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北师大版六年级下册数学全册教案

第一单元

单元教学内容：

面的旋转

圆柱的表面积

圆柱的体积

圆锥的体积

圆柱与圆锥

单元教学目标：

1、结合具体情境和操作活动，引导学生整体把握

2、从多种角度探索圆柱和圆锥的特征。

3、探索圆柱表面积的计算方法，发展空间观念。

4、经历圆柱和圆锥体积计算方法的探索过程，体会

“类比 ”的思想。

“点、线、面、体

”之间的联系。

5、在解决实际问题中用活所学知识，感受数学与生活的联系。

单元教材分析：



学生已经直观认识了长方体、正方体、圆柱和球，并初步了解了长方形、正方形、圆等

平面图形的性质，学习了这些图形的面积计算，学生还认识了长方体（正方体）

方体（正方体） 表面积与体积的含义及其计算方法。在此基础上，

柱的表面积、圆柱的体积、圆锥的体积等内容，并参与实践活动。

以下主要特点：


，掌握了长

、圆

本单元进一步学习圆柱和

本单元教材编写力图体现


圆锥的知识。本单元主要通过五个活动，引导学生学习面的旋转（圆柱和圆锥的认识）


1.结合具体情境和操作活动，引导学生经历

“点动成线 ”“线动成面 ”“面动成体 ”的过程，

体会 “点、线、面、体 ”之间的联系教材的第一个活动体现的内容是

“由平面图形经过旋转形

成几何体 ”，这不仅是对几何体形成过程的学习，同时体会面和体的关系也是发展空间观念

的重要途径， 这也是教材将此课题目定为

情境，鼓励学生进行观察，激活学生的生活经验，使学生经历

小旗， 引导学生结合空间想象体会立体图形的形成过程，


由面旋转成体的练习。



“面的旋转 ”的原因。 教材呈现了几个生活中的具体

“点动成线 ”“线动成面 ”“面动


成体 ”的过程。在结合具体情境感受的基础上，教材又设计了一个操作活动，通过快速旋转

发展空间观念。 教材还提供了若干





2.重视操作与思考、想象相结合，发展学生的空间观念操作与思考、想象相结合是学生

认识图形、 探索图形特征、发展空间观念的重要途径。在本单元中，教材重视学生操作活动

的安排，在每个主题活动中都安排了操作活动，促进学生理解数学知识、发展空间观念。如

形，并呈现了两种操作的方法：

种是用一张长方形纸卷成圆柱形。

一种是把圆柱形纸盒剪开，侧面展开后是一个长方形；

一张横着卷成一个圆柱形，

“圆柱的表面积 ”的教学中， 教材引导学生通过操作来说明圆柱的侧面展开后是一个怎样的图


另一

再如本单元的最后专门安排了一个

“用长方形纸卷圆柱形 ”

另一张竖着

然后组织学生将两张完全一样的长方形纸裁开，

引导学生发现规律， 深化对圆柱表


的实践活动， 先让学生用两张完全一样的长方形纸，

卷成一个圆柱形， 研究两个圆柱体积的大小；

把变化形状后的纸再卷成圆柱形，

面积、体积的认识，并体会变量之间的关系。


研究圆柱体积的变化，


3.引导学生经历圆柱和圆锥体积计算方法的探索过程，

一种重要的数学思想方法， 是合情推理时常用的方法。

体会类比等数学思想方法类比是

教材重视类比、 转化等数学思想方法

“底面积 ×高 ”，由

的渗透。在 “圆柱的体积 ”教学时，教材引导学生经历

“类比猜想 — 验证说明 ”的探索过程。由

于圆柱和长方体、正方体都是直柱体，而且长方体与正方体的体积都等于

此可以产生猜想：圆柱的体积计算方法也可能是





“底面积 ×高”。在形成猜想后，教材再引导


学生 “验证说明 ”自己的猜想。在 “圆锥的体积 ”教学时，教材继续渗透类比的思想，再次引导

manipulat
al esi
industrial control










or control mode ad programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
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nipulatcool 2.1 classificati on
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old i ndustrial equipment,buso orecommon. Minly these two relatively cheap and you can eetold- fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
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ntages in l

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contr ol. Optimization of PLC is th










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dapt to te coex lgicontrol, (2) only for thcurrent project, the lack
ch software resources, especially t
ng the runni
he ne ed for immedia
ng order of functi
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ons. Marked
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of copatibi lity and (3) not reforming the system with quipment improvements. S
s used tocontrol and meet its spee
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d, on the virtu
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ury emerged, micr
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ectronics processing technology w





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ol system for industrial a
the Programmable
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anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
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g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
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e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






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ogistics, mechani cal processi
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abr
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学生经历 “类比猜想 —验证说明 ”的探索过程。另外， 教材还注意转化、化曲为直等思想方
法的渗透，如在验证说明 “圆柱的体积＝底面积 ×高 ”时，引导学生把圆柱切割拼成近似的长
方体进行研究，体现了化曲为直的思想方法。







4.在解决实际问题中巩固所学知识，

用所学知识解决问题。如学习

感受数学与生活的联系圆柱和圆锥的知识在生活中

引导学生灵活运

有着较为广泛的应用， 教材在编排练习时， 选择了来自于现实生活的问题，

风管需要的铁皮的面积、 压路机压路的面积等， 由于实际情形变化比较多，

际情况灵活地选择有关数据进行计算。

“圆柱的表面积 ”时，鼓励学生计算薯片盒的包装纸的大小、通

需要学生根据实

在学习 “圆柱和圆锥的体积

”后，教材鼓励学生计算水

桶的容积、圆木的体积、 圆锥形小麦堆的体积、铅锤的质量等。这些实际问题的解决，将使
学生巩固对所学知识的理解，体会数学 知识在生活中的广泛应用，丰富对现实空间的认识，
逐步形成学好数学的情感和态度。




课时安排： 12 课时





















教学内容：面的旋转

教学目标：

1．通过初步认识圆柱和圆锥使学生感受到数学与生活的密切联系。

2．通过观察和动手操作等，初步体会

柱和圆锥的各部分名称。

教学重点：

1、联系生活，在生活中辨认圆柱和圆锥体的物体，并能抽象出几何图形的形状来。

2、通过观察，初步了解圆柱和圆锥的组成及其特点。

教学难点：

通过观察，初步了解圆柱和圆锥的组成及其特点。

教学用具：

各种面、圆柱和圆锥模型

教学过程：

一．活动一

如图： 将自行车后轮架支起，在后车车条上系上彩带。转动后车轮，观察并思考彩带
随着车轮 转动后形成的图形是什么？

学生根据发现的现象 （彩带随着车轮的转动形成了圆）说明自己的想法，并体验：

成线

二．活动二

观察下面各图，你发现了什么？

学生发现：

风筝的每一个节连起来看，形成了一个长方形；雨刷器扫过后形成一个半圆形
学生体验：线动成 面

点动

“点、线、面、体

”之间的关系，发展空间观念。

3．通过由面旋转成体的过程，认识圆柱和圆锥，了解圆柱和圆锥的基本特征，知道圆











三．活动三

如图：用纸片和小棒做成下面的小旗， 快速的旋状小棒， 观察并想象旋转后形成的图形，再
连一连。








manipulat
al esi
industrial control










or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
ss, hope desig
ne ha s be en ra pid development i
ood devel opme
ers
n industrial
nt of the technology makes a g
can i n yihu esin i
onme nt there is a
autoationas
ood optimizati
n the
separate subject.
on of produ ctive ca
nipulappli
pial, anrootshs
g n his e sin
cation bega
his uni que a dvantages,
n to filter int
such as: has
o weld
d co
abr
ogistics, mechani cal
patibi lity, wi de availa
d of resear
nd
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
dge has has must awarencan success of usin e cee s experience 1.2 anatr in ot h at an
very as as foaterialsimple movemecond generation meh sensors a
rocessi
bility,
ch r ofilau




ng, a
ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
1、学生实际动手操作，然后根据想象的图形连线

1—— 1（圆柱） 2—— 3（球） 3—— 4（圆锥）








4—— 2（圆台）



2、介绍：圆柱、圆锥、球的名称。并请学生根据自己的观察介绍一下这几个立体图
形的特点。指名请学生说。

小结：我们学过的长方体、正方体都是由平面围成的立体图形，今 天我们学习的圆柱、
圆锥和球也是立体图形，只是与长方体、正方体不同，围成的图形上可能有曲面。< br>










































四．找一找

请你找一找我们学过的立体图形

五．说一说

圆柱与圆锥有什么特点？和小组的同学互相说一说

圆柱：有两个面是大小相同的圆，有另一个面是曲面。

圆锥：它是由一个圆和一个曲面组成的。

六．认一认

圆柱的上下两个面叫做底面，它们是完全相同的两个圆。圆柱有一个曲面，叫做侧面。

圆柱两个底面之间的距离叫做高。

圆锥的底面是一个圆。 圆锥的侧面是一个曲面。

从圆锥顶点到底面圆心的距离是圆锥的

高。 (教师画出平面图进行讲解。并在图上标出各部分的名称。

七．练一练

1．找一找，下图中哪些部分的形状是圆柱或者圆锥？

再和同学们说一说生活中哪些物体的形状是圆柱或者圆锥的。

2．下面图形中是圆柱或圆锥的在括号里写出图形的名称，并标出地面的直径和高。

3．想一想，连一连

4．应用题

八．板书

)

九．随堂反思


















manipulator control mode a
al esi
industrial control
ner of th
computer use
software writing
教学内容：圆柱的表面积

第一课时

教学目标：

1．能根据具体情境，灵活运用圆柱表面积的计算方法解决生活中一些简单的问题，使











d programmabl e controllers introduction 2.1 S
contencontrolall
central colle
bout. Now in several ways in
ction
elect discussion with ma
context f indstal
nd distri bution system and transiti





nipulatcool 2.1 classificati on
toatn ca
on
n oen
of distributed
be se en i n three ways: (1) Programmable Logica
contr ol system










of control relaysand dscretelctronic circuitcan cotrol
l Controller (referred to as
in a
IPC); (2) Distri
alog ue h
bu
ndli ng, loop contro
d Control System (DCS for short), and (3) the Programmable
has beg















old i ndustrial equi pment,so orecommon. Minly these two relatively cheap and you can eetold-fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
h distri
contrast contrast 1, ea
d system has great adva
ch of the three technologi
ntages in l

oop regulati
es of origi
on, but only as a means of conti
s anevelenreqreen
uos rocess
s for fast data processing makes it inve
contr ol. Optimization of PLC is th











simple) industrial equipmet. Sohe can see them nowhowever t hese tw
nted the com
corre
puer. The m
spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
o contr ol mode s (relay and discrete ele

n the w ork order control, early




ctronic
h level of standardi
primary is repla
circuits) are these fatal flaws: (1) cannot a
at n, ca nse
ced relay this hulking system, focused on the switch



ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
s, is a ri
ng the runni
ch software resources, especially t
ng order of functi
he ne ed for immedia
ons. Marked
cy in
micr
he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
s used to
cent ury emerged, micr
control and meet its spee
o-el ectronics technol
d, on the virtu
og ha s devel ope d rapi dly, people soon microel
sta toatechy e sust
l model , real-time a nd i
ectronics processing technology w



ntial increase i
n computational re
ill e sed







n thelevel of industrial aut
quireme
the Programmable
nts. Distri buted system started w
gicalntroer at i

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
program as a ba
g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
d co
n thr ocee
e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






o welding, l
patibi lity, wi de availa
nd
of experience 1.2 manipulator i

ogistics, mechani cal processi
bility,
n bot h at home and




abr
ng, a
hardwar e is complet
学生感受到数学与生活的密切联系

2．通过想象、操作等活动，知道圆柱侧面展开后可以是一个长方形，加深对圆柱特征

的认识，发展空间观念。

3．结合具体情境和动手操作，探索圆柱侧面积的计算方法 ，掌握圆柱侧面积和表面
积的计算方法，能正确计算圆柱的侧面积和表面积。

教学重点：

使学生认识圆柱侧面展开图的多样性。

教学难点：

学生能够将展开图与圆柱体的各部分建立联系，

式。

教学用具：

课件、圆柱体的瓶子、剪子

教学过程：

一、创设情境，引起兴趣。

拿出圆柱体茶叶罐， 谁能说说圆柱由哪几部分组成的？想一想工人叔叔做这个茶叶罐是

怎样下料的？ （学生会说出做两个圆形的底面再加一个侧面） 那么大家猜猜侧面是怎样做成的
呢？（说说自己的猜想）

并推导出圆柱侧面积、

表面积的计算公






































二、自主探究，发现问题。

研究圆柱侧面积

1、独立操作：利用手中的材料（纸质小圆柱，长方形纸，剪刀）

证刚才的猜想。

2、观察对比：观察展开的图形各部分与圆柱体有什么关系？

3、小组交流：能用已有的知识计算它的面积吗？

4、小组汇报。

（选出一个学生已经展开的图形贴到黑板上）

，用自己喜欢的方式验

重点感受：圆柱体侧面如果沿着高展开是一个长方形。

方形与圆柱体上的那个面有什么关系？

体的高）

长方形的面积＝圆柱的侧面积即

圆柱的侧面积＝底面周长

如果已知底面半径为

×高

（这里要强调沿着高剪）这个长

(长方形的长是圆柱体底面周长、长方形的宽是圆柱

长×宽

＝底面周长 ×高，所以，

S 侧 == C

× h

S 侧 =2∏r ×h

r，圆柱的侧面积公式也可以写成：

如果圆柱展开是平行四边形，是否也适用呢？

学生动手操作 ,动笔验证 ,得出了同样适用的结论。 （因为刚才学生是用自己喜欢的方式剪

开的，所以可能已经出现了这种情况。

此时可以让已经得出平行四边形的学生介绍一下他的

剪法，然后大家拿出准备好的圆柱纸盒用此法展开）

研究圆柱表面积

1、现在请大家试着求出这个圆柱体茶叶罐用料多少。

学生测量，计算表面积。

2、圆柱体的表面积怎样求呢？

得出结论：圆柱的表面积 ＝ 圆柱的侧面积＋底面积 ×2 3、动
画：圆柱体表面展开过程

三、实际应用

1、解决书上的例题







manipulator control mode a
al esi
industrial control
ner of th
computer use
software writing










nd programmabl e controllers introduction 2.1 S
contencontrolall
central colle
bout. Now in several ways in
ction
elect discussion with ma
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
ss, hope desig
ne ha s be en ra pid development i
ood devel opme
ers
n industrial
nt of the technology makes a g
can i n yihu esin i
onme nt there is a
autoationas
ood optimizati
n the
separate subject.
on of produ ctive ca
nipulappli
pial, anrootshs
g n his e sin
cation bega
his uni que a dvantages,
n to filter int
such as: has
o weld
d co
abr
ogistics, mechani cal
patibi lity, wi de availa
d of resear
nd
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
dge has has must awarencan success of usin e cee s experience 1.2 anatr in ot h at an
very as as foaterialsimple movemecond generation meh sensors a
rocessi
bility,
ch r ofilau




ng, a
ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
2、填空


圆柱的侧面沿着高展开可能是（

（

）



）形，也可能是（


）形。第二种情况是因为

3、要求一个圆柱的表面积，一般需要知道哪些条件（

4、教材第六页试一试。

四、板书


圆柱体的表面积

圆柱的侧面积

↓

长方形





















）










＝

↑


底面周长 ×高

↑

长


→ S 侧＝ ch






面积

＝

＝

× 宽


圆柱的表面积

五、随堂反思：

圆柱的侧面积＋底面积 ×2

第二课时

教学目标：

1、进一步理解圆柱体侧面积和表面积的含义。

2、掌握求圆柱的侧面积、表面积的方法，并能运用到实际中解决问题。

教学重点：掌握求圆柱的侧面积、表面积的方法，并能运用到实际中解决问题。

教学难点：圆柱表面积的实际应用。

教学过程 ：

一、基本练习

说说计算方法

二、实际应用

求压路的面积是求什么？

说自己的想法，独立解答。

三、实践活动




四、课后反思


























manipulator control mode a
al esi
industrial control
ner of th
computer use
software writing
第三课时

教学目标：

1、进一步理解圆柱体侧面积和表面积的含义。

2、掌握求圆柱的侧面积、表面积的方法，并能运用到实际中解决问题。

教学重点：掌握求圆柱的侧面积、表面积的方法，并能运用到实际中解决问题。

教学难点：圆柱表面积的实际应用。

教学过程 ：

一、 实际应用

1、











d programmabl e controllers introduction 2.1 S
contencontrolall
central colle
bout. Now in several ways in
ction
elect discussion with ma
context f indstal
nd distri bution system and transiti





nipulatcool 2.1 classificati on
toatn ca
on
n oen
of distributed
be se en i n three ways: (1) Programmable Logica
contr ol system










of control relaysand dscretelctronic circuitcan cotrol
l Controller (referred to as
in a
IPC); (2) Distri
alog ue h
bu
ndli ng, loop contro
d Control System (DCS for short), and (3) the Programmable
has beg















old i ndustrial equi pment,so orecommon. Minly these two relatively cheap and you can eetold-fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
h distri
contrast contrast 1, ea
d system has great adva
ch of the three technologi
ntages in l

oop regulati
es of origi
on, but only as a means of conti
s anevelenreqreen
uos rocess
s for fast data processing makes it inve
contr ol. Optimization of PLC is th











simple) industrial equipmet. Sohe can see them nowhowever t hese tw
nted the com
corre
puer. The m
spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
o contr ol mode s (relay and discrete ele

n the w ork order control, early




ctronic
h level of standardi
primary is repla
circuits) are these fatal flaws: (1) cannot a
at n, ca nse
ced relay this hulking system, focused on the switch



ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
s, is a ri
ng the runni
ch software resources, especially t
ng order of functi
he ne ed for immedia
ons. Marked
cy in
micr
he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
s used to
cent ury emerged, micr
control and meet its spee
o-el ectronics technol
d, on the virtu
og ha s devel ope d rapi dly, people soon microel
sta toatechy e sust
l model , real-time a nd i
ectronics processing technology w



ntial increase i
n computational re
ill e sed







n thelevel of industrial aut
quireme
the Programmable
nts. Distri buted system started w
gicalntroer at i

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
program as a ba
g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
d co
n thr ocee
e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






o welding, l
patibi lity, wi de availa
nd
of experience 1.2 manipulator i

ogistics, mechani cal processi
bility,
n bot h at home and




abr
ng, a
hardwar e is complet
2、

3、

二、随堂反思

教学内容：圆柱的体积

第一课时

教学目标：

1．通过切割圆柱体，拼成近似的长方体，从而推导出圆柱的体积公式这一教学过程，

向学生渗透转化思想。

2．通过圆柱体体积公式的推导，培养学生的分析推理能力。

3．理解圆柱体体积公式的推导过程，掌握计算公式；会运用公式计算圆柱的体积。

教学重点：

教学难点：

教学用具：

教学过程：

一、










圆柱体体积的计算


圆柱体体积公式的推导


圆柱体学具、课件


复习引新

(2)d=4 分米；

1．求下面各圆的面积 (回答 )。

(1)r=1 厘米；





(3)C=6.28 米。


要求说出解题思路。

2．想一想：学习计算圆的面积时，是怎样得出圆的面积计算公式的



?指出：把一个圆等





分成若干等份，可以拼成一个近似的长方形。这个长方形的面积就是圆的面积。


3．提问：什么叫体积

4．已知长方体的底面积

积×高 )

?常用的体积单位有哪些

?

s 和高 h，怎样计算长方体的体积




?(板书：长方体的体积

=底面



















manipulat
al esi
industrial control
二、探索新知

1．根据学过的体积概念，说说什么是圆柱的体积。

(板书课题 )

2．怎样计算圆柱的体积呢

?我们能不能根据圆柱的底面可以像上面说的转化成一个长方

形，通过切、拼的方法，把圆柱转化为已学过的立体图形来计算呢， 现在我们大家一起来讨论。

3．公式推导。 (有条件的可分小组进行 )

(1)请同学指出圆柱体的底面积和高。

(2)回顾圆面积公式的推导。
(3)探索求圆柱体积的公式。

根据圆面积剪、 拼转化成长方形的思路，

我们也可以运用切拼转化的方法把圆柱体变成

(切拼转化 )

学过的几何形体来推导出圆柱的体积计算公式。你能想出怎样切、拼转化吗

?请同学们仔细











or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
ss, hope desig
ne ha s be en ra pid development i
ood devel opme
ers
n industrial
nt of the technology makes a g
can i n yihu esin i
onme nt there is a
autoationas
ood optimizati
n the
separate subject.
on of produ ctive ca
nipulappli
pial, anrootshs
g n his e sin
cation bega
his uni que a dvantages,
n to filter int
such as: has
o weld
d co
abr
ogistics, mechani cal
patibi lity, wi de availa
d of resear
nd
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
dge has has must awarencan success of usin e cee s experience 1.2 anatr in ot h at an
very as as foaterialsimple movemecond generation meh sensors a
rocessi
bility,
ch r ofilau




ng, a
ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
观察以下实验， 边观察边思考圆柱的体积、底面积、高与拼成的几何形体之间的关系。

演示圆柱体积公式推导演示教具：把圆柱的底面分成许多相等的扇形

然后把圆柱切开，照下图拼起来，

(4)讨论并得出结果。

你能根据这个实验得出圆柱的体积计算公式吗

越多，拼成的立体图形就越接近于长方体。

(图见教材 )就近似于一个长方体。可以想象，分成的扇形

教师

(数量一般为

16 个 )，

?为什么 ?让学生再讨论：圆柱体通过切

相等，这个长方

所以， 圆柱体的体积计算

拼，圆柱体转化成近似的长方体。这个长方体的底面积与圆柱体的底面积

体的高与圆柱体的高相等。 因为长方体的体积等于底面积乘以高，

(板书： V=Sh)

(5)小结。

圆柱的体积是怎样推导出来的

4．教学算一算

?计算圆柱的体积必须知道哪些条件？

公式是：圆柱的体积

=底面积 ×高 (板书：圆柱的体积

=底面积 ×高 )用字母表示：

审题。提问：你能独立完成这题吗 ?指名一同学板演，其余学生做在练习本上。集体订正：
列式依据是什么 ?应注意哪些问题 ?最后结果用体积单位 )



教学 “试一试 ”

小结：求圆柱的体积，必须知道底面积和高。如果不知道底面积，只知道半径 r，通过什么途径
求出圆柱的体积 ?如果知道 d 呢?知道 C 呢 ?知道 r、d、 C，都要先求出底面积再求体积。









三、巩固练习

练习册练习

四、课堂小结

这节课学习了什么内容

计算公式 V=Sh 。

五、板书：

?圆柱的体积怎样计算，这个公式是怎样得到的

?指出：这节课，

我们通过转化，把圆柱体切拼转化成长方体， ( 在课题下板书：圆柱些长方体 )得出了圆柱体的体积









六、随堂反思：



















manipulat
al esi
industrial control
第二课时

教学目标：

1．进一步理解和掌握圆柱的体积计算公式，并能应用到实际解决问题中。

2． 培养学生初步的空间观念和思维能力；让学生认识

教学重点：

理解和掌握圆柱的体积计算公式。

教学难点 ：

圆柱体积计算公式的推导。

教学过程：

一、基本练习

“转化 ”的思考方法。











or control mode ad programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti





nipulatcool 2.1 classificati on
toatn ca
on
n oen
of distributed
be se en i n three ways: (1) Programmable Logica
contr ol system










of control relaysand dscretelctronic circuitcan cotrol
l Controller (referred to as
in a
IPC); (2) Distri
alog ue h
bu
ndli ng, loop contro
d Control System (DCS for short), and (3) the Programmable
has beg















old i ndustrial equi pment,so orecommon. Minly these two relatively cheap and you can eetold-fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
h distri
contrast contrast 1, ea
d system has great adva
ch of the three technologi
ntages in l

oop regulati
es of origi
on, but only as a means of conti
s anevelenreqreen
uos rocess
s for fast data processing makes it inve
contr ol. Optimization of PLC is th











simple) industrial equipmet. Sohe can see them nowhowever t hese tw
nted the com
corre
puer. The m
spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
o contr ol mode s (relay and discrete ele

n the w ork order control, early




ctronic
h level of standardi
primary is repla
circuits) are these fatal flaws: (1) cannot a
at n, ca nse
ced relay this hulking system, focused on the switch



ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
s, is a ri
ng the runni
ch software resources, especially t
ng order of functi
he ne ed for immedia
ons. Marked
cy in
micr
he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
s used to
cent ury emerged, micr
control and meet its spee
o-el ectronics technol
d, on the virtu
og ha s devel ope d rapi dly, people soon microel
sta toatechy e sust
l model , real-time a nd i
ectronics processing technology w



ntial increase i
n computational re
ill e sed







n thelevel of industrial aut
quireme
the Programmable
nts. Distri buted system started w
gicalntroer at i

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
program as a ba
g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
d co
n thr ocee
e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






o welding, l
patibi lity, wi de availa
nd
of experience 1.2 manipulator i

ogistics, mechani cal processi
bility,
n bot h at home and




abr
ng, a
hardwar e is complet
二、实际应用

说解题思路

说说你的解题思路

这道题的注意的地方：单位的统一

说说哪个体积大？为什么？

上升的 2 厘米是什么

分别说说表面积和体积的计算方法。

三、实践活动

四、课后反思

圆锥的体积

第一课时

教学目标：

1、使学生理解求圆锥体积的计算公式．

2、会运用公式计算圆锥的体积．

3、培养学生初步的空间观念和思维能力；让学生认识

教学重点

圆锥体体积计算公式的推导过程．

教学难点

正确理解圆锥体积计算公式．

教学过程：

一、铺垫孕伏

1、提问：

（ 1）圆柱的体积公式是什么？
（ 2）投影出示圆锥体的图形，学生指图说出圆锥的底面、侧面和高．
“转化 ”的思考方法。







2、导入：同学们，前面我们已经认 识了圆锥，掌握了它的特征，那么圆锥的体积怎
样计算呢？这节课我们就来研究这个问题． （板书：圆锥的体积）

二、探究新知

（一）指导探究圆锥体积的计算公式．

1、教师谈话：

下面我们利用实验的方法来探究圆锥体积的计算方法． 老师给每组同学都准备了两个圆锥体
容 器，两个圆柱体容器和一些沙土．实验时，先往圆柱体（或圆锥体）容器里装满沙土

（用直尺将多余的沙土刮掉） ，倒人圆锥体（或圆柱体）容器里．倒的时候要注意，把两个
容 器比一比、量一量，看它们之间有什么关系，并想一想，通过实验你发现了什么？

2、学生分组实验

学生汇报实验结果

①圆柱和圆锥的底面积相等，

一次，又倒了一些，才装满．







高不相等， 圆锥体容器装满沙土往圆柱体容器里倒，








倒了


②圆柱和圆锥的底面积不相等，


高相等， 圆锥体容器装满沙土往圆柱体容器里倒，





倒了


两次，又倒了一些，才装满．

③圆柱和圆锥的底面积相等，

次，正好装满．

高相等， 圆锥体容器装满沙土往圆柱体容器里倒，

倒了三






manipulat
al esi
industrial control










or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
ss, hope desig
ne ha s be en ra pid development i
ood devel opme
ers
n industrial
nt of the technology makes a g
can i n yihu esin i
onme nt there is a
autoationas
ood optimizati
n the
separate subject.
on of produ ctive ca
nipulappli
pial, anrootshs
g n his e sin
cation bega
his uni que a dvantages,
n to filter int
such as: has
o weld
d co
abr
ogistics, mechani cal
patibi lity, wi de availa
d of resear
nd
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
dge has has must awarencan success of usin e cee s experience 1.2 anatr in ot h at an
very as as foaterialsimple movemecond generation meh sensors a
rocessi
bility,
ch r ofilau




ng, a
ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
⋯⋯

4、引导学生发现：

圆柱体的体积等于和它等底等高的圆锥体体积的


3 倍或圆锥的体积是和它等底等高圆

柱体积的 ．

板书：






5、推导圆锥的体积公式：用字母表示圆锥的体积公式．板书：

6、思考：要求圆锥的体积，必须知道哪两个条件？

7、反馈练习

圆锥的底面积是

圆锥的底面积是

（二）算一算






5，高是

3，体积是（

10，高是

9，体积是（

）



）







学生独立计算，集体订正．

说说解题方法

三、全课小结

通过本节的学习， 你学到了什么知识？ （从两个方面谈： 圆锥体体积公式的推导方法和公
式的应用）

四、课后反思






















第二课时

教学目标：

1、进一步掌握圆柱和圆锥体积的计算方法，能正确熟练地运用公式计算圆锥的体积。

2、进一步培养学生运用所学知识解决实际问题的能力和动手操作的能力。

3、进一步熟悉圆锥的体积计算

教学难点：

圆锥的体积计算

教学重点：

圆锥的体积计算

教学过程：

一、基本练习

圆锥体积计算公式

相邻两个面积单位之间的进率是多少？

相邻两个体积单位之间的进率是多少？

二、实际应用



占地面积是求得什么？
















manipulat
al esi
industrial control
三、实践活动

四、课后反思











or control mode ad programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti





nipulatcool 2.1 classificati on
toatn ca
on
n oen
of distributed
be se en i n three ways: (1) Programmable Logica
contr ol system










of control relaysand dscretelctronic circuitcan cotrol
l Controller (referred to as
in a
IPC); (2) Distri
alog ue h
bu
ndli ng, loop contro
d Control System (DCS for short), and (3) the Programmable
has beg















old i ndustrial equi pment,so orecommon. Minly these two relatively cheap and you can eetold-fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
h distri
contrast contrast 1, ea
d system has great adva
ch of the three technologi
ntages in l

oop regulati
es of origi
on, but only as a means of conti
s anevelenreqreen
uos rocess
s for fast data processing makes it inve
contr ol. Optimization of PLC is th











simple) industrial equipmet. Sohe can see them nowhowever t hese tw
nted the com
corre
puer. The m
spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
o contr ol mode s (relay and discrete ele

n the w ork order control, early




ctronic
h level of standardi
primary is repla
circuits) are these fatal flaws: (1) cannot a
at n, ca nse
ced relay this hulking system, focused on the switch



ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
s, is a ri
ng the runni
ch software resources, especially t
ng order of functi
he ne ed for immedia
ons. Marked
cy in
micr
he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
s used to
cent ury emerged, micr
control and meet its spee
o-el ectronics technol
d, on the virtu
og ha s devel ope d rapi dly, people soon microel
sta toatechy e sust
l model , real-time a nd i
ectronics processing technology w



ntial increase i
n computational re
ill e sed







n thelevel of industrial aut
quireme
the Programmable
nts. Distri buted system started w
gicalntroer at i

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
program as a ba
g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
d co
n thr ocee
e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






o welding, l
patibi lity, wi de availa
nd
of experience 1.2 manipulator i

ogistics, mechani cal processi
bility,
n bot h at home and




abr
ng, a
hardwar e is complet




第二单元


正比例和反比例








单元教学内容：

变化的量

正比例





画一画

反比例

观察与探究

图形的缩放

比例尺



单元教学目标：

1、结合具体情境，体会生活中存在着大量互相依赖的变量；在具体 情境中，尝试用
自己的语言描述两个变量之间的关系。



2、结 合丰富的实例，认识正比例或者反比例；能根据正比例和反比例的意义，判断
两个相关联的量是不是成正 比例或反比例

3、能找出生活中成正比例和反比例的实例，会利用正、反比例的有关指示解决 一些
简单的生活问题。

4、通过观察、操作与交流，体会比例持产生的必要性和实际意义，

了解比例尺的含义。



5、运用比例尺的有关知识，通过测量、 绘图、估算、计算等活动，学会解决生活中
的一些实际问题。






单元教材分析：

单元教材分析这部分内容是在学生已经学过比的意义、

习的。本单元教材编写力图体现以下主要特点。

中，从数学的角度研究变量和变量之间的关系，


来。同时， 研究现实世界中的变化规律，

：

将有助于人们更好地认识现实世界、

预测未

比的化简与比的应用的基础上学

1.提供具体情境， 使学生体会生活中存在大量互相依赖的量我们生活在一个变化的世界

也使学生从常量的世界进入了变量的世界，开始接

在一个变化过程中有两个

y 就叫做 x 的函数）是

描述应从小学阶段非正

触一种新的思维方式。我们知道，函数（函数可以直观地理解为：


变量 x,y,对于 x 的每一个变化的值， y 都有唯一确定的值与之对应，

研究现实世界变量之间关系的一个重要模型，

要内容。 而国际数学课程发展的趋势表明，

对变量之间关系的探索、

对它的学习一直是中学阶段数学学习的一个重

其实，以前学习的探索数、 形的变化规律，

而本章的正比例、 反比例本身

体会函数思想需要丰富的

有的变量之间是存在一定关系

使他们体会变量和变量之间相互

式地开始， 早期对函数的丰富经历是十分重要的。

字母表示数等， 已经为学生积累了研究变量之间关系的经验，


情境， 学生将在这些情境中，

感受到生活中存在着大量变量，

计了三个具体情境， 通过学生感兴趣的日常生活中的问题，

依赖的关系， 并尝试对这些关系进行大致地描述。

想的理解，应使他们对函数的多种表示

就是两个重要的函数。 函数是刻画变量之间相互关系的重要模型，

的，一个变量随另一个变量的变化而变化。因此，在正式学习正比例、反比例之前，教材设

多种研究表明， 为了有助于学生对函数思

——— 数值表示（表格） 、图像表示、解析表示（关

系式），有丰富的经历。因此，教材在呈现具体情境中变量之间的关系时，分别运用了表格

表示、图像表示、关系式表示的方法。在后面正比例、反比例的学习中，也十分重视三种方

式的结合。


2．提供丰富情境，引导学生经历从具体情境中抽象出正、反比例的过程正比例关系、

反比例关系是数学中比较重要的数量关系，


同时，学生理解正比例、 反比例的意义往往比较

困难。 为此，教材密切联系学生已有的生活经验和学习经验，


设计了系列情境，让学生体会

反比例在

生活中存在大量相关联的量，它们之间的关系有着共同之处，从而引发学生的讨论和思考，

并通过对具体问题的讨论， 使学生认识成正比例的量、 成反比例的量以及正比例、

生活中的广泛存在。 这些系列情境也为学生理解

背景和具体案例，例如教材从不同的角度

境，也包括正方形周长与边长、





manipulat
al esi
industrial control
“正比例 ”“反比例 ”的意义提供了丰富的直观

（实际生活、图形） 提供了有利于学生探索并理解

情境中有正例也有反例，


正比例意义的情境， 这些情境中既包括 “时间与路程 ”“购买苹果应付的钱数与质量

”等生活情

面积与边长等数学情境，


以引导学

生经历从具体情境中抽象概括出正比例的过程。












or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
ss, hope desig
ne ha s be en ra pid development i
ood devel opme
ers
n industrial
nt of the technology makes a g
can i n yihu esin i
onme nt there is a
autoationas
ood optimizati
n the
separate subject.
on of produ ctive ca
nipulappli
pial, anrootshs
g n his e sin
cation bega
his uni que a dvantages,
n to filter int
such as: has
o weld
d co
abr
ogistics, mechani cal
patibi lity, wi de availa
d of resear
nd
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
dge has has must awarencan success of usin e cee s experience 1.2 anatr in ot h at an
very as as foaterialsimple movemecond generation meh sensors a
rocessi
bility,
ch r ofilau




ng, a
ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
3.注重引导学生利用

“正、反比例 ”的意义解决实际问题，关注知识之间的联系正、反比

例在生活中有着广泛的应用， 教材不仅仅是在引入时为学生提供了丰富的现实情境，

还鼓励






学生寻找生活情境中成 “正、反比例 ”的量。如，设计 “找一找生活中成正、反比例的例子，
并与同伴交流 ”的题目，使学生认识到正、反比例的知识与日常生活的密切联系。同时，教

材还特别注重知识之间的联系，

呈现了大量学生以前学过的量与量之间的关系，

鼓励学生判

断它们之间的关系。如，底一定时，平行四边形的面积与高；圆的周长与直径。

4.在画图或解决实际问题等的活动中，体验比例尺的应用对于比例尺的知识，学生并不

陌生， 生活经验比较丰富，如地图上的比例尺等。

尽管如此， 比例尺的应用对于学生来说还

是比较抽象的， 教材结合具体的活动和实例， 贴近学生的生活经验， 让学生感受到比例尺的广
泛应用。如，在探究活动中，通过在方格纸上画小猫图 ，讨论哪只小猫长得更像乐乐，让















学生初步体会比例尺的应用。再如， 在实践活动中， 通过画自己卧室的平面图，设计巨人的教室，
进一步体会比例尺在生活中的应用。同时，通过 “你知道吗 ”栏目中的知识，了解比例尺的另一
种形式，拓宽学生的视野。




课时安排：





















15 课时
教学内容：变化的量

教学目标：

1．结合具体目标，体会生活中存在着大量互相依存的变量。

2．在具体情境中，尝试用自己的语言描述两个变量之间的关系。

教学重点：

结合具体目标，体会生活中存在着大量互相依存的变量。

教学难点：

在具体情境中，尝试用自己的语言描述两个变量之间的关系。

教学用具：

课件

教学过程：

活动一：观察并回答。

1、 下表是小明的体重变化情况。

观察表中所反映的内容，搞清楚表中所涉及的量是哪两个量？观察后请回答。

2、 上表中哪些量在发生变化？

3、 说一说小明 10 周岁前的体重是如何随年龄增长而变化的？



小结：小明的体重随年龄的增长而变化。






2—6 岁和

6---10

岁是体重的增长高峰。说明




这两个阶段是孩子成长的重要阶段。

4、体重一直会随年龄的增长而变化吗？这说明了什么？

说明：体重和年龄是一组相关联的量。但体重的增长是随着人的生长规律而确定的。

6、教育学生要合理饮食，适当控制自己的体重。

活动二：骆驼被称为 “沙漠之舟 ”，它的体温随时间的变化而发生较大的变化。

manipulator control mode a
al esi
industrial control
ner of th
computer use
software writing
观察书上统计图：

1、图中所反映的两个变化的量是哪两个？

2、横轴表示什么？纵轴表示什么？

同桌两人观察并思考，得出结论后，记录在书上，然后再在全班汇报说明。

3、

一天中，骆驼的体温最高是多少？最低是多少？











d programmabl e controllers introduction 2.1 S
contencontrolall
central colle
bout. Now in several ways in
ction
elect discussion with ma
context f indstal
nd distri bution system and transiti





nipulatcool 2.1 classificati on
toatn ca
on
n oen
of distributed
be se en i n three ways: (1) Programmable Logica
contr ol system










of control relaysand dscretelctronic circuitcan cotrol
l Controller (referred to as
in a
IPC); (2) Distri
alog ue h
bu
ndli ng, loop contro
d Control System (DCS for short), and (3) the Programmable
has beg

















old i ndustrial equi pment,so orecommon. Minly these two relatively cheap and you can eetold- fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
h distri
contrast contrast 1, ea
d system has great adva
ch of the three technologi
ntages in l

oop regulati
es of origi
on, but only as a means of conti
s anevelenreqreen
uos rocess
s for fast data processing makes it inve
contr ol. Optimization of PLC is th











simple) industrial equipmet. Sohe can see them nowhowever t hese tw
nted the com
corre
puer. The m
spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
o contr ol mode s (relay and discrete ele

n the w ork order control, early




ctronic
h level of standardi
primary is repla
circuits) are these fatal flaws: (1) cannot a
at n, ca nse
ced relay this hulking system, focused on the switch



ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
s, is a ri
ng the runni
ch software resources, especially t
ng order of functi
he ne ed for immedia
ons. Marked
cy in
micr
he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
s used to
cent ury emerged, micr
control and meet its spee
o-el ectronics technol
d, on the virtu
og ha s devel ope d rapi dly, people soon microel
sta toatechy e sust
l model , real-time a nd i
ectronics processing technology w



ntial increase i
n computational re
ill e sed







n thelevel of industrial aut
quireme
the Programmable
nts. Distri buted system started w
gicalntroer at i

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
program as a ba
g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
d co
n thr ocee
e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






o welding, l
patibi lity, wi de availa
nd
of experience 1.2 manipulator i

ogistics, mechani cal processi
bility,
n bot h at home and




abr
ng, a
hardwar e is complet

































4、 一天中，在什么时间范围内骆驼的体温在上升？在什么时间范围内骆驼的体温在
下降？

5、

第二天 8 时骆驼的体温与前一天

8 时的体温有什么关系？

6、

骆驼的体温有什么变化变化的规律吗？

活动三：某地的一位学生发现蟋蟀叫的次数与气温之间有如下的近似关系。

1、

蟋蟀 1 分叫的次数除以

7 再加 3，所得的结果与当时的气温值差不多。

2、

如果用

t 表示蟋蟀每分叫的次数，你能用公式表示这个近似关系吗？请你写出这

个关系式，全班展示，交流。

3、

你还发现生活中有哪两个量之间具有变化的关系？它们之间是怎样变化的？四人

小组交流你收集到的信息，选派代表请举例说明

4、

你还发现我们学过的数学知识中有哪些量之间具有变化的关系？

全课小结： 今天我们研究的两个量都是相关联的。

关系。 下一节课我们将深入研究具有相关联的两个量，

知识在数学上的应用。

课后反思：

它们之间在变化的时候都具有一定的

在变化时有相同的变化特征，

这样的

教学内容：正比例

教学目标：

1．利用正比例解决一些简单的生活问题，感受正比例关系在生活中的广泛应用。

2．能根据正比例的意义，判断两个相关联的量是不是成正比例。

3．结合丰富的事例，认识正比例。

教学重点：

1、结合丰富的事例，认识正比例。

2、能根据正比例的意义，判断两个相关联的量是不是成正比例。

教学难点：

能根据正比例的意义，判断两个相关联的量是不是成正比例。

教学用具：

课件

教学过程：

活动一：在情境中感受两种相关联的量之间的变化规律。

（一）情境一：

1、 观察图，分别把正方形的周长与边长，面积与边长的变化情况填入表格中。请根
据你的观 察，把数据填在表中。

2、填完表以后思考：正方形的周长与边长，面积与边长的变化是否有关系？它们的变

化分别有怎样的规律？规律相同吗？

说说从数据中发现了什么？

3、 小结：正方形的周长和面积都随边长的增加而增加，在变化过程中，正方形的周
长与边长的比值一定都是 4。正方形的面积一边长的比是边长，是一个不确定的值。

说说你发现的规律。

（二）情境二：

1、一种汽车行驶的速度为

2、请把下表填写完整。

3、从表中你发现了什么规律？

90 千米 小时。汽车行驶的时间和路程如下：














manipulat
al esi
industrial control










or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
ss, hope desig
ne ha s be en ra pid development i
ood devel opme
ers
n industrial
nt of the technology makes a g
can i n yihu esin i
onme nt there is a
autoationas
ood optimizati
n the
separate subject.
on of produ ctive ca
nipulappli
pial, anrootshs
g n his e sin
cation bega
his uni que a dvantages,
n to filter int
such as: has
o weld
d co
abr
ogistics, mechani cal
patibi lity, wi de availa
d of resear
nd
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
dge has has must awarencan success of usin e cee s experience 1.2 anatr in ot h at an
very as as foaterialsimple movemecond generation meh sensors a
rocessi
bility,
ch r ofilau




ng, a
ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
说说你发现的规律：路程与时间的比值（速度）相同。

（三）情境三：

1、一些人买一种苹果，购买苹果的质量和应付的钱数如下。

2、把表填写完整。

3、从表中发现了什么规律？

应付的钱数与质量的比值（也就是单价）相同。

4、说说以上两个例子有什么共同的特点。

小结：路程随时间的变化而变化， 在变化过程中路程与时间的比值相同； 应付的钱数随购买
苹果的质量的变化而变化，在变化过程中应付的钱数与质量的比值相同。

5、正比例关系：

（ 1）时间增加，所走的路程也相应增加，而且路程与时间的比 值（速度）相同。那
么我们说路程和时间成正比例。
（ 2）购买苹果应付的钱数与质量有什么关系？




















6、观察思考成正比例的量有什么特征？

一个量随另一个量的变化而变化，在变化过程中这两个量的比值相同。

（四）想一想：

1、正方形的周长与边长成正比例吗？面积与边长呢？为什么？

师小结：

（ 1）正方形的周长随边长的变化而变化，并且周长与边长的比值都是

的周长与边长成正比例。

请你也试着说一说。

（ 2）正方形的面积虽然也随边长的变化而变化，

所以正方形的面积和边长不成正比例。

请生用自己的语言说一说。

2、小明和爸爸的年龄变化情况如下：

小明的年龄岁



4，所以正方形

但面积与边长的比值是一个变化的值，

6



7



8

9

10

11

爸爸的年龄

岁

32

33







（ 1） 把表填写完整。
（ 2） 父子的年龄成正比例吗？为什么？
（ 3） 爸爸的年龄 =小明的年龄 +26。虽然小明岁数增加 ，爸爸岁数也增加，但是小明岁
数与爸爸岁数的比值随着时间发生变化，不是一个确定的值，所以父子的 年龄不成正比例。







与同桌交流，再集体汇报

在老师的小结中感受并总结正比例关系的特征

活动二：练一练。

1、

判断下面各题中的两个量，是否成正比例，并说明理由。

（ 1） 每袋大米的质量一定，大米的总质量和袋数。
（ 2） 一个人的身高和年龄。
（ 3） 宽不变，长方形的周长与长。
2、

根据下表中平行四边形的面积与高相对应的数值，判断当底是

们是是成正比例，并说明理由。

6 厘米的时候，它









manipulat
al esi
industrial control










or control mode ad programmabl e controllers introduction 2.1 S
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ntage. T
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contr ol. Optimization of PLC is th











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nted the com
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spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
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n the w ork order control, early




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h level of standardi
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at n, ca nse
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ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
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he ne ed for immedia
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he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
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opme nt of the trains, the success of PLC har











































control obj
are soare an
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appear often i
win
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autoationas
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by learn
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平行四边形的面积随高的变化而变化， 即平行四边形的面积与高的比值不变， 所以平行四边
形的面积与高成正比例。 （也可以用公式进行说明）

3、

买邮票的枚数与应付的钱数成正比例吗？填写表格。先填写表格，再说明理由

应付的钱数随购买的枚数的变化而变化， 而且比值不便。 所以应付的钱数与买邮票的枚数
成正比例。

4、找一找生活中成正比例的例子。

5、先自己独立完成，然后集体订正，说理由。

课后反思：

























教学内容：画一画

教学目标：

1、 在具体情境中，通过

所对应的变量的值。

3、利用正比例关系，解决生活中的一些简单问题。

教学重点：

1、在具体情境中，通过

所对应的变量的值。

教学难点：

1、会在方格纸上描出成正比例的量所对应的点，并能在图中根据一个变 量的值估计
它所对应的变量的值。

2、利用正比例关系，解决生活中的一些简单问题。

教学过程：

一 、复习

活动一；判断下面的量是否成正比例关系？

1、

每行人数一定，总人数和行数。

2、

长方形的长一定，宽和面积。

3、

长方体的底面积一定，体积和高。

4、

分子一定，分母和分数值。

5、

长方形的周长一定，长和宽。

6、

一个自然数和它的倒数。

7、

正方形的边长与周长。

8、

正方形的边长与面积。

9、

圆的半径与周长。

10、

圆的面积与半径。

11、

什么样的两个量叫做成正比例的量

二、新授


“画一画 ”的活动，初步认识正比例图象。

2、 会在方格纸上描出成正比例的量所对应的点，

并能在图中根据一个变量的值估计它

“画一画 ”的活动，初步认识正比例图象。

2、会在方格纸上描出成正比例的量所对应的点，并能在图中根据一个变量的值估计它

















活动二：探索一个数与它的

5 倍之间的关系。

1、 求出一个数的

5

倍，填写书上表格。自己独立完成。





manipulat
2、 判断一个数的

5

倍和这个数有怎样的关系？说说你判断的理由











or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
al esi
industrial control
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
cen





qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
l model , real-time a nd i









ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har
















































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to devel
has gradually mature
p as a factory a
ng evel oknwl
d, as at
utationanards. eca
ure a technology li
use robots are g
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nt of the technology makes a g
can i n yihu esin i
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separate subject.
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such as: has
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ha
om
nipulators have the envircertain amountof seen the mechancal arm is to use theprogram as a basis. Difference is that troot eg
小结：一个数和它的

5 倍之间具有正比例关系。

（图见书上）。请观察横轴表示什么？纵轴表

3、

根据上表，说出下图中各点的含义。

示什么？然后说说各点表示的含义。

4、

连接各点，你发现了什么？

注：所描的点都在同一条直线上。

5、

利用书上的图，把下表填完整。

6、

估计并找一找这组数据在统计图上的位置。

自己独立完成。

在统计图上估计一下，看看自己估计地是否准确

三、练习

活动三：试一试。

1、

在下图中描点，表示第

20 页两个表格中的数量关系。

2、

思考；连接各点，你发现了什么？

活动四：练一练。

1、

圆的半径和面积成正比例关系吗？为什么？

教师讲解：因为圆的面积和半径的比值不是一个常数。

2、

乘船的人数与所付船费为：

（数据见书上）

（ 1） 将书上的图补充完整。
（ 2） 说说哪个量没有变？
（ 3） 乘船人数与船费有什么关系？
（ 4） 连接各点，你发现了什么？
每人所需的乘船费用没有变化。

乘船费用与人数成正比例。

所有的点都在一条直线上。

3、

回答下列问题：

（ 1）圆的周长与直径成正比例吗？为什么？
圆的周长与直径成正比例关系。
（ 2） 根据右图，先估计圆的周长，再实际计算。
（ 3） 直径为 5 厘米的圆的周长估计值为（

（ 4） 直径为 15 厘米的圆的周长估计值为（）

），实际计算值为（） 。













，实际计算值为（） 。

4、把下表填写完整。试着在 第一题的图上描点，并连接各点，你发现了什么？（表格见
书上）所有的点都在同一条直线上。




四、课后反思：


















manipulator control mode a
al esi
industrial control
ner of th
computer use
software writing
教学内容：反比例

教学目标：

1、结合丰富的实例，认识反比例。

2、能根据反比例的意义，判断两个相关联的量是不是成反比例。











d programmabl e controllers introduction 2.1 S
contencontrolall
central colle
bout. Now in several ways in
ction
elect discussion with ma
context f indstal
nd distri bution system and transiti





nipulatcool 2.1 classificati on
toatn ca
on
n oen
of distributed
be se en i n three ways: (1) Programmable Logica
contr ol system










of control relaysand dscretelctronic circuitcan cotrol
l Controller (referred to as
in a
IPC); (2) Distri
alog ue h
bu
ndli ng, loop contro
d Control System (DCS for short), and (3) the Programmable
has beg















old i ndustrial equi pment,so orecommon. Minly these two relatively cheap and you can eetold- fashionedsimple (or

n t o refectse a e adva
Logical Controller (PLC for short). 2.1.2 PLC a
ntage. T
e IC and D
h distri
contrast contrast 1, ea
d system has great adva
ch of the three technologi
ntages in l

oop regulati
es of origi
on, but only as a means of conti
s anevelenreqreen
uos rocess
s for fast data processing makes it inve
contr ol. Optimization of PLC is th











simple) industrial equipmet. Sohe can see them nowhowever t hese tw
nted the com
corre
puer. The m
spg relay ee
n brought i
ds wa
n terms of hardware there,
s bor n, its main
si ng hig
use i
o contr ol mode s (relay and discrete ele

n the w ork order control, early




ctronic
h level of standardi
primary is repla
circuits) are these fatal flaws: (1) cannot a
at n, ca nse
ced relay this hulking system, focused on the switch



ore compatibility tool
controlli








dapt to te coex lgicontrol, (2) only for thcurrent project, t
s, is a ri
ng the runni
ch software resources, especially t
ng order of functi
he ne ed for immedia
ons. Marked
cy in
micr
he lack of com patibi lity and (3) not reforming the sy
operational systems. So the com
oprocessor i n the early 1970 of t












stem with qui pment impr ovements. Spring for te evelena's ern
puter can effectively control i
he 20th
s used to
cent ury emerged, micr
control and meet its spee
o-el ectronics technol
d, on the virtu
og ha s devel ope d rapi dly, people soon microel
sta toatechy e sust
l model , real-time a nd i
ectronics processing technology w



ntial increase i
n computational re
ill e sed







n thelevel of industrial aut
quireme
the Programmable
nts. Distri buted system started w
gicalntroer at i

anulatr i
echoly
of design let
successf ully com









s w seda a ist
nd t
desig
l robots in
rapi d evel
ners on in
ding,
schol
paintiplete like wel
se ,
opme nt of the trains, the success of PLC har











































control obj
are soare an
ctives often
simulation control
appear often i
win
n inal aut
big and succe
some usually
nts.
n. Istal
ssfevelenno
didn't opport
auati
conti
on technolog
s to developas actry
as gradually mature
utationanards. eca
ng level of
d, as mat
use robots are g
ure a technology li
ood devel opme
ne ha s be en ra pid development i
nt of the technology makes a g
ss, hope desig
n industrial
ood optimizati
ers
autoationas
n roctive
separate subject.
pital, and robot shows t
nipulappli
his uni que a dvantages,
cation bega
such as: has
by learn
ng, del
of has a must of consolidation, understand hasunitie s awarene ss i
cha nical arms are
n worl d range within some leadi
eqpped
knwldge has has must awaren
nipulators hav
can i n yihu esin in thecan success of usi
program as a ba
g n his e sin
very as as foaterialsimple movemecond generation meh sensors a
n to filter int
d co
n thr ocee
e the envir onme nt there is acertain amo untof seen the mechancal arm is to use thes. Diference is tat he robot beg






o welding, l
patibi lity, wi de availa
nd
of experience 1.2 manipulator i

ogistics, mechani cal processi
bility,
n bot h at home and




abr
ng, a
hardwar e is complet
3、利用反比例解决一些简单的生活问题，感受反比例关系在生活中的广泛应用。

教学重点：

认识反比例，能根据反比例的意义判断两个相关联的量是不是成反比例。

教学难点：

认识反比例，能根据反比例的意义判断两个相关联的量是不是成反比例。

教学过程：

一、复习

1、什么是正比例的量？

2、判断下面各题中的两种量是否成正比例？为什么？

（ 1）工作效率一定，工作时间和工作总量。
（ 2）每头奶牛的产奶量一定，奶牛的头数和产奶总量。
（ 3）正方形的边长和它的面积。














二、导入新课

利用反义词来导入今天研究的课题。今天研究两种量成反比例关系的变化规律。

三、进行新课

情境（一）

认识加法表中和是

12 的直线及乘法表中积是 12 的曲线。

引导学生发现规律：加法表中和是 12，一个加数随另一个加数的变化而变化；乘法表中
积是 12，一个乘数随另一个乘数的变化而变化。




情境（二）






让学生把汽车行 驶的速度和时间的表填完整，当速度发生变化时，时间怎样变化？每
两个相对应的数的乘积各是多少？你 有什么发现？独立观察，思考同桌交流，用自己
的语言表达

写出关系式：速度

×时间 =路程（一定）



观察思考并用自己的语言描述变化关系乘积（路程）一定




情境（三）








把杯数和每杯果汁量的表填完整， 当杯数发生变化时， 每杯果汁量怎样变化？每两个相对
应 的数的乘积各是多少？你有什么发现？用自己的语言描述变化关系

写出关系式：每杯果汁量

反比例意义

引导小结： 都有两种相关联通的量， 其中一种量变化，另一种量也随着变化，并且这两
种量中相对应的两个数的乘 积是一定的。这两种量之间是反比例关系。

活动四：想一想

P26 页第 1、2、3 题

关系式： X×Y=K （一定）

×杯数 =果汗总量（一定）

5、以上两个情境中有什么共同点？








manipulat
al esi
industrial control










or control mode and programmabl e controllers introduction 2.1 S
ner of th
computer use
software writing
elect discussion with ma
contencontrolall
central colle
bout. Now in several ways in
ction
context f indstal
nd distri bution system and transiti







nipulatcontr ol 2.1.1 classificati onof control relays
utati
on
n ca
of distributed
n oen
contr ol system in a
be se en i n three ways: (1) Programmable Logica
alog




and dscretel
l Controller (referred to as
ue ha
ctronic circuit

ndli ng, loop contro








can cotrolold i ndustrial equi pment,bu
IPC); (2) Distri
has beg
bute d Control System (
n t o refectse a e adva
DCS for short), and (3) the Programmable
ntage. T
Logical Controller (PLC for short). 2.1.2 PLC a
h dist




















o more common. Mainly these two relatively cheap and you can eetold-fashionedsimple (orsimple) i
bute
e IC and D
d system has great adva
contrast contrast 1, ea
ntages in l
ch of the three technologi
oop regulati

on, but only as a means of conti
es of origi
uos rocess
s anevelenreqreen
contr ol. Optimization of PLC is th
s for fast data processing makes it inve
corre

ndustrial equipme
nted the com
spg relay ee









t. Sohe can see them nowhowever t hese two contr ol mode s (relay and discrete electroniccircuits) are these fatal flaws: (1) cannot a
puer. The m
ds wa
n brought i
s bor n, its main
n terms of hardware there,
use i
si ng hig
n the w ork order control, early

primary is repla
h level of standardi
ced relay this hulking system, focused on the switch
atica nse
controlli









dapt to te coex lgicontrol, (2) only for thcurrent project, t
ore compatibility tool
ng the runni
s, is a ri
ng order of functi
ch soft ware resources, especially t
ons. Marked
he ne ed for immedia
micr
he lack of com patibi lity and (3) not reforming the sy
cy in
oprocessor i n the early 1970 of the 20th


stem with
operational systems. So the com
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qui pment impr ovements. Spring for t
puter can effectively control i
ury emerged, micr
s used to
o-el ectronics technol
e evelena's ern
control and meet its spee
og ha s devel ope d rapi dly, people soon microel






st
d, on the virtu
ectronics processing technology w
utation echloy the sust
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ntial increase in the
ill e sed
n computational re
rogram
quireme
able Logical Controller (that is