人教版六年级数学下册《数学思考》PPT

耳朵倾听，眼睛观察，嘴巴说话，用心思考。打一个字？聪六年级下数学思考——巧数线段.小组内的4个同学，每两个握一次手，一共可以握几次？思考：怎样做到不重复，不遗漏，有顺序①②③①②①一共握了：6次1+2+3=6(次)8个同学可以握多少次呢？我们教室里的40个同学又可以握多少次呢？有没有什么规律？我们可以从2个点开始，逐步增加点数来研究。alsolackthenecessaryunderstanding.Twoisthebusinessfoundationisnotsolid,thetextlevelisnothigh.Theirworkinthearmybefore,althoughtheunderstandingofthematerial,butalsojustonlyknowfur,textlevel,writingabilityisstillinalowlevelinterface.Theknowledgeisnotcomplete,especiallyitisverylittleaboutprofessionalsomedepartmentsknowknowledge,towriteChinesebutnotfalse,sometimesrelyononlinewritingorpresentationofready-madeone-sidedmaterials,unwillingtomakeadeepthinking,putallsortsofthingstogether,thepresentationqualityisnothigh,duetotheoverallqualityoftheirownqualityisnothigh,theleadershipofdepartmentscannotunderstand,itisdifficulttostandintheperspective合作探究发现规律小组合作要求：①连一连，完成表格②说一说你们的发现alsolackthenecessaryunderstanding.Twoisthebusinessfoundationisnotsolid,thetextlevelisnothigh.Theirworkinthearmybefore,althoughtheunderstandingofthematerial,butalsojustonlyknowfur,textlevel,writingabilityisstillinalowlevelinterface.Theknowledgeisnotcomplete,especiallyitisverylittleaboutprofessionalsomedepartmentsknowknowledge,towriteChinesebutnotfalse,sometimesrelyononlinewritingorpresentationofready-madeone-sidedmaterials,unwillingtomakeadeepthinking,putallsortsofthingstogether,thepresentationqualityisnothigh,duetotheoverallqualityoftheirownqualityisnothigh,theleadershipofdepartmentscannotunderstand,itisdifficulttostandintheperspectiveABalsolackthenecessaryunderstanding.Twoisthebusinessfoundationisnotsolid,thetextlevelisnothigh.Theirworkinthearmybefore,althoughtheunderstandingofthematerial,butalsojustonlyknowfur,textlevel,writingabilityisstillinalowlevelinterface.Theknowledgeisnotcomplete,especiallyitisverylittleaboutprofessionalsomedepartmentsknowknowledge,towriteChinesebutnotfalse,sometimesrelyononlinewritingorpresentationofready-madeone-sidedmaterials,unwillingtomakeadeepthinking,putallsortsofthingstogether,thepresentationqualityisnothigh,duetotheoverallqualityoftheirownqualityisnothigh,theleadershipofdepartmentscannotunderstand,itisdifficulttostandintheperspectiveBCalsolackthenecessaryunderstanding.Twoisthebusinessfoundationisnotsolid,thetextlevelisnothigh.Theirworkinthearmybefore,althoughtheunderstandingofthematerial,butalsojustonlyknowfur,textlevel,writingabilityisstillinalowlevelinterface.Theknowledgeisnotcomplete,especiallyitisverylittleaboutprofessionalsomedepartmentsknowknowledge,towriteChinesebutnotfalse,sometimesrelyononlinewritingorpresentationofready-madeone-sidedmaterials,unwillingtomakeadeepthinking,putallsortsofthingstogether,thepresentationqualityisnothigh,duetotheoverallqualityoftheirownqualityisnothigh,theleadershipofdepartmentscannotunderstand,itisdifficulttostandintheperspectiveABCD仔细观察这张表格，你能得到什么信息？3个点共连：1+2=3（条）4个点共连：1+2+3=6（条）5个点共连：1+2+3+4=10（条）根据规律，8个点能连几条线段？问题1＋2＋3＋4＋5＋6＋7能用简单方法计算吗？=28（条）=8×3＋4=(1＋7)＋(2＋6)＋(3＋5)＋4根据规律，你知道15个点能连多少条线段吗？问题1＋2＋3＋4＋5＋6+……+14=105（条）——15个点=15×7按照简单的方法计算，你发现了什么，试着归纳一下。n个点共连成线段：1+2+3+4+5+6+…+（n-1）再观察2354点数，增加条数和总条数之间有什么联系吗？你还有什么新发现吗？可以发现：3个点共连：3×2÷2=3（条）4个点共连：4×3÷2=6（条）5个点共连：5×4÷2=10（条）n个点共连成线段：n（n-1）÷2n个点共连成线段：1+2+3+4+5+6+…+（n-1）n（n-1）÷2今天我们一共有40个同学，每2位好朋友握手1次，大家一共要握手多少次？1+2+3+...…+39=（1＋39）×19＋20=780（次）1+2+3+...…+39=40×39÷2=780（次）答：40个同学一共要握手780次同学们，在我们生活中有许多看似复杂的问题，我们都可以尝试从简单问题去思考，逐步找到其中的规律，从而来解决复杂的问题。1.有几条线段？2.有几个角？321219876453458761+2+3+4+5+6+7+8=(1+8)×4×=36（条）9×8÷2=36(条)1+2+3+4+5+6+7=（1＋7）×3+4=28（个）×8×7÷2=28(个)三、巩固深化1.观察下图，想一想。(1)第7幅图有多少个棋子？第15幅图呢？每幅图各有多少个棋子？14916在数的过程中，你发现了什么？问题149161×12×23×34×4每行的棋子数×行数＝棋子总数问题1.第7幅图有多少个棋子？第15幅图呢？7×7＝49（个）15×15＝225（个）2.第n幅图每边有多少个棋子？一共有多少个棋子？每行有n个，有n行棋子总数=n2今天你学到了什么？从简单开始，有序思考用化繁为简，找到规律复杂的问题要善于退，足够地退，退到最原始而不失去重要性的地方，是学好数学的一个诀窍。不足之处，恳请大家给予批评指正多边形边数3456内角和180°360°540°720°（1）多边形内角和与它的边数有什么关系？（2）一个九边形的内角和是多少度？多边形内角和＝（边数-2）×180°（9-2）×180°＝1260°ABCD找规律（1）3，9，11，17，20，＿，＿，36，41，…+2+3+4+5（2）1，3，2，6，4，＿，＿，12，＿，…+3+3+3+3×2×2×2×226309816+6+6+6+6