苏教版五年级上册数学钉子板上的多边形课件(共16张PPT)

(共16张PPT)
第八单元 用字母表示数
钉子板上
的多边形
学习目标
1.探索钉子板上的多边形的面积与边上的钉子数之间的关系
2.用字母表示出钉子板上的多边形的面积与边上的钉子数之间的关系的规律
复习导入
复习导入
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引出问题
数一数，下面图形的面积？
厘
米
1
1厘米
数一数，下面图形的面积？
引出问题
厘
米
1
1厘米




数一数，下面图形的面积？
引出问题
想一想：钉子板上多边形的面积可能跟什么有关？
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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
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4
8
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观察上
表，你有
什么发现？
激活猜想
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、、
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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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②
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④
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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
当多边形内只有1枚钉子时，用n表示多边形上的钉子数，用S表示多边形的面积，那么面积S=n÷2
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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）÷2
充实猜想
当多边形内只有2枚钉子时，用n表示多边形上的钉子数，用S表示多边形的面积，那么面积S=（n＋2）÷2
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①
②
③
充实猜想
想一想，当a=3时， s与n之间有着怎样的关系？
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)
7
10
5.5
6.5
7
9
S =（n＋4）÷2
当a=3时，
充实猜想
当多边形内只有3枚钉子时，用n表示多边形上的钉子数，用S表示多边形的面积，那么面积S=（n＋4）÷2
当多边形内只有4枚钉子时，用n表示多边形上的钉子数，用S表示多边形的面积，那么面积S=（n＋6）÷2
当多边形内只有5枚钉子时，用n表示多边形上的钉子数，用S表示多边形的面积，那么面积S=（n＋8）÷2
当多边形内没有钉子时，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？
自主探究
当a=1时，S=n÷2
当a=2时，S=（n＋2） ÷2
当a=3时，S=（n＋4）÷2
概括规律
当a=4时，S=（n＋6）÷2
当a=5时，S=（n＋8）÷2
发现n加的数＝（多边形内钉子数－1）X 2
当多边形内没有钉子时，S=（n－2）÷2
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。
回顾探索和发现规律的过程，你有什么体会？
课堂小结