Magic Squares and Observations.

If you look at the instructions for how to do a magic square they have a specific progression on how to fill them in. Today, I"m only looking at the 3 x 3 grids but I plan to look to see if these observations for a 3 x 3 work for larger square and could lead to a interesting activity.  I used numbers for this but it could be done by hand or by excel.  

To create a 3 x 3 while using the digits of 1 to 9, start by putting the 1 in the middle cell of the top row.  

The next digit 2, is located one pace up and over but that puts you outside the grid so you end up placing the 2 in the bottom right most square.  The digit 3 is then placed right one and up one so again, you are off the grid and end up placing it in the first cell of the second row.  

The digit 4 is one cell down, just below the 3. 5 is then one cell to the right and one up and the 6 is also one right and one up so the 4, 5, 6 are on a diagonal from lowest left to highest right. To get to 7, you move one cell down.

To place the digit 8, you go right one cell and up one so you have to move to the top row, first cell.  The digit 9 ends up being placed in the last open cell between the 4 and the 2.

The next step would be to have students add up all the rows, columns, and diagonals, to make sure they all add up to 15.  If you are using numbers or excel, have the students create the math for the cells. 

Once this is set up, for all the cells, students can see they all add up to 15.

Now for the fun part, ask students if you rotate the magic square 90 degrees, 180 degrees, or 270 degrees, will it still work out properly?  I did it and yes, the magic square still adds up to 15 in all directions for all those rotations.

                                               

We all know it is but many students wouldn't and it makes a nice extension for the activity and it brings in the idea of rotation in an area other than geometry.  Let me know what you think, I'd love to hear.  Have a great day.