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15045144412:八年级数学上册 第七章 平行线的证明 第三节 平行线的判定(2)教案 (新版)北师大版

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平行线的判定
课 课题 型 1.运用实验验证、举反例验证、推理论证等方法来验证某些问题的结论正确与否. 教学 目标 2.经历观察、验证、归纳等过程,使学生对由这些方法所得到的结论产生怀疑,以此激 发学生的好奇心,从而认识证明的必要性,培养学生的推理意识. 3.了解检验数学结论的常用方法:实验验证、举出反例、推理论证等. 重点 难点 教学 用具 教学 二次备课 环节 第一环节:验证活动(1) 活动内容: 某学习小组发现,当 n=0,1,2,3 时,代数式 n -n+11 的值都是质数,于 是得到结论:对于所有自然数 n, n -n+11 的值都是 质数.你认为呢?与同伴 新课 导入 交流. 参考答案:列表归纳为 n n -n+11 是否为 是 质数 课 程 第二 环节:猜想并验证活动(2) 活动内容: 如图,假如用一根比地球的赤道长 1 米的铁丝将地球赤 讲 授 道围起来,那么铁丝与地球赤道之间的间隙能有多大(把地 球看成球形)?能放进一个红枣吗?能 放进一个拳头吗? 是 是 是 是 是 是 是 是 是 是 是
2 2 2

理解推理、论证的必要性 推理论证的过程

0 11

1 11

2 13

3 17

4 23

5 31

6 41

7 53

8 67

9 83

10 101

11 121 不



参考答案:设赤道周长为 c ,铁丝与地球赤道之间的间隙为 :

c ?1 c 1 ? ? ? 0.16(m) 2? 2? 2?
它们的间隙不仅能放进一个红枣,而且也能放进一个拳头. 第三环节:猜想并验证活动(3) 活动内容: 如图,四边形 ABCD 四边的中点 E、F、G、H,度量四边形 EF GH 的边和角, 你能发现什么结论?改变四边形 ABCD 的形状,还能得到类似的结论吗? 参考答案:连接 AC. ∵E、F、G、H 分别是四边形 ABCD 四边中点, ∴EF∥AC,EF=

1 1 AC;GH∥AC,GH= AC; 2 2
E B

∴EF 平行且等于 GH, ∴四边形 EFHG 为平行四边形. 第四环节:反馈练习

A

H

D G

F

C

活动内容:1.如图中两条线段 a 与 b 的长度相等吗?请你先观察,再度量一 下.

答案:a 与 b 的长度相等.

第 1 小题图

第 2 小题图

2.如图中三条线段 a、b、c,哪一条线段与线段 d 在同一直线上?请你先观察, 再用三角尺验证一下. 答案:线段 b 与线段 d 在同一直线上. 3.当 n 为正整数时,n +3n+1 的值一定是质数吗? 答案:经验证:当 n 为正整数时,n +3n+1 的值一定是质数 . 谈谈你这节课有什么收获? 小结
2 2

作业 课本第 217 页习题 6.1 第 2,3 题 布置 板书 设计 课后 反思


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