日历中的数学规律

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,*,日 历 中 的 数 学 规律,数学是思维的体操，学数学会使人越来越聪明！,1、了解日历中蕴含的数学规律,2、学会利用字母表示简单问题中的数量关系，并会验证得到的规律。,学习目标,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,2018,年,10,月的日历,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,一、创设情境：游戏,游戏规则：由同学从日历中任意框选出一个九宫格（3,3方框每格都要有数字），老师能迅速的说出这九宫格中的数字之和，你们相信吗？不信我们可以试试。,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,问题1：,观察日历，你能发现日历中的数字特点吗？,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,（1） 横行相邻的日期：,（2） 竖列相邻的日期：,二、合作研讨，探究规律,a,a+,1,a,a+,7,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,（3）下阶梯相邻的日期：,（4）上阶梯相邻的日期：,a,a,+8,a,a,+6,二、合作研讨，探究规律,问题2,:,（,1,）,观察日历，同一直线上相邻的三个数有哪几种情况,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,问题2,:,（,1,）,观察日历，同一直线上相邻的三个数有哪几种情况,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,（3）你能用含字母,a,的式子来表示横行相邻的三个数吗？你能验证规律吗？,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,（,2,）,你能找出横行相邻的三个数之间蕴含的规律吗？,（3）你能用含字母,a,的式子来表示横行相邻的三个数吗？你能验证规律吗？,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a,a,+1,a,-1,二、合作研讨，探究规律,结论：,三个,相邻,数之和,=,中间数的,3,倍,问题3,：,针对竖列、下阶梯、上阶梯的情况，如果设中间的数为,a,，你能用含字母,a,的式子来表示其它的两个数吗？他们又有什么规律？,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,竖列,a,a,-7,a+,7,下阶梯,上阶梯,a,a,+8,a,-8,a,-6,a,a,+6,结论：,三个,相邻,数之和,=,中间数的,3,倍,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,问题,4,：,（,1,）、,在“”型区域内，用含字母,a,的式子来表示这五个数，这五个数之间有什么规律？,二、合作研讨，探究规律,a,a,+7,a,+1,a,-1,a,-7,(,a,-1)+(,a,+1 )+,a,+(,a,-7)+(,a,+7)=,5,a,在,“,十,”,字形中，,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,五个数之和,=,正中间数,的,5,倍,五个数之和,=,正中间数的,5,倍,a,+6,a,+8,a,-8,a,-6,(,a,-6)+(,a,+6 )+,a,+(,a,-8)+(,a,+8)=,5,a,在,“,”,字形中,，,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,a,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,二、合作研讨，探究规律,二、合作研讨，探究规律,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,（,1,）,在日历上圈出一个33方框，请用含字母a的整式来表示这九个数,（,2,）,在,3,3,方格里的九个数，这九个数之和方框中的正中间的数有什么关系？,三、运用规律，解决问题,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,a,a-7,a+8,a-6,a-8,a+6,a+7,a-1,a+1,33,方框中，,九数之和,=,中间数的,9,倍,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,哪个同学可以进行课堂一开始的游戏大揭密呢？,三、运用规律，解决问题,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,四、当堂检测,1.,如图，用一个框竖着框住,3,个数，当你任意框出一竖列上相邻的三个数时，发现这三个数的和不可能是（）,(A)42 (B)60 (C)27 (D)81,D,日,一,二,三,四,五,六,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,四、当堂检测,2,、,如图，在排成每行七天的日历表中取下一个,3,3,的方块。若所有日期之和为,189,，则,n,的值为（ ）,A. 15 B.11 C. 21 D.24,n,216,C,四、当堂检测,3,、,有一些分别标有,6,、,12,、,18,、,24,、,的卡片，后一张卡片上的数比前一张卡片上的数大,6,，小明拿到了相邻的,3,张卡片，且卡片上的数字之和为,90.,（,1,）小明拿到了哪,3,张卡片？,（,2,）你能拿到相邻的,3,张卡片，使得这些卡片上的数之和是,86,吗？,五、谈谈你的收获,1,、本节课我们总结出规律有：,2,、,本节课的学习中，我们应用了哪些数学思想？,数学思想：（,1,）,由特殊到一般；,（,2,）分类讨论,