I am in the process of tutoring several students who will be going straight from my 6th grade advanced class to 7th grade Algebra. There are quite a few concepts and skills they will miss if I do not cover them outside of the regular class curriculum, so their parents have been gracious enough to allow me to work with them before school.
One of the concepts I need to cover is Pythagorean Theorem (which I'm really excited about because I was missing it from the 8th grade curriculum). Before I could just jump into good 'ole Pythagoras, I needed to introduce the concept of non-perfect squares, as all I am required to cover in the 6th grade curriculum is the concept of perfect squares.
As I often like to do, I wanted to start with what they knew, and build on that.