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王妞妞
地区： 山西省 - 阳泉市 - 矿 区 学校：阳泉市第十三中学 共1课时6.1 平方根 初中数学 人教2011课标版 1教学目标 ＜p＞知识与技能:（1）了解算术平方根的概念，会用根号表示一个非负数的算术平方根． （2）会求一些数的算术平方根过程与方法: 会用平方运算求某些非负数的算术平方根；＜br＞＜/p＞＜p＞情感价值观: 通过对实际生活中问题的解决，让学生体验数学与生活实际是紧密联系着的，通过探究活动培养动手能力和激发学生学习数学的兴趣。＜br＞＜/p＞ 2学情分析 ＜p＞ 算术平方根是初中数学中的重要概念，引入算术平方根，是解决实际问题的需要．作为《实数》的开篇第一课，掌握好算术平方根的概念和计算，一方面可为后续研究平方根、立方根提供方法上的借鉴，另一方面也是为认识无理数，完成数集的扩充，解决数学内部运算，以及二次根式的学习等作准备．＜br＞＜/p＞＜p＞ 算术平方根的概念分两个部分，分别是关于一个正数算术平方根的定义和关于0的算术平方根的规定．由算术平方根的概念引出其符号表示、读法及什么是被开方数．＜br＞＜/p＞＜p＞ 根据算术平方根的概念，可以利用互逆关系，求一些数的算术平方根．根据这些数的算术平方根的结果，不难归纳得出“被开方数越大，对应的算术平方根也越大”的结论，其间体现了从特殊到一般的思想方法．＜br＞＜/p＞ 3重点难点 ＜p＞＜p＞三、教学重点：＜/p＞＜p＞ 算术平方根的概念。＜/p＞＜p＞四、教学难点：＜/p＞＜p＞ 根据算术平方根的概念正确求出非负数的算术平方根。＜/p＞＜br＞＜/p＞ 4教学过程 4.1 第一学时 教学活动 活动1【导入】创设情境 ＜p＞＜strong＞问题1＜/strong＞ 学校要举行美术作品比赛，小鸥想裁出一块面积为25dm 的正方形画布，画上自己的得意之作参加比赛，这块正方形画布的边长应取多少？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生可能很快答出边长为5dm．＜br＞＜/p＞＜p＞＜strong＞追问＜/strong＞请说一说，你是怎样算出来的？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生理清解决问题的思路，回答，教师可结合图片强调思路．＜br＞＜/p＞＜p＞＜strong＞问题2＜/strong＞ 完成下表：＜br＞＜/p＞＜p＞正方形的面积/dm 1 9 16 36＜br＞＜/p＞＜p＞ 边长/dm＜br＞＜/p＞＜p＞＜strong＞师生活动:＜/strong＞学生可能很快答出．＜br＞＜/p＞＜p＞＜strong＞问题3＜/strong＞:你能指出问题1与问题2的共同特点吗？＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生可能回答：上述问题都是“已知一个正方形的面积，求这个正方形的边长”的问题，教师可引导学生进一步归纳为“已知一个正数的平方，求这个正数”的问题，从而揭示问题的本质．在此基础上教师给出算术平方根的定义．＜br＞＜/p＞ 活动2【讲授】新授 ＜p＞＜strong＞定义:＜/strong＞一般地，如果一个正数x 的平方等于a ，即x＜sup＞2＜/sup＞=a ，那么这个正数x 叫做a 的算术平方根．a 的算术平方根记为＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="7"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞，读作“根号a ”，a 叫做被开方数．＜br＞＜/p＞＜p＞＜strong＞问题4＜/strong＞ 上面就一个正数给出了算术平方根的定义，那么，你认为“0的算术平方根是多少？”“怎样表示”比较合适呢？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生不难回答“0的算术平方根是0”，可以表示为“＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="8"＞0＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞=0 ”；教师指明：算术平方根的概念包含“正数算术平方根”的定义和“0的算术平方根”的规定两部分.＜br＞＜/p＞ 活动3【活动】例题 ＜p＞＜strong＞例1＜/strong＞ 求下列各数的算术平方根：＜br＞＜/p＞＜p＞（1）100；（2）＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="fraction non-leaf"＞＜span mathquill-block-id="5" class="numerator"＞＜span mathquill-command-id="8"＞1＜/span＞＜span mathquill-command-id="9"＞6＜/span＞＜/span＞＜span mathquill-block-id="6" class="denominator"＞＜span mathquill-command-id="10"＞6＜/span＞＜span mathquill-command-id="11"＞4＜/span＞＜/span＞＜span style="display:inline-block; width:0"＞ ＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞（3）0．0001．＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：教师给出第（1）小题求数的算术平方根的思考过程，学生模仿独立完成第（2）、第（3）小题，两名学生板演后，全班交流．＜br＞＜/p＞＜p＞＜strong＞追问＜/strong＞从例1中，你能发现被开方数的大小与对应的算术平方根的大小之间有什么关系吗？＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生比较被开方数的大小以及其算术平方根的大小，试图归纳出结论．如有困难，教师再举一些具体例子加以引导，说明．＜br＞＜/p＞＜p＞＜strong＞设计意图：＜/strong＞通过求大小不同的三种形式的正数的算术平方根的实践，巩固求算术平方根的方法，由特殊到一般归纳出结论：被开方数越大，对应的算术平方根也越大．为下节课学习估计平方根的大小做准备．＜br＞＜/p＞ 活动4【练习】练习 ＜p＞＜strong＞练习＜/strong＞：求下列各数的算术平方根：＜br＞＜/p＞＜p＞0.0025 121 3＜sup＞2＜/sup＞＜br＞＜/p＞ 活动5【活动】例题2 ＜p＞＜strong＞例2＜/strong＞下列式子表示什么意思？求出下列各式的值。＜br＞＜/p＞＜p＞＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="7"＞1＜/span＞＜span mathquill-command-id="8"＞4＜/span＞＜span mathquill-command-id="9"＞4＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="10"＞6＜/span＞＜span mathquill-command-id="9"＞4＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 1.75)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="11" class="fraction non-leaf"＞＜span mathquill-block-id="12" class="numerator"＞＜span mathquill-command-id="15"＞9＜/span＞＜/span＞＜span mathquill-block-id="13" class="denominator"＞＜span mathquill-command-id="16"＞1＜/span＞＜span mathquill-command-id="17"＞6＜/span＞＜span mathquill-command-id="18"＞9＜/span＞＜/span＞＜span style="display:inline-block; width:0"＞ ＜/span＞＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生先说明所求式子的含义，然后三名学生板演，全班交流，教师点评．＜br＞＜/p＞＜p＞＜strong＞设计意图：＜/strong＞使学生熟悉算术平方根的符号表示，全面了解算术平方根．＜br＞＜/p＞ 活动6【活动】探究 ＜p＞＜strong＞追问＜/strong＞（1） 根据以上学习，你认为对于算术平方根中被开方数a 可以是哪些数？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生回答，教师明确：算术平方根中被开方数a 可以是正数或0，即非负数．＜br＞＜/p＞＜p＞＜strong＞追问（2）＜/strong＞＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="8"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞＜strong＞＜/strong＞是什么数？＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生思考、回答，教师点拨： ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="8"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞是非负数，即 ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="8"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ≥0＜br＞＜/p＞＜p＞＜strong＞设计意图＜/strong＞：通过不断追问，由学生思考解决，体会分类讨论，既加深学生对算术平方根的理解，又让学生养成全面考虑问题的习惯．＜br＞＜/p＞ 活动7【练习】练习 ＜p＞下列各式是否有意义，为什么？＜br＞＜/p＞＜p＞＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="12"＞−＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="11"＞3＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="13"＞−＜/span＞＜span mathquill-command-id="11"＞3＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 1.25)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="23"＞（＜/span＞＜span mathquill-command-id="24" class="binary-operator"＞−＜/span＞＜span mathquill-command-id="25"＞3＜/span＞＜span mathquill-command-id="26"＞）＜/span＞＜sup mathquill-command-id="18" mathquill-block-id="19" class="non-leaf"＞＜span mathquill-command-id="22"＞2＜/span＞＜/sup＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 2.1)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="47" class="fraction non-leaf"＞＜span mathquill-block-id="48" class="numerator"＞＜span mathquill-command-id="52"＞1＜/span＞＜/span＞＜span mathquill-block-id="49" class="denominator"＞＜span mathquill-command-id="73"＞1＜/span＞＜span mathquill-command-id="74"＞0＜/span＞＜sup mathquill-command-id="69" mathquill-block-id="70" class="non-leaf"＞＜span mathquill-command-id="72"＞2＜/span＞＜/sup＞＜/span＞＜span style="display:inline-block; width:0"＞ ＜/span＞＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞＜br＞＜/p＞ 活动8【活动】总结 ＜p＞师生共同回顾本节课所学内容，并请学生回答以下问题：＜br＞＜/p＞＜p＞a、知道什么叫算术平方根及表示方法＜br＞＜/p＞＜p＞b、求一个正数的算术平方根＜br＞＜/p＞＜p＞c、算术平方根成立的条件＜br＞＜/p＞＜p＞d、体会了合作、互帮、互助＜br＞＜/p＞ 活动9【导入】作业 ＜p＞教科书习题6．1 第1、2题．＜br＞＜/p＞6.1 平方根 课时设计 课堂实录6.1 平方根 1第一学时 教学活动 活动1【导入】创设情境 ＜p＞＜strong＞问题1＜/strong＞ 学校要举行美术作品比赛，小鸥想裁出一块面积为25dm 的正方形画布，画上自己的得意之作参加比赛，这块正方形画布的边长应取多少？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生可能很快答出边长为5dm．＜br＞＜/p＞＜p＞＜strong＞追问＜/strong＞请说一说，你是怎样算出来的？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生理清解决问题的思路，回答，教师可结合图片强调思路．＜br＞＜/p＞＜p＞＜strong＞问题2＜/strong＞ 完成下表：＜br＞＜/p＞＜p＞正方形的面积/dm 1 9 16 36＜br＞＜/p＞＜p＞ 边长/dm＜br＞＜/p＞＜p＞＜strong＞师生活动:＜/strong＞学生可能很快答出．＜br＞＜/p＞＜p＞＜strong＞问题3＜/strong＞:你能指出问题1与问题2的共同特点吗？＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生可能回答：上述问题都是“已知一个正方形的面积，求这个正方形的边长”的问题，教师可引导学生进一步归纳为“已知一个正数的平方，求这个正数”的问题，从而揭示问题的本质．在此基础上教师给出算术平方根的定义．＜br＞＜/p＞ 活动2【讲授】新授 ＜p＞＜strong＞定义:＜/strong＞一般地，如果一个正数x 的平方等于a ，即x＜sup＞2＜/sup＞=a ，那么这个正数x 叫做a 的算术平方根．a 的算术平方根记为＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="7"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞，读作“根号a ”，a 叫做被开方数．＜br＞＜/p＞＜p＞＜strong＞问题4＜/strong＞ 上面就一个正数给出了算术平方根的定义，那么，你认为“0的算术平方根是多少？”“怎样表示”比较合适呢？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生不难回答“0的算术平方根是0”，可以表示为“＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="8"＞0＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞=0 ”；教师指明：算术平方根的概念包含“正数算术平方根”的定义和“0的算术平方根”的规定两部分.＜br＞＜/p＞ 活动3【活动】例题 ＜p＞＜strong＞例1＜/strong＞ 求下列各数的算术平方根：＜br＞＜/p＞＜p＞（1）100；（2）＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="fraction non-leaf"＞＜span mathquill-block-id="5" class="numerator"＞＜span mathquill-command-id="8"＞1＜/span＞＜span mathquill-command-id="9"＞6＜/span＞＜/span＞＜span mathquill-block-id="6" class="denominator"＞＜span mathquill-command-id="10"＞6＜/span＞＜span mathquill-command-id="11"＞4＜/span＞＜/span＞＜span style="display:inline-block; width:0"＞ ＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞（3）0．0001．＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：教师给出第（1）小题求数的算术平方根的思考过程，学生模仿独立完成第（2）、第（3）小题，两名学生板演后，全班交流．＜br＞＜/p＞＜p＞＜strong＞追问＜/strong＞从例1中，你能发现被开方数的大小与对应的算术平方根的大小之间有什么关系吗？＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生比较被开方数的大小以及其算术平方根的大小，试图归纳出结论．如有困难，教师再举一些具体例子加以引导，说明．＜br＞＜/p＞＜p＞＜strong＞设计意图：＜/strong＞通过求大小不同的三种形式的正数的算术平方根的实践，巩固求算术平方根的方法，由特殊到一般归纳出结论：被开方数越大，对应的算术平方根也越大．为下节课学习估计平方根的大小做准备．＜br＞＜/p＞ 活动4【练习】练习 ＜p＞＜strong＞练习＜/strong＞：求下列各数的算术平方根：＜br＞＜/p＞＜p＞0.0025 121 3＜sup＞2＜/sup＞＜br＞＜/p＞ 活动5【活动】例题2 ＜p＞＜strong＞例2＜/strong＞下列式子表示什么意思？求出下列各式的值。＜br＞＜/p＞＜p＞＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="7"＞1＜/span＞＜span mathquill-command-id="8"＞4＜/span＞＜span mathquill-command-id="9"＞4＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="10"＞6＜/span＞＜span mathquill-command-id="9"＞4＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 1.75)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="11" class="fraction non-leaf"＞＜span mathquill-block-id="12" class="numerator"＞＜span mathquill-command-id="15"＞9＜/span＞＜/span＞＜span mathquill-block-id="13" class="denominator"＞＜span mathquill-command-id="16"＞1＜/span＞＜span mathquill-command-id="17"＞6＜/span＞＜span mathquill-command-id="18"＞9＜/span＞＜/span＞＜span style="display:inline-block; width:0"＞ ＜/span＞＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生先说明所求式子的含义，然后三名学生板演，全班交流，教师点评．＜br＞＜/p＞＜p＞＜strong＞设计意图：＜/strong＞使学生熟悉算术平方根的符号表示，全面了解算术平方根．＜br＞＜/p＞ 活动6【活动】探究 ＜p＞＜strong＞追问＜/strong＞（1） 根据以上学习，你认为对于算术平方根中被开方数a 可以是哪些数？＜br＞＜/p＞＜p＞＜strong＞师生活动＜/strong＞：学生回答，教师明确：算术平方根中被开方数a 可以是正数或0，即非负数．＜br＞＜/p＞＜p＞＜strong＞追问（2）＜/strong＞＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="8"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞＜strong＞＜/strong＞是什么数？＜br＞＜/p＞＜p＞＜strong＞师生活动：＜/strong＞学生思考、回答，教师点拨： ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="8"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞是非负数，即 ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="4" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="5" class="non-leaf sqrt-stem"＞＜var mathquill-command-id="8"＞a＜/var＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ≥0＜br＞＜/p＞＜p＞＜strong＞设计意图＜/strong＞：通过不断追问，由学生思考解决，体会分类讨论，既加深学生对算术平方根的理解，又让学生养成全面考虑问题的习惯．＜br＞＜/p＞ 活动7【练习】练习 ＜p＞下列各式是否有意义，为什么？＜br＞＜/p＞＜p＞＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="12"＞−＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="11"＞3＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 0.9)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="13"＞−＜/span＞＜span mathquill-command-id="11"＞3＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 1.25)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="23"＞（＜/span＞＜span mathquill-command-id="24" class="binary-operator"＞−＜/span＞＜span mathquill-command-id="25"＞3＜/span＞＜span mathquill-command-id="26"＞）＜/span＞＜sup mathquill-command-id="18" mathquill-block-id="19" class="non-leaf"＞＜span mathquill-command-id="22"＞2＜/span＞＜/sup＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞ ＜span style="font-size:20px" class="mathquill-rendered-math"＞＜span class="textarea"＞＜textarea data-cke-editable="1" contenteditable="false"＞＜/textarea＞＜/span＞＜span mathquill-command-id="8" class="non-leaf"＞＜span style="-webkit-transform:scale(1, 2.1)" class="scaled sqrt-prefix"＞√＜/span＞＜span mathquill-block-id="9" class="non-leaf sqrt-stem"＞＜span mathquill-command-id="47" class="fraction non-leaf"＞＜span mathquill-block-id="48" class="numerator"＞＜span mathquill-command-id="52"＞1＜/span＞＜/span＞＜span mathquill-block-id="49" class="denominator"＞＜span mathquill-command-id="73"＞1＜/span＞＜span mathquill-command-id="74"＞0＜/span＞＜sup mathquill-command-id="69" mathquill-block-id="70" class="non-leaf"＞＜span mathquill-command-id="72"＞2＜/span＞＜/sup＞＜/span＞＜span style="display:inline-block; width:0"＞ ＜/span＞＜/span＞＜/span＞＜/span＞＜/span＞＜span＞ ＜/span＞＜br＞＜/p＞ 活动8【活动】总结 ＜p＞师生共同回顾本节课所学内容，并请学生回答以下问题：＜br＞＜/p＞＜p＞a、知道什么叫算术平方根及表示方法＜br＞＜/p＞＜p＞b、求一个正数的算术平方根＜br＞＜/p＞＜p＞c、算术平方根成立的条件＜br＞＜/p＞＜p＞d、体会了合作、互帮、互助＜br＞＜/p＞ 活动9【导入】作业 ＜p＞教科书习题6．1 第1、2题．＜br＞＜/p＞Tags：平方根,课堂,实录
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