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钉子板上的多边形
苏教版五年级数学（上）
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1㎝
1㎝
1cm²
9cm²
10cm²
想一想：钉子板上多边形的面积可能跟什么有关？
引出问题：
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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
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2
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4
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3
3.5
6
7
4
8
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观察上表，你有什么发现？
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：
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1㎝
1㎝
、、
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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
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1㎝
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图形中间点的个数
用a来表示
当a=1时
充实猜想：
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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
想一想，当a=2时，s与n之间有着怎样的关系？
当a=2时，s=n÷2+1
充实猜想：
小组合作，先在钉子板上围出内部
有3个钉子的不同多边形，再完成下表：
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
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