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,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,日历中的数学知识,花城中学,王海涛,这是,2011,年某月的日历，你能发现日历中的数字有什么规律吗,?,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,日历中,相邻三数,之间有什么关系？,探究一,:,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,横行,三个相邻数的大小关系,a,a+1,后者比前者多,1,能用字母表示吗,?,探究一,:,a-1,a,a-7,a+7,(2),竖列,三个相邻数大小关系,下比上多,7,能用字母表示吗,?,探究一,:,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,(3),左上右下对角线,上三个相邻数大小关系,右下比左上多,8,a,a+8,a-8,能用字母表示吗,?,探究一,:,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a-6,a,a+6,(4),左下右上对角线,上三个相邻数大小关系,左下比右上多,6,能用字母表示吗,?,探究一,:,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,同一直线上相邻三,个数，,首尾两数之和,与,中间数,的关系？,探究一,:,同一直线上相邻三,个数，,首尾两数之和,=2,中间数,(1),水平三邻数,:,a-1,a,a+1,(2),竖直三邻数,:,a,a-7,a+7,(3),斜下三邻数,:,a,a+8,a-8,(4),斜上三邻数,a-6,a,a+6,(a-1)+(a+1)=_,2a,(a-7)+(a+7),=_,2a,(a-8)+(a+8)=_,2a,(a-6)+(a+6)=_,2a,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,探究一,:,同一直线上相邻三,个数，,首尾两数之和,=2,中间数,归纳1：,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,探究二,:,日历中,相邻,四个数,有何关系？,用字母怎样表示？,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a,a+1,a+8,a+7,对角的,两数,之和相等,a+(a+8)=,(a+1)+(a+7)=,2a+8,2a+8,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a,a+1,a+6,a+7,两端的,两数之和,等于,中间,两数之和,a+(a+7)=,(a+1)+(a+6)=,2a+7,2a+7,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a,a-6,a+6,a+12,两端的,两数之和,等于,中间,两数之和,a+(a+6)=,(a-6)+(a+12)=,2a+6,2a+6,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,探究二,:,1,、,对角的,两数之和相等,2,、两端的,两数之和,等于,中间,两数之和,归纳2：,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,探究三,:,日历中,3,3,方框内,九数之和,与方框中,正中间的数,有何等量关系？,33,方框中：,九数之和,=,9,中间数,这个关系在,其它方框,中成立吗,?,(3),这个关系对,任何一个月,的日历都成立吗,?,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,探究三,:,33,方框中：,九数之和,=,9,中间数,2011,年某月 日历,(4),这个规律也能用,字母说明,吗,?,a,a-7,a+8,a-6,a-8,a+6,a+7,a-1,a+1,(a-8)+,(a-7),+(a-6)+,(a-1),+,a,+,(a+1),(a+6)+,(a+7),+(a+8),=_,9a,33,方框中，,九数之和,等于,中间数的九倍。,3,4,5,10,11,12,17,18,19,归纳3：,(5),你还能发现正方形方框中九数之间的 其它关系吗,?,a,a-7,a+8,a-6,a-8,a+6,a+7,a-1,a+1,11,12,10,18,19,17,3,4,5,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,在下图所圈的区域中，,所有数之和,与,正中心的数,何关系,?,能用,字母,表示并验证这个关系吗,?,探究四,2011,年 某 月日历,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a,a+7,a+1,a-1,a-7,(a-1),+,(a+1),+,a,+,(a-7),+,(a+7),=,5a,在,+,字形中，,五个数之和,=,5,正中心的数,星期日,星期一,星期二,星期三,星期四,星期五,星期六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,在,H,形区域中，,七个数之和,=,7,正中心的数,a,a-1,a+6,a+8,a-6,a-8,a+1,(a-8)+(a-1),+,(a+6),+,a,+,(a-6),+,(a+1)+(a+8),=,7a,总结：,1、同一直线上相邻三个数，,首尾两数之和=2中间数,2、对角的两数之和相等,3、两端的两数之和等于中间两数之和,总结：,4、33方框中，九数之和等于中间数的九倍。,5、在+字形中，五个数之和=5正中心的数,6、在 H 形区域中，七个数之和=7正中心的数,在下列表格中涂颜色的数字是否符合前面发现的结论,?,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,变形拓展,在下列表格中涂颜色的数字是否符合前面发现的结论,?,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,变形拓展,1,、下,图,的数阵是由一些奇数排成的,.,（,1,）观察图,1,框中的四个数之间的关系，请你用字母表示这样的框中四个数之间的关系,.,（,2,）若框住的四个数之,和为,200,，求这四个数,.,（,3,）是否存在这样的四,个数，它们的和为,250,？,为什么？,习题,1,谢谢大家，,再见！,
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