Rectangular Arrays to Teach Multiplication

Date: Thu, 10 Nov 1994 12:28:42 -0700 (MST)
From: Anonymous
Subject: multiplication

I'm Glen, hi! I teach fourth grade math. Are rectangular arrays 
the best way to teach multiplication?

Thanks for your time.

Date: Thu, 10 Nov 1994 16:10:13 -0500 (EST)
From: Dr. Ken
Subject: Re: multiplication

Hello there, Glen!

Well, I'm not sure we're really your best resource on this question.  
I'm happy to tell you my opinion, but I've never been a math teacher 
nor have I graduated from college yet, so I may not be of much help 
to you.

I think that it's very important for students to see the relationship
between addition and multiplication, i.e. that mulitiplying 7 by 5 is 
the same thing as adding seven fives together.  And let them discover 
(lead them to it if they need some help) that adding seven fives together 
will give you the same result as adding five sevens together.  I mean, 
that's a pretty deep result for a fourth-grader.  I know I was excited.

I think that using rectangular arrays is a good way to visualize
mulitiplication, but I also think that kids should be well-grounded 
in symbol manipulation, i.e. writing out 7 + 7 + 7 + 7 + 7 and seeing 
that it equals 35.  Gaining familiarity with this kind of manipulation 
will help them when they start to learn Algebraic manipulation of 
variables.

Of course, these are just a couple of ideas.  Perhaps another Math 
Doctor will have other ideas.

-Ken "Dr." Math