While Kaylee's conjecture may seem obvious to adults and older students, it helps the students make connections between a "square number," such as 5 times 5 equals 25, and a geometric model of a square with 5 rows of 5 square units per row. It also helps the students be more precise and careful as they make observations.
You may notice that this is setting the stage for a far less obvious conjecture that is encountered in middle school, namely, that the difference between two consecutive square numbers, n2 and (n + 1)2 is 2n + 1. For example, the difference between 192 and 202 is 2 x 19 + 1. By definition, 2n + 1 is an odd number. As you look at the sequence of consecutive squares and compute the differences between each consecutive pair, you always get odd numbers: 1, 3, 5, 7, . . . 39, 41, etc.