冀教版七年级下册数学 8.5.2平方差公式 教案

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名称 冀教版七年级下册数学 8.5.2平方差公式 教案
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更新时间 2022-05-30 07:16:39

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平方差公式
教学#= 774;计思想
因为ߕ= 6;法公式实际上是整式&= #20056;法的特殊情况,因= 492;,呈现方式是直接推= ;演.所以本节教学过&#= 31243;以学生做自主活动È= 26;主线来组织,根据学= 生的探究情况补充讲= 5299;.乘法公式有平方।= 6;公式和完全平方公式&= #20004;部分,本节课主要#= 762;解平方差公式. <= span style=3D'mso-themecolor:text1'>
首先通过一般多= ;项式的乘法结果来引&#= 36215;学生的兴趣:两个É= 08;项式具备什么特征,= 合并同类项后的结果= 6159;一个二项式.再通๠= 7;一起探究中的几个计&= #31639;引发学生思考,让= 398;生观察算式及结果,= ;发现其中规律.这一&#= 29615;节鼓励学生大胆表ů= 98;意见 , = 215;极与小组同伴合作 = , #= 752;论,交流然后统一意= ;见,师生共同总结出&#= 20844;式内容,分析公式ń= 67;构.再通过探究公式= 的几何背景进一步认= 5782;公式.最后给出例ག= 4;使学生对公式( a+b= A= 289;( a-b= A= 289; =3D= a2-b2 = 340; a A= 292; b = 547;义有更进一步理解,= ;从而对公式的掌握和&#= 36816;用达到灵活和准确ʌ= 94;
教学目标
知识与技能: =
1 .会推导平方差公= 335;,理解平方差公式的= ;几何意义.
2 .掌握平方差公式A= 292;能用平方差公式进行= ;相关运算.
3 .提高发现问题、= 506;索规律的能力
过程与方法: =
1 .经历探究平方差= 844;式的过程,让学生明= ;确这一公式来源于整&#= 24335;乘法,又可以用于ă= 72;式的乘法辩证思想.=
2 .掌握两数和乘以$= 825;两数的差的公式结构= ;特征,培养从一般到&#= 29305;殊,再从特殊到一ō= 24;的思想方法
情感态度价值观= ;:
1 .感知数学公式的 = 467;构美、和谐美,在灵= ;活运用中体验数学的&#= 20048;趣
2. 以探索、归纳公式= 1644;简单运用公式这一ਤ= 8;学情景,增加学习数&= #23398;和使用的信心
教学重点和难点= ;
%= 325;点:
1 = . 对平方差公式的理Š= 99;,掌握 平方差公&#= 24335; 的结构特征,熟练平方差公&#= 24335; 进行简单计算. =
2 = .平方差公式的应用= 5294;
难点: 理Š= 99;理解两数和乘以它们= 的差公式的几何意义= 1450;特点,理解公式中ढ= 3;母 a 、 b 的 的广泛含&#= 20041;,代数推理能力的á= 21;养.
关键:准确的找= ;出因式中哪个式子是a A= 292;哪个式子是 b A= 292;然后把原式写成公式= ;所具备的结构,再按&#= 20844;式进行运算
教é= 98;方法
学生探索归纳与ਢ= 5;师讲授结合
教Ð= 55;准备:
投影仪
课ą= 02;安排
1 课时
教学过程设计 =
一、 &nb= sp; 创设情境
从前,有-个狡ஆ= 2;的庄园主,把-块边&= #38271;为a 米的正方形土ࢸ= 0;租给张老汉种植.第&= #20108;
年,他对= 352;老汉说:“我把这块= 地的-边减少5 米= ,相邻的另-边= 686;加5 米= ,继续租给你,= 199;金不变,你也没有吃= ;亏,你看如何? ”
张老汉-听,觉得å= 09;像没有吃亏,就答应= 道:“好吧.”回到ê= 78;中,他把这事和邻居= 们-讲,大家都说:= 220;张老汉,你吃亏了! ”张老汉非常吃= ;惊.你知道张老汉是&#= 21542;吃亏了吗? 学习了本节课௚= 0;知识,你将能轻松地&= #35299;决这个问题啦。
二、!= 258;主探索
课本 P86 ( 1 )( 2 A= 289;( 3 A= 289;( 4 A= 289;
谈一谈:
①上面四个式子= 中,两个乘式之间有= 0160;么特点?
②乘积合并同类= 项后是几项式?这个= 2810;项式有什么特点?
学生活动:组内= ;讨论,分工合作一起&#= 21160;脑、动笔进行探讨ʌ= 92;然后小组之间互相交= 流,发表自己的见解= 5294;
( 每个算式都是两个= 968;的和与这两个数的差= ;相乘,运算结果是这&#= 20004;个数的平方差 )

总结大家的#= 752;论结果,得出平方差公ó= 35;:( = a+b )( a-b ) =3Da2-b2 = .两个数的= 644;与这两个数的差的积= ;,等于这两个数的平&#= 26041;差. A= 288;板书)
= 2 .认识公式的结构&= #29305;征
( 1 )公式左边= 159;两个二项式相乘,这= ;两个二项式中有一项&#= 26159;完全相同,另一项É= 14;为相反数,右边是相= 同项的平方减去相反= 5968;的平方.
( 2 )公式中的= 383;母 a = 644; b = 487;以是数,也可以是式= ;(包括单项式、多项&#= 24335;等),只要符合平Ą= 41;差的结构特征,就可= 以运用公式.
为了帮助学生认= ;识平方差公式特点,&#= 32473;出下列三个变形,É= 74;中学会确定相同与相= 反项,并正确表示运= 1639;结果.
( -a+b ) (-a-b)=3D( )2-( )2

( b+a ) (-b-a)=3D( )2-( )2

( b-a ) (-b-a)=3D( )2-( )2

学生活动:= 635;结结构特征,对上述= ;三个变形进行计算,&#= 20174;而加深对平方差公ó= 35;的认识
= 3 .用图形进一步验&= #35777;平方差公式
给出下图,提出ߍ= 9;列问题让学生思考:<= /span>
( 1 )请你表示 8-5-1 两个图中( 10&= #8212;4 A= 289;中阴影部分的面积.= ;
( 2 )(如果将&= 452;影部分拼成一个长方= ;形(如图 10&= #8212;5 A= 289;,这个长方形的长和= ;宽分别是多少?你能&#= 34920;示出它的面积吗?ʌ= 89;两个图形的面积之间= 有什么关系?
( 3 )(比较( 1 A= 289;和( 2 A= 289;的结果,你能验证平= ;方差公式吗?)请你&#= 32467;合图形,对平方差Ð= 44;式( = a+b )( a-b ) =3Da2-b2 $= 827;行解释.
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3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
3Dwww.dearedu.c=
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= = &nb= sp;


3D"www.dearedu.com,www.dearedu.com,www.dearedu.com,www.dearedu.com,ww=




= 图 8-5-1





(1 A= 289; = &nb= sp; = A= 288; 2 A= 289;
学生活动:分组= ;讨论,了解公式的几&#= 20309;背景,进一步认识Ð= 44;式.
4 .= 做一做
填写下ƃ= 54;表格,使学生加深对= 公式的理解

算式
与平方差公式中 a= &#= 23545;应的项
与平方差公式中 b= &#= 23545;应的项
写成就 &= #8220;a2-b2” &#= 30340;形式
计算结果

( m+2 ) (m-2)
&= nbsp;
&= nbsp;
&= nbsp;
&= nbsp;

(2m+3)(2m-3)
&= nbsp;
&= nbsp;
&= nbsp;
&= nbsp;

(x+2y)(-x+2y)
&= nbsp;
&= nbsp;
&= nbsp;
&= nbsp;

(1+3y)= (1-3y)
&= nbsp;
&= nbsp;
&= nbsp;
&= nbsp;
体会平方= 046;公式中 a A= 292; b = 340;含义,准确地找出因= ;式中哪个式子是 a A= 292;哪个式子是 b A= 294;
例 1 计算
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( 1 )前两题教= 072;引导学生分析题目条= ;件是否符合平方差公&#= 24335;特征,并让学生说Ñ= 86;本题中 a A= 292; b = 998;别表示什么.
( 2 )第三题计= 639;时把 = 475;成一个数,把 3b<= /span> = 475;成另一个数,直接写= ;出 (-<= st1:chmetcnv UnitName=3D"a" SourceValue=3D"5" HasSpace=3D"False" Negative=3D"False" Numb= erType=3D"1" TCSC=3D"0" w:st=3D"on">5a)2- A= 288; 3b<= /span> A= 289; 2 = 518;得出结果 . = 240;此,我们在计算中,= ;先要分析题目的数字&#= 29305;征,然后正确应用ñ= 79;方差公式,就能比较= 简捷地得到答案.
( 3 )教师引导= 398;生发现,只需将 <= span style=3D'mso-themecolor:text1'>(m+= n) = 013;的两项交换位置,就= ;可用平方差公式进行&#= 35745;算.
5 .= 课堂练习
课本 P88= = 451;习 1 = 289; 2 <= span style=3D'mso-spacerun:yes'> 习题 1 = 289; 2 A= 288; 1 A= 289;( 3 A= 289;、 4 A= 288; 1 A= 289;
教师巡视学生练= ;习情况,请不同解法&#= 30340;学生,或发生错误į= 40;学生板演,教师和学= 生一起分析解法.
三z= 89;小结
1 .什么是&#= 24179;方差公式?
2 .运用公式要注意= 160;么?
(1) 要符合公式特征৔= 5;能运用平方差公式;<= /span>
(2) 有些式子表面不೦= 1;应用公式,但实质能&= #24212;用公式,要注意变= 418;.
四、作业
P88 习= 题 2 A= 288; 2 A= 289;( 4 A= 289;、 3 = 289; 4 A= 288; 2 A= 289;
五、板书设计 =

乘法公式( 1= &#= 65289;
做一做几&#= 20309;背景 1=

(图)
平方差公式: <= span style=3D'font-family:SimSun;color:black;mso-bidi-font-weight:bold'>৶= 6;究结果学生板演 <= o:p>
注意事项 <= o:p>

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