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在中学代数课本中有一例:“一个容器盛滿纯药液20升,第一次倒出若干升后,用水加滿,第二次又例出同样的升数,这时容器里只剩下纯药液5升,每次倒出的液体是多少升?”这一类问题是分数问題、百分数问题的实际应用,不仅在工农业生产中经常要碰到,而且学生在高一、高二学习等比数列、指数方程等內容时,也要碰到这一类的应用題。根据以往经验了解到,学生理解这个问題是不够深透的,说明教法上有改进的必要。首先我们对学生的知识状况摸了一下底,进行了分析研究,发现学生对“分数的三个基本问題”印象不深。而这一类问题,不仅要运用“已知一个数的几分之几求这个数的方法”,而且“溶液”、“浓度”、“溶质”三者的变化多,学生更感到难以捉摸。其次我们考虑到本题一般有下列三种列式方法:(设每次倒出x升液体)
In the middle school algebra textbook, there is an example: “A container full of 20 liters of pure liquid. After the first time a few liters are poured out, the water is used to fill up. The second time, the same litre is given, and only the pure drug remains in the container. 5 litres of liquid, how many litres of liquid is poured out each time?” This type of problem is the practical application of the fractional problem and the percentage problem, not only in the industrial and agricultural production, but also in the student’s learning in the high school and high school. In the case of series, exponential equations, etc., this type of application should also be encountered. Based on past experience, it is understood that students understand this issue is not enough to explain the need for improvement in teaching methods. First of all, we touched the students’ knowledge status and analyzed them. We found that students were not impressed by the “three basic questions of scores”. This type of problem requires not only the use of ”a few fractions of a known number to find this number,“ but also the ”solution,“ ”concentration,“ and ”solute," which are more elusive. Secondly, we consider that there are generally the following three column methods in this question: (Set up x liters of liquid every time)