Magic Squares 1 – Anti-Magic Squares

I’ve never found much success asking children to use the numbers 1 to 9 to create a magic square in which each of the rows, columns, and the two diagonals totals the same number.

True, you can give them a nudge by telling them the central number has to be 5 and / or that the magic total is 15, but I’m rather against telling children anything in what’s supposed to be an exploration.  In any case, for most children it’s not helpful enough, and failed attempts don’t give much helpful feedback that enables you to do better next time – instead of the “Trial and Improvement” we like to see, it’s Trial and Error and then Trial and Error again.

Consequently, for most children it’s a frustrating exercise in failure – they’ve been given a challenge and failed it, perhaps after putting a lot of time and effort into it.  So it’s not a very rewarding task at all.

That’s not the only disadvantage.  What does the teacher do when one or two children do succeed?  Apart from rotations and reflections there’s only the one solution (green cards), so you can’t ask them to find any more, and if finding the 3×3 magic square presents plenty of problems, you can be sure finding a 4×4 magic square can definitely be crossed off the list of potential extensions.

So how do you get round all these problems?  Easy, dead easy.  Simply reverse the task, and ask children to find an Anti-Magic Square, where the rows, columns and diagonals all add up to different totals (example: yellow cards).  Whatever array you choose is bound to give three different totals or more, so children are getting some success immediately, and the task then becomes to build on success rather than failure and to do better than your last attempt.

There are further advantages.  There’s more than one solution (no, I’ve no idea how many), and if anyone really wants to, finding a 4×4 Anti-Magic Square is a worthwhile challenge.

MAGIC SQ

PS: one final benefit: have some digit cards available on Open Evenings, and let parents have a go at creating an Anti-Magic Square!

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2 responses

  1. […] Magic Squares 1 – Anti-Magic Squares (established1962.wordpress.com) Another idea for 3 x 3 squares […]

  2. […] Magic Squares 1 – Anti-Magic Squares (established1962.wordpress.com) Another idea for 3 x 3 squares […]

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