最新垂线教学设计人教版 垂线的教学方法(八篇)
人的记忆力会随着岁月的流逝而衰退,写作可以弥补记忆的不足,将曾经的人生经历和感悟记录下来,也便于保存一份美好的回忆。范文书写有哪些要求呢?我们怎样才能写好一篇范文呢?下面我给大家整理了一些优秀范文,希望能够帮助到大家,我们一起来看一看吧。
垂线教学设计人教版 垂线的教学方法篇一
1、使学生掌握过直线上一点作直线的垂线和过直线外一点作直线的垂线的方法。
2、了解点到直线的距离的概念,明白从直线外一点到这条直线所画的垂直线段最短。
垂直的画法。
理解“点到直线的距离”的概念。
教具:三角板、电脑、投影。
学具:三角板。
一、复习铺垫
1、让学生画两条互相垂直的直线。
(1)学生独立作画,教师巡视检查。
(2)投影学生作品,及时评讲。
(3) 说一说:哪一条直线是哪一条直线的垂线?什么是垂足?在哪里?(学生讲时,教师在作品中指出)。
2、 今天,我们进一步学习画垂线的方法。
二、探究新课
1、过直线上的一点,作已知直线的垂线.
(1)例2 过直线上a点,作直线的垂线.(教师示范后学生练习)
画的方法和步骤
把三角板的一条直角边与直线重合.
沿直线移动三角板,使直角顶点与a点重合.
从a点起,沿另一直角边画一条直线.
过a点新画出的直线,就是原直线的垂线.
指名到黑板上试画过直线上的点的直线的垂线,其余同学在本上试画.教师巡视指导.
(2)练习:过直线上的点作直线的垂线:
2、过直线外一点画这条直线的垂线.
(1)例 过直线外一点b,作这条直线的垂线.(可以先让学生小组交流,尝试作图,展示几张作品,让一名学生示范画,老师在一边傍述作图方法)
画的方法和步骤:
把三角板的一条直角边与已知直线重合.
沿直线移动三角板,使三角板另一条直角边过已知b点.
从直角的顶点起,沿另一直角边画一条直线.
新画出的这条直线就是过线外b点所求的垂线.
(2)练习:过直线外的点作直线的垂线:
3.理解垂线的性质,建立距离的概念.
把直线外一点a与直线上任意一点连接起来,可以画多少条线段?哪一条最短?
(1) 画出一条直线和直线外一点(师生同步)
(2) 每人画4条
(3)测量每条线段的长度
(4)你所画的线段中,哪一条最短?
引导学生得出:从直线外一点到这条直线所画的垂直线段最短,它的长度叫做这点到直线的距离.
师指出:从直线外一点到这条直线所画垂直线段的长度实际上距离就是垂线线段的长度.
4.画垂线的应用.
我们可以应用画垂线的方法画长方形和正方形.
例 画一个长2、5厘米,宽2厘米的长方形和正方形.
提问:正方形和长方形的特征是什么?
引导学生明确:它们的对边相等,相邻的两条边互相垂直.
画的步骤如下:
先画一条2、5厘米长的线段;
过两个端点在线段的同侧画两条与它垂直的线段,每条线段长2厘米;
把这两条线段的端点连接起来.
同学们在本上画一个边长2厘米的正方形.
教师行间巡视,加强指导.
5、拓展题:让我来当工程师
新建一座大楼,要接水,又接电,怎样接,最省料?水管
大楼、
水管
5.小结.启发性提问:
(1)过一点怎样作已知直线的垂线/
(2)从直线外一点到这条直线,可以画多少条线段?什么样的线段最短?
(3)什么叫做距离?
(三)巩固反馈1、课本第69页第5、6、7、8题。
(四)作业设计
1、课本第68页第4(1)、(3)题。
2、理解记忆作图方法,熟记什么叫距离。
垂线教学设计人教版 垂线的教学方法篇二
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垂线教学设计人教版 垂线的教学方法篇三
垂线的认识
1.使学生认识垂线,会判断两条直线相交是不是互相垂直,会用三角板画垂线。
2.使学生知道垂线的性质,理解测定点到直线的距离的方法。
判断两条直线相交是不是互相垂直
理解点到直线的距离
(一)动手操作,得出概念:
1.请任意画两条直线(有两种情况)
2.相交 不相交,但经过延长也是相交的
3.不相交,且经过延长也不相交
4.今天我们研究直线相交的情况。
5.请画两条直线使相交,想一想二条直线相交分几种情况。
a
b
(1) (2)
4.图2中四个角相等吗?
图1中角1是直角,是90度,那么其它三只角会是什么角呢?
5.小结:
两条直线相交成直角时,这两条直线互相垂直;
其中一条直线是另一条直线的垂线,它们的交点叫做垂足。
试一试:
说一说图1中——是——的垂线。(体现相互性)
6、举例说明 生活中有这样的情况吗?
(二)应用实践:
1.判断下列哪组是相互垂直。
(体现不同的方位)
2.从直线外一点画一条直线的垂线
(1)哪一条线是垂线?
(2)哪一条线段最长?
(3)哪一条线段最短?
(4)从中你得到了什么启发?
结论1:从直线外一点到直线的距离,与这条直线垂直的线段最短。展开阅读全文
结论2:从直线外一点到这条直线所画的垂直线段的长度,叫做这点到直线的距离。
3.画下列直线的垂线:p61 1
4.过一点画下列直线的垂线:p61 2
5.韩家篓要修一条公路,请你帮助设计一条最近的连接公路的路:p 61 3
6、p61 4 5
(三)总结提高:
1.垂直、垂线、垂足的定义,区别。
2.会画垂线。
(四)作业:
作业本展开阅读全文
垂线教学设计人教版 垂线的教学方法篇四
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垂线教学设计人教版 垂线的教学方法篇六
1、使学生明确垂线的重要性质,直线外一点到这条直线间的距离垂线最短。学会用三角板准确的画垂线。
2、培养学生良好的学习习惯。初步培养学生空间想象能力。
3、通过动手操作活动,使学生经历画垂线的过程,培养学生的作图能力。。
4、通过活动,让学生从中感受到学习的乐趣,体会到成功的喜悦,从而提高学习的兴趣。
学会用三角板准确的画垂线
准确的画出垂线。使学生明确垂线的重要性质,直线外一点到这条直线间的距离垂线最短。
1、创设情境
(1)你还记得什么叫垂直吗?
(2)生活中哪里有互相垂直的现象?
2、提出学习目标:
(1)学会用三角板准确画垂线。
(2)什么叫点到直线的距离?
1、小组内个人展示
学生独立自学、完成例题2(教师相机的进行指导,收集学生的学习信息,重在让学生展示不同的思维方法和错例,特别是引导小组内学生之间的交流与探讨)。完成后在小组内按学困生→中等生→优生的顺序进行展示,小组内互相交流、帮助、质疑问难。
2、全班展示(以小组为单位)
(1)、过直线上一点画这条直线的垂线
学生汇报画法:
三角板上有一个角是直角,通常可以用三角尺来画垂线。
①先画一条直线。
②把三角板的一条直角边与这条直线重合,沿着另一条直角边画出的直线就是前一条直线的垂线(直角顶点是垂足)。
师强调:让三角板的直角顶点落在给定的这点上。
(2)、过直线外一点画这条直线的垂线
学生汇报画法:
①用三角板的一条直角边与已知直线重合;
②然后沿着已知直线移动三角板,用三角板的另一条直角边紧靠已知点;
③最后沿着三角板的另一条直角边画一条直线,这条直线就是已知直线的垂线。
师强调:
一般用左手持三角板,右手画线。当要求直线通过其一点时,要考虑到笔画的粗细度,三角板的边与已知点之间可稍留一些空隙。最后让我们标注上垂直符号。
(3)、学习点到直线的距离
①直线外一点a与直线上任意一点连接起来,可以画出很多条线段。
②这些线段中,哪条最短?(垂直线段的长度最短)
你是怎么知道的?(可以目测,也可以用尺测量)
这条垂直的线段有几条?(只有1条)
说明它很特殊,于是它也有个专用的名字,看书66页最后一段,全班齐读。
边展示边引发知识的冲突,让学生更深层次的进行思考:
1、针对同学的展示,学生自由质疑问难。
2、教师引导学困生提出问题:同学们,你在学习中碰到困难了吗?能把你遇到的确困难说给大家听吗?那你对同学的展示会有什么时候想法与建议吗?
1、基本练习。
完成练习十一第4题(1)画一画
2、小组探究,实际应用:
(1)完成练习十一第5题
测定跳远成绩时,怎样测量比较准确?为什么?
(2)完成练习十一第6题
垂线教学设计人教版 垂线的教学方法篇七
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垂线教学设计人教版 垂线的教学方法篇八
本节的重点是会用两直线垂直的定义判定两条直线垂直和点到直线的距离的概念。两直线垂直的定义中虽然强调“有一个角是直角”,但实际上由对顶角和邻补角的性质,可以得到其他三个角也都是直角,因此不指定哪一个角是直角,实际上无论哪一个角是直角,都可以判定两直线垂直。反过来,已知两直线垂直,那么它们的四个交角中无论哪一个角都是直角。对于点到直线的距离,一定要给学生强调距离是垂线段的长度,是一个数量,而不能误认为是垂线段本身。本节课的内容较多,垂线的性质、画法、垂线段的性质以及点到直线的距离,都是重点。
理解垂线的定义,点到直线的距离,掌握垂线的性质,会过一点画已知直线的垂线。经历画已知直线的垂线,测量两点之间的距离比较、归纳理解垂线的两个性质。培养学生合作交流的方法和意识,以及数学在实际生活中的应用意识。
启发式、讨论式以及讲练结合的教学方法。
(一)导入新课
1、相交线:两条直线有且只有一个交点的两条直线叫相交线。
展示教具:把两根细木条看作是两条直线,固定木条a,转动木条b,当b的位置变化时,a、b所成的角α会发生什么变化。当α =90°时,其他三个角有什么变化?这时a与b有什么关系呢?
2、垂线的定义:当直线a与直线b相交所构成的四个角中有一个角为直角时,其它三个角也都成为直角,
此时,直线a,b互相垂直,记作“a⊥b”,它们的交点o叫做垂足。
3、垂直的表示方法:符号表示
(二)讲授新课
1、垂线的性质
经过直线a上(外)一点p画a的垂线,可以画几条?
在同一平面内,经过直线上或直线外一点,有且只有一条直线与已知直线垂直。
2、垂线的.画法
①作一条已知直线的垂线(提示利用垂直定义)。
分别用直角三角板作垂线和用量角器作垂线
②过一点作已知直线的垂线(注意点与直线的两种位置关系)。
③图形演示,总结画法。
总结画垂线的方法:“一靠、二过、三画”
一靠:把三角板的一条直角边靠在已知直线上;(垂直定义的运用,有90°角就有垂直)二过:让三角板的另一条直角边经过已知的点;三画:沿着直角边经过已知点画直线。”
3、垂线段
思考:有人不慎掉入有鳄鱼的湖中。如图,他在p点,应选择什么样的路线尽快游到岸边m呢?
概念:作线段pb⊥直线m,如图,垂足为b,我们就把线段pb叫做点p到直线m的垂线段。
过直线外一点作已知直线的垂线,这点与垂足间的线段叫垂线段。
提出问题:垂线与垂线段有何区别和联系?
区别:垂线是直线,垂线段是线段联系:垂线和垂线段都有垂直关系。
4、垂线段的性质
如图:线段pa,pb,pc,pd谁最短?请你用直尺量一量,和你的同伴一起检验你的猜测是否正确?
直线外一点与直线上的各点连结的线段中,线段最短。
5、点到直线的距离
点到直线的距离:从直线外一点到这条直线的垂线段的线段长度叫点到直线的距离。
6、知识应用
例1、如下图,已知ab⊥cd,垂足为o,oe是一条射线,且∠aoe=35°,求∠boe、∠coe的度数。
解:∵ ab⊥cd ∴∠aoc=90°
∵∠aoe=35°
∴∠coe=55°,∠boe=∠boc+∠coe=145°
(三)课堂练习:课本p137练习1 、2
如图,已知直线ab与cd相交于点o,ob平分eod,°=+9021,问:图中的线是否存在互相垂直的关系,若有,请写出哪些线互相垂直,并说明理由;若无,直接说明理由.
(四)课堂小结:
①通过本节课的学习,你学会了哪些知识;②通过本节课的学习,你最大的体验是什么;③通过本节课的学习,你掌握了哪些学习数学的方法?
(五)布置作业: