Physics: Hello Mr Galileo Galilei. Your method used in Dialogue on Two New Sciences laid the groundwork for the scientific revolution. Your statement of inertia predates Newton, and is for us a step towards rigorous description of motion. Hot wheels on ramps are even like your spheres of old.
Math: where does the square root come from? From actual squares! Have you seen the square root of two? All that is needed is to construct a square with an area of two.
Related Awesome Quote
If you can both listen to children and accept their answers not as things to just be judged right or wrong but as pieces of information which may reveal what the child is thinking you will have taken a giant step towards becoming a master teacher rather than merely a disseminator of information.
JA Easley, Jr. & RE Zwoyer