八年级数学教案示例：立方根

这是一份八年级数学教案示例：立方根，共5页。教案主要包含了教学目标，教学重点和难点，教学方法，教学手段，教学过程等内容，欢迎下载使用。
八年级数学教案示例：立方根　　一、教学目标1.了解立方根和开立方的概念;2.会用根号表示一个数的立方根，掌握开立方运算;3.培养学生用类比的思想求立方根的运算能力;4.由立方与立方根的教学，渗透数学的转化思想;5.通过立方根符号的引入体验数学的简洁美.二、教学重点和难点教学重点：立方根的概念与性质.教学难点：会求某些数的立方根.三、教学方法启发式，讲练结合四、教学手段幻灯片.五、教学过程(一)复习提问请同学们回忆一下，平方根我们是如何定义的?平方根有哪些性质?在同学们回答后，启发学生是否可试着给数的立方根下个定义.1.立方根的概念：如果一个数的立方等于a，这个数就叫做a的立方根.(也称数a的三次方根)用数学式表示为：若x3=a，则x叫做a的立方根，或称x叫做a的三次方根.2.立方根的表示方法：类似于平方根德表示方法，数a的立方根我们用符号                              来表示.读作“三次根号下a”，其中a叫做被开方数，3叫做根指数，注意，在前面我们学习平方根的表示方法说过当根指数为2时可以省略不写，现在是立方根了，这个根指数3是绝对不可省的，否则就会与平方根混淆了，例如                                                        表示125的立方根，而                                                        则表示125的算术平方根.                                                        练习：用根号表示下列各数的立方根：                                                                                                                                                               3.开立方概念：求一个数的立方根的运算，叫做开立方.                 4.开立方运算与立方运算互为逆运算.因此，我们可以根据立方运算来求一些数的立方根.例1. 求下列各数的立方根：                                               解：(1)∵(-2)3=-8，                                                                                                       (2)∵23=8，                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           (4)∵ (0.6)3=0.216，                                                                                                                                                                                                                                                                               (5)∵03=0，                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               下面我们思考这样一个问题：一个正数有几个平方根?负数有没有平方根?一个正数有几个立方根?负数有没有立方根?请学生来回答这个问题.由前面刚刚做过的题我们不难看出像8、0.126、103、                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    这样的正数，有一个正的立方根;像-8、                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    、                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    这样的负数有一个负的立方根;0的立方根是0.由此我们得了立方根的性质.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    5.立方根的性质：(1)正数有一个正的立方根.(2)负数有一个负的立方根.宋以后，京师所设小学馆和武学堂中的教师称谓皆称之为“教谕”。至元明清之县学一律循之不变。明朝入选翰林院的进士之师称“教习”。到清末，学堂兴起，各科教师仍沿用“教习”一称。其实“教谕”在明清时还有学官一意，即主管县一级的教育生员。而相应府和州掌管教育生员者则谓“教授”和“学正”。“教授”“学正”和“教谕”的副手一律称“训导”。于民间，特别是汉代以后，对于在“校”或“学”中传授经学者也称为“经师”。在一些特定的讲学场合，比如书院、皇室，也称教师为“院长、西席、讲席”等。(3)0的立方根是0.这里我们不妨与平方根的性质做个比较，平方根中，正数有两个平方根，它们互为相反数，正数只有一个正的立方根;在平方根中负数是没有平方根的，而负数有一个负的立方根;平方根与立方根唯一相同之处是0的平方根，立方根都是它本身.家庭是幼儿语言活动的重要环境，为了与家长配合做好幼儿阅读训练工作，孩子一入园就召开家长会，给家长提出早期抓好幼儿阅读的要求。我把幼儿在园里的阅读活动及阅读情况及时传递给家长，要求孩子回家向家长朗诵儿歌，表演故事。我和家长共同配合，一道训练，幼儿的阅读能力提高很快。