Effect

Nikit and Sam are invited up to the interactive white board to slide the numbers 1 to 9 into the 3 x 3 grid so that every row and column adds up to 15. The computer tells them their totals so that they can see how they are getting on. Can they do it before 2 minutes is up? With a few hints (cough, cough) from me they soon complete the task with seconds to spare. As they return to their seats I then offer to show the class how to build magic squares of any size (odd by odd) in record time.

By the end of the lesson, Nikit and Sam, along with many others, have drawn out perfect magic squares of many sizes. Nikit even managed 15 by 15!

Method

Place the 1 in the middle of the top row. Then simply carry on writing down the numbers in order according to three simple rules:

1) The next number is placed NORTH-EAST of the one you have just written.

2) If the box you want to write in is full, then write the next number SOUTH instead of North-East, i.e. in the box below the one you have just written.

3) If you go off the page, then just “wrap around” – top comes back in at the bottom, and right comes back in on the left.

Here’s my partial completion of a 7 x 7 Magic Square:

and so on.

My record on the board is a 21 x 21 square, which I began before I had realised that I would be writing 441 numbers!

These days I use this as a taster lesson for Year 6 children visiting Oaks Park for a sample Maths Lesson. We begin by trying to make the total 15 in as many ways as we can, and then agree that 5 has to go in the middle. When someone has found a solution to the 3 x 3 challenge (there are several, such as reflections and rotations), we share it with the others. As a quick extension, I ask the brightest to find me an anti-magic square, where all the totals are different.