苏教版五年级数学上册《钉子板上的多边形》课件
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多边形的面积/平
方厘米 (s)
2 3 3.5 4
多边形边上的钉子
数/枚 (n)
4 6 7 8
图形中间 点的个数 用a来表 示。
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第八单元 用字母表示数
课件PPT
4 钉子板上 的多边形
复习导入
课件PPT
复习导入
课件PPT
复习导入
课件PPT
引出问题
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课件PPT
数一数，下面图形的面积？
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n=10 n=9 n=9 n=8 ●
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s=6 s=5.5 s=6.5 s=7 ●
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充实猜想
S=n÷2
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图形编号
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s n 多方边厘形米的( 面)积/平 多数边/枚形边(上的) 钉子
①
6
10
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5.5
9
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3
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5
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充实猜想
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课件PPT
7 5.5
6.5
多边形边上的
钉子数/枚 (n)
10 7 9
当a=3时， S =n÷2+2
自主探究
课件PPT
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。
概括规律
课件PPT
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)
课堂小结
课件PPT
回顾探索和发现规律的过程，你有什 么体会？
要善于从不同的多变形中找到它们的相同点。
用含有字母的式子表示规律，简明易记。
探索规律时，要认真观察、反复比较，发 现规律后要验证。
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引出问题
1厘米 厘1
米
课件PPT
数一数，下面图形的面积？
引出问题
1厘米 厘1
米
课件PPT
数一数，下面图形的面积？
激活猜想
课件PPT
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3.5
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4
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激活猜想
图形编号
① ② ③ ④
课件PPT
S=n÷2
多边形的面积 多边形边上的
/平方厘米(s) 钉子数/枚(n)
2
4
3
6
3.5
7
4
8
数学是研究千变万化中不变的规律 ——开普勒
进行验证
课件PPT
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多边形的面积/平 多边形边上的钉子
方厘米
数/枚
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充实猜想
课件PPT
图形 编号 ① ② ③
多边形内部的钉
子数/枚 (a)
3 3 3
多边形的面积/
平方厘米 (s)
●
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●
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●●
●
多边形的面积/平
方厘米 (s)
2 3 3.5 4
多边形边上的钉子
数/枚 (n)
4 6 7 8
图形中间 点的个数 用a来表 示。
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第八单元 用字母表示数
课件PPT
4 钉子板上 的多边形
复习导入
课件PPT
复习导入
课件PPT
复习导入
课件PPT
引出问题
●
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课件PPT
数一数，下面图形的面积？
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s=6 s=5.5 s=6.5 s=7 ●
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充实猜想
S=n÷2
课件PPT
图形编号
①
②
③
④
1㎝
●
①
②
③
④
充实猜想
1㎝
课件PPT
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图形编号
s n 多方边厘形米的( 面)积/平 多数边/枚形边(上的) 钉子
①
6
10
②
5.5
9
③
3
4
④
5
8
充实猜想
1㎝
课件PPT
7 5.5
6.5
多边形边上的
钉子数/枚 (n)
10 7 9
当a=3时， S =n÷2+2
自主探究
课件PPT
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。
概括规律
课件PPT
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)
课堂小结
课件PPT
回顾探索和发现规律的过程，你有什 么体会？
要善于从不同的多变形中找到它们的相同点。
用含有字母的式子表示规律，简明易记。
探索规律时，要认真观察、反复比较，发 现规律后要验证。
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引出问题
1厘米 厘1
米
课件PPT
数一数，下面图形的面积？
引出问题
1厘米 厘1
米
课件PPT
数一数，下面图形的面积？
激活猜想
课件PPT
1㎝
●
●
●
●
●
●
③
3.5
7
④
4
8
激活猜想
图形编号
① ② ③ ④
课件PPT
S=n÷2
多边形的面积 多边形边上的
/平方厘米(s) 钉子数/枚(n)
2
4
3
6
3.5
7
4
8
数学是研究千变万化中不变的规律 ——开普勒
进行验证
课件PPT
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图形编号
多边形的面积/平 多边形边上的钉子
方厘米
数/枚
①
2
4
②
3
6
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①
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充实猜想
课件PPT
图形 编号 ① ② ③
多边形内部的钉
子数/枚 (a)
3 3 3
多边形的面积/
平方厘米 (s)