冀教版七年级下册数学 8.1同底数幂的乘法 教案

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名称 冀教版七年级下册数学 8.1同底数幂的乘法 教案
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更新时间 2022-05-30 07:10:37

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8.1 = 同底= ;数幂的乘法 = = 教学= ;设计
教学෹= 4;计说明 = <= /o:p>
同底数幂的乘法਷= 9;幂的运算性质之一,&= #23427;和幂的另两个运算= 615;质 —— = 4130;的乘方和积的乘方ᦁ= 2;都是学习整式乘法的&= #22522;础,在幂的三个运= 639;性质中,同底数幂的= ;乘法性质是最基本的&#= 65294;学好同底数幂的乘Ė= 61;性质的基础是正确理= 解底数、指数、幂的= 7010;念和乘方的意义.ਢ= 5;学时做到不要生硬地&= #25552;出问题,应力求顺= 046;自然、水到渠成.讲= ;课要注意联系过去尚&#= 19981;甚巩固的知识,将Ą= 32;旧知识有机地融合在= 一起.
教学௤= 6;标 = <= /o:p>
1 .掌握同底= 968;幂的乘法性质,通过= ;幂的运算法则的学习&#= 65292;培养对公式比较与ť= 82;别能力,从而提高能= 准确迅速地进行整式= 0056;法运算的能力; =
2 .能正确熟 = 451;地进行同底数幂的乘= ;法运算.
过程与方法
经历同底数幂乘ૢ= 1;运算性质的获得过程&= #65292;在探究同底数幂乘= 861;法则的过程中,培养= ;学生的归纳、概括能&#= 21147;,感悟归纳推理在ă= 68;学发现中的价值,同= 时渗透由未知转化为= 4050;知的化归思想. =
情感、态度与价ࠆ= 0;观
在计算、归纳和ઍ= 0;括的活动中,体验发&= #29616;的乐趣,从而增强= 398;生学好数学的信心.= ;
教学ດ= 5;点和难点 = <= /o:p>
教学重点:同底ਤ= 8;幂的乘法运算法则及&= #20854;应用.
教学难点:同底ਤ= 8;幂的乘法法则的推导&= #36807;程.
教学ਬ= 1;法: = <= /o:p>
引导启发法
教学ऎ= 6;体 = <= /o:p>
多媒体课件,投ঋ= 3;片.
教学๠= 7;程设计 = <= /o:p>
一、ߝ= 2;流与探究 = <= /o:p>
教师:在 an = 6825;个表达式中, a 是什么? n 是什么?它= 340;含义是什么?
当 a= n = 0316;为运算时,又读作ߠ= 0;么?
学生: a = 6159;底数, n 是指数, an = 1448;读作 a 的 n = 7425;幂.
教师:(多媒体৛= 7;影出示习题)用学过&= #30340;知识做下面的习题A= 292;在做题的过程中,认= ;真观察,积极思考,&#= 20114;相研究,看看能发Ĩ= 16;什么.
计算: <= /o:p>
( 1 = 5289; 22×23<= /span>

( 2 = 5289; 54×53<= /span>

( 3 = 5289; ( - 3)2×( = 5293; 3)2

( 4 = 5289; ()2×()4

( 5 = 5289; ( - <= span style=3D'position:relative;top:13.0pt;mso-text-raise:-13.0pt'>)3× ( - <= span style=3D'position:relative;top:13.0pt;mso-text-raise:-13.0pt'>)4

( 6 = 5289; 103×104

( 7 = 5289; 2m ×2n =

( 8 = 5289; ()m×()n (m , n = 6159;正整数 )

(学生开始= 570;题,互相研究、讨论= ;,气氛热烈,教师巡&#= 35270;、指点,待学生充Ñ= 98;讨论有所发现后,提= 问有何发现)
学生 A = 5306;根据乘方的意义,ࡤ= 7;以得到:
( 1 = 5289; 22×23=3D25

( 2 = 5289; 54×53=3D57

( 3 = 5289; ( - 3)2×( = 5293; 3)2=3D( = 5293; 3)5……

教师:刚才 A 同学说出了= 681;据乘方的意义计算上= ;面各题所得结果,计&#= 31639;是否准确?
学生:计算准确ᦁ= 4;
教师:通过刚才௚= 0;计算和研究,发现什&= #20040;规律性的结论了吗A= 311;
学生 B = 5306;不管底数是什么数ᦁ= 2;只要底数相同,结果&= #23601;是指数相加.
教师:请你举例෾= 8;明.
学生 B = 1040;前边黑板上板书:
22×23=3D = 5288; 2×2 ) ×= ; = 5288; 2×2×2 = 5289; =3D2×2×2×2×2=3D2= 5

底数不变,= 351;数 2+3=3D5

教师:其他= 960;个题是否也有这样的= ;规律呢?特别是后两&#= 20010;?
学生:都有这样௚= 0;规律.
教师:请以习题ᦀ= 8; 7 )为例再加= 197;说明.
学生 C = 1040;前边黑板上板书:
2m ×2n=3D(2×2×̷= 0;×2×2×2)×(2×2×…×2)=3D(2&ti= mes;2×…×2)=3D2m+n

<= !--[if mso & !supportInlineShapes & supportFields]> SHAPE \* MERGEFORMAT <= !--[if mso & !supportInlineShapes & supportFields]> SHAPE \* MERGEFORMAT <= span lang=3DEN-US style=3D'font-size:12.0pt;line-height:150%;color:black'><= /o:p>

m 个 2n = 0010; 2(m+n) 个 2=

底数 2 不变,指数 m+n . <= /o:p>
教师:大家对刚৔= 5;两个同学发现的规律&= #26377;无异议?
学生:没有. =
教师:那么,下༣= 4;大家一起来看更一般&= #30340;形式: am·an = 5288; m , n = 7117;是正整数),运用࠵= 8;才得到的规律如何来&= #35745;算呢?(学生举手A= 292;踊跃板演)
学生 D = 1040;前边黑板上板书:
am×an=3D(a= ×a×…×a×a×a)×(a×a×R= 30;×a)=3D(a×a×…×a)=3Dam+n

<= !--[if mso & !supportInlineShapes & supportFields]> SHAPE \* MERGEFORMAT <= !--[if mso & !supportInlineShapes & supportFields]> SHAPE \* MERGEFORMAT <= span lang=3DEN-US style=3D'font-size:12.0pt;line-height:150%;color:black'><= /o:p>

m 个 a n = 0010; a (m+n) 个 a=

教师:既然#= 268;律都是相同的,能否= ;将中间过程省略,将&#= 35745;算过程简化呢?
学生:能.
教师:将中间过ఴ= 3;省略,就得到 am·an=3Dam+= n = 5288; m , n = 7117;是正整数)
在这里 m = 5292; n 都是正整数A= 292;底数 a 是什么数呢A= 311;
学生 1 = 5306; a 是任何数都= 487;以.
学生 2 = 5306; a 必须是有理= 968;.
学生 3 = 5306; a 不能是 0 . <= /o:p>
教师:既然大家ल= 5;底数 a 是什么样的= 968;意见不统一,下面大= ;家代入一些数实验一&#= 19979;,然后互相交流,ť= 52;论一下.(学生纷纷= 代入数值实验、讨论= 5292;课堂气氛热烈)待ण= 8;生讨论后:
教师:请得到结෹= 0;的同学发表意见.
学生 1 = 5306;底数可以是任何数ᦁ= 2;但我们学的数都是有&= #29702;数,所以 a 是任意有理= 968;.
学生 2 = 5306;底数 a 可以是字母A= 294;
学生 3 = 5306;底数 a 可以是代数= 335;.
教师:刚才几个ࡧ= 6;学说的很好,底数 a 确实可以是= 219;何数,将来我们学的= ;数不都是有理数,另&#= 22806;底数 a 还可以代数= 335;.
教师:请大家思್= 1;,刚才我们一起研究&= #30340;这种乘法应该叫什= 040;乘法呢?
学生:同底数幂௚= 0;乘法.
教师:刚才大家๩= 0;过计算,互相研究得&= #21040;的是同底数幂的乘= 861;运算的方法,现在大= ;家思考一下,如何用&#= 20320;的语言来叙述这个Ű= 16;算的方法呢?(学生= 积极思考,教师板书= 5838;题后提问)
学生 1 = 5306;底数不改变,指数ࡃ= 2;起来.
学生 2 = 5306;把底数照写,指数௥= 6;加.
学生 3 = 5306;底数不变,指数相ࡃ= 2; .

教师:(边= 465;述边板书)刚才几个= ;同学归纳的很好,同&#= 24213;数幂相乘,底数不Ö= 64;,指数相加.
教师:下面运用৓= 2;学的知识来判断以下&= #30340;计算是否正确,如= 524;有错误,请改正.(= ;投影出示判断题)
( 1 = 5289; a3·a2=3Da6<= o:p>

( 2 = 5289; b4·b4=3D2b4=

( 3 = 5289; x5+x5=3Dx10

( 4 = 5289; y7·y=3Dy8

教师逐个提&= 382;学生解答.
教师:接下来,๡= 6;用同底数幂的乘法来&= #20570;下面的例题(投影= 986;示例题)
例 1 = 5306;计算
( <= /span>1 = ) <= span style=3D'mso-themecolor:text1'>26&t= imes;23 ;  = ;  ( 2 = ) <= span lang=3DEN-US style=3D'font-size:12.0pt;line-height:150%;font-family:"Times = New Roman"; color:black'>a <= span lang=3DEN-US style=3D'font-size:12.0pt;line-height:150%;font-family:"Times = New Roman"; color:black'>2 ·a4 ; <= span style=3D'mso-themecolor: text1'>
( <= /span>3 = ) xm ·xm<= /i>+1 ; <= span style=3D'mso-themecolor: text1'> ( 4 = ) <= span style=3D'mso-themecolor:text1'> .
两名同学到前面੖= 9;板演,其他同学练习&= #65292;教师巡视指点,待= 840;体同学做完,对照板= ;演改错,强调解题中&#= 30340;注意问题.
教师:现在我们ߌ= 8;起来运用本课所学的&= #30693;识解决一个实际问'= 064;.(投影出示课本引= ;例)
例 2 = 2826;阳系的形状像一个ߣ= 7;太阳为中心的大圆盘&= #65292;光通过这个圆盘半= 452;的时间约为 ,光的速度 = 422;为 .求太阳系= 340;直径.
解: <= !--[if gte vml 1]>
( km = 5289;.
答:太阳系的直঍= 2;约为 km . <= /o:p>
一名同学到前面ਖ਼= 5;演,其他同学练习,&= #24453;学生做完后发现板= 436;同学有错误.
教师:大家一起੖= 9;看王鑫同学的板演,&= #21457;现有问题的请发言A= 294;
学生李某:最后ಮ= 7;果 12 ×109 km = 6159;错的,不符合科学৙= 6;术法的要求.
教师:请你给他ਟ= 3;正.
学生李某到前面ਟ= 3;正 1.2 ×1010 km
教师:科学技术ૢ= 1;,如何记数,怎样要&= #27714;?
学生王某:把一ߑ= 0;较大的数写成 a×10n = 5292;其中 1≤a<10 = 5294;
教师:现在大家ߌ= 8;起来想一想: am·an·ap = 1561;于什么?( m , n = 5292; p 是正整数) ( 全体学生举= 163;,要求发言 )

学生高某: am·an·ap=3Dam+n+p

教师:现在= 105;们大家来互相考一考= ;,请每位同学为你的&#= 21516;桌出三道同底数幂È= 56;法的计算题,计算量= 不要太大,如果同桌= 0986;的题你全对,而你࠲= 6;的题同学有错,你就&= #33719;胜.(同学之间互= 456;出题,气氛热烈,效= ;果较好)
待学生完成后,ਢ= 5;师引导学生分析出错&= #30340;原因,强调注意问'= 064;.
教师:好了,现ࢷ= 2;让我们一起来回顾一&= #19979;本节课我们研究的= 869;容,有什么收获和体= ;会,大家一起来谈一&#= 35848;.
学生 1 = 5306;我们学习了同底数७= 0;的乘法,我会做同底&= #25968;幂乘法的计算题.
学生 2 = 5306;我学会了如何进行ࡧ= 6;底数幂的乘法,底数&= #19981;变,指数相加.
学生 3 = 5306;我们能运用同底数७= 0;的乘法来解决实际问&= #39064;.
学生 4 = 5306;大家一起研究、讨෹= 0;、交流、学习很快乐&= #65294;
学生 5 = 5306;同学之间互相考一್= 1;,方法很好,等于一&= #19979;做了 6 个题,感觉$= 824;不多,愿意做,挺有= ;意思.
教师:大家谈的๿= 7;非常好!
二、෿= 8;堂练习 = <= /o:p>
课本 P= 69 = 2451;习
三、෿= 8;时小结 = <= /o:p>
本节课由同学们೽= 8;己探究得到了同底数&= #24130;的乘法法则: ( m = 5292; n 伟正整数)A= 294;也就是说:同底数幂= ;相乘,底数不变,指&#= 25968;相加.底数 a 可以是一个= 968;,可以是一个单项式= ;,还可以是多项式.&#= 34429;然法则比较简单,į= 42;在计算时仍然要注意= :一是不要搞错符号= 5307;二是指数为 1 时不要遗漏A= 307;三是不要与合并同类= ;项混淆.
四、෿= 8;后作业 = <= /o:p>
课本 P69 A 组 1 = 2289; 2 、 3 = 9064;写在作业本上, = A 组其余题目= 889;在书上;
B 组题 1 ( 1 = 5289;、 2 题中等程度= 398;生完成, 1 ( 2 = 5289;、 3 数学程度好= 340;学生讨论完成 .

五、板书设计 = = <= /o:p>
3D"文本框:
<= span lang=3DEN-US style=3D'font-size:12.0pt;line-height:150%;color:black'><= /o:p>



&= nbsp;

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