From: Marielouise (for Teacher2Teacher Service)
Date: Oct 14, 1998 at 21:48:05
Subject: Re: Multiplying negative integers

I wrote the following answer recently for the same question. Perhaps it will
give you some ideas.

"If you asked me how I would teach this, I am certain that my answer is
different from the teacher next door or in the school down the way. Each of
us has developed our own ways that we believe to be consistent and most of
the time convincing.

I like to start with understanding what 3 x 4 means. I tell students that 3 x
4 = 4 + 4 + 4.  Multiplication is repetitive addition.

Therefore, 3 x 4 = 12.

Similarly 3 x (-4) = (-4) + (-4) + (-4) or (-12).

The point is to understand that (-3) x 4 is subtracting 4 three times.

(-3) x 4 = -(4) - (4) - (4) = -12.

Logically (-3) x (-4) is substracting (-4) three times.

(-3) x (-4) = - (-4) - (-4) - (-4) = 4 + 4 + 4 = 12.

Try this and see if you can convince your students.

 -Marielouise, for the Teacher2Teacher service