平面图形的周长和面积的复习课
济南市明湖小学 李伟
教学
内容
财务内部控制制度的内容财务内部控制制度的内容人员招聘与配置的内容项目成本控制的内容消防安全演练内容
:
教科书第97页内容，及相应练习
题
快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题
教材分析:
平面图形的周长和面积是小学阶段平面图形的主要内容。因此在六年级下册的复习中，处在一个比较重要的地位。借助本节课，使学生理解平面图形各种公式的推导过程，尤其是直线图形中的面积公式以及圆的周长和面积公式。通过复习巩固，帮助学生进一步掌握这部分知识，为后面的立体图形打好基础。 学情分析:
学生通过前阶段的学习，基本掌握了各种平面图形的周长和面积的计算方法，但是由于时间的迁移等各种原因，学生对于公式的推导过程有所淡忘，导致在应用公式解决实际问题中，常常遇到问题，从而影响学生的进一步学习。老师所要做的就是引导学生借助各种素材，进一步建立这些知识间的联系，从而起到巩固复习的目的。
学习目标:
1(使学生掌握周长和面积的含义。
2(使学生知道平面图形的周长和面积的公式是怎样推导出来的。掌握已学平面
图形周长和面积的
计算公式
六西格玛计算公式下载结构力学静力计算公式下载重复性计算公式下载六西格玛计算公式下载年假计算公式
，并会计算它的周长和面积。
3(让学生在解决问题的过程中，体验学习数学的乐趣，培养创新意识。 教学重难点:
1. 平面图形周长和面积计算公式的推导过程，尤其是面积公式的推导过程; 2. 借助公式，解决简单的实际问题。
教具、学具准备:
学生课前准备梳理的框架图、教师准备课件。
教学过程:
一、整理回顾，明确周长和面积的含义:
1.什么是平面图形的周长和面积,
教师提出问题:什么是平面图形的周长,什么是平面图形的面积, leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
让不同的学生根据自己的理解，说一说什么是周长,什么是面积, 明确:围成一个图形的所有边长的总和，叫作它们的周长。
物体的
表
关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf
面或围成平面图形的大小，叫做它们的面积。 2.课件演示:
课件演示周长和面积的含义，让学生齐读。
明确:计算周长时，应该用长度单位，计算面积时，应该用面积单位。 (设计意图:让学生根据自己的理解说什么是周长和面积，通过回顾，从概念上进一步明确它们的含义，以及使用的单位，从而为下面的复习做好铺垫。) 二、小组合作交流梳理:
师:我们明确了周长和面积的意义，课前要求大家梳理了平面图形周长和面积的
计算方法，根据平面图形的面积完成他们之间关系的框架图;并且复习回顾
了面积公式的推导过程。(课件展示)
1.小组内交流整理的公式和梳理的框架:
师:下面请同学们把整理的平面图形周长和面积的计算公式和梳理的框架在小组
内交流，待会介绍给大家。
小组活动，师巡视指导。
(设计意图:要求学生在家提前整理，在小组内进行交流，使学生明确
知识点
高中化学知识点免费下载体育概论知识点下载名人传知识点免费下载线性代数知识点汇总下载高中化学知识点免费下载
以及重难点和发现自身存在问题，并带着问题和收获进行交流，寻求帮助) 2.小组汇报:
生先介绍面积和周长公式，再根据推倒的过程介绍梳理的框架。 师引导，学生补充。(如:平行四边形不仅可以连接长方形，还可以连接正方形等)
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
(设计意图:通过初次汇报，使学生对平面图形的周长和面积的计算公式和内部关系初步感知，为下面的拓展和练习做准备)
3.再次梳理平面图形面积公式的推导:
师:刚才这个小组根据推导过程进行了梳理，下面请同学们在小组内按照这位同
学梳理的思路，进一步回忆一下这些平面图形的面积公式是如何推导的, 生小组活动，师巡视指导。
4.小组汇报:
借助学具和视频展台带领大家复习，师适时点拨，生发问
师同时引导不同观点的学生补充，
(设计意图:在初次汇报的基础上，再次进行讨论汇报，目的是使学生更好地理解平面图形周长和面积公式的推导过程，并且对于某些特殊情况进行补充，以达到复习巩固的目的)
4.归纳概括
师:刚才我们结合梳理思路复习了平面图形的面积公式的推导，不知道大家注意
到了没有，这些平面图形中，除了由曲线围成的圆以外，剩下的五个图形的
面积公式可不可以统一成一个图形的面积公式呢,小组内商量商量，待会把
你的想法介绍一下。
生独立小组讨论
汇报:(如果学生根据图形演变来说，适时进行课件演示，如果学生根据举例来说，可以根据学生讲解板书。)
明确可以统一成用梯形的面积公式表示
(设计意图:将平面图形的面积除圆之外都概括成一种图形的面积公式，目的并不是真正的统一，而是训练学生观察图形间、知识间的联系，从而发展学生的创造性思维)
三、练习巩固
师:请大家仔细看这两组图形，认真审题。(课件)
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
生:1、周长不等，面积相等
2、。周长相等，面积不等，因为„„
问:如果两个平面图形的周长相等，塔门的面积一定相等吗, (板书:意义、计算方法、运用)，请大家看这里。
(如果时间允许，出示5个判断，如果不允许，直接拿出教具出判断。) 判断:
1、三角形的面积等于平行四边形面积的一半。
2、同底等高的三角形，他们的形状不一定相等，但面积一定相等。 3、半径是2厘米的圆，周长和面积相等。
师:大家仔细看，把一个长方形拉成一个平行四边形，长方形和平行四边形的周长和面积不变，对不对呢,
生:不对，周长不变，面积变了，因为底没变，高缩小了。
(设计意图:通过有针对性、有梯度的练习让学生应用所学的知识解决实际问题，让学生更好地理解和掌握)
师:同学们真的很棒，本节课大家有什么收获,
生:„„
师:这节课我们重点对平面图形的意义及计算方法进行了梳理和复习，课下请同学们再以小组为单位整理与本节课内容有关的容易出错的题型，下节课进行汇报。
这节课就上到这儿，下课。
蓝色为修改部分 绿色为设计意图 红色为修改理由
平面图形的周长和面积的复习课
济南市明湖小学 李伟
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
教学内容:
教科书第97页内容，及相应练习题
教材分析:
《平面图形的周长和面积》是六年级下学期总复习《空间与图形》中的一节课。它是在复习学过平面图形的特点的基础上进行教学的，是一节复习课。教材把这一内容安排在“空间与图形”的第二课时，意图是让学生在整理知识中进一步体验各平面图形之间的关系。教材的例题首先通过小精灵提问:“说说什么是平面图形的周长、什么是平面图形的面积。”旨在让学生通过复习,明确平面图形周长和面积的意义。接着教材通过图示，要求学生写出各图形的周长和面积的计算公式，并说一说这些计算公式是怎样推导出的。不仅是让学生掌握长方形、正方形、三角形、梯形、圆等基本平面图形的周长和面积计算公式及其推导过程,加以熟练的运用,更重要的是这一图示引导学生构建平面图形的周长与面积的知识网络,形成知识体系，让学生进一步感受数学知识间的相互联系，巩固学生的空间观念，提高学生的学习能力。
学情分析:
学生通过前阶段的学习，基本掌握了各种平面图形的周长和面积的计算方法，但是由于时间的迁移等各种原因，学生对于公式的推导过程有所淡忘，导致在应用公式解决实际问题中，常常遇到问题，从而影响学生的进一步学习。老师所要做的就是引导学生借助各种素材，进一步建立这些知识间的联系，从而起到巩固复习的目的。 leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
教学目标:
1.引导学生回忆整理平面图形的周长和面积的公式及推导过程; 2.引导学生探索知识间的相互联系，构建知识网络，从而加深对知识的理解，领会学习方法;
3.渗透“事物之间是相互联系的”的思想，体验数学与生活的联系。 (本节课的教学目标主要是通过复习计算公式和面积公式的推导过
程，帮助学生构建知识网络，理解图形间的关系，利用公式解决
实际问题，有待于在下节课中去体现)
教学重难点:
1. 整理相关知识，形成知识网络，探索知识间的内在联系。 2. 平面图形周长和面积计算公式的推导过程，尤其是面积公式的推
导过程。
教具、学具准备:
学生课前准备梳理的框架图、平面图形的模型，教师准备课件。 教学过程:
一、引入课题，明确周长和面积的意义:
师:同学们上节课我们复习了平面图形的特征，到目前为止我们学习
了哪些平面图形,
引导学生说出所学过的六种平面图形。
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
(因为毕竟这是下学期的复习内容，回顾学过哪些平面图形，对于下
面进一步的复习会有很大的帮助)
师:什么是平面图形的周长和面积呢,
明确:
围成一个图形的所有边长的总和，叫作它们的周长。
物体的表面或围成平面图形的大小，叫做它们的面积。 师:我们一起来回顾一下。(课件出示周长和面积的意义) 师:那我们今天就一起来复习平面图形的周长和面积。(引出课题) (设计意图:让学生根据自己的理解说什么是周长和面积，通过回顾，从概念上进一步明确它们的含义，以及使用的单位，从而为下面的复习做好铺垫。)
二、复习回顾平面图形周长和面积的计算公式:
1、明确任务:
师:刚才大家所说的就是周长和面积的意义，(板书:意义) leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
课前老师给大家布置了三个任务，一起来回顾一下是哪三个任
务，
(课件出示:1、整理复习平面图形的周长和面积的计算公式。2、
整理复习平面图形面积公式的推导过程。3、根据面积公式的推
导过程，梳理它们之间的关系。)
(通过磨课发现，原来设计的两个课前任务，尤其是第一个任务，目标比较模糊，学生在课下不容易操作，以及课上解决这一任务时，产生了比较混乱的现象，严重影响教学效率。因此，由原来的两个任务改为三个任务，这样每个任务都比较单一，目的性也更强了) 2、复习计算公式:
师:我们先来看第一个任务，哪位同学把整理的平面图形的计算公式给大家介绍一下,
明确:
长方形的周长=(长+宽)×2，用字母表示是C=2 (a+b)，
正方形的周长=边长×4 ，用字母表示是C=4a，
圆的周长=圆周率×直径=2×圆周率×半径，用字母表示是C=Лd
或 C=2Лr，
长方形的面积=长×宽，用字母表示是 S=ab，
2,正方形的面积=边长×边长，用字母表示是S=a，
平行四边形的面积=底长×高，用字母表示是S=ah，
三角形的面积=底长×高?2，用字母表示是S=ah?2， leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
梯形的面积=(上底长下底长)×高?2，用字母表示是S=(a+b) h
?2，
2圆的面积=Л×半径×半径，用字母表示是S=Л×r (设计意图:要求学生在家提前整理，借助学生的汇报，进一步明确周长和面积的计算公式)
三、复习面积公式的推导过程:
师:刚才xx带领我们复习了周长和面积的计算方法，(板书:计算方
法)那这些平面图形的面积公式又是如何推导出来的呢,(课件
出示:第二个任务)下面请同学们在小组内互相说一说。 (每当进行下一个任务时，先让学生明确要进行什么任务了，对于提高课堂效率很有帮助)
生:小组活动„„
师:哪个小组带领大家复习一下,
组:(借助学具展示)„„
此环节生生间、师生间会展开交流，可能会出现以下几个比较集中的问题:
(1)两个完全一样的三角形除了可以拼成平行四边形，还可能拼成什么图形,
两个完全一样的直角三角形，可以拼成长方形;两个完全一样的等腰直角三角形，可以拼成正方形。
(2)可不可以说平行四边形的面积就是三角形面积的二倍, 平行四边形的面积是与他等底等高的三角形面积的2倍。 leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
(3)两个完全一样的梯形，除了可以拼成平行四边形外，还可以拼成什么图形,
两个完全一样的直角梯形，可以拼成长方形;两个完全一样的直角梯形，上底与下底的和等于高时，可以拼成正方形。
2(4)圆的面积公式是如何推导出S=Л×r
因为拼成的平行四边形的底是圆周长的一半，而高是圆的半径，周长
2的一半就是Лr，所以面积就是Лr×r=Л×r
(5)圆可不可以拼成正方形,
不能，因为拼成的平行四边形的底是圆周长的一半，而高是圆的半径，底永远是高的Л倍。
(通过磨课发现，学生出现的问题，多集中在这几点上，然而这几个知识点的处理对于下面构建框架图是很有必要的)
(设计意图:在初次汇报的基础上，再次进行讨论汇报，目的是使学生更好地理解平面图形周长和面积公式的推导过程，并且对于某些特殊情况进行补充，以达到复习巩固的目的)
四、梳理图形间的关系:
师:从他们组的介绍当中，有没有发现他们的推导过程体现着图像间
的内在联系，课前还要求同学们根据面积公式的推导过程梳理了
它们之间的关系，(课件出示:第三个任务)小组内再互相的说
一说，根据他们的介绍可以进一步进行补充。
生:„„(小组活动，梳理框架图，重点说根据什么这样梳理,) 师:哪个小组把你们的想法给大家说一说,
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
生:正方形的面积是根据长方形的面积推导出来的，平行四边形的面
积是根据长方形或正方形的面积推导出来的，三角形和梯形、圆
形的面积是根据平行四边形的面积推导出来的。
引导学生根据刚才的面积公式的推导过程进行补充。
师:刚才大家所说的，都是根据刚才推导过程中的发现。这样我们就
可以将关系图进一步明确。(借助黑板上的模型梳理关系图)
(借助模型在黑板上去构建框架图，这样更加直观，更利于学生的理解和交流)
(设计意图:通过初次汇报，使学生对平面图形的周长和面积的计算公式和内部关系初步感知，为下面的拓展和练习做准备) 五、公式的统一:
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
师:刚才我们结合推倒过程梳理了图形间的关系，不知道大家注意到
了没有，这些平面图形中，除了由曲线围成的圆以外，剩下的五
个图形的面积公式可不可以统一成一种图形的面积公式呢, 生:(独立思考)
师:谁来说说你的想法,(学生可能会有以下几种想法:) 生1:长方形，因为正方形是一个特殊的长方形，可以用长方形的面
积公式，而平行四边形沿高剪下，可以拼成一个长方形，而三
角形与梯形虽然说要除以2，单也可以变成长方形。 生2:平行四边形的面积
师:但我也有我自己的想法，大家想知道吗,(课件)大家仔细观察，
这是什么图形,(梯形)看发生了什么变化,(变成三角形了)
也就是说变成了一个上底为(0)的特殊的梯形，在仔细观察发
生什么变化,(长方形)，现在变成了一个上底和下底相等的特
殊梯形，那这个呢,(平行四边形)。
现在你再想想可以统一成那个图形的公式呢,板书:
s=(a+a)b?2
=2ab?2
=ab
s=(a+0)b?2
=ab?2
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
师:面积公式可以统一成梯形面积的公式，这恐怕是大家没有想到的。
看来平面图形的周长和面积中蕴含着丰富的知识等待着我们去
发现。
(这一部分是本节课的一个升华，也是难点。即使让学生小组去讨论，理解起来有一定的难度，所以让学生直接独立思考，把自己的第一感受说出来。其实这里并没有真正意义上的对与错，学生说出是长方形或平行四边形，正是由于他们理解了根据面积公式推导过程构建的图形间的关系。而后教师借助课件演示引导学生初步感知。) (设计意图:将平面图形的面积除圆之外都概括成一种图形的面积公式，目的并不是真正的统一，而是训练学生观察图形间、知识间的联系，从而发展学生的创造性思维)
六、巩固练习:
1、师:请大家仔细看这两组图形，认真审题，每组中的两个图形的周长和面积相等吗,(课件)
师:有想法了吗,谁来说一说,
生:1、周长不等，面积相等
2、周长相等，面积不等，因为„„
那下面这两道题对吗,
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
1.如果两个平面图形的周长相等，则它们的面积一定相等。 2.如果两个平面图形的面积相等，则它们的周长一定相等。 (借助上面的习题，让学生进一步感知周长相等的图形面积不一定相等，面积相等的图形周长不一定相等。)
2.师:大家仔细看，把一个长方形拉成一个平行四边形，长方形和平行四边形的周长和面积不变，对不对呢,
生:不对，周长不变，面积变了，因为底没变，高缩小了。 3.判断:
(1)三角形的面积等于平行四边形面积的一半。
(2)同底等高的三角形，他们的形状不一定相等，但面积一定相等。 (3)半径是2厘米的圆，周长和面积相等。
(设计意图:通过有针对性、有梯度的练习让学生应用所学的知识解决实际问题，让学生更好地理解和掌握)
师:看来我们在面对这类问题是，还要灵活的运用。
七、小结:
师:同学们真的很棒，这节课我们重点对平面图形的意义及计算方法
进行了梳理和复习，课下请同学们再以小组为单位，整理与本节leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
课内容有关的容易出错的题型，下节课进行汇报。(课件出示课
下小组需要完成你的任务)
(设计意图:在本节课的复习基础上，留给学生课下的小组任务，整
理易错的题型，下节课进行汇报。为下节课的复习做好准备。) 这节课就上到这儿，下课。
平面图形的周长和面积
教学过程:
一、引入课题，明确周长和面积的意义:
师:同学们上节课我们复习了平面图形的特征，到目前为止我们学习了哪些平面
图形,
生:长方形、正方形、平行四边形、梯形和圆形。
(课件出示六个平面图形)
师:什么是平面图形的周长和面积呢,
生:围成一个图形的所有边长的总和，叫作它们的周长。
生:物体的表面或围成平面图形的大小，叫做它们的面积。
师:我们一起来回顾一下。(课件出示周长和面积的意义)
生:(齐读)
师:那我们今天就一起来复习平面图形的周长和面积。(指板书) 二、复习回顾平面图形周长和面积的计算公式:
1、明确任务:
师:刚才大家所说的就是周长和面积的意义，(板书:意义)
课前老师给大家布置了三个任务，一起来回顾一下是哪三个任务，
(课件出示:1、整理复习平面图形的周长和面积的计算公式。2、整理复习
平面图形面积公式的推导过程。3、根据面积公式的推导过程，梳理它们之
间的关系。)
2、复习计算公式:
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
师:我们先来看第一个任务，哪位同学把整理的平面图形的计算公式给大家介绍一下,
生:大家看，这是我整理出来的周长公式和面积公式， 先一起来看周长公式吧。
长方形的周长=(长+宽)×2，用字母表示是C=2 (a+b)，正方形的周长=边
长×4 ，用字母表示是C=4a，圆的周长=圆周率×直径=2×圆周率×半径，
用字母表示是C=Лd 或 C=2Лr，
然后再让我们一起来看面积公式吧，长方形的面积=长×宽，用字母表示是
2,S=ab，正方形的面积=边长×边长，用字母表示是S=a，平行四边形的面积
=底长×高，用字母表示是S=ah，三角形的面积=底长×高?2，用字母表示
是S=ah?2，梯形的面积=(上底长下底长)×高?2，用字母表示是S=(a+b)
2h?2，圆的面积=Л×半径×半径，用字母表示是S=Л×r
大家和我整理的一样吗,
生:一样
生:那我们在用这些公式计算周长面积时应注意哪些问题呢,
生1:我觉得有两点，第一点是在计算周长时应用长度单位，计算面积时应用面
积单位，第二点是计算三角形和平行四边形面积时注意底、高相对应。 生:说得非常好，还有其他的吗,
生2:在计算梯形和三角形面积时别忘了除以2.
生3:我发现你整理的有一个问题，平行四边形和三角形的面积公式是底×高，
底×高?2，不是长×高。
师:我刚才也注意到这个细节了，什么时候是“长”,
生:长方形。
师:平行四边形和三角形称为“底”。
大家的掌声说明张思雨整理的公式对大家是非常有帮助的，并且提出了需要注意
的问题，我们在解决问题时，需要把注意的这些问题融入到实际情况之中。 三、复习面积公式的推导过程:
师:刚才张思雨带领我们复习了周长和面积的计算方法，(板书:计算方法)那
这些平面图形的面积公式又是如何推导出来的呢,(课件出示:第二个任务)
下面请同学们在小组内互相说一说。
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
生:小组活动„„
师:哪个小组带领大家复习一下,
组:大家看这是一个平行四边形，沿平行四边形的高剪下，是一个三角形，把三角形移到右边来，拼成了一个长方形， 长方形的面积和平行四边形的面积相等，因为我们学过长方形的面积是长乘宽，所以我用长方形的面积来推导平行四边形的面积，长方形的长等于平行四边形的底，长方形的宽等于平行四边形的高，因为长方形的面积是长乘宽，所以平行四边形的面积是底乘高。大家还有问题吗, 生:能拼成长方形，还能拼成什么图形呢,
组:还能拼成正方形
生:在什么情况下能拼成正方形,
组:当平行四边形的底和高相等时，可以拼成正方形
师:我们把他拼成正方形，不仅仅是为了拼，而是借助正方形的面积公式推导出
平行四边形的面积公式。
组:大家看，我用两个完全一样的三角形，拼成一个平行四边形，平行四边形的
面积是三角形面积的两倍，因为我们学过平行四边形的面积怎么求，所以用
平行四边形的面积来推导三角形的面积。平行四边形的底等于三角形的底，
平行四边形的高等于三角形的高，因为平行四边形的面积是底乘高，所以三
角形的面积是底乘高除以2，大家还有什么问题吗,
生:拼成平行四边形的面积和三角形面积有什么关系吗,
组:拼成的平行四边形的面积是三角形面积的2倍。
生:除了可以拼成长方形，还可以拼成什么图形?
组:还可以拼成长方形和正方形
生:在什么情况下可以拼成长方形和正方形,
组:当至两个完全一样的直角三角形时，可以拼成长方形，当你是两个完全一样
的等腰直角三角形时，可以拼成正方形。所以也可以借助长方形和正方形来
推导三角形的面积怎么求。
生:为什么最后要除以2呢,
组:因为拼成的平行四边形的面积是三角形面积的两倍。
师:大家千万别忘了要除以2，他在提醒大家这一点。
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
生:两个面积一样，但周长不一样的三角形，可以拼成一个平行四边形吗, 师:你的问题就是说，不完全一样的两个三角形可以拼成平行四边形吗, 组:不能，因为我们一开始说了，需要两个完全一样的三角形。 师:我这里有不一样的三角形，大家看看能拼吗,
生:不能。
师:既然不能就不能借助他的面积来推导三角形的面积公式了。
刚才李胜康问可以拼成其他图形吗, 他们组桌可以拼成长方形或正方形，
光说了，没有展示，大家看这里，这两个三角形完全一样吗,(完全一样)，
经你目测是什么图形,(直角等腰三角形)可以拼成什么图形,(正方形)
那是不是可以借助正方形的面积来推导三角形的面积,你们组现在迅速拼
一下长方形。
组:大家看这是两个完全一样的梯形，拼成一个平行四边形，它的面积是梯形面积的2倍，平行四边形的底等于梯形的上底加下底的和，平行四边形的高等于梯形的高，因为平行四边形的面积是底乘高，所以梯形的面积是上底加下底的和乘高除以2，大家还有问题吗,
生:除了可以拼成平行四边形进行推导，还可以拼成什么图形进行推导, 组:还可以拼成长方形或正方形。
生:在什么情况下拼成长方形或正方形呢,
组:在是直角梯形的情况下，可以拼成长方形，在上底和下底的和等于高的时候
可以拼成正方形。
师:是不是这种情况,两个完全一样的直角梯形，拼成长方形。什么情况下拼成
正方形,你能把你的想法再说一说吗,
组:在上底和下底的和等于高的时候可以拼成正方形。
师:是不是这种情况,(展示)
组:大家看我手中的这个图形，是将一个圆等分成若干等分，拼成了一个近似的
平行四边形，平行四边形的底是圆的周长的一半，平行四边形的高是圆的半
径，因为平行四边形的面积是底乘高，所以圆的面积是圆的周长的一半乘半
径，也就是圆周率乘半径的平方。大家还有问题吗,
生:为什么周长的一半乘半径，可以用圆周率成半径的平方。
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
2组:因为周长用Лd表示，而d=2r，所以用S=Л×r表示圆的面积。 生:我也有一种想法，周长除了可以用Лd表示，还可以用2Лr表示，所以周长
2的一半，就是2Лr?2，再乘r，就是Л×r。
师:大家觉得他俩的推导过程哪一个更清晰,(第二个)
生:把这个圆分的分数更多一些，可以拼成正方形吗,
组:不能，因为底是圆周长的一半，也就是Лr，而高是r，底是高的3.14倍，
所以不能拼成正方形。
师:拼成的图形的底是半径的Л倍，所以不能拼成正方形。
师:他们讲的好不好，掌声表示感谢。
四、梳理图形间的关系:
师:从他们组的介绍当中，有没有发现他们的推导过程体现着图像间的内在联系，
课前还要求同学们根据面积公式的推导过程梳理了它们之间的关系，(课件
出示:第三个任务)小组内再互相的说一说，根据他们的介绍可以进一步进
行补充。
生:„„(小组活动，梳理框架图，重点说根据什么这样梳理,) 师:哪个小组把你们的想法给大家说一说,
生:这是我们组根据面积公式的推导过程梳理的关系图，正方形的面积是根据长
方形的面积推导出来的，平行四边形的面积是根据长方形或正方形的面积推
导出来的，三角形和梯形、圆形的面积是根据平行四边形的面积推导出来的，
大家还有其他意见吗,
生:我来补充一下，三角形和梯形还可以用长方形和正方形的面积来推导，而圆
形分的份数够多，还可以拼成长方形，用长方形来进行推导。 师:刚才大家所说的，都是根据刚才推导过程中的发现。这样我们就可以将关系
图进一步明确。(借助黑板上的模型梳理关系图)
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
师:同学们的表现太棒了，让我们用掌声感谢他们的精彩发言。 五、公式的统一:
师:刚才我们结合推倒过程梳理了图形间的关系，不知道大家注意到了没有，这
些平面图形中，除了由曲线围成的圆以外，剩下的五个图形的面积公式可不
可以统一成一种图形的面积公式呢,
生:(独立思考)
师:谁来说说你的想法,
生1:长方形，因为正方形是一个特殊的长方形，可以用长方形的面积公式，而
平行四边形沿高剪下，可以拼成一个长方形，而三角形与梯形虽然说要除
以2，单也可以变成长方形。
生2:平行四边形的面积
师:刚才两位同学是对的，因为他们都说出了自己的想法。但我也有我自己的想
法大家想知道吗,(课件)大家仔细观察，这是什么图形,(梯形)看发生
了什么变化,(变成三角形了)也就是说变成了一个上底为(0)的特殊的
梯形，在仔细观察发生什么变化,(长方形)，现在变成了一个上底和下底
相等的特殊梯形，那这个呢,(平行四边形)。
现在你再想想可以统一成那个图形的公式呢,
生:梯形
师:我们再想一想，因为三角形可以看成是上底为0的梯形。
s=(a+a)b?2
=2ab?2
=ab
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
s=(a+0)b?2
=ab?2
师:面积公式可以统一成梯形面积的公式，这恐怕是大家没有想到的。看来平面
图形的周长和面积中蕴含着丰富的知识等待着我们去发现。 六、巩固练习:
1、师:请大家仔细看这两组图形，认真审题，每组中的两个图形的周长和面积相等吗,(课件)
师:有想法了吗,谁来说一说,
生1:第一幅图我认为面积相等。周长不等。因为平行四边形沿高剪下，拼成一个长方形，长方形的面积和平行四边形的面积相等，这条边是斜的，所以他们的周长不相等，这是我的想法。
生2:我觉得他们的周长应该是相等的，
生3:我同意刘润瑜的观点，斜线是最长的。
师:他注意到了这一条边，你注意到了吗,我们一起来看一下(课件)那条长,在直角三角形中斜边是最长的，而面积呢,(相等)刚才这几问同学都是想把平行四边形转化为长方形，我们还可不可以用最近本的求面积的方法,数方格，我们一起来数一下，他的长是(6)，宽是(3)，面积是(18)，平行四边形的底是(6)，高是(3)，面积是(18)，相等吗,(相等)那第二幅图呢,
生:周长相等，面积不等。
师:把他移到这边，我们仔细观察，面积正好少了(一个圆形)，周长呢,(相等)
师:看来我们在面对这类问题是，还要灵活的运用。
七、小结:
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
师:同学们真的很棒，这节课我们重点对平面图形的意义及计算方法进行了梳理
和复习，课下请同学们再以小组为单位，整理与本节课内容有关的容易出错
的题型，下节课进行汇报。这节课就上到这儿，下课。
leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slider 2x80 1.00 1.50 5.00 1 I50 jacked with electrical equipment 4 flat emergency gate slot of sluice and dam 6.2x2.0 of 2 2 .50 2.00 4.00 5 sand spillway gate door leaf 1.5x1.5 1 1.50 1.50 to 3.00 slider screw hoist electrical equipment 6 50.00 2.50 1 sand sluice working gate slot of overflow dam 1.5x1.5 1 3.00 2.00 2.00 7 water inlet trashrack gate leaf 2.0 Fixed X3.5 1 3.00 3.00 3.00 8 water inlet door leaf 2.0x2.5 slider 1 3.00 3.00 3.00 screw hoist 80.00 3.50 1.00 9 electrical equipment working gate slot of the intake 2.0x2.5 1 3.00 ... Tables 9.3.1 to be put into the main construction equipment number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric welding machine BX-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-500-3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-automatic cutting machine CG1-30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature control box CWK-18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 hoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compresso
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