钉子板上的多边形课件公开课.ppt

苏 教 版 五 年 级 数 学（上） ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1㎝ 1㎝ 1cm2 9cm2 10cm2 引出问题： ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1㎝ 1㎝ ① ② ③ ④ 图形编号 多边形的面积/平方厘米 多边形边上的钉子数/枚 ① ② ③ ④ ● ● ● 2 ● 4 ● ● ● ● ● 3 3.5 6 7 4 8 、●、 ● ● ● ● ● ● ● ● ● ● ● ● ● ● 激活猜想： 图形编号 多边形的面积/平方厘米 多边形边上的钉子数/枚 ① 2 4 ② 3 6 ③ 3.5 7 ④ 4 8 (s) (n) S=n÷2 数学是研究千变万化中不变的规律 ——开普勒 激活猜想： ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1㎝ 1㎝ 、、 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● n=10 s=6 n=9 s=5.5 n=9 s=6.5 n=8 s=7 进行验证： 图形编号 多边形的面积/平方厘米 多边形边上的钉子数/枚 ① 2 4 ② 3 6 ③ 3.5 7 ④ 4 8 (s) (n) S=n÷2 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1㎝ 1㎝ ① ② ③ ④ ● ● ● ● ● ● ● ● ● 、●、 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 图形中间点的个数 用a来表示 充实猜想： ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 1㎝ 1㎝ ① ② ③ ④ 图形编号 多边形的面积/平方厘米 多边形边上的钉子数/枚 ① ② ③ ④ (s) (n) 6 10 5.5 9 3 4 5 8 充实猜想： 图形 编号 多边形内部的钉子数/枚 多边形的面积/平方厘米 多边形边上的钉子数/枚 ① 3 ② 3 ③ 3 (s) (n) (a) 自主探究： 请先在小