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Magic Squares for 3rd and 4th Grade

Date: Sat, 5 Nov 1994 14:23:21 -0800
From: Peter Darby
Subject: Magic Squares

HELP - I am an administrator with a grade 3 teacher for a wife - her
children love to do Magic Squares (rows, columns and diagonals add up to
the same number) - is there an easy way to create these squares - suitable
for grade 3 or 4?  Is there a source of examples?

Peter Darby, Deputy Superintendent
County of Red Deer #23, 4758 32 Street, Red Deer, AB T4N 0M8

From: Dr. Ken
Date: Mon, 7 Nov 1994 11:01:01 -0500 (EST)

Hello there!

Great question!  Magic squares give rise to a whole bunch of interesting
mathematics.  I recommend to you the book "The Joy of Mathematics" by 
Theoni Pappas.  It gives a fantastic treatment of all kinds of beautiful
mathematical phenomena, including Magic Squares, Fibonacci numbers, and 
all kinds of other neat stuff.  Unfortunately, we don't have the book here in
our library (I've got it at home and we've got the sequel here), so I'm
afraid I won't be of much direct personal help to you.  Perhaps another one
of our Math Doctors here has had more experience with them, so you may get
another response from them!  In the meantime, though, check out that book.
It'll be loads of fun for you, your wife, _and_ your kids!

-Ken "Dr." Math

From: Dr. Ethan
Date: Tue, 8 Nov 1994 11:30:27 -0500 (EST)

                I think that you were already given a source for examples
(Joy of Mathematics).  So to answer your other question here is a
way to produce magic squares that I thought out this morning.  They aren't
very interesting but for third and fourth graders, I doubt that they would
notice a pattern.

        n+1   n+2  n-3  Or variation 2  n+1  n-5  n+4

        n-4    n   n+4                  n+3   n   n-3

        n+3   n-2  n-1                  n-4  n+5  n-1

        More generally this could be

        n-a       n-b     n+a+b

        n+2a+b     n      n-2a-b

        n-a-b     n+b     n+a

        However, for some choices of a and b you will get numbers 
repeated, which as I recall may not not be allowed.
        Hope this helps; maybe you think of a similar way to get magic
squares of size four. If not, write back and I will send you one.
        Ethan, Doctor On Call

Date: Wed, 9 Nov 1994 22:28:08 -0700
From: Peter Darby
Subject: Re: Magic Squares

Thank you for your help - I breath easier - we will try to find the book

It's good to know that Dr Math is IN!
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