图形中间点的个数用a来表示
当a=1时，
S =n÷2
合作交流
要求：
（1）每4人一小组，每人画一个内部有2枚钉子的多边形 （2）数一数，算一算多边形的面积和它边上的钉子数
（3）每人把获得的数据在小组内交流，并记录在表格中
（4）观察表格中的数据，小组交流：你有什么发现？
充实猜想
图形编号 ① 多边形的面积/平 多边形边上的 钉子数/枚（n） 方厘米（S） 6 10 5.5 9 4 3 5 8
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n=10 s =6
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n =9 s=5.5
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n =9 s=6.5
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n =8 s= 7
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比较发现
② ③ ④
当a=2时，
S =n÷2+1
1㎝
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1㎝
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①
②
③
图形 编号
多边形内部的钉 多边形的面积/ 子数/枚 (a) 平方厘米 (s)
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图形编号 ①
多边形的面积/平方厘米
多边形边上的钉子数/枚
2
4 6
②
③ ④
3 3.5
4
7
8
进行验证
1㎝
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1㎝
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、 ● 、
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多边形边上的 钉子数/枚 (n) 10 7 9
①
② ③
3 3 3
7 5.5
6.5
当a=3时，
S =n÷2+2
如果多边形内有4枚、5枚…钉子，它 的面积与它边上的钉子数的关系会怎样变 化？如果多边形的内部没有钉子呢？ 请先在小组内说说自己的想法，再通 过围一围、算一算进行验证。
当a=1时，S=n÷2
当a=2时，S=n÷2+1 当a=3时，S=n÷2+2 …… 你能用一个式子，表示出s与n之 间的关系吗？ 当a=x时，S=n÷2+(x-1)
1㎝ 1㎝
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图形编号 ① ② ③ ④
多边形的面积/平 多边形边上的 钉子数/枚（n） 方厘米（S） 2 4 3 6 7 3.5 4 8