数学广角——鸡兔同笼.ppt

状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,单击此处编辑母版标题样式,编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,R,四年级下册,数学广角,鸡兔同笼,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,笼子里有若干只鸡和兔。从上面数，有,8个头，从下面数，有26只脚。鸡和兔各有,几只？,探究新知,1,一只鸡有 只脚,一只兔有 只脚,分析：,8,2,4,枚举法,鸡,8,7,6,5,兔,0,1,脚,16,18,1.,当鸡有,8,只时，兔子,0,只，共,16,只脚；,2.,当鸡有,7,只时，兔子,1,只，共,18,只脚；,3.,当鸡有,6,只时，兔子,2,只，共,20,只脚；,2,20,3,22,4,4,24,3,5,26,2,6,28,1,7,30,0,8,32,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,思考：这一题用枚举法好不好做？,假设法,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,352=70,94-70=24,思考：相差的,24,只脚是怎么产生的？,假设笼子里都是鸡，共有 只脚。,笼子里实际有,94,只脚，相差 只脚。,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,假设法,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,因为笼子还有兔子，现在我们要将笼子里的部分鸡换成兔子，将,1,只鸡换成,1,只兔子，增加 了,只脚；增加,24,只脚需要换 只鸡。,2,242=12,假设法,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,所以兔子就有 只,鸡有 只。,242=12,35-12=23,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,方法总结：,首先，假设笼中全是鸡或者兔子，求出假设时的脚数，然后把假设时的脚数与实际情况相比较，找到差距和造成差距的原因，最后经过调整找到正确结果。,注意：假设法是设鸡得兔，或设兔得鸡；假设全是鸡，最后求出来的是兔子的数量。,抬腿法,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,假设笼子中的鸡和兔都训练有素，只要主人一吹口哨，鸡立马抬起一只脚，开始表演金鸡独立，兔子也会立刻抬起两只脚卖萌；,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,吹哨法,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,942=47,现在地上一共有 只脚，,这时，每只鸡,1,只脚，每只兔子,2,只脚，也就是说笼子里只要有一只兔子，脚的总数就比头的总数多,1,；,吹哨法,笼子里有若干只鸡和兔。从上面数，有,35,个头，从下面数，有,94,只脚。鸡和兔各有几只？,47-35=12,脚的总数与头的总数之差,兔子有 只,鸡有 只。,12,35-12=23,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,闯关练习,1.,有龟和鹤共,40,只，龟的腿和鹤的腿共有,112,条。龟、鹤各有几只？,（,1,）如果,都是鹤。,如果都是鹤，就有,402,80,条腿，比题目中少,112,80,32,条腿。,那么需要用龟换鹤，换上一只龟，腿的总数就多,2,条，有,322,16,只龟。,所以有,40,16,24,只鹤。,解答：,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,如果都是龟，就有,404,160,条腿，比题目中多,160,112,48,条腿。,那么需要用鹤换龟，换上一只鹤，腿的总数就少,2,条，有,482,24,只鹤。,所以有,40,24,16,只龟。,（,2,）,如果,都是龟。,假如让鹤抬起一条腿，龟抬起两条腿，还有,1122,56,条腿。,这时，只要有一只龟，则腿的总数就比头的总数多,1,。,这时腿的总数与头的总数之差,56-40,16,，就是龟的只数，所以有,40,16,24,只鹤。,（,3,）,抬腿法。,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,1.有鸡和兔共20只，有56只脚。鸡（）只，兔（）只。,2.,小方有面值2角和5角的邮票共12枚，面值总额39角。2角的邮票有（）枚，5角的邮票有（）枚。,12,8,7,5,闯关练习,假设全买篮球，,426=252,（元）,252-210=42,（元）,排球：,42(42-28)=3(,个,),篮球：,6-3=3(,个,),2.,篮球和排球各买了几个？,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,状元成才路,1.,课本练习二十四，第,1,、,2,、,3,题；,2.,完成练习册本课时的习题。,课后作业,