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分数的产生和意义分数的产生和意义分数的产生和意义分数的产生和意义马郎小学 陈伟 像刚才在进行测量，分物或计算时，像刚才在进行测量，分物或计算时，往往不能正好得到整数的结果，这时常往往不能正好得到整数的结果，这时常用分数表示。用分数表示。分数走过的历史分数走过的历史 我国的数学古书九章算术是世界上系我国的数学古书九章算术是世界上系统地叙述分数的最早著作，它所总结的分数运统地叙述分数的最早著作，它所总结的分数运算方法和现代所用的方法是基本一致的。像算方法和现代所用的方法是基本一致的。像 这这样系统地叙述，印度迟至公元样系统地叙述，印度迟至公元7 世纪才出现，世纪才出现，而欧洲则在而欧洲则在 15世纪以后，才逐渐形成现代的分世纪以后，才逐渐形成现代的分数的算法。足见我国古人的伟大数学智慧。数的算法。足见我国古人的伟大数学智慧。一个物体、一些物体等都可以看作一个整体，把这个整体平均一个物体、一些物体等都可以看作一个整体，把这个整体平均分成分成若干份若干份，这样的，这样的一份或几份一份或几份都可以用分数来表示。都可以用分数来表示。一个物体:如一个苹果、一张纸片、一块布 一个计量单位：如1米、1千克、1平方米 由许多物体组成的一个整体：如一堆沙、全班同学、12面旗帜、6个苹果单位“1”111122334568、读出下面的分数、读出下面的分数,并说出每一个分数的分数单位。并说出每一个分数的分数单位。分数单位分数单位161711 51181100162711187100415图中的涂色部分能不能用下面的分数表示？3459352413181416231213134猜猜一共有几枝？1616猜猜一共有几枝？25猜猜一共有几枝？13猜猜一共有几枝？ba拓展练习：拓展练习：1.把单位把单位“1”平均分成平均分成a份，表示这样的份，表示这样的 b份的分数是（份的分数是（），分数单位是），分数单位是（）。）。2.分数单位是分数单位是 的分数你能写几个？的分数你能写几个？171a17273747576777练一练一、填空1、把（、把（）平均分成（）平均分成（），表示这样的（），表示这样的（）或（）或（）的数，叫做分数。）的数，叫做分数。2、是把单位是把单位“1”平均分成（平均分成（）份，表示这样（）份，表示这样（）份的数。）份的数。3.把把5米长的绳子平均分成米长的绳子平均分成2份份,这里单位这里单位“1”是是(),每份是每份是5米的米的()4、的分数单位是（的分数单位是（），有（），有（）个这样的分数单位，再添上（）个这样的分数单位，再添上（）个这样的分数单位就是自然数）个这样的分数单位就是自然数1二、判断二、判断1、把单位、把单位“1”分成几份分成几份,表示这样一份或几份的数叫做分数表示这样一份或几份的数叫做分数()2、把单位把单位“1”平均分成若干份平均分成若干份,表示其中一份或几份的数表示其中一份或几份的数,叫做分数单位叫做分数单位()3、1 和和 单位单位“1”相等相等()4、把单位、把单位“1”平均分成平均分成8份，取其中的份，取其中的5份，就是份，就是 八分之五八分之五 （）三、思考：下图中涂色部分占全图的几分之几？（）（）通过今天的学习，我们知道了在很早以通过今天的学习，我们知道了在很早以前我们人类为了解决实际生产和生活中不能用前我们人类为了解决实际生产和生活中不能用整数表示结果的问题，就已经开始用分数来表整数表示结果的问题，就已经开始用分数来表示了，经过几千年的发展，我们对于分数的应示了，经过几千年的发展，我们对于分数的应用也变得更熟练更广泛。希望通过学习，我们用也变得更熟练更广泛。希望通过学习，我们每一位同学也能更多的了解分数，更好的学习每一位同学也能更多的了解分数，更好的学习分数知识。分数知识。1.Chinese except friendships to be more lasting.2.Different foundations for friendships.3.Westerns expect friends to be independent.4.Chinese usually expect more from their friends.Chinese except friendships to be more lasting.For Chinese a true friendship endures throughout life changes.Chinese are friends even if they havent spoken for 20 years.If you shared something at one time,then all your life you are friends.This is the best of guanxi(关系关系),the Wide Web that connects Chinese through time and space.So,we can say Chinese invented the Internet long before Bill Gates was born.In North America,even the relationship in which people feel close and tell each other personal problems may not survive life changes such as moving to another city,graduation from a university or marriage.If the people do not see each other regularly,the relationship is likely to die.Different foundations for friendships.Chinese friends share“things in common”:a task,a class,the hometown.Friendships are formed by people who work or go to school together.You may or may not like the person,but if he or she can do something for you because of his position or job,you can be friends.But in North America,business and friendship are kept separate.The friendships are usually tied to specific activities.A person may have work friends and leisure(休闲时休闲时)activity friends.Also friends tend to have similar financial circumstances,because friendship in the West is based on equality.Westerns expect friends to be independent.Why?Its because their friendship is mostly a matter of providing emotional support and spending time together,so they do not feel comfortable in a relationship in which one person is giving more and the other is dependent on what is giving.A westerner will respond to a friends trouble by asking“What do you want to do?”The idea is to help the friend to think out the problem and discover the solution he or she really wants and then to support the solution.Chinese friends give each other more concrete help.A Chinese will use personal connections to help a friend get something hard to obtain.They give each other money and might help each other out financially over a long time.Chinese usually expect more from their friends.In the West,you can certainly ask a friend to do something with you,but you recognize that your friend may say no,if he or she gives you as reason.You would not expect a friend to drop everything to respond to a non-urgent need such as shopping.Nor would you expect a friend to recognize and respond to your wishes without stating them.A friend in China is someone who offers help without waiting to be asked.There are few limits to what you can expect from a friend.You can feel free to tell your friend what he or she can or should do or help or please you.Good friends are like stars.You dont always see them,but you know they are always there.
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