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Topic: Surprisingly easy way to teach negative integer multiplication - is
it sound?

Replies: 14   Last Post: Sep 11, 2011 7:45 AM

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 Bill Dubuque Posts: 1,739 Registered: 12/6/04
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.