I got owned by one of my students today in math class which doesn’t happen terribly often to me. Here’s the situation, see if you can tell whose solution is really a better way to approach this problem.
My student, instead of approaching this problem from my algebraic method using the distance formula drew some triangles and using the Pythagorean theorem to solve the problem. Her solution was much easier to understand and easier to work out. No one even completed the problem the way I was suggesting to do it. So I got owned.
You can’t discover these kinds of interesting solutions to problems if you require rigid step-by-step solutions. I got some professional development today and some advice from my 16 year student. She said, "Triangles are your friends." I gotta say, I agree with her.