无理数估计大小的问题既是一类经典问题,又经常出现在高考试题中.对估计精度要求不高的问题,往往利用函数的性质就可以解决;而对估计精度要求较高的问题,学生往往不知道如何入手.针对这种现象,尝试从两个典型问题出发,探讨让学生在独立思考的基础上,自主探究,在总结解题规律的过程中,提升学生的理性思维. The problem of estimating the size of irrational numbers is not only a classic problem, but also often occurs in the high-test questions. The problem of low estimation accuracy is often solved by the nature of the function; students often do not have the problem of high accuracy. Knowing how to get started, aiming at this kind of phenomenon, we try to start from two typical problems and discuss how to allow students to independently explore on the basis of independent thinking. In the process of summarizing problem-solving rules, we can improve students’ rational thinking.