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正、反比例的意义
教学目标
1.使学生理解正、反比例的意义,能够初步判断两种相关联的量是否成比例,成什么比例.
2.通过观察、比较、归纳,提高学生综合概括推理的能力.
3.渗透辩证唯物主义的观点,进行“运用变化观点”的启蒙教育.
教学重点
理解正反比例的意义,掌握正反比例的变化的规律.
教学难点
理解正反比例的意义,掌握正反比例的变化的规律.
教学过程
一、导入新课
(一)昨天老师买了一些苹果,吃了一部分,你能想到什么?
(二)教师提问
1.你为什么马上能想到还剩多少呢?
2.是不是因为吃了的和剩下的是两种相关联的量?
教师板书:两种相关联的量
(三)教师谈话
在实际生活中两种相关的量是很多的,例如总价和单价是两种相关联的量,总价和
数量也是两种相关联的量.你还能举出一些例子吗?
二、新授教学
(一)成正比例的量
例1.一列火车行驶的时间和所行的路程如下表:
时间(时) |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
…… |
路程(千米) |
90 |
180 |
270 |
360 |
450 |
540 |
630 |
720 |
…… |
1.写出路程和时间的比并计算比值.
(1)
(2) 2表示什么?180呢?比值呢?
(3) 这个比值表示什么意义?
(4) 360比5可以吗?为什么?
……
2.思考
(1)180千米对应的时间是多少?4小时对应的路程又是多少?
(2)在这一组题中上边的一列数表示什么?下边一列数表示什么?所求出的比值呢?
教师板书:时间、路程、速度
(3)速度是怎样得到的?
教师板书:
(4)路程比时间得到了速度,速度也就是比值,比值相当于除法中的什么?
(5)在这组题中谁与谁是两种相关联的量?它们是如何相关联的?举例说明变化规律.
3.小结:有什么规律?
教师板书:商不变
(二)成反比例的量
1.华丰机械厂加工一批机器零件,每小时加工的数量和所需的加工时间如下表.
工效(个) |
10 |
20 |
30 |
40 |
50 |
60 |
…… |
时间(时) |
60 |
30 |
20 |
15 |
12 |
10 |
…… |
2.教师提问
(1)计算工效和时间的乘积.
(2)这一组题中涉及了几种量?谁与谁是相关联的量?
(3)请你举例说明谁与谁是相对应的两个数?
(4)在这一组题中两种相关联的量是如何变化的?(举例说明)
3.小结:有什么规律?(板书:积不变)
(三)不成比例的量
1.出示表格
运走的吨数 |
10 |
20 |
30 |
40 |
剩下的吨数 |
90 |
80 |
70 |
60 |
总吨数(和不变) |
100 |
100 |
100 |
100 |
2.教师提问
(1)总吨数是怎样得到的?
(2)谁与谁是两种相关联的量?
(3)它们又是怎样变化的?变化的规律是什么?
运走的吨数少,剩下的吨数多;运走的吨数多,剩下的吨数少;总和不变
(四)结合三组题观察、讨论、总结变化规律.
讨论题:
1.这三组题每组题中谁与谁是两种相关联的量?
2.在变化过程中,它们的异同点是什么?
共同点:都有两种相关联的量,一种量变化,另一量也随着变化
不同点:第一组商不变,第二组积不变,第三组和不变.
总结:
3.分别概括正、反比例的意义
4.强调第三组题中两种相关联的量叫做不成比例
5.教师提问
(1)两种量成正比例必须具备什么条件?
(2)两种量成反比例必须具备什么条件?
(五)字母关系式
三、巩固练习
判断下面各题是否成比例?成什么比例?
1.一种圆珠笔
总价(元) |
1.2 |
2.4 |
3.6 |
4.8 |
6 |
7.2 |
支数 |
1 |
2 |
3 |
4 |
5 |
6 |
单价(元) |
1 |
2 |
4 |
5 |
10 |
支数 |
100 |
50 |
25 |
20 |
10 |
(1)表中有哪两种相关联的量?
(2)说出几组这两种量中相对应的两个数的比
(3)每组等式说明了什么?
(4)两种相关的量是否成比例?成什么比例?
2.当速度一定,时间路程成什么比例?
当时间一定,路程和速度成什么比例?
当路程一定,速度和时间成什么比例?
3.长方形的面一定,长和宽
4.修一条路,已修的米数和剩下的米数.
四、课堂总结
今天这节课我们初步了解了正反比例的意义,并能运用正反比例的意义判断一些简单的问题.通过正反比例意义的对比,使我们进一步认识到,要判断两种相关联的量是成正比例关系还是反比例的关系,要抓住两种相关联的量的变化规律,这是本质.
五、课后作业
(一)判断下面每题中的两种量是不是成正比例,并说明理由.
1.苹果的单价一定,购买苹果的数量和总价.
2.轮船行驶的速度一定,行驶的路程和时间.
3.每小时织布米数一定,织布总米数和时间.
4.长方形的宽一定,它的面积和长.
(二)判断下面每题中的两种量是不是成反比例,并说明理由.
1.煤的总量一定,每天的烧煤量和能够烧的天数.
2.种子的总量一定,每公顷的播种量和播种的公顷数.
3.李叔叔从家到工厂,骑自行车的速度和所需时间.
4.华容做12道数学题,做完的题和没有做的题.
六、板书设计
评论人 | 评论内容 | 评论时间 | 打分 |
【Mark】 | m1NgIC http://www.y7YwKx7Pm6OnyJvolbcwrWdoEnRF29pb.com | 2016/5/12 14:16:39 | 3分 |
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