何玉侠 2020-11-10 10:35
<table><tbody><tr class="firstRow"><td width="43" style="border: 1px solid windowtext; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">课题</span></strong></p></td><td width="525" colspan="3" style="border-top: 1px solid windowtext; border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-image: initial; border-left: none; padding: 0px 7px;"><p style="text-align:center"><span style=";font-family:宋体;color:black">3.1</span><span style=";font-family:宋体;color:black">不等关系和不等式（2）</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">教材</span></strong></p></td><td width="525" colspan="3" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">全日制普通高中课程标准试验教科书（必修5）</span></p></td></tr><tr style=";height:29px"><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">授课</span></strong></p></td><td width="525" colspan="3" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><br/></td></tr><tr style=";height:29px"><td width="43" rowspan="3" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">三</span></strong></p><p><strong><span style=";font-family:宋体;color:black">维</span></strong></p><p><strong><span style=";font-family:宋体;color:black">目</span></strong></p><p><strong><span style=";font-family:宋体;color:black">标</span></strong></p></td><td width="96" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">知识与技能 </span></p></td><td width="429" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">掌握不等式的基本性质，会用不等式的性质证明简单的不等式。</span></p></td></tr><tr style=";height:30px"><td width="96" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">过程与方法</span></p></td><td width="429" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="margin-left:0"><span style=";font-family:宋体;color:black">通过解决具体问题，</span><span style=";font-family:宋体;color:black">理解证明不等式的逻辑推理方法。</span></p></td></tr><tr style=";height:42px"><td width="96" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">情感态度</span></p><p><span style=";font-family:宋体;color:black">与价值观</span></p></td><td width="429" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">通过对不等式性质的掌握，培养学生灵活应变的解题能力</span><span style=";font-family:宋体;color:black">和逻辑推理能力。</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">重点</span></strong></p></td><td width="525" colspan="3" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">掌握不等式的性质和利用不等式的性质证明简单的不等式。</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">难点</span></strong></p></td><td width="525" colspan="3" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p><span style=";font-family:宋体;color:black">利用不等式的性质求字母系数或代数式的范围。</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">准备</span></strong></p></td><td width="525" colspan="3" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:150%"><span style=";line-height:150%;font-family:宋体;color:black">多媒体课件</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">教学方法</span></strong></p></td><td width="525" colspan="3" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">启发引导，类比探究，讲练结合</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">教学</span></strong></p><p><strong><span style=";font-family:宋体;color:black">过程</span></strong></p></td><td width="408" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="text-align:center;line-height:16px"><span style=";font-family:宋体;color:black">教学情境设计</span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="margin-top:0;margin-right:62px;margin-bottom: 0;margin-bottom:0;text-indent:48px;line-height:16px"><span style=";font-family:宋体;color:black">设计意图 设计意图</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">创</span></strong></p><p><strong><span style=";font-family:宋体;color:black">设</span></strong></p><p><strong><span style=";font-family:宋体;color:black">情</span></strong></p><p><strong><span style=";font-family:宋体;color:black">境</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p></td><td width="408" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">我们知道，等式有一些基本性质，如</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"><img width="149" height="92" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">不等式是否有类似性质呢？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">带着这个问题，我们进入本节课的学习！</span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">从学生熟悉的知识点入手，通过类比和设问，激发学生学习兴趣，引入新课.</span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">探</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">究</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">新</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">知</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">探</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">究</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">新</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">知</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p></td><td width="408" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">探究 </span><span style=";font-family:宋体;color:black">不等式的性质</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考1：若1班人数比2班多，则2班人数比1班少，反之亦然.从数学的观点分析，这里反映了一个不等式性质，你能用数学符号语言表述这个不等式性质吗？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（1）a＞b </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="21" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> b</span><span style=";font-family:宋体;color:black">＜a（对称性）</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考2：若1班人数比2班多，2班人数比3班多，那么1班人数比3班多，这里反映出的不等式性质如何用数学符号语言表述？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（2）a＞b，b＞c </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> a</span><span style=";font-family:宋体;color:black">＞c；</span></p><p style="text-indent:35px;line-height:16px"><span style=";font-family:宋体;color:black">c</span><span style=";font-family:宋体;color:black">＜b，b＜a </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> c</span><span style=";font-family:宋体;color:black">＜a（传递性）</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考3：若1班人数比<a></a><a>2班多</a>，如果每班增加同样多的人或减少同样多的人，则1班人数仍然比2班多，这里反映出的不等式性质如何用数学符号语言表述？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（3）a＞b </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> a+c</span><span style=";font-family:宋体;color:black">＞b+c（可加性）</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考4：若1班的男生比2班多，1班的女生也比2班多，则1班的人数比2班多. 这里反映出的不等式性质如何用数学符号语言表述？ </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（4）a＞b，c＞d</span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> a+c</span><span style=";font-family:宋体;color:black">＞b+d（同向不等式的可加性）</span></p><p style="line-height:16px"><strong><span style=";font-family:宋体;color:black">注意：</span></strong><span style=";font-family:宋体;color:black">同向不等式具有可加性，但同向不等式不具有可减性。</span></p><p style="text-indent:42px;line-height:16px"><span style=";font-family:宋体;color:black">如：8>3，-2>-9，但8-(-2)<3-(-9).</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考5：如果a＞b，c＞0，那么ac与bc的大小关系如何？如果a＞b，c＜0，那么ac与bc的大小关系如何？为什么？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"><img width="269" height="109" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（5）a＞b，c＞0 </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> ac</span><span style=";font-family:宋体;color:black">＞bc；</span></p><p style="text-indent:35px;line-height:16px"><span style=";font-family:宋体;color:black">a</span><span style=";font-family:宋体;color:black">＞b，c＜0 </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> ac</span><span style=";font-family:宋体;color:black">＜bc.（可乘性）</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考6：如果a＞b＞0，c＞d＞0，那么ac与bd的大小关系如何？为什么？</span></p><p style="text-indent:29px"><span style=";font-family:宋体;color:black">证明：</span><span style=";font-family:宋体;color:black;position:relative;top:7px"><img width="87" height="21" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="64" height="19" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black">①</span></p><p style="text-indent:56px"><span style=";font-family: 宋体;color:black">又</span><span style=";font-family:宋体;color:black;position:relative;top:7px"><img width="92" height="21" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black">∴</span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="53" height="19" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black">② </span></p><p style="text-indent:21px"><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black">由 ①、②可得</span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="53" height="19" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"><img width="3" height="3" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（6）a＞b＞0，c＞d＞0 </span><span style=";font-family:宋体;color:black;position:relative;top:4px"><img width="19" height="15" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> ac</span><span style=";font-family:宋体;color:black">＞bd.（同向不等式的可乘性)</span></p><p style="text-indent:29px;line-height:16px"><span style=";font-family:宋体;color:black">注：这一推论可以推广到任意有限个两边都是正数的同向不等式两边分别相乘<img width="3" height="3" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/>这就是说，两个或者更多个两边都是正数的同向不等式两边分别相乘，所得不等式与原不等式同向<img width="3" height="3" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考7：如果a＞b＞0，n∈N*，那么a<sup>n</sup>与b<sup>n</sup>的大小关系如何？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（7）</span><span style=";font-family:宋体;color:black;position:relative;top:7px"><img width="212" height="24" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family: 宋体;color:black">（可乘方性）</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">思考8：如果a＞b＞0，n∈N*，那么</span><span style=";font-family:宋体;color:black;position:relative;top:5px"><img width="24" height="23" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family: 宋体;color:black">与</span><span style=";font-family:宋体;color:black;position:relative;top:5px"><img width="23" height="23" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black">的大小关系如何？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">（8）</span><span style=";font-family:宋体;color:black;position:relative;top:7px"><img width="225" height="25" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span><span style=";font-family:宋体;color:black"> </span><span style=";font-family:宋体;color:black">（可开方性）</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">【<strong>探究总结</strong>】不等式的性质是证明不等式和解不等式的理论基础，必须熟练掌握，注意不等式性质中的条件.</span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">通过实例引导学生探究不等式的性质，培养学生勇于探索的情感和态度。. </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">通过简单的推理和证明，加深对不等式性质的了解。</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p></td></tr><tr><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">尝</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">试</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">运</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">用</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">尝</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">试</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">运</span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black"> </span></strong></p><p><strong><span style=";font-family:宋体;color:black">用</span></strong></p></td><td width="408" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><strong><span style=";font-family:宋体;color:black">类型一 不等式的性质的理解</span></strong></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">例1.判断对错：</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"><img width="161" height="150" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><img width="252" height="183" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/><span style=";font-family:宋体;color:black"></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">【题后小结】利用不等式判断正误的两种方法</span></p><p style="margin-left:24px;line-height: 16px"><span style=";font-family:宋体;color:black">(1) </span><span style=";font-family:宋体;color:black">直接法：对于说法正确的，要利用不等式的相关性质证明；对于说法错误的只需举出一个反例即可.</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">(2)</span><span style=";font-family:宋体;color:black">特殊值法.</span></p><p style="line-height:16px"><strong><span style=";font-family:宋体;color:black">类型二 不等式的性质的应用</span></strong></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">1. </span><span style=";font-family:宋体;color:black">已知<span style="position:relative;top:5px"><img width="84" height="17" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span>求证：<span style="position:relative;top:16px"><img width="43" height="41" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span></span></p><p style="line-height:16px"><br/></p><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span><p><br/></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><br/> <p style="text-indent:14px;line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px">你还有其他证明方法吗？还可以利用作差法.</span></p><p style="line-height:16px"><br/></p><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span><p><br/></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black;position:relative;top:16px"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><br/> <p style="line-height:16px"><span style=";font-family:宋体;color:black">2</span><span style=";font-family:宋体;color:black">．如果12＜a＜60，15＜b＜36，求a－b及 的取值范围.</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"><img width="196" height="248" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif" alt=" "/></span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">【题后小结】</span></p><p style="line-height:150%"><span style=";line-height:150%;font-family:宋体;color:black">1.</span><span style=";line-height:150%;font-family:宋体;color:black">不等式证明常用的方法（1）利用性质（2）作差法</span></p><p style="margin-left:21px;line-height:150%"><span style=";position:absolute;z-index:251667456;left:0px;margin-left:150px;margin-top: 1514px;width:18px;height:56px"><img width="12" height="37" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position:absolute;z-index:251666432;left:0px;margin-left:527px;margin-top: 1477px;width:20px;height:56px"><img width="13" height="37" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";line-height:150%;font-family:宋体;color:black">2.</span><span style="font-family:宋体">欲求</span>a<span style="font-family: 宋体">－</span>b<span style="font-family:宋体">的取值范围，先求－</span>b<span style="font-family:宋体">的取值范围，欲求</span> <span style="font-family:宋体">的取值范</span></p><p style="margin-left:21px;line-height:150%"><span style="font-family:宋体">围，先求</span> <span style="font-family:宋体">的取值范围</span>,<span style="font-family:宋体">再用不等式的性质求解。</span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">通过简单的判断，使学生进一步理解不等式的性质。让学生及时巩固新知。</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">利用不等式的性质证明简单的不等式或求代数式的范围。</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black"> </span></p></td></tr><tr style=";height:103px"><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p style="line-height:150%"><strong><span style=";line-height:150%;font-family:宋体;color:black">课</span></strong></p><p style="line-height:150%"><strong><span style=";line-height:150%;font-family:宋体;color:black">堂</span></strong></p><p style="line-height:150%"><strong><span style=";line-height:150%;font-family:宋体;color:black">练</span></strong></p><p style="line-height:150%"><strong><span style=";line-height:150%;font-family:宋体;color:black">习</span></strong></p></td><td width="408" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style=";text-autospace:none"><span style=";font-family:宋体;color:black">1.</span><span style=";font-family:宋体;color:black">若</span><span style=";font-family:宋体;color:black">a</span><span style=";font-family:宋体;color:black">，</span><span style=";font-family: 宋体;color:black">b</span><span style=";font-family:宋体;color:black">，</span><span style=";font-family:宋体;color:black">c</span><span style=";font-family:宋体;color:black">，</span><span style=";font-family:宋体;color:black">d</span><span style=";font-family:宋体;color:black">均为实数，且有下列结论：</span></p><p style=";text-autospace:none"><span style=";position:absolute;z-index:251672576;left:0px;margin-left:580px;margin-top: 1545px;width:56px;height:56px"><img width="37" height="37" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";font-family:宋体;color:black">甲：若</span><span style=";font-family:宋体;color:black">a>b>0</span><span style=";font-family: 宋体;color:black">，则</span><span style=";font-family: 宋体;color:black">ac>bc</span><span style=";font-family:宋体;color:black">； </span><span style=";position:absolute;z-index:251671552;left:0px;margin-left:108px;margin-top: 1556px;width:48px;height:48px"><img width="32" height="32" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";font-family:宋体;color:black"> 乙：若</span><span style=";font-family:宋体;color:black">a>b</span><span style=";font-family:宋体;color:black">，则</span><span style=";font-family:宋体;color:black">a-c>b-c</span><span style=";font-family:宋体;color:black">；</span></p><p style="line-height:150%;text-autospace:none"><span style=";line-height:150%;font-family:宋体;color:black">丙：若 ，</span><span style=";line-height:150%;font-family: 宋体;color:black">ab>0</span><span style=";line-height:150%;font-family:宋体;color:black">，则</span><span style=";line-height:150%;font-family: 宋体;color:black">bc>ad</span><span style=";line-height:150%;font-family:宋体;color:black">；丁：若</span><span style=";line-height:150%;font-family: 宋体;color:black">a>b</span><span style=";line-height:150%;font-family:宋体;color:black">，</span><span style=";line-height:150%;font-family: 宋体;color:black">c<d</span><span style=";line-height:150%;font-family:宋体;color:black">,</span><span style=";line-height:150%;font-family: 宋体;color:black">cd</span><span style=";line-height:150%;font-family:宋体;color:black">≠0</span><span style=";line-height:150%;font-family:宋体;color:black">，则 </span></p><p style="line-height:150%;text-autospace:none"><span style=";line-height:150%;font-family:宋体;color:black">以上结论中错误的个数是</span><span style=";line-height:150%;font-family:宋体;color:black">(</span><span style=";line-height:150%;font-family:宋体;color:black"> C </span><span style=";line-height:150%;font-family: 宋体;color:black">)</span></p><p style="line-height:16px"><span style=";position:absolute;z-index:251673600;left:0px;margin-left:384px;margin-top: 1608px;width:54px;height:51px"><img width="36" height="34" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";font-family:宋体;color:black">A.0</span> <span style=";font-family: 宋体;color:black"> </span> <span style=";font-family:宋体;color:black">B.1</span> <span style=";font-family:宋体;color:black"> C.2</span> <span style=";font-family: 宋体;color:black"> </span> <span style=";font-family:宋体;color:black">D.3</span></p><p style="line-height:150%"><span style=";position:absolute;z-index:251670528;left:0px;margin-left:275px;margin-top: 1612px;width:19px;height:57px"><img width="13" height="38" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";line-height:150%;font-family:宋体;color:black">2.</span><span style=";line-height:150%;font-family:宋体;color:black">若6<a<8，12<b<16，则 的范围是_____.</span></p><p style="line-height:150%;text-autospace:none"><span style=";position:absolute;z-index:251669504;left:0px;margin-left:366px;margin-top: 1626px;width:126px;height:57px"><img width="84" height="38" src="http://study.teacheredu.cn/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";line-height:150%;font-family:宋体;color:black">3.已知</span><span style=";line-height:150%;font-family: 宋体;color:black">a>b>0</span><span style=";line-height:150%;font-family:宋体;color:black">，c<d<0，e<0，</span><span style=";line-height:150%;font-family:宋体;color:black">求证: </span></p><p style="line-height:16px;text-autospace:none"><span style=";font-family:宋体;color:black"> </span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">巩固本节课所学的知识，反馈课堂教学信息．</span></p></td></tr><tr style=";height:97px"><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p><strong><span style=";font-family:宋体;color:black">学习</span></strong></p><p><strong><span style=";font-family:宋体;color:black">小结</span></strong></p></td><td width="408" colspan="2" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">通过这堂课的学习你有哪些收获？</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">1.</span><span style=";font-family:宋体;color:black">不等式的基本性质；</span></p><p style="line-height:16px"><span style=";font-family:宋体;color:black">2.</span><span style=";font-family:宋体;color:black">不等式基本性质的应用.</span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">对于不等式的性质方面的收获进行小结.</span></p></td></tr><tr style=";height:57px"><td width="43" style="border-right: 1px solid windowtext; border-bottom: 1px solid windowtext; border-left: 1px solid windowtext; border-image: initial; border-top: none; padding: 0px 7px;"><p style="line-height:150%"><strong><span style=";line-height:150%;font-family: 宋体;color:black">巩固</span></strong></p><p style="line-height:150%"><strong><span style=";line-height:150%;font-family: 宋体;color:black">作业</span></strong></p></td><td width="408" colspan="2" valign="bottom" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:150%"><span style=";line-height:150%;font-family:宋体">不等关系与不等式（2）作业(见附页）</span></p><p style="text-align:center;line-height:16px"><span style=";font-family:宋体;color:black"> </span></p></td><td width="117" style="border-top: none; border-left: none; border-bottom: 1px solid windowtext; border-right: 1px solid windowtext; padding: 0px 7px;"><p style="line-height:16px"><span style=";font-family:宋体;color:black">进一步巩固所学知识.</span></p></td></tr></tbody></table><p><br/></p>