Educating Risa

Do you remember playing with magic squares as a kid? I loved them, and I thought Daegan might too—and that they’d be another way to practice his addition facts. The classic magic square is a 3-by-3 grid that uses each integer from 1 to 9 only once, and where the sum of each row, column, or diagonal is 15:

There are in fact many different magic squares; the common elements being only that the vertical, horizontal, and diagonal sums add to the same total, and that each integer in the grid can be used only once. I found some simple magic squares on this site, and used them as templates to make magic squares for Daegan to try. We did the “sum of 12” magic square, which uses the integers 0 through 8, and the classic “sum of 15” magic square, which uses the integers 1 through 9. I filled in four of the answers to make things quite easy to start off with, as we’re still working on basic addition facts, not complex puzzle-solving strategies. Here’s the magic squares sheet I made up. Note that for each column, the answers are simply rotations of one another.

We used plastic number tokens (from a dollar-store version of Sudoku, the game board from which has long since disintegrated) to fill in the squares, making the sheets reusable. Here’s Daegan in deep thought with the sum-to-12 grid:

Even though a magic square uses three numbers for each sum (whether across, down, or diagonal), this activity gave Daegan lots of practice on his basic (two number) addition facts, as he had to sum the two to work out the missing number. This is how he solved the above square, adding down the columns first (e.g., 6+5 = 11) and then subtracting that sum from 12 to get the missing number (12-11 = 1).

Here’s the completed square:

He employed the same strategies on the ‘sum of 15’ square. First, he put on the tokens for the numbers already filled in on the grid:

Then, he selected which square to solve for next. Daegan had a bit of difficulty understanding which square(s) to begin solving first. In the above picture, we do not yet have enough information to solve the lower right corner square, for example. But all in all, and despite some moments of frustration, he had fun with these puzzles: