七年级数学上册 2.2代数式教案 沪科版

七年级数学上册 2.2代数式教案 沪科版 2.2 代数式 学习目标 1( 会列代数式，能解释一些简单代数式的实际意义。 2( 掌握单项式的系数、次数，多项式的项、项数、次数等概念;会辨别单项式、多项式。 3( 了解代数式、整式等概念。 4( 会求代数式的值，感受代数式求值可以理解为一个转换过程或某种算法，会利用代数式 求值推断代数式所反映的规律。 教材解读 一、 温故 1( 不等号:,、,、?、?、?。 2( 多位数用各位上的数字 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 示:如 23,2，10，3234,2，100，3，10，4，。 二、知新 1(代数式 ?用加、减、乘(乘方)、除等运算符号把数或表示数的字母连接而成的式子，叫做代 1s222k,190aa，b,rh数式。如:，，，4，，，等都是代数式。 aav3 2(单项式 ?由数与字母的乘积组成的代数式叫做单项式，单独的一个数或一个字母也是单项式。 1224a,3,rh如 ，，，，等都是单项式; aa3 1224a,3,rh?单项式中的数字因数叫做这个单项式的系数。如 ，，，，的系aa3 1,3,411数分别是，，，，; 3 1224a,3,rh?单项式中所有字母的指数之和叫做这个单项式的次数。如 ，a，，a，3 03121的次数分别是，，，，。 3(多项式 22k,1a，bx，2x,3?几个单项式的和叫做多项式。如:，，等都是多项式; ?在多项式中，每个单项式叫做多项式的项，多项式的每一项都包括它前面的符号。其 22,93x,2y中不含字母的项，叫做常数项。如的项是:、、，其中常数项3x,2y,9 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 ,99是，而不是; ?一个多项式含有几项，这个多项式就叫做几项式。一个多项式中次数最高项的次数， 2叫做这个多项式的次数。如是三次四项式。 4ab,3ab，2a,1 4(单项式与多项式统称为整式。即单项式、多项式都是整式。 重点剖析 3x,113222xa，b,10例1 下列代数式:，，，，，,,,其中abx,3x，46,2x2R 哪些是单项式,哪些是多项式,哪些是整式, 32x,10解: 单项式:，， ab; 2 3x,12a，b多项式:，，; x,3x，42 3x,1322xa，b,10整式:ab，，，，x,3x，4,。 22 注意:?整式是单项式与多项式的统称。?分母中含有字母的代数式一定不是整式，也就一定不是单项式，也不是多项式。 例2 说出下列多项式的项，并说明是几次几项式: 13222343a,ab，3ab,b,1x,2x，x,5?;?。 4 4343,5x,2x，x,5,2xx解:?的项是、、、，它是四次四项式。 x 1,ba,ab，3ab,b,1,1,ab3aba?的项是、、、、，它是四次44 五项式。 注意:?多项式的项包括前面的符号;?在求多项式的次数之前要先确定每一项的次数， 0其中次数最高项的次数就是这个多项式的次数;?常数项的次数为。 222b,,4a,a,b，3a,b例3 已知，，求代数式的值。 3 2b,,4a,解:当，时， 3 222222,(),(,4)，3，,(,4)a,b，3a,b 33 45,,16，2，4,,9。 99 注意:?将相应的字母换成数字，运算符号、原来的数字不变。?如果字母给出的数值是负数，代入时必须加括号。?如果字母给出的数值是分数，作乘方运算时也必须添上括号。?如果代数式中省略了乘号，代入数值后必须添上乘号。 1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-2012.12 4 CO2 gas shielded welding machine ZXG400 1 Wuhan 1996 30 good workshop -3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-500-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-machine BXlding mber manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric wet 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 nue slo0 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 gatsluice 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 3.0 1 sand50 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 ider 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 .leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slhoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compressoelding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric w-rol box CWK12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature cont30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.-chine CG1automatic cutting ma-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-- 2 - 227例4 已知代数式的值为，求代数式的值。 x，x，32x，2x,3 2分析:若由条件先求出值，再代入中计算，则很麻烦，并且到现在为止2x，2x,3x 22,7我们还不会解这个方程。可由条件求得，再将 要求 对教师党员的评价套管和固井爆破片与爆破装置仓库管理基本要求三甲医院都需要复审吗 值的代数式进,4x，x，3x，x 行变形，然后整体代入求值。 22,7解:?，?， ,4x，x，3x，x 22,32，4,3,5?,(),。 22x，2x,3x，x 注意:本题通过将代数式变形，然后“整体代入”来求代数式的值。“整体代入”不是求出代数式里各个字母的值，而是把与这些字母有关的某个代数式的值整体代入，达到求解的目的。 错点反思 2232,ab8例5 指出下列单项式的系数和次数:?;?;?,。 a3 881错解:?的系数是，次数是; 0?的系数和次数都是; a 22322,ab2,,?的系数是，次数是6。 33 88反思:?的系数是，其中不含字母所以次数不是1，而是0;?单独一个字母的a 22,,系数和次数都是1，次数不是0;?误认为是字母，实际上是常数，不是字母，所以,,3是系数，次数为5。 88正解:?的系数是，次数是0; 1?a的系数和次数都是; 22322,ab25,,,?的系数是，次数是。 33 ,注意:?是常数，不是字母;?单项式的次数是所有字母的指数和，不能加上系数中的指数;?若单项式是单独的一个数字，则它的系数是它本身，次数是0。 例6 用代数式表示: bmnaa?与的4倍的和;?与平方差;?比大20,的数。 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 on barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.1218KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulati-op 2012.12 9 automatic temperature control box CWKelding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine worksh30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric w-machines welding machine BXautomatic cutting machine CG1-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-5 Workshop 2006 95 good carbon arc gouging machine ZXG 1250 4 Wuhan electric welding machine 2012.12-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding -3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-500--re to enter time 1 AC electric welding machine BXnt number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now whequipme9 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 eate 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 rack glectrical 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 trashf 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 eent 4 flat emergency gate slot oleaf 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 equipm- 3 - 用心 爱心 专心 2错解:?;?;?+20,。 a,ba(4m，n) b反思:?混同了“与的和的4倍”;?混同了“与的平方的差”;?错在将百mna 分数等同于一般的数。 22m，4n正解:?;?;?(1+20,)。 a,ba 注意:列代数式时要弄清楚题中的数量关系，运算顺序，书写代数式时要 规范 编程规范下载gsp规范下载钢格栅规范下载警徽规范下载建设厅规范下载 。 方法总结 1(代数式的判定方法 不含等号，也不含不等号的式子就是代数式。含等号，或含不等号的式子就不是代数式。,5ax,3,4如，都是代数式;,2，都不是代数式。 a3x,7y 2(整式的判定方法 xa,b分母不是字母的代数式就是整式。分母是字母的代数式就不是整式。如，，，8y2223x都是整式，，都不是整式。 a,x，y 3(单项式和多项式的判定方法 不含加号或减号的整式就是单项式，含加号或减号的整式就是多项式。 4(单项式是由数字因数和字母因式两部分组成。数字因数就是单项式的系数。单项式 ,33的系数应包括前面的符号，比如单项式的系数是“”而不是“”。单项式的系 ,1,1111数是“”或“”时，“”通常省略不写，“”中的“”也通常省略不写，但“,” 1号不能省略。因此只含有字母因式的单项式不能认为它们没有系数，它们的系数是“”或,1“”。 5(单项式次数仅与单项式中所有字母的指数有关，而与系数无关。单项式中单独出现 21，2，1,41的字母，其指数“”通常略去不写，但计算次数时不可丢失。如的次数是3xyz 0，2，0,2次，而不是次。 126x,x,56(多项式的项及项的系数应包括它前面的符号，比如，多项式的第二项2 1111x是，而不是，第二项的系数是，而不是。 ,x, 2222 7(求代数式的值的步骤 ?代入，即用数值代替代数式里的字母。 12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature cont30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.-chine CG1automatic cutting ma-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-2012.12 4 CO2 gas shielded welding machine ZXG400 1 Wuhan 1996 30 good workshop -3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-500-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-machine BXlding mber manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric wet 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 nue slo0 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 gatsluice 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 3.0 1 sand50 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 ider 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 .leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slhoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compressoelding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric w-rol box CWK- 4 - ?计算，即按照代数式指明的运算顺序，计算出结果。 注意:?书写格式，在把字母所取的数值代入代数式时，必须写上“当„„时”，表示 这个代数式的值是在这种情况下求得的。 ?求某些代数式的值时，有时采取整体代入法来求。 知识巩固 一、填空题: 2,,ab1(是________次单项式，系数是________。 5 22(多项式是 ________次________项式，其中最高次项是________，常数项 2x,3xy，1 是________。 12m，122,ab，ab,3a,53(已知多项式是六次四项式，则是________。 m4 4(将原价为元的药品降价30%出售，则降价后此药品售价为________元。 a 2275a，2b，53a，6b，4(若的值为，则代数式的值是________。 二、选择题: (下列式子符合代数式的书写格式的是( )。 6 113,m(a,b)2abA(?40 B( C( D( aa437(下列说法正确的是( )。 A( 单项式既没有系数，也没有次数 m 5B( 单项式5×10的系数是5 ,2006C( 也是单项式 2,3,3,xD( 的系数是 22a,5b8(代数式用语言叙述正确的是( )。 5bbA(a与的平方差 B(a的平方减5乘以的平方 b5baaC(的平方与的平方的5倍的差 D(与的差的平方 三、解答题: 3422x,y,,9(当，时，求代数式的值。 x，y,x,y55 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 on barrel 4 Wuhan 11 2009 140 good electric welding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.1218KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulati-op 2012.12 9 automatic temperature control box CWKelding machine 2012 6 a good workshop 2012.12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine worksh30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric w-machines welding machine BXautomatic cutting machine CG1-500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-5 Workshop 2006 95 good carbon arc gouging machine ZXG 1250 4 Wuhan electric welding machine 2012.12-400 1 Wuhan 1996 30 good workshop 2012.12 4 CO2 gas shielded welding machine ZXG300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding -3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-500--re to enter time 1 AC electric welding machine BXnt number equipment name model number manufacturer name year of purchase has been using classes maintenance situation now whequipme9 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 eate 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 rack glectrical 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 trashf 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 eent 4 flat emergency gate slot oleaf 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 equipm- 5 - 用心 爱心 专心 bb[10(用代数式表示:?的平方;?、平方和;?与和的平方;?与和的一yaax4y 半。 能力提高 23419201.一列单项式:，，，，„„，，，„„ ,3x,19x20x2x4x,x ?你能说出排列有什么规律吗, ?写出第99个，第2006个单项式; n，1?写出第个，第个单项式。 n a，b1a,b2a，2b,,2(当时，求代数式的值。 a,b2a，ba,b 33x,2x,,23(当时，代数式ax,bx,1的值为1000，求时，代数式ax,bx,1的值。 4(水泥厂以每年产量增长10%的速度发展，如果第一年的产量是，那么第二年的产量是a 多少,第三年的产量是多少, 5.为了节约用水，某市自来水公司采取以下收费方法:每户每月用水不超过10t，收费1.5元/t;每户每月用水超过10t，超过的部分按3元/t收费。现在已知小明家2月份用水txx,10),请用代数式表示小明家2月份应交水费多少元,如果,16，那么小明家2月份应x 交水费多少元, -500 2 Wuhan 2010 80 good electric welding machine workshop 2012.12 6 Wuhan welding semi-1250 4 Wuhan electric welding machine 2012.12 5 Workshop 2006 95 good carbon arc gouging machine ZXG-2012.12 4 CO2 gas shielded welding machine ZXG400 1 Wuhan 1996 30 good workshop -3 2 Wuhan 2010 2012.12 3 102 good workshop Silicon rectifier welding machines welding machine ZXG-500-300 2 Wuhan 2010 120 good electric welding machine workshop 2012.12 2 AC welding machines welding machine BX-machine BXlding mber manufacturer name year of purchase has been using classes maintenance situation now where to enter time 1 AC electric wet 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 nue slo0 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 gatsluice 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 3.0 1 sand50 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 ider 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 .leaf of sluice and dam 6.2x2.0 7.00 7.00 electric hoist 1 2.50 slhoist 1T~5T 2012.12 14 5, Jiangsu wujin 2011 22 good workshop 2010, China air compressoelding machine workshop 2012.12 truck crane 25T 1 car loan good workshop 2012.12 12 flatbed 1 lease a good workshop 13 18KW 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 10 insulation barrel 4 Wuhan 11 2009 140 good electric w-rol box CWK12 8 Baking box 400 degrees 1 Wuhan 2010 150 good electric welding machine workshop 2012.12 9 automatic temperature cont30 1 machine shop 2009 212 good 2012.12 7 manual cutting device 2 Wuhan electric welding machine 2012 6 a good workshop 2012.-chine CG1automatic cutting ma- 6 -