Investigating a mathematical principle in elementary mathematics lesson is important in that it is one of the main purposes of school mathematics and that many topics in mathematics lessons are related to mathematical principles. However, there have been lack of studies that provide teachers with a detailed guideline of how to design and implement a mathematics lesson in a way for students to explore a mathematical principle. Given this, this study selected two specific teachers who implemented lessons of investigating the mathematical principle involved in comparing numbers with similar topics, and analyzed their lessons in terms of 18 analytic elements related to the design and implementation of a mathematics lesson. This paper closes with specific suggestions on how to design and implement a lesson for elementary students to investigate a mathematical principle.