“点子图”在数学教学中的妙用
数学教学是数学活动的教学,是师生之间,学生之间交往互动与共同发展的过程。
教师是学生数学活动的组织者,引导者与合作者;可以根据学生的具体情况,有创造地设计教学过程,恰当地运用“点子图”,能通过形象生动地数形结合,让学生直观地理解算理,让学生在解决问题的过程中,通过多样化的数学学习活动,不断感悟﹑不断总结。从而提高学生理解问题的能力。
一:“点子图”在计算中的妙用
人教版三年级下册第63页例1:“到书店买书,一套12本,每本24元,一共要付多少钱?”教师引导学生理解问题的意义,知道要求出12个24是多少,并列出算式24×12后,教师可以出示12个24的点子图,让学生通过圈一圈,画一画来理解两位数乘两位数的计算过程。
算法一: 24×10=240 24×2=48 240+48=288
让学生在点子图中圈出前10行就是10个24,后2行就是2个24,合起来就是12个24.
算法二: 20×12=240 4×12=48 240+48=288
同样让学生在点子图中圈出左边20列就是12个20,剩下的就是12个4,合起来就是12个24.
算法三:20×10=200 4×12=48 20×2=40 200+48+40=288
算法四:20×10=200 4×12=48 24×2=48 200+48+48-2×2=288 这两种算法,可以让学生了解一下,只要让学生圈出20个10是哪些,学生自然不难明白后面再怎么算。
用点子图作为学生研究算理的素材,把数字用圆点来表示,一个数字代表一个小圆点,非常直观;凸显了乘法的意义,几个相同的数相加用乘法计算的方法在图上一目了然。所有的点子数相加就是计算的结果,契合了先分后合的计算方法。可以说达到了完美的数形结合。二:“点子图”在简算中的妙用
在第二学段的数学学习中,课标指出,应增进学生对运算意义的理解,应重视口算,加强估算,鼓励算法多样化,避免繁杂的运算。而让学生熟练运用简算知识则会让学生的计算能力显著提高。在小学阶段的简算运算定律中,乘法分配律是变化最多,也最不容易理解掌握的,教师可以通过点子图的形象演示,让学生深刻理解乘法分配律的算理。
人教版四年级下册第36页例3:“一共有25个小组,每组里4人负责挖坑、种树,2人负责抬水、浇树。一共有多少名同学参加了
这次植树活动?”
先让学生分开看,前4行是25个4,即4×25;后2行是25个2,即2×25;一共4×25+2×25名同学。如果合起来竖着看看,一大列就是4+2个25,一共(4+2)×25名同学。25个4加25个2就是25个6,乘法分配律的算理就非常明晰了。对算理深刻理解,才能举一反三,灵活运用,而且不容易出错。
三:“点子图”在解决问题中的妙用
学生在小学阶段要学会综合运用所学的知识和方法解决简单的实际问题,获得运用数学解决问题的思考方法。因此,在教学时,教师要引导学生从不同角度探索多种解决问题的方法。
人教版三年级下册第99页例1:“每个方阵有8行,每行有10人。3个方阵一共有多少人?”
对于这道例题,我巧妙地利用点子图来代替三个方阵,学生们或圈或画,清晰明了,取得了非常巧妙的教学效果。其一:妙在方便学生动手。教师课前发给每名学生一张点子图,在出示题目读完题,划出条件和问题后,就让学生在点子图上圈出先算什么,再算什么。简洁清晰的点子图,非常便于学生圈画出自己的想法。其二:妙在简洁
清晰一目了然。点子图分成三部分,分别代表三个方阵,每个方阵8行,每行10人。
共有三种解决方法:
第一种:先求出一个方阵有多少人,再求3个方阵有多少人?
第二种:从整体上横着看,把3个方阵的第一横行看成一大行,求出一大行有30人,一共有这样的8大行。
第三种:把3个方阵摞起来竖着看,可以先求3个方阵一大列共有多少人,一共有这样的10列。
每个方阵有8行×3个方阵
就像教育家张英宙所说:“解决数学应用问题的本质是数学建模.”只要学生的数学思维模式建立起来了,那学习数学知识就会循序渐进,水到渠成。
槐荫区大杨小学
李德霞
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点子图和方格图集团文件发布号:(9816-UATWW-MWUB-WUNN-INNUL-
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姓名:班级:(友情提醒,请节约使用。) 一 二三四······················································································································································································································································································································································································································································································································································································································································································································································································································································································································································
姓名:班级:(友情提醒,请节约使用。) ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ··························· ···························
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