发布人：叶海波
所在工作坊： 宜都市初中数学1坊
时间日期：2018-10-10 至 2018-12-31
59讨论 18人
发布人：叶海波
所在工作坊： 宜都市初中数学1坊
时间日期：2018-10-10 至 2018-12-31
59讨论 18人
<p><strong><span style="font-size:20px;font-family:仿宋">人教版八年级数学第十六章</span></strong></p><p style="text-align:center;text-indent:12px"><strong><span style="font-size:24px;font-family:宋体">《二次根式的除法》</span></strong><strong> </strong><strong><span style="font-size:24px;font-family: 宋体">教学设计</span></strong></p><p><strong><span style="font-size:19px;font-family:宋体">教学目标：</span></strong></p><p><span style="font-size:19px">1.</span><span style="font-size:19px;font-family:宋体">知识与技能</span></p><p><span style="font-size:19px">(1)</span><span style="font-size:19px;font-family:宋体">理解二次根式的除法法则和商的算术平方根法则</span><span style="font-size:19px">.</span></p><p><span style="font-size:19px">(2)</span><span style="font-size:19px;font-family:宋体">运用这两个法则进行运算</span><span style="font-size:19px">.</span></p><p><span style="font-size:19px">2.</span><span style="font-size:19px;font-family:宋体">过程与方法</span></p><p><span style="font-size:19px">(1)</span><span style="font-size:19px;font-family:宋体">先由具体数据发现规律，导出二次根式的除法法则并运用它进行计算</span><span style="font-size:19px">.</span></p><p><span style="font-size:19px">(2)</span><span style="font-size:19px;font-family:宋体">再利用逆向思维，得出商的算术平方根法则并运用它进行解题和化简</span><span style="font-size:19px">.</span></p><p><span style="font-size:19px">(3)</span><span style="font-size:19px;font-family:宋体">最后综合运用以上两个规律进行解题</span><span style="font-size:19px">. </span></p><p><span style="font-size:19px"> 3.</span><span style="font-size:19px;font-family:宋体">情感、态度与价值观</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">通过探究二次根式的除法法则培养学生由特殊到一般的探究精神，让学生推导商的算术平方根法则以训练逆向思维，通过严谨解题，增强学生准确解题的能力，引导学生从特殊到一般总结归纳的方法以及类比的方法解决数学问题</span><span style="font-size:19px">.</span></p><p><strong><span style="font-size:19px;font-family:宋体">学情分析：</span></strong><strong><span style="font-size:19px"> </span></strong></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">本节内容主要是在进行二次根式的除法运算时，分母含根号的处理方式上，学生可能会出现困难或容易失误，在除法运算中，可以先计算后利用商的算术平方根的性质来进行，也可以先利用分式的性质，去掉分母中的根号，再结合乘法法则和积的算术平方根的性质来进行</span><span style="font-size:19px">.</span><span style="font-size:19px;font-family:宋体">二次根式的除法与分式的运算类似，如果分子、分母中含有相同的因式，可以直接约去，以简化运算。教学中不能只是列举题型，应以各级各类习题为载体，引导学生把握运算过程，估计运算结果，明确运算方向</span><span style="font-size:19px">.</span></p><p><strong><span style="font-size:19px;font-family:宋体">重点难点</span></strong><strong><span style="font-size:19px"> </span></strong></p><p><span style="font-size:19px;font-family:宋体">重点</span><span style="font-size:19px">:</span><span style="font-size:19px;font-family:宋体">二次根式的除法法则</span></p><p><span style="font-size:19px;font-family:宋体">难点</span><span style="font-size:19px">:</span><span style="font-size:19px;font-family:宋体">二次根式的化简</span></p><p><strong><span style="font-size:19px;font-family:宋体">教学过程：</span></strong></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">一、问题发现，感受新知</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">问题</span><span style="font-size:19px">1 </span><span style="font-size:19px;font-family:宋体">设长方形的面积为</span><em><span style="font-size:19px">S</span></em><span style="font-size:19px;font-family: 宋体">，其中一边长为</span><em><span style="font-size:19px">a</span></em><span style="font-size:19px">,</span><span style="font-size:19px;font-family: 宋体">则另一边长表示为：</span><span style="position:relative;top:16px"><img width="28" height="35" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></p><p style="text-indent:47px"><span style="font-size:19px;font-family:宋体">问题</span><span style="font-size:19px">2 </span><span style="font-size:19px;font-family: 宋体">已知</span><em><span style="font-size:19px">S= </span></em><span style="position:relative;top:4px"><img width="33" height="23" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><em><span style="font-size:19px"> </span></em><em><span style="font-size:19px;font-family:宋体">，</span></em><em><span style="font-size:19px">a= </span></em><span style="position:relative;top:5px"><img width="24" height="24" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><em><span style="font-size:19px"> </span></em><span style="font-size:19px">,</span><span style="font-size:19px;font-family:宋体">那么求另一边长时如何列式</span><span style="font-size:19px">? </span><span style="font-size:19px;font-family:宋体">答：</span><span style="position:relative;top:19px"><img width="36" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px;font-family:宋体">；</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">问题</span><span style="font-size:19px">3 </span><span style="font-size:19px;font-family:宋体">上面列式是什么运算</span><span style="font-size:19px">?</span><span style="font-size:19px;font-family: 宋体">又该如何计算呢</span><span style="font-size:19px">?</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">导入课题：二次根式的除法</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">二、合作探究，获取新知</span></p><p><span style="font-size:19px"> 1.</span><span style="font-size:19px;font-family:宋体">阅读教材</span><span style="font-size:19px">P8</span><span style="font-size:19px;font-family:宋体">，计算并发现规律</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">（</span><span style="font-size:19px">1</span><span style="font-size:19px;font-family:宋体">）</span><span style="position:relative;top:19px"><img width="28" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span>=<span style="text-decoration:underline;"><span style="position:relative;top:16px"><img width="16" height="41" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></span><span style="font-family:宋体">，</span><span style="position:relative;top:17px"><img width="28" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span>=<span style="text-decoration:underline;"><span style="position:relative;top:16px"><img width="16" height="41" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></span><span style="font-family:宋体">，</span><span style="position:relative;top:19px"><img width="67" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">（</span><span style="font-size:19px">2</span><span style="font-size:19px;font-family:宋体">）</span><span style="position:relative;top:19px"><img width="35" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span>=<span style="text-decoration:underline;"><span style="position:relative;top:16px"><img width="16" height="41" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></span><span style="font-family:宋体">，</span><span style="position:relative;top:17px"><img width="35" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span>=<span style="text-decoration:underline;"><span style="position:relative;top:16px"><img width="16" height="41" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></span><span style="font-family:宋体">，</span><span style="position:relative;top:19px"><img width="81" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></p><p style="text-indent:47px"><span style="font-size:19px">(3)</span><span style="font-size:19px;font-family:宋体">＝</span><span style="font-size:19px;font-family:宋体">，</span><span style="font-size:19px;font-family:宋体">＝</span><span style="font-size:19px;font-family:宋体">，</span><span style="text-decoration:underline;"><span style="font-size:19px;font-family:宋体">＝</span></span><span style="font-size:19px;font-family:宋体">；</span></p><p><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">二次根式的除法法则：</span><span style="font-size:19px;font-family:宋体">＝</span><span style="font-size:19px">(<em>a</em></span><span style="font-size:19px;font-family:宋体">≥</span><span style="font-size:19px">0</span><span style="font-size:19px;font-family:宋体">，</span><em><span style="font-size:19px">b</span></em><span style="font-size:19px">>0)</span><span style="font-size:19px;font-family: 宋体">．</span></p><p style="text-indent:37px"><span style="font-size:19px">2.</span><span style="font-size:19px;font-family:宋体">例</span><span style="font-size:19px">1</span><span style="font-size:19px;font-family:宋体">：计算</span></p><p style="text-indent:37px"><br/></p><table><tbody><tr class="firstRow"><td width="60"><br/></td><td width="60"><br/></td></tr><tr><td><br/></td><td><img width="160" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></td></tr></tbody></table><p><span style="font-size:19px"> </span></p><p><br/></p><p><br/> </p><p style="text-indent:37px"><span style="font-size:19px">3.</span><span style="font-size:19px;font-family:宋体">试回顾如何计算</span><span style="position:relative;top:5px"><img width="72" height="24" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px">? .</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">想一想：如何计算</span> <span style="position:relative;top:16px"><img width="93" height="41" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">呢？</span></p><p style="text-indent:37px"><span style=";position: absolute;z-index:251649536;left:0px;margin-left:252px;margin-top:11px;width:276px;height:25px"><img width="276" height="25" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px;font-family:宋体">二次根式的除法扩充法则：</span></p><p style="text-indent:37px"><span style=";position: relative;z-index:251650560"><span style="left:0px;position:absolute;left:36px;top:-1px;width:116px;height:47px"><img width="116" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></span><span style="font-size:19px"> </span></p><p><br/> </p><p style="text-indent:37px"><span style=";position: absolute;z-index:251651584;left:0px;margin-left:36px;margin-top:31px;width:153px;height:48px"><img width="153" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px">4.</span><strong> </strong><span style="font-size:19px;font-family:宋体">商的算术平方根的性质及应用</span></p><p style="text-indent:37px"><span style="font-size:19px"> </span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">记住成立的条件！</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">利用它可以进行二次根式的化简</span><span style="font-size:19px">.</span></p><p style="text-indent:37px"><span style="font-size:19px">5.</span> <span style="font-size:19px;font-family:宋体">例</span><span style="font-size:19px">2 </span><span style="font-size:19px;font-family:宋体">化简</span></p><p style="text-indent:37px"><span style="font-size:19px">A</span><span style="font-size:19px;font-family:宋体">组</span><span style="position:relative;top:17px"><img width="59" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span> <span style="position:relative;top:17px"><img width="55" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-family:宋体">（用不同的方法求解）</span></p><p style="text-indent:37px"><span style="font-size:19px">6.</span><span style="font-size:19px;font-family:宋体">分母有理化：把分母中的根号化去</span><span style="font-size: 19px">,</span><span style="font-size:19px;font-family:宋体">使分母变成有理数的这个过程就叫做分母有理化</span><span style="font-size:19px">.</span></p><p style="text-indent:37px"><br/></p><table><tbody><tr class="firstRow"><td width="36"><br/></td><td width="36"><br/></td></tr><tr><td><br/></td><td><img width="232" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></td></tr></tbody></table><p><span style="font-size:19px"> </span></p><p><br/></p><p><br/> </p><p style="text-indent:37px"><span style="font-size:19px">7.</span><span style="font-size:19px;font-family:宋体">例</span><span style="font-size:19px">2 </span><span style="font-size:19px;font-family:宋体">化简</span></p><p style="text-indent:37px"><span style=";position: absolute;z-index:251653632;left:0px;margin-left:84px;width:160px;height:48px"><img width="160" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px">B</span><span style="font-size:19px;font-family:宋体">组</span></p><p style="text-indent:37px"><span style=";position: absolute;z-index:251654656;left:0px;margin-left:156px;margin-top:31px;width:28px;height:44px"><img width="28" height="44" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size: 19px">8.</span><span style="font-size:19px;font-family:宋体">课堂小游戏：角色扮演，我问你答</span></p><p style="text-indent:37px"><strong><span style="font-size:19px;font-family:宋体">例：</span></strong><span style="font-size: 19px;font-family:宋体">我是式子</span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">，</span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">我的化简结果在哪里？</span></p><p style="text-indent:75px"><span style="font-size:19px;font-family:宋体">我是</span><span style="font-size:19px"> </span><span style="position:relative;top:5px"><img width="24" height="24" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">，我是（）的化简结果？</span></p><p style="text-indent:37px"><span style="font-size:19px">9.</span><span style="font-size:19px;font-family:宋体">最简二次根式：满足如下两个特点：</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">（</span><span style="font-size:19px">1</span><span style="font-size:19px;font-family: 宋体">）被开方数中不含分母；</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">（</span><span style="font-size:19px">2</span><span style="font-size:19px;font-family: 宋体">）被开方数中不含能开得尽方的因数或因式</span></p><p style="text-indent:37px"><span style="font-size:19px">(</span><span style="font-size:19px;font-family:宋体">简记为：一根号无分母，分母无根号；二不能再开方）</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">三、课堂练习，深化新知</span></p><p style="text-indent:37px"><span style="font-size:19px">1.</span><span style="font-size:19px;font-family:宋体">计算</span><span style="position:relative;top:19px"><img width="55" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">的结果是（</span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">）</span></p><p style="text-indent:37px"><span style="font-size:19px">A. 3 B. 5 C. 6 D. 8</span></p><p style="text-indent:16px"><span style=";position: absolute;z-index:251655680;left:0px;margin-left:72px;width:47px;height:44px"><img width="47" height="44" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:32px;font-family:黑体"> </span><span style="font-size:19px">2.</span><span style="font-size:19px;font-family:宋体">把</span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">化简得</span><span style="font-size:19px">( )</span></p><p style="text-indent:37px"><span style=";position: absolute;z-index:251660800;left:0px;margin-left:168px;margin-top:31px;width:237px;height:47px"><img width="237" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: absolute;z-index:251659776;left:0px;margin-left:432px;width:40px;height:23px"><img width="40" height="23" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: absolute;z-index:251658752;left:0px;margin-left:300px;margin-top:10px;width:44px;height:23px"><img width="44" height="23" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: absolute;z-index:251657728;left:0px;margin-left:156px;margin-top:10px;width:54px;height:23px"><img width="54" height="23" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: absolute;z-index:251656704;left:0px;margin-left:72px;margin-top:10px;width:53px;height:23px"><img width="53" height="23" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size:19px">A. B. C. D. </span></p><p style="text-indent:37px"><span style="font-size:19px">3</span><span style="font-size:19px;font-family:宋体">在二次根式</span><span style="font-size:19px"> </span><span style="font-size:19px;font-family:宋体">中属于最简二次根式的是</span><span style="font-size:19px"> <span style="text-decoration:underline;"> </span> </span></p><p style="text-indent:37px"><span style=";position: absolute;z-index:251662848;left:0px;margin-left:396px;margin-top:11px;width:31px;height:24px"><img width="31" height="24" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: absolute;z-index:251661824;left:0px;margin-left:240px;margin-top:11px;width:32px;height:24px"><img width="32" height="24" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size: 19px">4. </span><span style="font-size:19px;font-family:宋体">已知长方形的面积</span><span style="font-size:19px">S= , </span><span style="font-size:19px;font-family:宋体">若一边长</span><em><span style="font-size:19px">a</span></em><span style="font-size:19px">= ,</span><span style="font-size:19px;font-family:宋体">则</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">另一边长</span><em><span style="font-size:19px">b</span></em><span style="font-size:19px">= <span style="text-decoration:underline;"> </span> </span></p><p style="text-indent:37px"><span style=";position: absolute;z-index:251666944;left:0px;margin-left:108px;margin-top:51px;width:143px;height:47px"><img width="143" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: absolute;z-index:251665920;left:0px;margin-left:336px;margin-top:10px;width:131px;height:25px"><img width="131" height="25" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style=";position: relative;z-index:251664896"><span style="left:0px;position:absolute;left:216px;top:-1px;width:61px;height:47px"><img width="61" height="47" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span></span><span style=";position: absolute;z-index:251663872;left:0px;margin-left:108px;width:63px;height:48px"><img width="63" height="48" src="http://study.yanxiu.jsyxsq.com/proj/static/ueditor/themes/default/images/spacer.gif"/></span><span style="font-size: 19px">5.</span><span style="font-size:19px;font-family:宋体">化简：</span></p><p style="text-indent:37px"><span style="font-size:19px"> </span></p><p style="text-indent:37px"><span style="font-size:19px"> </span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">四、课堂小结，巩固新知</span></p><p style="text-indent:37px"><span style="font-size:19px;font-family:宋体">（小组交流，集体反馈）</span></p><p style="text-indent:37px"><span style="font-size:19px">1.</span><span style="font-size:19px;font-family:宋体">二次根式的除法法则</span></p><p style="text-indent:37px"><span style="font-size:19px">2.</span><span style="font-size:19px;font-family:宋体">分母有理化</span></p><p style="text-indent:37px"><span style="font-size:19px">3.</span><span style="font-size:19px;font-family:宋体">最简二次根式</span></p><p style="text-indent:37px"><span style="font-size:19px"> </span></p><p><br/></p>