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求代数式值是初中代数的重要内容,也是数学竞赛中的常见题型.这类题涉及的知识面很广,有些题难度较大,不易直接求解,需要打破常规,树立“求异”思想,广开思维渠道,从不同的角度去分析探索,而构造法就是一种重要而灵活的思维方式,是最富活力的数学转化方法之一,如果恰当地运用,可以另辟蹊径,难题巧解,同时有利于发展同学们的思维品质和探索创新能力.下面通过具体的实例来说明构造法在求代数式值中的应用.
Finding algebraic type values is an important part of junior high school algebra, and it is also a common question in mathematics competitions. Such questions involve a wide range of knowledge, some of which are difficult and difficult to solve directly, and need to break the routine and establish the “seeking differences” mentality. Widely open the way of thinking, from different perspectives to analyze and explore, and the construction method is an important and flexible way of thinking. It is one of the most dynamic methods of mathematics transformation. If it is used properly, it can be used to find new paths and solve difficult problems. It is conducive to the development of the students’ thinking quality and the ability to explore and innovate. The following is a concrete example to illustrate the application of the construction method in algebraic expressions.