# Magic Squares Even Ordered 4n x 4n Multiples

After a fun week working with odd ordered magic squares and watching the children follow a complicated algorithm, I wanted to continue with even ordered magic squares. The 6x6, 10x10, 14x14 algorithm is a little too much but the 4x4, 8x8, 12x12, etc. is very achievable.

We first discussed an unusual discovery, that the only magic square not possible is 2x2. Although the magic number should be 5, it is not achievable. A 1x1 Magic Square was fun to discuss and prove.

Most of the fun was working with the children to create 4x4 diagonals across any grid (see the pdf). Page one of the pdf. sets out the rules with an example of a 4x4. Then, the rest of the pdf has 8x8, through 20x20 with the 4x4 diagonals already included. For those Mathletes who want to challenge themselves to create the diagonals, the second pdf has the empty cell grids. The key is to count out from the corner vertex every four squares or vertices.

The children should practice finding the magic number by taking any column and adding the numbers since they are already lined up for addition. Remember to move your single digit numbers to the right to the units digit column or ones digit.

The last page of the first pdf is for the 4-6th graders to try to find the magic number with the algebraic equation we used last week: (n^3 + n)/2.

AttachmentSize
Magic_Squares_Even_Ordered_4nx4n.pdf940.13 KB
Magic_Square_Empty_Grids_8x8_12X12_16x16_20X20.pdf24.78 KB