
Re: Surprisingly easy way to teach negative integer multiplication  is it sound?
Posted:
Sep 8, 2011 1:18 AM


Bhushit Joshipura <joshipura@gmail.com> wrote: > > I am not a mathematician. This just worked out with my seven year old. > He barely knows negative numbers. > > His text book was trying to teach multiplication of positive integers > using a number line(!) "For m*n, take m steps and jump such m steps n > times". Very clear, in rear view mirror. The kid was having hard time. > > I tried two number lines  Cartesian way. "Take m steps, take a left > turn and walk n steps. Draw a rectangle and count squares". It was > bound to be easier. > > The kid asked a question: "What if I take a *right* turn instead?" > > Then I realized that along the whole number line, if you take left, > you end up multiplying with a positive number and if you take right, > you end up multiplying a negative number. It stands correct while > multiplying negative numbers with negative numbers also. Squares above > the number line are positive, below are negative. > > To my surprise, the kid also got negative number (integers only for > now) multiplication slam dunk. > > Now two questions: > 1. This trick works but is it sound? > 2. Can we tame division also using two number lines?
There are *many* interesting prior discussions here on the law of signs. E.g. see these threads http://groups.google.com/groups/search?q=group%3A*math*++author%3Adubuque+law+signs
Bill Dubuque

