Magic Squares:

A classic math puzzle. Try to arrange your cards (1-9) into a 3x3 grid, so that every row, every column, and both diagonals all add to the same number. Can kids figure out what that number has to be even before solving the Magic Square? (Hints in the title of this game, and below in Learning Notes.)

Magic Squares:

See the variation above for instructions on making a Magic Square. Children will likely need some assistance. Help them break down the challenge into parts:

First, guide them in figuring out what the "magic sum" should be (that is, what each row, column, and diagonal should add up to). Ask what the sum of all 9 cards is. This is a great chance to be clever about adding up numbers. Look for pairs that add to 10 first: 1 + 9, 2 + 8, 3 + 7, and 4 + 6. These add to 40, with the 5 still uncounted. So the sum is 45. Since the sum of each of the three rows has to be the same, we know that each row must be a third of 45, or 15. We've found our magic number.

Second, ask the child to form 3 rows that each add to 15. For this step, ignore columns and diagonals. This can be tough, depending on the age and ability of the child. But it's good addition practice, and good practice in number sense ("If this row is too big, I need to switch out one number with a smaller number.").

Third, now that there are 3 rows that each add to 15, challenge your child to rearrange the cards so that each column also equals 15. They can do this by switching numbers within a row. This keeps the sum of each row the same.

Fourth, try to get the diagonals to equal 15. This part is the toughest. The trick is to realize that you can move a whole column to another position, or a whole row. Let your child try this for a bit. When it's done, the Magic Square should have the 5 in the center. Here's one possible arrangement (though there are more):

Remember grouping all the pairs that add to 10 earlier? Those pairs are all hiding in this square on either side of the 5. The 1 and 9 are on opposite squares on either side of the 5. So are the 2 and 8, 3 and 7, and 4 and 6!

Tic-Tac-Toe:

Once you've made your Magic Square, copy it onto a piece of paper. Then play a few games of Fifteen again. This time, as you play, keep track of which cards each player chooses by marking an X for one player, and an O for the other player on the Magic Square. It won't take long for your child to recognize that playing Fifteen is just the same as playing Tic-Tac-Toe on a Magic Square! (This is why Fifteen so often ends in a draw, just like Tic-Tac-Toe.)