析8*动脑思考明确新知一般地，不等式xa（0a）的解集是,a a；不等式xa（0a）的解集是,aaU试一试：写出不等式xa,与xa（0a）的解集总结强化理解记忆强调特点15*巩固知识典型例题例解下列各不等式：（1）310 x；（2）26x?分析：将不等式化成xa或xa的形式后求解解（1）由不等式310 x，得13x，所以原不等式的分析讲解强调细节思考主动求解进一步巩固知识点20（2）（1）文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1教学过程教师行为学生行为教学意图时间解集为11,33U；（2）由不等式26x?，得3x,，所以原不等式的解集为3,3*运用知识强化练习教材练习2.4.1解下列各不等式：（1）28x；（2）2.6x；（3）10 x巡视辅导解题交流反馈学习效果25*实际操作探索新知问题如何通过xa（0a）求解不等式213x解决在 不 等 式213x中，设21mx，则 不 等 式213x化为3m，其解集为33m，即3213x利用不等式的性质，可以求出解集总结可以通过“变量替换”的方法求解不等式axbc或axbc（0c）质疑引导演示归纳思考观察体会理解通过实例使学生初步领会变量替换的思想30*动脑思考感悟新知不等式axbc或axbc（0c）可以通过“变量替换”的方法求解实际运算中，可以省略变量替换的书写过程即axbccaxbcaxbcaxbcaxbc或说明强调理解记忆归纳方法便于学生应用35*巩固知识典型例题例 2解不等式213x,引领分析思路观察思考领会巩固知识强调45文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1教学过程教师行为学生行为教学意图时间解由原不等式可得3213x剟，于是224x剟，即12x剟，所以原不等式的解集为1,2例 3解不等式257x解由原不等式得257x或257x，整理，得6x或1x，所以原不等式的解集为,61,U讲解主动求解不等式求解的细节*运用知识强化练习教材练习2.4.2 解下列各不等式：（1）49x；（2）1142x,；（3）546x；（4）1122x巡视指导求解交流反馈学习效果60*归纳小结强化思想本次课学了哪些内容重点和难点各是什么*自我反思目标检测本次课采用了怎样的学习方法你是如何进行学习的你的学习效果如何引导总结反思交流培养学生总结学习过程能力65讨论交流总结阅读教材本章阅读与欣赏数学家华罗庚，小组讨论交流：1.我所知道的华罗庚；2.我要向华罗庚学习引导倾听讨论交流培养学生学习品质75*继续探索活动探究(1)读书部分：教材章节，学习与训练；(2)书面作业：教材习题，学习与训练训练题说明记录80教 学 反 思：本 节 课 内 容 可 以 分 成 两 节 课 来 进 行，前 一 节 课 主 要 讲 解文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 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HB10K6F10J4L4 ZT9A6Q3J1P1x()x(0)a aoa a或型的不等式，后一节课主要讲解(0)(0)axbc caxbc c或者型的不等式。当然如果班级学生理解能力强，反应快，掌握好，也可以一节课完成。含绝对值的不等式有三种解法，一是根据绝对值的意义，二是两边平方，转化成一元二次不等式来解，三是分类讨论。结合中职生的实际情况，本节课主要学习第一种解法。后两种可以在复习课的时候选讲。教学主要通过数形结合，通过观察数轴来解含绝对值的不等式，教学中一定要反复强调结合图像，否则学生容易出错。由于知识点比较简单，可以多提问，提高学生学习热情，尤其是中等生和差生，有机会表现自己，借此提高学习数学的积极性。教学板书：含有绝对值的不等式一、原理：x()a ao的解集是：x（-，-a）（a,+）x()a ao 的解集是：x（-a,a）二、例题讲解：例 1：解下列不等式（1）310 x；（2）26x?例 2解不等式213x,例 3解不等式257x文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 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ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1文档编码:CO3N9G3Z3N8 HB10K6F10J4L4 ZT9A6Q3J1P1
